Coverage for /usr/local/lib/python3.11/dist-packages/pyrocko/trace.py: 76%

1745 statements  

« prev     ^ index     » next       coverage.py v6.5.0, created at 2024-01-10 08:51 +0000

1# https://pyrocko.org - GPLv3 

2# 

3# The Pyrocko Developers, 21st Century 

4# ---|P------/S----------~Lg---------- 

5 

6''' 

7Basic signal processing for seismic waveforms. 

8''' 

9 

10import time 

11import math 

12import copy 

13import logging 

14import hashlib 

15from collections import defaultdict 

16 

17import numpy as num 

18from scipy import signal 

19 

20from pyrocko import util, orthodrome, pchain, model, signal_ext 

21from pyrocko.util import reuse 

22from pyrocko.guts import Object, Float, Int, String, List, \ 

23 StringChoice, Timestamp 

24from pyrocko.guts_array import Array 

25from pyrocko.model import squirrel_content 

26 

27# backward compatibility 

28from pyrocko.util import UnavailableDecimation # noqa 

29from pyrocko.response import ( # noqa 

30 FrequencyResponse, Evalresp, InverseEvalresp, PoleZeroResponse, 

31 ButterworthResponse, SampledResponse, IntegrationResponse, 

32 DifferentiationResponse, MultiplyResponse) 

33 

34 

35guts_prefix = 'pf' 

36 

37logger = logging.getLogger('pyrocko.trace') 

38 

39 

40g_tapered_coeffs_cache = {} 

41g_one_response = FrequencyResponse() 

42 

43 

44@squirrel_content 

45class Trace(Object): 

46 

47 ''' 

48 Create new trace object. 

49 

50 A ``Trace`` object represents a single continuous strip of evenly sampled 

51 time series data. It is built from a 1D NumPy array containing the data 

52 samples and some attributes describing its beginning and ending time, its 

53 sampling rate and four string identifiers (its network, station, location 

54 and channel code). 

55 

56 :param network: network code 

57 :param station: station code 

58 :param location: location code 

59 :param channel: channel code 

60 :param extra: extra code 

61 :param tmin: system time of first sample in [s] 

62 :param tmax: system time of last sample in [s] (if set to ``None`` it is 

63 computed from length of ``ydata``) 

64 :param deltat: sampling interval in [s] 

65 :param ydata: 1D numpy array with data samples (can be ``None`` when 

66 ``tmax`` is not ``None``) 

67 :param mtime: optional modification time 

68 

69 :param meta: additional meta information (not used, but maintained by the 

70 library) 

71 

72 The length of the network, station, location and channel codes is not 

73 resricted by this software, but data formats like SAC, Mini-SEED or GSE 

74 have different limits on the lengths of these codes. The codes set here are 

75 silently truncated when the trace is stored 

76 ''' 

77 

78 network = String.T(default='', help='Deployment/network code (1-8)') 

79 station = String.T(default='STA', help='Station code (1-5)') 

80 location = String.T(default='', help='Location code (0-2)') 

81 channel = String.T(default='', help='Channel code (3)') 

82 extra = String.T(default='', help='Extra/custom code') 

83 

84 tmin = Timestamp.T(default=Timestamp.D('1970-01-01 00:00:00')) 

85 tmax = Timestamp.T() 

86 

87 deltat = Float.T(default=1.0) 

88 ydata = Array.T(optional=True, shape=(None,), serialize_as='base64+meta') 

89 

90 mtime = Timestamp.T(optional=True) 

91 

92 cached_frequencies = {} 

93 

94 def __init__(self, network='', station='STA', location='', channel='', 

95 tmin=0., tmax=None, deltat=1., ydata=None, mtime=None, 

96 meta=None, extra=''): 

97 

98 Object.__init__(self, init_props=False) 

99 

100 time_float = util.get_time_float() 

101 

102 if not isinstance(tmin, time_float): 

103 tmin = Trace.tmin.regularize_extra(tmin) 

104 

105 if tmax is not None and not isinstance(tmax, time_float): 

106 tmax = Trace.tmax.regularize_extra(tmax) 

107 

108 if mtime is not None and not isinstance(mtime, time_float): 

109 mtime = Trace.mtime.regularize_extra(mtime) 

110 

111 if ydata is not None and not isinstance(ydata, num.ndarray): 

112 ydata = Trace.ydata.regularize_extra(ydata) 

113 

114 self._growbuffer = None 

115 

116 tmin = time_float(tmin) 

117 if tmax is not None: 

118 tmax = time_float(tmax) 

119 

120 if mtime is None: 

121 mtime = time_float(time.time()) 

122 

123 self.network, self.station, self.location, self.channel, \ 

124 self.extra = [ 

125 reuse(x) for x in ( 

126 network, station, location, channel, extra)] 

127 

128 self.tmin = tmin 

129 self.deltat = deltat 

130 

131 if tmax is None: 

132 if ydata is not None: 

133 self.tmax = self.tmin + (ydata.size-1)*self.deltat 

134 else: 

135 raise Exception( 

136 'fixme: trace must be created with tmax or ydata') 

137 else: 

138 n = int(round((tmax - self.tmin) / self.deltat)) + 1 

139 self.tmax = self.tmin + (n - 1) * self.deltat 

140 

141 self.meta = meta 

142 self.ydata = ydata 

143 self.mtime = mtime 

144 self._update_ids() 

145 self.file = None 

146 self._pchain = None 

147 

148 def __str__(self): 

149 fmt = min(9, max(0, -int(math.floor(math.log10(self.deltat))))) 

150 s = 'Trace (%s, %s, %s, %s)\n' % self.nslc_id 

151 s += ' timerange: %s - %s\n' % ( 

152 util.time_to_str(self.tmin, format=fmt), 

153 util.time_to_str(self.tmax, format=fmt)) 

154 

155 s += ' delta t: %g\n' % self.deltat 

156 if self.meta: 

157 for k in sorted(self.meta.keys()): 

158 s += ' %s: %s\n' % (k, self.meta[k]) 

159 return s 

160 

161 @property 

162 def codes(self): 

163 from pyrocko.squirrel import model 

164 return model.CodesNSLCE( 

165 self.network, self.station, self.location, self.channel, 

166 self.extra) 

167 

168 @property 

169 def time_span(self): 

170 return self.tmin, self.tmax 

171 

172 @property 

173 def summary_entries(self): 

174 return ( 

175 self.__class__.__name__, 

176 str(self.codes), 

177 self.str_time_span, 

178 '%g' % (1.0/self.deltat)) 

179 

180 @property 

181 def summary_stats_entries(self): 

182 return tuple('%13.7g' % v for v in ( 

183 self.ydata.min(), 

184 self.ydata.max(), 

185 self.ydata.mean(), 

186 self.ydata.std())) 

187 

188 @property 

189 def summary(self): 

190 return util.fmt_summary(self.summary_entries, (10, 20, 55, 0)) 

191 

192 @property 

193 def summary_stats(self): 

194 return self.summary + ' | ' + util.fmt_summary( 

195 self.summary_stats_entries, (12, 12, 12, 12)) 

196 

197 def __getstate__(self): 

198 return (self.network, self.station, self.location, self.channel, 

199 self.tmin, self.tmax, self.deltat, self.mtime, 

200 self.ydata, self.meta, self.extra) 

201 

202 def __setstate__(self, state): 

203 if len(state) == 11: 

204 self.network, self.station, self.location, self.channel, \ 

205 self.tmin, self.tmax, self.deltat, self.mtime, \ 

206 self.ydata, self.meta, self.extra = state 

207 

208 elif len(state) == 12: 

209 # backward compatibility 0 

210 self.network, self.station, self.location, self.channel, \ 

211 self.tmin, self.tmax, self.deltat, self.mtime, \ 

212 self.ydata, self.meta, _, self.extra = state 

213 

214 elif len(state) == 10: 

215 # backward compatibility 1 

216 self.network, self.station, self.location, self.channel, \ 

217 self.tmin, self.tmax, self.deltat, self.mtime, \ 

218 self.ydata, self.meta = state 

219 

220 self.extra = '' 

221 

222 else: 

223 # backward compatibility 2 

224 self.network, self.station, self.location, self.channel, \ 

225 self.tmin, self.tmax, self.deltat, self.mtime = state 

226 self.ydata = None 

227 self.meta = None 

228 self.extra = '' 

229 

230 self._growbuffer = None 

231 self._update_ids() 

232 

233 def hash(self, unsafe=False): 

234 sha1 = hashlib.sha1() 

235 for code in self.nslc_id: 

236 sha1.update(code.encode()) 

237 sha1.update(self.tmin.hex().encode()) 

238 sha1.update(self.tmax.hex().encode()) 

239 sha1.update(self.deltat.hex().encode()) 

240 

241 if self.ydata is not None: 

242 if not unsafe: 

243 sha1.update(memoryview(self.ydata)) 

244 else: 

245 sha1.update(memoryview(self.ydata[:32])) 

246 sha1.update(memoryview(self.ydata[-32:])) 

247 

248 return sha1.hexdigest() 

249 

250 def name(self): 

251 ''' 

252 Get a short string description. 

253 ''' 

254 

255 s = '%s.%s.%s.%s, %s, %s' % (self.nslc_id + ( 

256 util.time_to_str(self.tmin), 

257 util.time_to_str(self.tmax))) 

258 

259 return s 

260 

261 def __eq__(self, other): 

262 return ( 

263 isinstance(other, Trace) 

264 and self.network == other.network 

265 and self.station == other.station 

266 and self.location == other.location 

267 and self.channel == other.channel 

268 and (abs(self.deltat - other.deltat) 

269 < (self.deltat + other.deltat)*1e-6) 

270 and abs(self.tmin-other.tmin) < self.deltat*0.01 

271 and abs(self.tmax-other.tmax) < self.deltat*0.01 

272 and num.all(self.ydata == other.ydata)) 

273 

274 def almost_equal(self, other, rtol=1e-5, atol=0.0): 

275 return ( 

276 self.network == other.network 

277 and self.station == other.station 

278 and self.location == other.location 

279 and self.channel == other.channel 

280 and (abs(self.deltat - other.deltat) 

281 < (self.deltat + other.deltat)*1e-6) 

282 and abs(self.tmin-other.tmin) < self.deltat*0.01 

283 and abs(self.tmax-other.tmax) < self.deltat*0.01 

284 and num.allclose(self.ydata, other.ydata, rtol=rtol, atol=atol)) 

285 

286 def assert_almost_equal(self, other, rtol=1e-5, atol=0.0): 

287 

288 assert self.network == other.network, \ 

289 'network codes differ: %s, %s' % (self.network, other.network) 

290 assert self.station == other.station, \ 

291 'station codes differ: %s, %s' % (self.station, other.station) 

292 assert self.location == other.location, \ 

293 'location codes differ: %s, %s' % (self.location, other.location) 

294 assert self.channel == other.channel, 'channel codes differ' 

295 assert (abs(self.deltat - other.deltat) 

296 < (self.deltat + other.deltat)*1e-6), \ 

297 'sampling intervals differ %g, %g' % (self.deltat, other.delta) 

298 assert abs(self.tmin-other.tmin) < self.deltat*0.01, \ 

299 'start times differ: %s, %s' % ( 

300 util.time_to_str(self.tmin), util.time_to_str(other.tmin)) 

301 assert abs(self.tmax-other.tmax) < self.deltat*0.01, \ 

302 'end times differ: %s, %s' % ( 

303 util.time_to_str(self.tmax), util.time_to_str(other.tmax)) 

304 

305 assert num.allclose(self.ydata, other.ydata, rtol=rtol, atol=atol), \ 

306 'trace values differ' 

307 

308 def __hash__(self): 

309 return id(self) 

310 

311 def __call__(self, t, clip=False, snap=round): 

312 it = int(snap((t-self.tmin)/self.deltat)) 

313 if clip: 

314 it = max(0, min(it, self.ydata.size-1)) 

315 else: 

316 if it < 0 or self.ydata.size <= it: 

317 raise IndexError() 

318 

319 return self.tmin+it*self.deltat, self.ydata[it] 

320 

321 def interpolate(self, t, clip=False): 

322 ''' 

323 Value of trace between supporting points through linear interpolation. 

324 

325 :param t: time instant 

326 :param clip: whether to clip indices to trace ends 

327 ''' 

328 

329 t0, y0 = self(t, clip=clip, snap=math.floor) 

330 t1, y1 = self(t, clip=clip, snap=math.ceil) 

331 if t0 == t1: 

332 return y0 

333 else: 

334 return y0+(t-t0)/(t1-t0)*(y1-y0) 

335 

336 def index_clip(self, i): 

337 ''' 

338 Clip index to valid range. 

339 ''' 

340 

341 return min(max(0, i), self.ydata.size) 

342 

343 def add(self, other, interpolate=True, left=0., right=0.): 

344 ''' 

345 Add values of other trace (self += other). 

346 

347 Add values of ``other`` trace to the values of ``self``, where it 

348 intersects with ``other``. This method does not change the extent of 

349 ``self``. If ``interpolate`` is ``True`` (the default), the values of 

350 ``other`` to be added are interpolated at sampling instants of 

351 ``self``. Linear interpolation is performed. In this case the sampling 

352 rate of ``other`` must be equal to or lower than that of ``self``. If 

353 ``interpolate`` is ``False``, the sampling rates of the two traces must 

354 match. 

355 ''' 

356 

357 if interpolate: 

358 assert self.deltat <= other.deltat \ 

359 or same_sampling_rate(self, other) 

360 

361 other_xdata = other.get_xdata() 

362 xdata = self.get_xdata() 

363 self.ydata += num.interp( 

364 xdata, other_xdata, other.ydata, left=left, right=left) 

365 else: 

366 assert self.deltat == other.deltat 

367 ioff = int(round((other.tmin-self.tmin)/self.deltat)) 

368 ibeg = max(0, ioff) 

369 iend = min(self.data_len(), ioff+other.data_len()) 

370 self.ydata[ibeg:iend] += other.ydata[ibeg-ioff:iend-ioff] 

371 

372 def mult(self, other, interpolate=True): 

373 ''' 

374 Muliply with values of other trace ``(self *= other)``. 

375 

376 Multiply values of ``other`` trace to the values of ``self``, where it 

377 intersects with ``other``. This method does not change the extent of 

378 ``self``. If ``interpolate`` is ``True`` (the default), the values of 

379 ``other`` to be multiplied are interpolated at sampling instants of 

380 ``self``. Linear interpolation is performed. In this case the sampling 

381 rate of ``other`` must be equal to or lower than that of ``self``. If 

382 ``interpolate`` is ``False``, the sampling rates of the two traces must 

383 match. 

384 ''' 

385 

386 if interpolate: 

387 assert self.deltat <= other.deltat or \ 

388 same_sampling_rate(self, other) 

389 

390 other_xdata = other.get_xdata() 

391 xdata = self.get_xdata() 

392 self.ydata *= num.interp( 

393 xdata, other_xdata, other.ydata, left=0., right=0.) 

394 else: 

395 assert self.deltat == other.deltat 

396 ibeg1 = int(round((other.tmin-self.tmin)/self.deltat)) 

397 ibeg2 = int(round((self.tmin-other.tmin)/self.deltat)) 

398 iend1 = int(round((other.tmax-self.tmin)/self.deltat))+1 

399 iend2 = int(round((self.tmax-other.tmin)/self.deltat))+1 

400 

401 ibeg1 = self.index_clip(ibeg1) 

402 iend1 = self.index_clip(iend1) 

403 ibeg2 = self.index_clip(ibeg2) 

404 iend2 = self.index_clip(iend2) 

405 

406 self.ydata[ibeg1:iend1] *= other.ydata[ibeg2:iend2] 

407 

408 def max(self): 

409 ''' 

410 Get time and value of data maximum. 

411 ''' 

412 

413 i = num.argmax(self.ydata) 

414 return self.tmin + i*self.deltat, self.ydata[i] 

415 

416 def min(self): 

417 ''' 

418 Get time and value of data minimum. 

419 ''' 

420 

421 i = num.argmin(self.ydata) 

422 return self.tmin + i*self.deltat, self.ydata[i] 

423 

424 def absmax(self): 

425 ''' 

426 Get time and value of maximum of the absolute of data. 

427 ''' 

428 

429 tmi, mi = self.min() 

430 tma, ma = self.max() 

431 if abs(mi) > abs(ma): 

432 return tmi, abs(mi) 

433 else: 

434 return tma, abs(ma) 

435 

436 def set_codes( 

437 self, network=None, station=None, location=None, channel=None, 

438 extra=None): 

439 

440 ''' 

441 Set network, station, location, and channel codes. 

442 ''' 

443 

444 if network is not None: 

445 self.network = network 

446 if station is not None: 

447 self.station = station 

448 if location is not None: 

449 self.location = location 

450 if channel is not None: 

451 self.channel = channel 

452 if extra is not None: 

453 self.extra = extra 

454 

455 self._update_ids() 

456 

457 def set_network(self, network): 

458 self.network = network 

459 self._update_ids() 

460 

461 def set_station(self, station): 

462 self.station = station 

463 self._update_ids() 

464 

465 def set_location(self, location): 

466 self.location = location 

467 self._update_ids() 

468 

469 def set_channel(self, channel): 

470 self.channel = channel 

471 self._update_ids() 

472 

473 def overlaps(self, tmin, tmax): 

474 ''' 

475 Check if trace has overlap with a given time span. 

476 ''' 

477 return not (tmax < self.tmin or self.tmax < tmin) 

478 

479 def is_relevant(self, tmin, tmax, selector=None): 

480 ''' 

481 Check if trace has overlap with a given time span and matches a 

482 condition callback. (internal use) 

483 ''' 

484 

485 return not (tmax <= self.tmin or self.tmax < tmin) \ 

486 and (selector is None or selector(self)) 

487 

488 def _update_ids(self): 

489 ''' 

490 Update dependent ids. 

491 ''' 

492 

493 self.full_id = ( 

494 self.network, self.station, self.location, self.channel, self.tmin) 

495 self.nslc_id = reuse( 

496 (self.network, self.station, self.location, self.channel)) 

497 

498 def prune_from_reuse_cache(self): 

499 util.deuse(self.nslc_id) 

500 util.deuse(self.network) 

501 util.deuse(self.station) 

502 util.deuse(self.location) 

503 util.deuse(self.channel) 

504 

505 def set_mtime(self, mtime): 

506 ''' 

507 Set modification time of the trace. 

508 ''' 

509 

510 self.mtime = mtime 

511 

512 def get_xdata(self): 

513 ''' 

514 Create array for time axis. 

515 ''' 

516 

517 if self.ydata is None: 

518 raise NoData() 

519 

520 return self.tmin \ 

521 + num.arange(len(self.ydata), dtype=num.float64) * self.deltat 

522 

523 def get_ydata(self): 

524 ''' 

525 Get data array. 

526 ''' 

527 

528 if self.ydata is None: 

529 raise NoData() 

530 

531 return self.ydata 

532 

533 def set_ydata(self, new_ydata): 

534 ''' 

535 Replace data array. 

536 ''' 

537 

538 self.drop_growbuffer() 

539 self.ydata = new_ydata 

540 self.tmax = self.tmin+(len(self.ydata)-1)*self.deltat 

541 

542 def data_len(self): 

543 if self.ydata is not None: 

544 return self.ydata.size 

545 else: 

546 return int(round((self.tmax-self.tmin)/self.deltat)) + 1 

547 

548 def drop_data(self): 

549 ''' 

550 Forget data, make dataless trace. 

551 ''' 

552 

553 self.drop_growbuffer() 

554 self.ydata = None 

555 

556 def drop_growbuffer(self): 

557 ''' 

558 Detach the traces grow buffer. 

559 ''' 

560 

561 self._growbuffer = None 

562 self._pchain = None 

563 

564 def copy(self, data=True): 

565 ''' 

566 Make a deep copy of the trace. 

567 ''' 

568 

569 tracecopy = copy.copy(self) 

570 tracecopy.drop_growbuffer() 

571 if data: 

572 tracecopy.ydata = self.ydata.copy() 

573 tracecopy.meta = copy.deepcopy(self.meta) 

574 return tracecopy 

575 

576 def crop_zeros(self): 

577 ''' 

578 Remove any zeros at beginning and end. 

579 ''' 

580 

581 indices = num.where(self.ydata != 0.0)[0] 

582 if indices.size == 0: 

583 raise NoData() 

584 

585 ibeg = indices[0] 

586 iend = indices[-1]+1 

587 if ibeg == 0 and iend == self.ydata.size-1: 

588 return 

589 

590 self.drop_growbuffer() 

591 self.ydata = self.ydata[ibeg:iend].copy() 

592 self.tmin = self.tmin+ibeg*self.deltat 

593 self.tmax = self.tmin+(len(self.ydata)-1)*self.deltat 

594 self._update_ids() 

595 

596 def append(self, data): 

597 ''' 

598 Append data to the end of the trace. 

599 

600 To make this method efficient when successively very few or even single 

601 samples are appended, a larger grow buffer is allocated upon first 

602 invocation. The traces data is then changed to be a view into the 

603 currently filled portion of the grow buffer array. 

604 ''' 

605 

606 assert self.ydata.dtype == data.dtype 

607 newlen = data.size + self.ydata.size 

608 if self._growbuffer is None or self._growbuffer.size < newlen: 

609 self._growbuffer = num.empty(newlen*2, dtype=self.ydata.dtype) 

610 self._growbuffer[:self.ydata.size] = self.ydata 

611 self._growbuffer[self.ydata.size:newlen] = data 

612 self.ydata = self._growbuffer[:newlen] 

613 self.tmax = self.tmin + (newlen-1)*self.deltat 

614 

615 def chop( 

616 self, tmin, tmax, inplace=True, include_last=False, 

617 snap=(round, round), want_incomplete=True): 

618 

619 ''' 

620 Cut the trace to given time span. 

621 

622 If the ``inplace`` argument is True (the default) the trace is cut in 

623 place, otherwise a new trace with the cut part is returned. By 

624 default, the indices where to start and end the trace data array are 

625 determined by rounding of ``tmin`` and ``tmax`` to sampling instances 

626 using Python's :py:func:`round` function. This behaviour can be changed 

627 with the ``snap`` argument, which takes a tuple of two functions (one 

628 for the lower and one for the upper end) to be used instead of 

629 :py:func:`round`. The last sample is by default not included unless 

630 ``include_last`` is set to True. If the given time span exceeds the 

631 available time span of the trace, the available part is returned, 

632 unless ``want_incomplete`` is set to False - in that case, a 

633 :py:exc:`NoData` exception is raised. This exception is always raised, 

634 when the requested time span does dot overlap with the trace's time 

635 span. 

636 ''' 

637 

638 if want_incomplete: 

639 if tmax <= self.tmin-self.deltat or self.tmax+self.deltat < tmin: 

640 raise NoData() 

641 else: 

642 if tmin < self.tmin or self.tmax < tmax: 

643 raise NoData() 

644 

645 ibeg = max(0, t2ind(tmin-self.tmin, self.deltat, snap[0])) 

646 iplus = 0 

647 if include_last: 

648 iplus = 1 

649 

650 iend = min( 

651 self.data_len(), 

652 t2ind(tmax-self.tmin, self.deltat, snap[1])+iplus) 

653 

654 if ibeg >= iend: 

655 raise NoData() 

656 

657 obj = self 

658 if not inplace: 

659 obj = self.copy(data=False) 

660 

661 self.drop_growbuffer() 

662 if self.ydata is not None: 

663 obj.ydata = self.ydata[ibeg:iend].copy() 

664 else: 

665 obj.ydata = None 

666 

667 obj.tmin = obj.tmin+ibeg*obj.deltat 

668 obj.tmax = obj.tmin+((iend-ibeg)-1)*obj.deltat 

669 

670 obj._update_ids() 

671 

672 return obj 

673 

674 def downsample( 

675 self, ndecimate, snap=False, demean=False, ftype='fir-remez', 

676 cut=False): 

677 

678 ''' 

679 Downsample (decimate) trace by a given integer factor. 

680 

681 Antialiasing filter details: 

682 

683 * ``iir``: A Chebyshev type I digital filter of order 8 with maximum 

684 ripple of 0.05 dB in the passband. 

685 * ``fir``: A FIR filter using a Hamming window and 31 taps and a 

686 well-behaved phase response. 

687 * ``fir-remez``: A FIR filter based on the Remez exchange algorithm 

688 with ``45*ndecimate`` taps and a cutoff at 75% Nyquist frequency. 

689 

690 Comparison of the digital filters: 

691 

692 .. figure :: ../../static/downsampling-filter-comparison.png 

693 :width: 60% 

694 :alt: Comparison of the downsampling filters. 

695 

696 See also :py:meth:`Trace.downsample_to`. 

697 

698 :param ndecimate: 

699 Decimation factor, avoid values larger than 8. 

700 :type ndecimate: 

701 int 

702 

703 :param snap: 

704 Whether to put the new sampling instants closest to multiples of 

705 the sampling rate (according to absolute time). 

706 :type snap: 

707 bool 

708 

709 :param demean: 

710 Whether to demean the signal before filtering. 

711 :type demean: 

712 bool 

713 

714 :param ftype: 

715 Which FIR filter to use, choose from ``'iir'``, ``'fir'``, 

716 ``'fir-remez'``. Default is ``'fir-remez'``. 

717 

718 :param cut: 

719 Whether to cut off samples in the beginning of the trace which 

720 are polluted by artifacts of the anti-aliasing filter. 

721 :type cut: 

722 bool 

723 ''' 

724 newdeltat = self.deltat*ndecimate 

725 b, a, n = util.decimate_coeffs(ndecimate, None, ftype) 

726 if snap: 

727 ilag = int(round((math.ceil( 

728 (self.tmin+(n//2 if cut else 0)*self.deltat) / 

729 newdeltat) * newdeltat - self.tmin) / self.deltat)) 

730 else: 

731 ilag = (n//2 if cut else 0) 

732 

733 data = self.ydata.astype(num.float64) 

734 if data.size != 0: 

735 if demean: 

736 data -= num.mean(data) 

737 y = signal.lfilter(b, a, data) 

738 self.ydata = y[n//2+ilag::ndecimate].copy() 

739 else: 

740 self.ydata = data 

741 

742 self.tmin += ilag * self.deltat 

743 self.deltat = reuse(self.deltat*ndecimate) 

744 self.tmax = self.tmin+(len(self.ydata)-1)*self.deltat 

745 self._update_ids() 

746 

747 def downsample_to( 

748 self, deltat, snap=False, allow_upsample_max=1, demean=False, 

749 ftype='fir-remez', cut=False): 

750 

751 ''' 

752 Downsample to given sampling rate. 

753 

754 Tries to downsample the trace to a target sampling interval of 

755 ``deltat``. This runs :py:meth:`downsample` one or several times. If 

756 ``allow_upsample_max`` is set to a value larger than 1, intermediate 

757 upsampling steps are allowed, in order to increase the number of 

758 possible downsampling ratios. 

759 

760 If the requested ratio is not supported, an exception of type 

761 :py:exc:`pyrocko.util.UnavailableDecimation` is raised. 

762 

763 The downsampled trace will be shorter than the input trace because the 

764 anti-aliasing filter introduces edge effects. If `cut` is selected, 

765 additionally, polluted samples in the beginning of the trace are 

766 removed. The approximate amount of cutoff which will be produced by a 

767 given downsampling configuration can be estimated with 

768 :py:func:`downsample_tpad`. 

769 

770 See also: :meth:`Trace.downsample`. 

771 

772 :param deltat: 

773 Desired sampling interval in [s]. 

774 :type deltat: 

775 float 

776 

777 :param allow_upsample_max: 

778 Maximum allowed upsampling factor of the signal to achieve the 

779 desired sampling interval. Default is ``1``. 

780 :type allow_upsample_max: 

781 int 

782 

783 :param snap: 

784 Whether to put the new sampling instants closest to multiples of 

785 the sampling rate (according to absolute time). 

786 :type snap: 

787 bool 

788 

789 :param demean: 

790 Whether to demean the signal before filtering. 

791 :type demean: 

792 bool 

793 

794 :param ftype: 

795 Which FIR filter to use, choose from ``'iir'``, ``'fir'``, 

796 ``'fir-remez'``. Default is ``'fir-remez'``. 

797 

798 :param cut: 

799 Whether to cut off samples in the beginning of the trace which 

800 are polluted by artifacts of the anti-aliasing filter. 

801 :type demean: 

802 bool 

803 ''' 

804 

805 upsratio, deci_seq = _configure_downsampling( 

806 self.deltat, deltat, allow_upsample_max) 

807 

808 if demean: 

809 self.drop_growbuffer() 

810 self.ydata = self.ydata.astype(num.float64) 

811 self.ydata -= num.mean(self.ydata) 

812 

813 if upsratio > 1: 

814 self.drop_growbuffer() 

815 ydata = self.ydata 

816 self.ydata = num.zeros( 

817 ydata.size*upsratio-(upsratio-1), ydata.dtype) 

818 self.ydata[::upsratio] = ydata 

819 for i in range(1, upsratio): 

820 self.ydata[i::upsratio] = \ 

821 float(i)/upsratio * ydata[:-1] \ 

822 + float(upsratio-i)/upsratio * ydata[1:] 

823 self.deltat = self.deltat/upsratio 

824 

825 for i, ndecimate in enumerate(deci_seq): 

826 self.downsample( 

827 ndecimate, snap=snap, demean=False, ftype=ftype, cut=cut) 

828 

829 def resample(self, deltat): 

830 ''' 

831 Resample to given sampling rate ``deltat``. 

832 

833 Resampling is performed in the frequency domain. 

834 ''' 

835 

836 ndata = self.ydata.size 

837 ntrans = nextpow2(ndata) 

838 fntrans2 = ntrans * self.deltat/deltat 

839 ntrans2 = int(round(fntrans2)) 

840 deltat2 = self.deltat * float(ntrans)/float(ntrans2) 

841 ndata2 = int(round(ndata*self.deltat/deltat2)) 

842 if abs(fntrans2 - ntrans2) > 1e-7: 

843 logger.warning( 

844 'resample: requested deltat %g could not be matched exactly: ' 

845 '%g' % (deltat, deltat2)) 

846 

847 data = self.ydata 

848 data_pad = num.zeros(ntrans, dtype=float) 

849 data_pad[:ndata] = data 

850 fdata = num.fft.rfft(data_pad) 

851 fdata2 = num.zeros((ntrans2+1)//2, dtype=fdata.dtype) 

852 n = min(fdata.size, fdata2.size) 

853 fdata2[:n] = fdata[:n] 

854 data2 = num.fft.irfft(fdata2) 

855 data2 = data2[:ndata2] 

856 data2 *= float(ntrans2) / float(ntrans) 

857 self.deltat = deltat2 

858 self.set_ydata(data2) 

859 

860 def resample_simple(self, deltat): 

861 tyear = 3600*24*365. 

862 

863 if deltat == self.deltat: 

864 return 

865 

866 if abs(self.deltat - deltat) * tyear/deltat < deltat: 

867 logger.warning( 

868 'resample_simple: less than one sample would have to be ' 

869 'inserted/deleted per year. Doing nothing.') 

870 return 

871 

872 ninterval = int(round(deltat / (self.deltat - deltat))) 

873 if abs(ninterval) < 20: 

874 logger.error( 

875 'resample_simple: sample insertion/deletion interval less ' 

876 'than 20. results would be erroneous.') 

877 raise ResamplingFailed() 

878 

879 delete = False 

880 if ninterval < 0: 

881 ninterval = - ninterval 

882 delete = True 

883 

884 tyearbegin = util.year_start(self.tmin) 

885 

886 nmin = int(round((self.tmin - tyearbegin)/deltat)) 

887 

888 ibegin = (((nmin-1)//ninterval)+1) * ninterval - nmin 

889 nindices = (len(self.ydata) - ibegin - 1) / ninterval + 1 

890 if nindices > 0: 

891 indices = ibegin + num.arange(nindices) * ninterval 

892 data_split = num.split(self.ydata, indices) 

893 data = [] 

894 for ln, h in zip(data_split[:-1], data_split[1:]): 

895 if delete: 

896 ln = ln[:-1] 

897 

898 data.append(ln) 

899 if not delete: 

900 if ln.size == 0: 

901 v = h[0] 

902 else: 

903 v = 0.5*(ln[-1] + h[0]) 

904 data.append(num.array([v], dtype=ln.dtype)) 

905 

906 data.append(data_split[-1]) 

907 

908 ydata_new = num.concatenate(data) 

909 

910 self.tmin = tyearbegin + nmin * deltat 

911 self.deltat = deltat 

912 self.set_ydata(ydata_new) 

913 

914 def stretch(self, tmin_new, tmax_new): 

915 ''' 

916 Stretch signal while preserving sample rate using sinc interpolation. 

917 

918 :param tmin_new: new time of first sample 

919 :param tmax_new: new time of last sample 

920 

921 This method can be used to correct for a small linear time drift or to 

922 introduce sub-sample time shifts. The amount of stretching is limited 

923 to 10% by the implementation and is expected to be much smaller than 

924 that by the approximations used. 

925 ''' 

926 

927 i_control = num.array([0, self.ydata.size-1], dtype=num.int64) 

928 t_control = num.array([tmin_new, tmax_new], dtype=float) 

929 

930 r = (tmax_new - tmin_new) / self.deltat + 1.0 

931 n_new = int(round(r)) 

932 if abs(n_new - r) > 0.001: 

933 n_new = int(math.floor(r)) 

934 

935 assert n_new >= 2 

936 

937 tmax_new = tmin_new + (n_new-1) * self.deltat 

938 

939 ydata_new = num.empty(n_new, dtype=float) 

940 signal_ext.antidrift(i_control, t_control, 

941 self.ydata.astype(float), 

942 tmin_new, self.deltat, ydata_new) 

943 

944 self.tmin = tmin_new 

945 self.set_ydata(ydata_new) 

946 self._update_ids() 

947 

948 def nyquist_check(self, frequency, intro='Corner frequency', warn=True, 

949 raise_exception=False): 

950 

951 ''' 

952 Check if a given frequency is above the Nyquist frequency of the trace. 

953 

954 :param intro: string used to introduce the warning/error message 

955 :param warn: whether to emit a warning 

956 :param raise_exception: whether to raise an :py:exc:`AboveNyquist` 

957 exception. 

958 ''' 

959 

960 if frequency >= 0.5/self.deltat: 

961 message = '%s (%g Hz) is equal to or higher than nyquist ' \ 

962 'frequency (%g Hz). (Trace %s)' \ 

963 % (intro, frequency, 0.5/self.deltat, self.name()) 

964 if warn: 

965 logger.warning(message) 

966 if raise_exception: 

967 raise AboveNyquist(message) 

968 

969 def lowpass(self, order, corner, nyquist_warn=True, 

970 nyquist_exception=False, demean=True): 

971 

972 ''' 

973 Apply Butterworth lowpass to the trace. 

974 

975 :param order: order of the filter 

976 :param corner: corner frequency of the filter 

977 

978 Mean is removed before filtering. 

979 ''' 

980 

981 self.nyquist_check( 

982 corner, 'Corner frequency of lowpass', nyquist_warn, 

983 nyquist_exception) 

984 

985 (b, a) = _get_cached_filter_coeffs( 

986 order, [corner*2.0*self.deltat], btype='low') 

987 

988 if len(a) != order+1 or len(b) != order+1: 

989 logger.warning( 

990 'Erroneous filter coefficients returned by ' 

991 'scipy.signal.butter(). You may need to downsample the ' 

992 'signal before filtering.') 

993 

994 data = self.ydata.astype(num.float64) 

995 if demean: 

996 data -= num.mean(data) 

997 self.drop_growbuffer() 

998 self.ydata = signal.lfilter(b, a, data) 

999 

1000 def highpass(self, order, corner, nyquist_warn=True, 

1001 nyquist_exception=False, demean=True): 

1002 

1003 ''' 

1004 Apply butterworth highpass to the trace. 

1005 

1006 :param order: order of the filter 

1007 :param corner: corner frequency of the filter 

1008 

1009 Mean is removed before filtering. 

1010 ''' 

1011 

1012 self.nyquist_check( 

1013 corner, 'Corner frequency of highpass', nyquist_warn, 

1014 nyquist_exception) 

1015 

1016 (b, a) = _get_cached_filter_coeffs( 

1017 order, [corner*2.0*self.deltat], btype='high') 

1018 

1019 data = self.ydata.astype(num.float64) 

1020 if len(a) != order+1 or len(b) != order+1: 

1021 logger.warning( 

1022 'Erroneous filter coefficients returned by ' 

1023 'scipy.signal.butter(). You may need to downsample the ' 

1024 'signal before filtering.') 

1025 if demean: 

1026 data -= num.mean(data) 

1027 self.drop_growbuffer() 

1028 self.ydata = signal.lfilter(b, a, data) 

1029 

1030 def bandpass(self, order, corner_hp, corner_lp, demean=True): 

1031 ''' 

1032 Apply butterworth bandpass to the trace. 

1033 

1034 :param order: order of the filter 

1035 :param corner_hp: lower corner frequency of the filter 

1036 :param corner_lp: upper corner frequency of the filter 

1037 

1038 Mean is removed before filtering. 

1039 ''' 

1040 

1041 self.nyquist_check(corner_hp, 'Lower corner frequency of bandpass') 

1042 self.nyquist_check(corner_lp, 'Higher corner frequency of bandpass') 

1043 (b, a) = _get_cached_filter_coeffs( 

1044 order, 

1045 [corner*2.0*self.deltat for corner in (corner_hp, corner_lp)], 

1046 btype='band') 

1047 data = self.ydata.astype(num.float64) 

1048 if demean: 

1049 data -= num.mean(data) 

1050 self.drop_growbuffer() 

1051 self.ydata = signal.lfilter(b, a, data) 

1052 

1053 def bandstop(self, order, corner_hp, corner_lp, demean=True): 

1054 ''' 

1055 Apply bandstop (attenuates frequencies in band) to the trace. 

1056 

1057 :param order: order of the filter 

1058 :param corner_hp: lower corner frequency of the filter 

1059 :param corner_lp: upper corner frequency of the filter 

1060 

1061 Mean is removed before filtering. 

1062 ''' 

1063 

1064 self.nyquist_check(corner_hp, 'Lower corner frequency of bandstop') 

1065 self.nyquist_check(corner_lp, 'Higher corner frequency of bandstop') 

1066 (b, a) = _get_cached_filter_coeffs( 

1067 order, 

1068 [corner*2.0*self.deltat for corner in (corner_hp, corner_lp)], 

1069 btype='bandstop') 

1070 data = self.ydata.astype(num.float64) 

1071 if demean: 

1072 data -= num.mean(data) 

1073 self.drop_growbuffer() 

1074 self.ydata = signal.lfilter(b, a, data) 

1075 

1076 def envelope(self, inplace=True): 

1077 ''' 

1078 Calculate the envelope of the trace. 

1079 

1080 :param inplace: calculate envelope in place 

1081 

1082 The calculation follows: 

1083 

1084 .. math:: 

1085 

1086 Y' = \\sqrt{Y^2+H(Y)^2} 

1087 

1088 where H is the Hilbert-Transform of the signal Y. 

1089 ''' 

1090 

1091 y = self.ydata.astype(float) 

1092 env = num.abs(hilbert(y)) 

1093 if inplace: 

1094 self.drop_growbuffer() 

1095 self.ydata = env 

1096 else: 

1097 tr = self.copy(data=False) 

1098 tr.ydata = env 

1099 return tr 

1100 

1101 def taper(self, taperer, inplace=True, chop=False): 

1102 ''' 

1103 Apply a :py:class:`Taper` to the trace. 

1104 

1105 :param taperer: instance of :py:class:`Taper` subclass 

1106 :param inplace: apply taper inplace 

1107 :param chop: if ``True``: exclude tapered parts from the resulting 

1108 trace 

1109 ''' 

1110 

1111 if not inplace: 

1112 tr = self.copy() 

1113 else: 

1114 tr = self 

1115 

1116 if chop: 

1117 i, n = taperer.span(tr.ydata, tr.tmin, tr.deltat) 

1118 tr.shift(i*tr.deltat) 

1119 tr.set_ydata(tr.ydata[i:i+n]) 

1120 

1121 taperer(tr.ydata, tr.tmin, tr.deltat) 

1122 

1123 if not inplace: 

1124 return tr 

1125 

1126 def whiten(self, order=6): 

1127 ''' 

1128 Whiten signal in time domain using autoregression and recursive filter. 

1129 

1130 :param order: order of the autoregression process 

1131 ''' 

1132 

1133 b, a = self.whitening_coefficients(order) 

1134 self.drop_growbuffer() 

1135 self.ydata = signal.lfilter(b, a, self.ydata) 

1136 

1137 def whitening_coefficients(self, order=6): 

1138 ar = yulewalker(self.ydata, order) 

1139 b, a = [1.] + ar.tolist(), [1.] 

1140 return b, a 

1141 

1142 def ampspec_whiten( 

1143 self, 

1144 width, 

1145 td_taper='auto', 

1146 fd_taper='auto', 

1147 pad_to_pow2=True, 

1148 demean=True): 

1149 

1150 ''' 

1151 Whiten signal via frequency domain using moving average on amplitude 

1152 spectra. 

1153 

1154 :param width: width of smoothing kernel [Hz] 

1155 :param td_taper: time domain taper, object of type :py:class:`Taper` or 

1156 ``None`` or ``'auto'``. 

1157 :param fd_taper: frequency domain taper, object of type 

1158 :py:class:`Taper` or ``None`` or ``'auto'``. 

1159 :param pad_to_pow2: whether to pad the signal with zeros up to a length 

1160 of 2^n 

1161 :param demean: whether to demean the signal before tapering 

1162 

1163 The signal is first demeaned and then tapered using ``td_taper``. Then, 

1164 the spectrum is calculated and inversely weighted with a smoothed 

1165 version of its amplitude spectrum. A moving average is used for the 

1166 smoothing. The smoothed spectrum is then tapered using ``fd_taper``. 

1167 Finally, the smoothed and tapered spectrum is back-transformed into the 

1168 time domain. 

1169 

1170 If ``td_taper`` is set to ``'auto'``, ``CosFader(1.0/width)`` is used. 

1171 If ``fd_taper`` is set to ``'auto'``, ``CosFader(width)`` is used. 

1172 ''' 

1173 

1174 ndata = self.data_len() 

1175 

1176 if pad_to_pow2: 

1177 ntrans = nextpow2(ndata) 

1178 else: 

1179 ntrans = ndata 

1180 

1181 df = 1./(ntrans*self.deltat) 

1182 nw = int(round(width/df)) 

1183 if ndata//2+1 <= nw: 

1184 raise TraceTooShort( 

1185 'Samples in trace: %s, samples needed: %s' % (ndata, nw)) 

1186 

1187 if td_taper == 'auto': 

1188 td_taper = CosFader(1./width) 

1189 

1190 if fd_taper == 'auto': 

1191 fd_taper = CosFader(width) 

1192 

1193 if td_taper: 

1194 self.taper(td_taper) 

1195 

1196 ydata = self.get_ydata().astype(float) 

1197 if demean: 

1198 ydata -= ydata.mean() 

1199 

1200 spec = num.fft.rfft(ydata, ntrans) 

1201 

1202 amp = num.abs(spec) 

1203 nspec = amp.size 

1204 csamp = num.cumsum(amp) 

1205 amp_smoothed = num.empty(nspec, dtype=csamp.dtype) 

1206 n1, n2 = nw//2, nw//2 + nspec - nw 

1207 amp_smoothed[n1:n2] = (csamp[nw:] - csamp[:-nw]) / nw 

1208 amp_smoothed[:n1] = amp_smoothed[n1] 

1209 amp_smoothed[n2:] = amp_smoothed[n2-1] 

1210 

1211 denom = amp_smoothed * amp 

1212 numer = amp 

1213 eps = num.mean(denom) * 1e-9 

1214 if eps == 0.0: 

1215 eps = 1e-9 

1216 

1217 numer += eps 

1218 denom += eps 

1219 spec *= numer/denom 

1220 

1221 if fd_taper: 

1222 fd_taper(spec, 0., df) 

1223 

1224 ydata = num.fft.irfft(spec) 

1225 self.set_ydata(ydata[:ndata]) 

1226 

1227 def _get_cached_freqs(self, nf, deltaf): 

1228 ck = (nf, deltaf) 

1229 if ck not in Trace.cached_frequencies: 

1230 Trace.cached_frequencies[ck] = deltaf * num.arange( 

1231 nf, dtype=float) 

1232 

1233 return Trace.cached_frequencies[ck] 

1234 

1235 def bandpass_fft(self, corner_hp, corner_lp): 

1236 ''' 

1237 Apply boxcar bandbpass to trace (in spectral domain). 

1238 ''' 

1239 

1240 n = len(self.ydata) 

1241 n2 = nextpow2(n) 

1242 data = num.zeros(n2, dtype=num.float64) 

1243 data[:n] = self.ydata 

1244 fdata = num.fft.rfft(data) 

1245 freqs = self._get_cached_freqs(len(fdata), 1./(self.deltat*n2)) 

1246 fdata[0] = 0.0 

1247 fdata *= num.logical_and(corner_hp < freqs, freqs < corner_lp) 

1248 data = num.fft.irfft(fdata) 

1249 self.drop_growbuffer() 

1250 self.ydata = data[:n] 

1251 

1252 def shift(self, tshift): 

1253 ''' 

1254 Time shift the trace. 

1255 ''' 

1256 

1257 self.tmin += tshift 

1258 self.tmax += tshift 

1259 self._update_ids() 

1260 

1261 def snap(self, inplace=True, interpolate=False): 

1262 ''' 

1263 Shift trace samples to nearest even multiples of the sampling rate. 

1264 

1265 :param inplace: (boolean) snap traces inplace 

1266 

1267 If ``inplace`` is ``False`` and the difference of tmin and tmax of 

1268 both, the snapped and the original trace is smaller than 0.01 x deltat, 

1269 :py:func:`snap` returns the unsnapped instance of the original trace. 

1270 ''' 

1271 

1272 tmin = round(self.tmin/self.deltat)*self.deltat 

1273 tmax = tmin + (self.ydata.size-1)*self.deltat 

1274 

1275 if inplace: 

1276 xself = self 

1277 else: 

1278 if abs(self.tmin - tmin) < 1e-2*self.deltat and \ 

1279 abs(self.tmax - tmax) < 1e-2*self.deltat: 

1280 return self 

1281 

1282 xself = self.copy() 

1283 

1284 if interpolate: 

1285 n = xself.data_len() 

1286 ydata_new = num.empty(n, dtype=float) 

1287 i_control = num.array([0, n-1], dtype=num.int64) 

1288 tref = tmin 

1289 t_control = num.array( 

1290 [float(xself.tmin-tref), float(xself.tmax-tref)], 

1291 dtype=float) 

1292 

1293 signal_ext.antidrift(i_control, t_control, 

1294 xself.ydata.astype(float), 

1295 float(tmin-tref), xself.deltat, ydata_new) 

1296 

1297 xself.ydata = ydata_new 

1298 

1299 xself.tmin = tmin 

1300 xself.tmax = tmax 

1301 xself._update_ids() 

1302 

1303 return xself 

1304 

1305 def fix_deltat_rounding_errors(self): 

1306 ''' 

1307 Try to undo sampling rate rounding errors. 

1308 

1309 See :py:func:`fix_deltat_rounding_errors`. 

1310 ''' 

1311 

1312 self.deltat = fix_deltat_rounding_errors(self.deltat) 

1313 self.tmax = self.tmin + (self.data_len() - 1) * self.deltat 

1314 

1315 def sta_lta_centered(self, tshort, tlong, quad=True, scalingmethod=1): 

1316 ''' 

1317 Run special STA/LTA filter where the short time window is centered on 

1318 the long time window. 

1319 

1320 :param tshort: length of short time window in [s] 

1321 :param tlong: length of long time window in [s] 

1322 :param quad: whether to square the data prior to applying the STA/LTA 

1323 filter 

1324 :param scalingmethod: integer key to select how output values are 

1325 scaled / normalized (``1``, ``2``, or ``3``) 

1326 

1327 ============= ====================================== =========== 

1328 Scalingmethod Implementation Range 

1329 ============= ====================================== =========== 

1330 ``1`` As/Al* Ts/Tl [0,1] 

1331 ``2`` (As/Al - 1) / (Tl/Ts - 1) [-Ts/Tl,1] 

1332 ``3`` Like ``2`` but clipping range at zero [0,1] 

1333 ============= ====================================== =========== 

1334 

1335 ''' 

1336 

1337 nshort = int(round(tshort/self.deltat)) 

1338 nlong = int(round(tlong/self.deltat)) 

1339 

1340 assert nshort < nlong 

1341 if nlong > len(self.ydata): 

1342 raise TraceTooShort( 

1343 'Samples in trace: %s, samples needed: %s' 

1344 % (len(self.ydata), nlong)) 

1345 

1346 if quad: 

1347 sqrdata = self.ydata**2 

1348 else: 

1349 sqrdata = self.ydata 

1350 

1351 mavg_short = moving_avg(sqrdata, nshort) 

1352 mavg_long = moving_avg(sqrdata, nlong) 

1353 

1354 self.drop_growbuffer() 

1355 

1356 if scalingmethod not in (1, 2, 3): 

1357 raise Exception('Invalid argument to scalingrange argument.') 

1358 

1359 if scalingmethod == 1: 

1360 self.ydata = mavg_short/mavg_long * float(nshort)/float(nlong) 

1361 elif scalingmethod in (2, 3): 

1362 self.ydata = (mavg_short/mavg_long - 1.) \ 

1363 / ((float(nlong)/float(nshort)) - 1) 

1364 

1365 if scalingmethod == 3: 

1366 self.ydata = num.maximum(self.ydata, 0.) 

1367 

1368 def sta_lta_right(self, tshort, tlong, quad=True, scalingmethod=1): 

1369 ''' 

1370 Run special STA/LTA filter where the short time window is overlapping 

1371 with the last part of the long time window. 

1372 

1373 :param tshort: length of short time window in [s] 

1374 :param tlong: length of long time window in [s] 

1375 :param quad: whether to square the data prior to applying the STA/LTA 

1376 filter 

1377 :param scalingmethod: integer key to select how output values are 

1378 scaled / normalized (``1``, ``2``, or ``3``) 

1379 

1380 ============= ====================================== =========== 

1381 Scalingmethod Implementation Range 

1382 ============= ====================================== =========== 

1383 ``1`` As/Al* Ts/Tl [0,1] 

1384 ``2`` (As/Al - 1) / (Tl/Ts - 1) [-Ts/Tl,1] 

1385 ``3`` Like ``2`` but clipping range at zero [0,1] 

1386 ============= ====================================== =========== 

1387 

1388 With ``scalingmethod=1``, the values produced by this variant of the 

1389 STA/LTA are equivalent to 

1390 

1391 .. math:: 

1392 s_i = \\frac{s}{l} \\frac{\\frac{1}{s}\\sum_{j=i}^{i+s-1} f_j} 

1393 {\\frac{1}{l}\\sum_{j=i+s-l}^{i+s-1} f_j} 

1394 

1395 where :math:`f_j` are the input samples, :math:`s` are the number of 

1396 samples in the short time window and :math:`l` are the number of 

1397 samples in the long time window. 

1398 ''' 

1399 

1400 n = self.data_len() 

1401 tmin = self.tmin 

1402 

1403 nshort = max(1, int(round(tshort/self.deltat))) 

1404 nlong = max(1, int(round(tlong/self.deltat))) 

1405 

1406 assert nshort < nlong 

1407 

1408 if nlong > len(self.ydata): 

1409 raise TraceTooShort( 

1410 'Samples in trace: %s, samples needed: %s' 

1411 % (len(self.ydata), nlong)) 

1412 

1413 if quad: 

1414 sqrdata = self.ydata**2 

1415 else: 

1416 sqrdata = self.ydata 

1417 

1418 nshift = int(math.floor(0.5 * (nlong - nshort))) 

1419 if nlong % 2 != 0 and nshort % 2 == 0: 

1420 nshift += 1 

1421 

1422 mavg_short = moving_avg(sqrdata, nshort)[nshift:] 

1423 mavg_long = moving_avg(sqrdata, nlong)[:sqrdata.size-nshift] 

1424 

1425 self.drop_growbuffer() 

1426 

1427 if scalingmethod not in (1, 2, 3): 

1428 raise Exception('Invalid argument to scalingrange argument.') 

1429 

1430 if scalingmethod == 1: 

1431 ydata = mavg_short/mavg_long * nshort/nlong 

1432 elif scalingmethod in (2, 3): 

1433 ydata = (mavg_short/mavg_long - 1.) \ 

1434 / ((float(nlong)/float(nshort)) - 1) 

1435 

1436 if scalingmethod == 3: 

1437 ydata = num.maximum(self.ydata, 0.) 

1438 

1439 self.set_ydata(ydata) 

1440 

1441 self.shift((math.ceil(0.5*nlong) - nshort + 1) * self.deltat) 

1442 

1443 self.chop( 

1444 tmin + (nlong - nshort) * self.deltat, 

1445 tmin + (n - nshort) * self.deltat) 

1446 

1447 def peaks(self, threshold, tsearch, 

1448 deadtime=False, 

1449 nblock_duration_detection=100): 

1450 

1451 ''' 

1452 Detect peaks above a given threshold (method 1). 

1453 

1454 From every instant, where the signal rises above ``threshold``, a time 

1455 length of ``tsearch`` seconds is searched for a maximum. A list with 

1456 tuples (time, value) for each detected peak is returned. The 

1457 ``deadtime`` argument turns on a special deadtime duration detection 

1458 algorithm useful in combination with recursive STA/LTA filters. 

1459 ''' 

1460 

1461 y = self.ydata 

1462 above = num.where(y > threshold, 1, 0) 

1463 deriv = num.zeros(y.size, dtype=num.int8) 

1464 deriv[1:] = above[1:]-above[:-1] 

1465 itrig_positions = num.nonzero(deriv > 0)[0] 

1466 tpeaks = [] 

1467 apeaks = [] 

1468 tzeros = [] 

1469 tzero = self.tmin 

1470 

1471 for itrig_pos in itrig_positions: 

1472 ibeg = itrig_pos 

1473 iend = min( 

1474 len(self.ydata), 

1475 itrig_pos + int(math.ceil(tsearch/self.deltat))) 

1476 ipeak = num.argmax(y[ibeg:iend]) 

1477 tpeak = self.tmin + (ipeak+ibeg)*self.deltat 

1478 apeak = y[ibeg+ipeak] 

1479 

1480 if tpeak < tzero: 

1481 continue 

1482 

1483 if deadtime: 

1484 ibeg = itrig_pos 

1485 iblock = 0 

1486 nblock = nblock_duration_detection 

1487 totalsum = 0. 

1488 while True: 

1489 if ibeg+iblock*nblock >= len(y): 

1490 tzero = self.tmin + (len(y)-1) * self.deltat 

1491 break 

1492 

1493 logy = num.log( 

1494 y[ibeg+iblock*nblock:ibeg+(iblock+1)*nblock]) 

1495 logy[0] += totalsum 

1496 ysum = num.cumsum(logy) 

1497 totalsum = ysum[-1] 

1498 below = num.where(ysum <= 0., 1, 0) 

1499 deriv = num.zeros(ysum.size, dtype=num.int8) 

1500 deriv[1:] = below[1:]-below[:-1] 

1501 izero_positions = num.nonzero(deriv > 0)[0] + iblock*nblock 

1502 if len(izero_positions) > 0: 

1503 tzero = self.tmin + self.deltat * ( 

1504 ibeg + izero_positions[0]) 

1505 break 

1506 iblock += 1 

1507 else: 

1508 tzero = ibeg*self.deltat + self.tmin + tsearch 

1509 

1510 tpeaks.append(tpeak) 

1511 apeaks.append(apeak) 

1512 tzeros.append(tzero) 

1513 

1514 if deadtime: 

1515 return tpeaks, apeaks, tzeros 

1516 else: 

1517 return tpeaks, apeaks 

1518 

1519 def peaks2(self, threshold, tsearch): 

1520 

1521 ''' 

1522 Detect peaks above a given threshold (method 2). 

1523 

1524 This variant of peak detection is a bit more robust (and slower) than 

1525 the one implemented in :py:meth:`Trace.peaks`. First all samples with 

1526 ``a[i-1] < a[i] > a[i+1]`` are masked as potential peaks. From these, 

1527 iteratively the one with the maximum amplitude ``a[j]`` and time 

1528 ``t[j]`` is choosen and potential peaks within 

1529 ``t[j] - tsearch, t[j] + tsearch`` 

1530 are discarded. The algorithm stops, when ``a[j] < threshold`` or when 

1531 no more potential peaks are left. 

1532 ''' 

1533 

1534 a = num.copy(self.ydata) 

1535 

1536 amin = num.min(a) 

1537 

1538 a[0] = amin 

1539 a[1: -1][num.diff(a, 2) <= 0.] = amin 

1540 a[-1] = amin 

1541 

1542 data = [] 

1543 while True: 

1544 imax = num.argmax(a) 

1545 amax = a[imax] 

1546 

1547 if amax < threshold or amax == amin: 

1548 break 

1549 

1550 data.append((self.tmin + imax * self.deltat, amax)) 

1551 

1552 ntsearch = int(round(tsearch / self.deltat)) 

1553 a[max(imax-ntsearch//2, 0):min(imax+ntsearch//2, a.size)] = amin 

1554 

1555 if data: 

1556 data.sort() 

1557 tpeaks, apeaks = list(zip(*data)) 

1558 else: 

1559 tpeaks, apeaks = [], [] 

1560 

1561 return tpeaks, apeaks 

1562 

1563 def extend(self, tmin=None, tmax=None, fillmethod='zeros'): 

1564 ''' 

1565 Extend trace to given span. 

1566 

1567 :param tmin: begin time of new span 

1568 :param tmax: end time of new span 

1569 :param fillmethod: ``'zeros'``, ``'repeat'``, ``'mean'``, or 

1570 ``'median'`` 

1571 ''' 

1572 

1573 nold = self.ydata.size 

1574 

1575 if tmin is not None: 

1576 nl = min(0, int(round((tmin-self.tmin)/self.deltat))) 

1577 else: 

1578 nl = 0 

1579 

1580 if tmax is not None: 

1581 nh = max(nold - 1, int(round((tmax-self.tmin)/self.deltat))) 

1582 else: 

1583 nh = nold - 1 

1584 

1585 n = nh - nl + 1 

1586 data = num.zeros(n, dtype=self.ydata.dtype) 

1587 data[-nl:-nl + nold] = self.ydata 

1588 if self.ydata.size >= 1: 

1589 if fillmethod == 'repeat': 

1590 data[:-nl] = self.ydata[0] 

1591 data[-nl + nold:] = self.ydata[-1] 

1592 elif fillmethod == 'median': 

1593 v = num.median(self.ydata) 

1594 data[:-nl] = v 

1595 data[-nl + nold:] = v 

1596 elif fillmethod == 'mean': 

1597 v = num.mean(self.ydata) 

1598 data[:-nl] = v 

1599 data[-nl + nold:] = v 

1600 

1601 self.drop_growbuffer() 

1602 self.ydata = data 

1603 

1604 self.tmin += nl * self.deltat 

1605 self.tmax = self.tmin + (self.ydata.size - 1) * self.deltat 

1606 

1607 self._update_ids() 

1608 

1609 def transfer(self, 

1610 tfade=0., 

1611 freqlimits=None, 

1612 transfer_function=None, 

1613 cut_off_fading=True, 

1614 demean=True, 

1615 invert=False): 

1616 

1617 ''' 

1618 Return new trace with transfer function applied (convolution). 

1619 

1620 :param tfade: rise/fall time in seconds of taper applied in timedomain 

1621 at both ends of trace. 

1622 :param freqlimits: 4-tuple with corner frequencies in Hz. 

1623 :param transfer_function: FrequencyResponse object; must provide a 

1624 method 'evaluate(freqs)', which returns the transfer function 

1625 coefficients at the frequencies 'freqs'. 

1626 :param cut_off_fading: whether to cut off rise/fall interval in output 

1627 trace. 

1628 :param demean: remove mean before applying transfer function 

1629 :param invert: set to True to do a deconvolution 

1630 ''' 

1631 

1632 if transfer_function is None: 

1633 transfer_function = g_one_response 

1634 

1635 if self.tmax - self.tmin <= tfade*2.: 

1636 raise TraceTooShort( 

1637 'Trace %s.%s.%s.%s too short for fading length setting. ' 

1638 'trace length = %g, fading length = %g' 

1639 % (self.nslc_id + (self.tmax-self.tmin, tfade))) 

1640 

1641 if freqlimits is None and ( 

1642 transfer_function is None or transfer_function.is_scalar()): 

1643 

1644 # special case for flat responses 

1645 

1646 output = self.copy() 

1647 data = self.ydata 

1648 ndata = data.size 

1649 

1650 if transfer_function is not None: 

1651 c = num.abs(transfer_function.evaluate(num.ones(1))[0]) 

1652 

1653 if invert: 

1654 c = 1.0/c 

1655 

1656 data *= c 

1657 

1658 if tfade != 0.0: 

1659 data *= costaper( 

1660 0., tfade, self.deltat*(ndata-1)-tfade, self.deltat*ndata, 

1661 ndata, self.deltat) 

1662 

1663 output.ydata = data 

1664 

1665 else: 

1666 ndata = self.ydata.size 

1667 ntrans = nextpow2(ndata*1.2) 

1668 coeffs = self._get_tapered_coeffs( 

1669 ntrans, freqlimits, transfer_function, invert=invert, 

1670 demean=demean) 

1671 

1672 data = self.ydata 

1673 

1674 data_pad = num.zeros(ntrans, dtype=float) 

1675 data_pad[:ndata] = data 

1676 if demean: 

1677 data_pad[:ndata] -= data.mean() 

1678 

1679 if tfade != 0.0: 

1680 data_pad[:ndata] *= costaper( 

1681 0., tfade, self.deltat*(ndata-1)-tfade, self.deltat*ndata, 

1682 ndata, self.deltat) 

1683 

1684 fdata = num.fft.rfft(data_pad) 

1685 fdata *= coeffs 

1686 ddata = num.fft.irfft(fdata) 

1687 output = self.copy() 

1688 output.ydata = ddata[:ndata] 

1689 

1690 if cut_off_fading and tfade != 0.0: 

1691 try: 

1692 output.chop(output.tmin+tfade, output.tmax-tfade, inplace=True) 

1693 except NoData: 

1694 raise TraceTooShort( 

1695 'Trace %s.%s.%s.%s too short for fading length setting. ' 

1696 'trace length = %g, fading length = %g' 

1697 % (self.nslc_id + (self.tmax-self.tmin, tfade))) 

1698 else: 

1699 output.ydata = output.ydata.copy() 

1700 

1701 return output 

1702 

1703 def differentiate(self, n=1, order=4, inplace=True): 

1704 ''' 

1705 Approximate first or second derivative of the trace. 

1706 

1707 :param n: 1 for first derivative, 2 for second 

1708 :param order: order of the approximation 2 and 4 are supported 

1709 :param inplace: if ``True`` the trace is differentiated in place, 

1710 otherwise a new trace object with the derivative is returned. 

1711 

1712 Raises :py:exc:`ValueError` for unsupported `n` or `order`. 

1713 

1714 See :py:func:`~pyrocko.util.diff_fd` for implementation details. 

1715 ''' 

1716 

1717 ddata = util.diff_fd(n, order, self.deltat, self.ydata) 

1718 

1719 if inplace: 

1720 self.ydata = ddata 

1721 else: 

1722 output = self.copy(data=False) 

1723 output.set_ydata(ddata) 

1724 return output 

1725 

1726 def drop_chain_cache(self): 

1727 if self._pchain: 

1728 self._pchain.clear() 

1729 

1730 def init_chain(self): 

1731 self._pchain = pchain.Chain( 

1732 do_downsample, 

1733 do_extend, 

1734 do_pre_taper, 

1735 do_fft, 

1736 do_filter, 

1737 do_ifft) 

1738 

1739 def run_chain(self, tmin, tmax, deltat, setup, nocache): 

1740 if setup.domain == 'frequency_domain': 

1741 _, _, data = self._pchain( 

1742 (self, deltat), 

1743 (tmin, tmax), 

1744 (setup.taper,), 

1745 (setup.filter,), 

1746 (setup.filter,), 

1747 nocache=nocache) 

1748 

1749 return num.abs(data), num.abs(data) 

1750 

1751 else: 

1752 processed = self._pchain( 

1753 (self, deltat), 

1754 (tmin, tmax), 

1755 (setup.taper,), 

1756 (setup.filter,), 

1757 (setup.filter,), 

1758 (), 

1759 nocache=nocache) 

1760 

1761 if setup.domain == 'time_domain': 

1762 data = processed.get_ydata() 

1763 

1764 elif setup.domain == 'envelope': 

1765 processed = processed.envelope(inplace=False) 

1766 

1767 elif setup.domain == 'absolute': 

1768 processed.set_ydata(num.abs(processed.get_ydata())) 

1769 

1770 return processed.get_ydata(), processed 

1771 

1772 def misfit(self, candidate, setup, nocache=False, debug=False): 

1773 ''' 

1774 Calculate misfit and normalization factor against candidate trace. 

1775 

1776 :param candidate: :py:class:`Trace` object 

1777 :param setup: :py:class:`MisfitSetup` object 

1778 :returns: tuple ``(m, n)``, where m is the misfit value and n is the 

1779 normalization divisor 

1780 

1781 If the sampling rates of ``self`` and ``candidate`` differ, the trace 

1782 with the higher sampling rate will be downsampled. 

1783 ''' 

1784 

1785 a = self 

1786 b = candidate 

1787 

1788 for tr in (a, b): 

1789 if not tr._pchain: 

1790 tr.init_chain() 

1791 

1792 deltat = max(a.deltat, b.deltat) 

1793 tmin = min(a.tmin, b.tmin) - deltat 

1794 tmax = max(a.tmax, b.tmax) + deltat 

1795 

1796 adata, aproc = a.run_chain(tmin, tmax, deltat, setup, nocache) 

1797 bdata, bproc = b.run_chain(tmin, tmax, deltat, setup, nocache) 

1798 

1799 if setup.domain != 'cc_max_norm': 

1800 m, n = Lx_norm(bdata, adata, norm=setup.norm) 

1801 else: 

1802 ctr = correlate(aproc, bproc, mode='full', normalization='normal') 

1803 ccmax = ctr.max()[1] 

1804 m = 0.5 - 0.5 * ccmax 

1805 n = 0.5 

1806 

1807 if debug: 

1808 return m, n, aproc, bproc 

1809 else: 

1810 return m, n 

1811 

1812 def spectrum(self, pad_to_pow2=False, tfade=None): 

1813 ''' 

1814 Get FFT spectrum of trace. 

1815 

1816 :param pad_to_pow2: whether to zero-pad the data to next larger 

1817 power-of-two length 

1818 :param tfade: ``None`` or a time length in seconds, to apply cosine 

1819 shaped tapers to both 

1820 

1821 :returns: a tuple with (frequencies, values) 

1822 ''' 

1823 

1824 ndata = self.ydata.size 

1825 

1826 if pad_to_pow2: 

1827 ntrans = nextpow2(ndata) 

1828 else: 

1829 ntrans = ndata 

1830 

1831 if tfade is None: 

1832 ydata = self.ydata 

1833 else: 

1834 ydata = self.ydata * costaper( 

1835 0., tfade, self.deltat*(ndata-1)-tfade, self.deltat*ndata, 

1836 ndata, self.deltat) 

1837 

1838 fydata = num.fft.rfft(ydata, ntrans) 

1839 df = 1./(ntrans*self.deltat) 

1840 fxdata = num.arange(len(fydata))*df 

1841 return fxdata, fydata 

1842 

1843 def multi_filter(self, filter_freqs, bandwidth): 

1844 

1845 class Gauss(FrequencyResponse): 

1846 f0 = Float.T() 

1847 a = Float.T(default=1.0) 

1848 

1849 def __init__(self, f0, a=1.0, **kwargs): 

1850 FrequencyResponse.__init__(self, f0=f0, a=a, **kwargs) 

1851 

1852 def evaluate(self, freqs): 

1853 omega0 = 2.*math.pi*self.f0 

1854 omega = 2.*math.pi*freqs 

1855 return num.exp(-((omega-omega0) 

1856 / (self.a*omega0))**2) 

1857 

1858 freqs, coeffs = self.spectrum() 

1859 n = self.data_len() 

1860 nfilt = len(filter_freqs) 

1861 signal_tf = num.zeros((nfilt, n)) 

1862 centroid_freqs = num.zeros(nfilt) 

1863 for ifilt, f0 in enumerate(filter_freqs): 

1864 taper = Gauss(f0, a=bandwidth) 

1865 weights = taper.evaluate(freqs) 

1866 nhalf = freqs.size 

1867 analytic_spec = num.zeros(n, dtype=complex) 

1868 analytic_spec[:nhalf] = coeffs*weights 

1869 

1870 enorm = num.abs(analytic_spec[:nhalf])**2 

1871 enorm /= num.sum(enorm) 

1872 

1873 if n % 2 == 0: 

1874 analytic_spec[1:nhalf-1] *= 2. 

1875 else: 

1876 analytic_spec[1:nhalf] *= 2. 

1877 

1878 analytic = num.fft.ifft(analytic_spec) 

1879 signal_tf[ifilt, :] = num.abs(analytic) 

1880 

1881 enorm = num.abs(analytic_spec[:nhalf])**2 

1882 enorm /= num.sum(enorm) 

1883 centroid_freqs[ifilt] = num.sum(freqs*enorm) 

1884 

1885 return centroid_freqs, signal_tf 

1886 

1887 def _get_tapered_coeffs( 

1888 self, ntrans, freqlimits, transfer_function, invert=False, 

1889 demean=True): 

1890 

1891 cache_key = ( 

1892 ntrans, self.deltat, freqlimits, transfer_function.uuid, invert, 

1893 demean) 

1894 

1895 if cache_key in g_tapered_coeffs_cache: 

1896 return g_tapered_coeffs_cache[cache_key] 

1897 

1898 deltaf = 1./(self.deltat*ntrans) 

1899 nfreqs = ntrans//2 + 1 

1900 transfer = num.ones(nfreqs, dtype=complex) 

1901 hi = snapper(nfreqs, deltaf) 

1902 if freqlimits is not None: 

1903 kmin, kmax = hi(freqlimits[0]), hi(freqlimits[3]) 

1904 freqs = num.arange(kmin, kmax)*deltaf 

1905 coeffs = transfer_function.evaluate(freqs) 

1906 if invert: 

1907 if num.any(coeffs == 0.0): 

1908 raise InfiniteResponse('%s.%s.%s.%s' % self.nslc_id) 

1909 

1910 transfer[kmin:kmax] = 1.0 / coeffs 

1911 else: 

1912 transfer[kmin:kmax] = coeffs 

1913 

1914 tapered_transfer = costaper(*freqlimits, nfreqs, deltaf) * transfer 

1915 else: 

1916 if invert: 

1917 raise Exception( 

1918 'transfer: `freqlimits` must be given when `invert` is ' 

1919 'set to `True`') 

1920 

1921 freqs = num.arange(nfreqs) * deltaf 

1922 tapered_transfer = transfer_function.evaluate(freqs) 

1923 

1924 g_tapered_coeffs_cache[cache_key] = tapered_transfer 

1925 

1926 if demean: 

1927 tapered_transfer[0] = 0.0 # don't introduce static offsets 

1928 

1929 return tapered_transfer 

1930 

1931 def fill_template(self, template, **additional): 

1932 ''' 

1933 Fill string template with trace metadata. 

1934 

1935 Uses normal python '%(placeholder)s' string templates. The following 

1936 placeholders are considered: ``network``, ``station``, ``location``, 

1937 ``channel``, ``tmin`` (time of first sample), ``tmax`` (time of last 

1938 sample), ``tmin_ms``, ``tmax_ms``, ``tmin_us``, ``tmax_us``, 

1939 ``tmin_year``, ``tmax_year``, ``tmin_month``, ``tmax_month``, 

1940 ``tmin_day``, ``tmax_day``, ``julianday``. The variants ending with 

1941 ``'_ms'`` include milliseconds, those with ``'_us'`` include 

1942 microseconds, those with ``'_year'`` contain only the year. 

1943 ''' 

1944 

1945 template = template.replace('%n', '%(network)s')\ 

1946 .replace('%s', '%(station)s')\ 

1947 .replace('%l', '%(location)s')\ 

1948 .replace('%c', '%(channel)s')\ 

1949 .replace('%b', '%(tmin)s')\ 

1950 .replace('%e', '%(tmax)s')\ 

1951 .replace('%j', '%(julianday)s') 

1952 

1953 params = dict( 

1954 zip(('network', 'station', 'location', 'channel'), self.nslc_id)) 

1955 params['tmin'] = util.time_to_str( 

1956 self.tmin, format='%Y-%m-%d_%H-%M-%S') 

1957 params['tmax'] = util.time_to_str( 

1958 self.tmax, format='%Y-%m-%d_%H-%M-%S') 

1959 params['tmin_ms'] = util.time_to_str( 

1960 self.tmin, format='%Y-%m-%d_%H-%M-%S.3FRAC') 

1961 params['tmax_ms'] = util.time_to_str( 

1962 self.tmax, format='%Y-%m-%d_%H-%M-%S.3FRAC') 

1963 params['tmin_us'] = util.time_to_str( 

1964 self.tmin, format='%Y-%m-%d_%H-%M-%S.6FRAC') 

1965 params['tmax_us'] = util.time_to_str( 

1966 self.tmax, format='%Y-%m-%d_%H-%M-%S.6FRAC') 

1967 params['tmin_year'], params['tmin_month'], params['tmin_day'] \ 

1968 = util.time_to_str(self.tmin, format='%Y-%m-%d').split('-') 

1969 params['tmax_year'], params['tmax_month'], params['tmax_day'] \ 

1970 = util.time_to_str(self.tmax, format='%Y-%m-%d').split('-') 

1971 params['julianday'] = util.julian_day_of_year(self.tmin) 

1972 params.update(additional) 

1973 return template % params 

1974 

1975 def plot(self): 

1976 ''' 

1977 Show trace with matplotlib. 

1978 

1979 See also: :py:meth:`Trace.snuffle`. 

1980 ''' 

1981 

1982 import pylab 

1983 pylab.plot(self.get_xdata(), self.get_ydata()) 

1984 name = '%s %s %s - %s' % ( 

1985 self.channel, 

1986 self.station, 

1987 time.strftime('%d-%m-%y %H:%M:%S', time.gmtime(self.tmin)), 

1988 time.strftime('%d-%m-%y %H:%M:%S', time.gmtime(self.tmax))) 

1989 

1990 pylab.title(name) 

1991 pylab.show() 

1992 

1993 def snuffle(self, **kwargs): 

1994 ''' 

1995 Show trace in a snuffler window. 

1996 

1997 :param stations: list of :py:class:`pyrocko.model.station.Station` 

1998 objects or ``None`` 

1999 :param events: list of :py:class:`pyrocko.model.event.Event` objects or 

2000 ``None`` 

2001 :param markers: list of :py:class:`pyrocko.gui.snuffler.marker.Marker` 

2002 objects or ``None`` 

2003 :param ntracks: float, number of tracks to be shown initially (default: 

2004 12) 

2005 :param follow: time interval (in seconds) for real time follow mode or 

2006 ``None`` 

2007 :param controls: bool, whether to show the main controls (default: 

2008 ``True``) 

2009 :param opengl: bool, whether to use opengl (default: ``False``) 

2010 ''' 

2011 

2012 return snuffle([self], **kwargs) 

2013 

2014 

2015def snuffle(traces, **kwargs): 

2016 ''' 

2017 Show traces in a snuffler window. 

2018 

2019 :param stations: list of :py:class:`pyrocko.model.station.Station` objects 

2020 or ``None`` 

2021 :param events: list of :py:class:`pyrocko.model.event.Event` objects or 

2022 ``None`` 

2023 :param markers: list of :py:class:`pyrocko.gui.snuffler.marker.Marker` 

2024 objects or ``None`` 

2025 :param ntracks: int, number of tracks to be shown initially (default: 12) 

2026 :param follow: time interval (in seconds) for real time follow mode or 

2027 ``None`` 

2028 :param controls: bool, whether to show the main controls (default: 

2029 ``True``) 

2030 :param opengl: bool, whether to use opengl (default: ``False``) 

2031 ''' 

2032 

2033 from pyrocko import pile 

2034 from pyrocko.gui.snuffler import snuffler 

2035 p = pile.Pile() 

2036 if traces: 

2037 trf = pile.MemTracesFile(None, traces) 

2038 p.add_file(trf) 

2039 return snuffler.snuffle(p, **kwargs) 

2040 

2041 

2042def downsample_tpad( 

2043 deltat_in, deltat_out, allow_upsample_max=1, ftype='fir-remez'): 

2044 ''' 

2045 Get approximate amount of cutoff which will be produced by downsampling. 

2046 

2047 The :py:meth:`Trace.downsample_to` method removes some samples at the 

2048 beginning and end of the trace which is downsampled. This function 

2049 estimates the approximate length [s] which will be cut off for a given set 

2050 of parameters supplied to :py:meth:`Trace.downsample_to`. 

2051 

2052 :param deltat_in: 

2053 Input sampling interval [s]. 

2054 :type deltat_in: 

2055 float 

2056 

2057 :param deltat_out: 

2058 Output samling interval [s]. 

2059 :type deltat_out: 

2060 float 

2061 

2062 :returns: 

2063 Approximate length [s] which will be cut off. 

2064 

2065 See :py:meth:`Trace.downsample_to` for details. 

2066 ''' 

2067 

2068 upsratio, deci_seq = _configure_downsampling( 

2069 deltat_in, deltat_out, allow_upsample_max) 

2070 

2071 tpad = 0.0 

2072 deltat = deltat_in / upsratio 

2073 for deci in deci_seq: 

2074 b, a, n = util.decimate_coeffs(deci, None, ftype) 

2075 # n//2 for the antialiasing 

2076 # +deci for possible snap to multiples 

2077 # +1 for rounding errors 

2078 tpad += (n//2 + deci + 1) * deltat 

2079 deltat = deltat * deci 

2080 

2081 return tpad 

2082 

2083 

2084def _configure_downsampling(deltat_in, deltat_out, allow_upsample_max): 

2085 for upsratio in range(1, allow_upsample_max+1): 

2086 dratio = (upsratio/deltat_in) / (1./deltat_out) 

2087 deci_seq = util.decitab(int(round(dratio))) 

2088 if abs(dratio - round(dratio)) / dratio < 0.0001 and deci_seq: 

2089 return upsratio, [deci for deci in deci_seq if deci != 1] 

2090 

2091 raise util.UnavailableDecimation('ratio = %g' % (deltat_out / deltat_in)) 

2092 

2093 

2094def _all_same(xs): 

2095 return all(x == xs[0] for x in xs) 

2096 

2097 

2098def _incompatibilities(traces): 

2099 if not traces: 

2100 return None 

2101 

2102 params = [ 

2103 (tr.ydata.size, tr.ydata.dtype, tr.deltat, tr.tmin) 

2104 for tr in traces] 

2105 

2106 if not _all_same(params): 

2107 return params 

2108 else: 

2109 return None 

2110 

2111 

2112def _raise_incompatible_traces(params): 

2113 raise IncompatibleTraces( 

2114 'Given traces are incompatible. Sampling rate, start time, ' 

2115 'number of samples and data type must match.\n%s\n%s' % ( 

2116 ' %10s %-10s %12s %22s' % ( 

2117 'nsamples', 'dtype', 'deltat', 'tmin'), 

2118 '\n'.join( 

2119 ' %10i %-10s %12.5e %22s' % ( 

2120 nsamples, dtype, deltat, util.time_to_str(tmin)) 

2121 for (nsamples, dtype, deltat, tmin) in params))) 

2122 

2123 

2124def _ensure_compatible(traces): 

2125 params = _incompatibilities(traces) 

2126 if params: 

2127 _raise_incompatible_traces(params) 

2128 

2129 

2130def _almost_equal(a, b, atol): 

2131 return abs(a-b) < atol 

2132 

2133 

2134def get_traces_data_as_array(traces): 

2135 ''' 

2136 Merge data samples from multiple traces into a 2D array. 

2137 

2138 :param traces: 

2139 Input waveforms. 

2140 :type traces: 

2141 list of :py:class:`pyrocko.Trace <pyrocko.trace.Trace>` objects 

2142 

2143 :raises: 

2144 :py:class:`IncompatibleTraces` if traces have different time 

2145 span, sample rate or data type, or if traces is an empty list. 

2146 

2147 :returns: 

2148 2D array as ``data[itrace, isample]``. 

2149 :rtype: 

2150 :py:class:`numpy.ndarray` 

2151 ''' 

2152 

2153 if not traces: 

2154 raise IncompatibleTraces('Need at least one trace.') 

2155 

2156 _ensure_compatible(traces) 

2157 

2158 return num.vstack([tr.ydata for tr in traces]) 

2159 

2160 

2161def make_traces_compatible( 

2162 traces, 

2163 dtype=None, 

2164 deltat=None, 

2165 enforce_global_snap=True, 

2166 warn_snap=False): 

2167 

2168 eps_snap = 1e-3 

2169 

2170 if not traces: 

2171 return [] 

2172 

2173 traces = list(traces) 

2174 

2175 dtypes = [tr.ydata.dtype for tr in traces] 

2176 if not _all_same(dtypes) or dtype is not None: 

2177 

2178 if dtype is None: 

2179 dtype = float 

2180 logger.warning( 

2181 'make_traces_compatible: Inconsistent data types - converting ' 

2182 'sample datatype to %s.' % str(dtype)) 

2183 

2184 for itr, tr in enumerate(traces): 

2185 tr_copy = tr.copy(data=False) 

2186 tr_copy.set_ydata(tr.ydata.astype(dtype)) 

2187 traces[itr] = tr_copy 

2188 

2189 deltats = [tr.deltat for tr in traces] 

2190 if not _all_same(deltats) or deltat is not None: 

2191 if deltat is None: 

2192 deltat = max(deltats) 

2193 logger.warning( 

2194 'make_traces_compatible: Inconsistent sampling rates - ' 

2195 'downsampling to lowest rate among input traces: %g Hz.' 

2196 % (1.0 / deltat)) 

2197 

2198 for itr, tr in enumerate(traces): 

2199 if tr.deltat != deltat: 

2200 tr_copy = tr.copy() 

2201 tr_copy.downsample_to(deltat, snap=True, cut=True) 

2202 traces[itr] = tr_copy 

2203 

2204 tmins = num.array([tr.tmin for tr in traces]) 

2205 is_aligned = num.abs(num.round(tmins / deltat) * deltat - tmins) \ 

2206 > deltat * eps_snap 

2207 

2208 if enforce_global_snap or any(is_aligned): 

2209 tref = util.to_time_float(0.0) 

2210 else: 

2211 # to keep a common subsample shift 

2212 tref = num.max(tmins) 

2213 

2214 tmins_snap = num.round((tmins - tref) / deltat) * deltat + tref 

2215 need_snap = num.abs(tmins_snap - tmins) > deltat * eps_snap 

2216 if num.any(need_snap): 

2217 if warn_snap: 

2218 logger.warning( 

2219 'make_traces_compatible: Misaligned sampling - introducing ' 

2220 'subsample shifts for proper alignment.') 

2221 

2222 for itr, tr in enumerate(traces): 

2223 if need_snap[itr]: 

2224 tr_copy = tr.copy() 

2225 if tref != 0.0: 

2226 tr_copy.shift(-tref) 

2227 

2228 tr_copy.snap(interpolate=True) 

2229 if tref != 0.0: 

2230 tr_copy.shift(tref) 

2231 

2232 traces[itr] = tr_copy 

2233 

2234 tmins = num.array([tr.tmin for tr in traces]) 

2235 nsamples = num.array([tr.ydata.size for tr in traces]) 

2236 tmaxs = tmins + (nsamples - 1) * deltat 

2237 

2238 tmin = num.max(tmins) 

2239 tmax = num.min(tmaxs) 

2240 

2241 if tmin > tmax: 

2242 raise IncompatibleTraces('Traces do not overlap.') 

2243 

2244 nsamples_must = int(round((tmax - tmin) / deltat)) + 1 

2245 for itr, tr in enumerate(traces): 

2246 if not (_almost_equal(tr.tmin, tmin, deltat*eps_snap) 

2247 and _almost_equal(tr.tmax, tmax, deltat*eps_snap)): 

2248 

2249 traces[itr] = tr.chop( 

2250 tmin, tmax, 

2251 inplace=False, 

2252 want_incomplete=False, 

2253 include_last=True) 

2254 

2255 xtr = traces[itr] 

2256 assert _almost_equal(xtr.tmin, tmin, deltat*eps_snap) 

2257 assert int(round((xtr.tmax - xtr.tmin) / deltat)) + 1 == nsamples_must 

2258 xtr.tmin = tmin 

2259 xtr.tmax = tmax 

2260 xtr.deltat = deltat 

2261 xtr._update_ids() 

2262 

2263 return traces 

2264 

2265 

2266class IncompatibleTraces(Exception): 

2267 ''' 

2268 Raised when traces have incompatible sampling rate, time span or data type. 

2269 ''' 

2270 

2271 

2272class InfiniteResponse(Exception): 

2273 ''' 

2274 This exception is raised by :py:class:`Trace` operations when deconvolution 

2275 of a frequency response (instrument response transfer function) would 

2276 result in a division by zero. 

2277 ''' 

2278 

2279 

2280class MisalignedTraces(Exception): 

2281 ''' 

2282 This exception is raised by some :py:class:`Trace` operations when tmin, 

2283 tmax or number of samples do not match. 

2284 ''' 

2285 

2286 pass 

2287 

2288 

2289class NoData(Exception): 

2290 ''' 

2291 This exception is raised by some :py:class:`Trace` operations when no or 

2292 not enough data is available. 

2293 ''' 

2294 

2295 pass 

2296 

2297 

2298class AboveNyquist(Exception): 

2299 ''' 

2300 This exception is raised by some :py:class:`Trace` operations when given 

2301 frequencies are above the Nyquist frequency. 

2302 ''' 

2303 

2304 pass 

2305 

2306 

2307class TraceTooShort(Exception): 

2308 ''' 

2309 This exception is raised by some :py:class:`Trace` operations when the 

2310 trace is too short. 

2311 ''' 

2312 

2313 pass 

2314 

2315 

2316class ResamplingFailed(Exception): 

2317 pass 

2318 

2319 

2320def minmax(traces, key=None, mode='minmax', outer_mode='minmax'): 

2321 

2322 ''' 

2323 Get data range given traces grouped by selected pattern. 

2324 

2325 :param key: a callable which takes as single argument a trace and returns a 

2326 key for the grouping of the results. If this is ``None``, the default, 

2327 ``lambda tr: (tr.network, tr.station, tr.location, tr.channel)`` is 

2328 used. 

2329 :param mode: ``'minmax'`` or floating point number. If this is 

2330 ``'minmax'``, minimum and maximum of the traces are used, if it is a 

2331 number, mean +- standard deviation times ``mode`` is used. 

2332 

2333 param outer_mode: ``'minmax'`` to use mininum and maximum of the 

2334 single-trace ranges, or ``'robust'`` to use the interval to discard 10% 

2335 extreme values on either end. 

2336 

2337 :returns: a dict with the combined data ranges. 

2338 

2339 Examples:: 

2340 

2341 ranges = minmax(traces, lambda tr: tr.channel) 

2342 print ranges['N'] # print min & max of all traces with channel == 'N' 

2343 print ranges['E'] # print min & max of all traces with channel == 'E' 

2344 

2345 ranges = minmax(traces, lambda tr: (tr.network, tr.station)) 

2346 print ranges['GR', 'HAM3'] # print min & max of all traces with 

2347 # network == 'GR' and station == 'HAM3' 

2348 

2349 ranges = minmax(traces, lambda tr: None) 

2350 print ranges[None] # prints min & max of all traces 

2351 ''' 

2352 

2353 if key is None: 

2354 key = _default_key 

2355 

2356 ranges = defaultdict(list) 

2357 for trace in traces: 

2358 if isinstance(mode, str) and mode == 'minmax': 

2359 mi, ma = num.nanmin(trace.ydata), num.nanmax(trace.ydata) 

2360 else: 

2361 mean = trace.ydata.mean() 

2362 std = trace.ydata.std() 

2363 mi, ma = mean-std*mode, mean+std*mode 

2364 

2365 k = key(trace) 

2366 ranges[k].append((mi, ma)) 

2367 

2368 for k in ranges: 

2369 mins, maxs = num.array(ranges[k]).T 

2370 if outer_mode == 'minmax': 

2371 ranges[k] = num.nanmin(mins), num.nanmax(maxs) 

2372 elif outer_mode == 'robust': 

2373 ranges[k] = num.percentile(mins, 10.), num.percentile(maxs, 90.) 

2374 

2375 return ranges 

2376 

2377 

2378def minmaxtime(traces, key=None): 

2379 

2380 ''' 

2381 Get time range given traces grouped by selected pattern. 

2382 

2383 :param key: a callable which takes as single argument a trace and returns a 

2384 key for the grouping of the results. If this is ``None``, the default, 

2385 ``lambda tr: (tr.network, tr.station, tr.location, tr.channel)`` is 

2386 used. 

2387 

2388 :returns: a dict with the combined data ranges. 

2389 ''' 

2390 

2391 if key is None: 

2392 key = _default_key 

2393 

2394 ranges = {} 

2395 for trace in traces: 

2396 mi, ma = trace.tmin, trace.tmax 

2397 k = key(trace) 

2398 if k not in ranges: 

2399 ranges[k] = mi, ma 

2400 else: 

2401 tmi, tma = ranges[k] 

2402 ranges[k] = min(tmi, mi), max(tma, ma) 

2403 

2404 return ranges 

2405 

2406 

2407def degapper( 

2408 traces, 

2409 maxgap=5, 

2410 fillmethod='interpolate', 

2411 deoverlap='use_second', 

2412 maxlap=None): 

2413 

2414 ''' 

2415 Try to connect traces and remove gaps. 

2416 

2417 This method will combine adjacent traces, which match in their network, 

2418 station, location and channel attributes. Overlapping parts are handled 

2419 according to the ``deoverlap`` argument. 

2420 

2421 :param traces: input traces, must be sorted by their full_id attribute. 

2422 :param maxgap: maximum number of samples to interpolate. 

2423 :param fillmethod: what to put into the gaps: 'interpolate' or 'zeros'. 

2424 :param deoverlap: how to handle overlaps: 'use_second' to use data from 

2425 second trace (default), 'use_first' to use data from first trace, 

2426 'crossfade_cos' to crossfade with cosine taper, 'add' to add amplitude 

2427 values. 

2428 :param maxlap: maximum number of samples of overlap which are removed 

2429 

2430 :returns: list of traces 

2431 ''' 

2432 

2433 in_traces = traces 

2434 out_traces = [] 

2435 if not in_traces: 

2436 return out_traces 

2437 out_traces.append(in_traces.pop(0)) 

2438 while in_traces: 

2439 

2440 a = out_traces[-1] 

2441 b = in_traces.pop(0) 

2442 

2443 avirt, bvirt = a.ydata is None, b.ydata is None 

2444 assert avirt == bvirt, \ 

2445 'traces given to degapper() must either all have data or have ' \ 

2446 'no data.' 

2447 

2448 virtual = avirt and bvirt 

2449 

2450 if (a.nslc_id == b.nslc_id and a.deltat == b.deltat 

2451 and a.data_len() >= 1 and b.data_len() >= 1 

2452 and (virtual or a.ydata.dtype == b.ydata.dtype)): 

2453 

2454 dist = (b.tmin-(a.tmin+(a.data_len()-1)*a.deltat))/a.deltat 

2455 idist = int(round(dist)) 

2456 if abs(dist - idist) > 0.05 and idist <= maxgap: 

2457 # logger.warning('Cannot degap traces with displaced sampling ' 

2458 # '(%s, %s, %s, %s)' % a.nslc_id) 

2459 pass 

2460 else: 

2461 if 1 < idist <= maxgap: 

2462 if not virtual: 

2463 if fillmethod == 'interpolate': 

2464 filler = a.ydata[-1] + ( 

2465 ((1.0 + num.arange(idist-1, dtype=float)) 

2466 / idist) * (b.ydata[0]-a.ydata[-1]) 

2467 ).astype(a.ydata.dtype) 

2468 elif fillmethod == 'zeros': 

2469 filler = num.zeros(idist-1, dtype=a.ydata.dtype) 

2470 a.ydata = num.concatenate((a.ydata, filler, b.ydata)) 

2471 a.tmax = b.tmax 

2472 if a.mtime and b.mtime: 

2473 a.mtime = max(a.mtime, b.mtime) 

2474 continue 

2475 

2476 elif idist == 1: 

2477 if not virtual: 

2478 a.ydata = num.concatenate((a.ydata, b.ydata)) 

2479 a.tmax = b.tmax 

2480 if a.mtime and b.mtime: 

2481 a.mtime = max(a.mtime, b.mtime) 

2482 continue 

2483 

2484 elif idist <= 0 and (maxlap is None or -maxlap < idist): 

2485 if b.tmax > a.tmax: 

2486 if not virtual: 

2487 na = a.ydata.size 

2488 n = -idist+1 

2489 if deoverlap == 'use_second': 

2490 a.ydata = num.concatenate( 

2491 (a.ydata[:-n], b.ydata)) 

2492 elif deoverlap in ('use_first', 'crossfade_cos'): 

2493 a.ydata = num.concatenate( 

2494 (a.ydata, b.ydata[n:])) 

2495 elif deoverlap == 'add': 

2496 a.ydata[-n:] += b.ydata[:n] 

2497 a.ydata = num.concatenate( 

2498 (a.ydata, b.ydata[n:])) 

2499 else: 

2500 assert False, 'unknown deoverlap method' 

2501 

2502 if deoverlap == 'crossfade_cos': 

2503 n = -idist+1 

2504 taper = 0.5-0.5*num.cos( 

2505 (1.+num.arange(n))/(1.+n)*num.pi) 

2506 a.ydata[na-n:na] *= 1.-taper 

2507 a.ydata[na-n:na] += b.ydata[:n] * taper 

2508 

2509 a.tmax = b.tmax 

2510 if a.mtime and b.mtime: 

2511 a.mtime = max(a.mtime, b.mtime) 

2512 continue 

2513 else: 

2514 # make short second trace vanish 

2515 continue 

2516 

2517 if b.data_len() >= 1: 

2518 out_traces.append(b) 

2519 

2520 for tr in out_traces: 

2521 tr._update_ids() 

2522 

2523 return out_traces 

2524 

2525 

2526def rotate(traces, azimuth, in_channels, out_channels): 

2527 ''' 

2528 2D rotation of traces. 

2529 

2530 :param traces: list of input traces 

2531 :param azimuth: difference of the azimuths of the component directions 

2532 (azimuth of out_channels[0]) - (azimuth of in_channels[0]) 

2533 :param in_channels: names of the input channels (e.g. 'N', 'E') 

2534 :param out_channels: names of the output channels (e.g. 'R', 'T') 

2535 :returns: list of rotated traces 

2536 ''' 

2537 

2538 phi = azimuth/180.*math.pi 

2539 cphi = math.cos(phi) 

2540 sphi = math.sin(phi) 

2541 rotated = [] 

2542 in_channels = tuple(_channels_to_names(in_channels)) 

2543 out_channels = tuple(_channels_to_names(out_channels)) 

2544 for a in traces: 

2545 for b in traces: 

2546 if ((a.channel, b.channel) == in_channels and 

2547 a.nslc_id[:3] == b.nslc_id[:3] and 

2548 abs(a.deltat-b.deltat) < a.deltat*0.001): 

2549 tmin = max(a.tmin, b.tmin) 

2550 tmax = min(a.tmax, b.tmax) 

2551 

2552 if tmin < tmax: 

2553 ac = a.chop(tmin, tmax, inplace=False, include_last=True) 

2554 bc = b.chop(tmin, tmax, inplace=False, include_last=True) 

2555 if abs(ac.tmin - bc.tmin) > ac.deltat*0.01: 

2556 logger.warning( 

2557 'Cannot rotate traces with displaced sampling ' 

2558 '(%s, %s, %s, %s)' % a.nslc_id) 

2559 continue 

2560 

2561 acydata = ac.get_ydata()*cphi+bc.get_ydata()*sphi 

2562 bcydata = -ac.get_ydata()*sphi+bc.get_ydata()*cphi 

2563 ac.set_ydata(acydata) 

2564 bc.set_ydata(bcydata) 

2565 

2566 ac.set_codes(channel=out_channels[0]) 

2567 bc.set_codes(channel=out_channels[1]) 

2568 rotated.append(ac) 

2569 rotated.append(bc) 

2570 

2571 return rotated 

2572 

2573 

2574def rotate_to_rt(n, e, source, receiver, out_channels=('R', 'T')): 

2575 ''' 

2576 Rotate traces from NE to RT system. 

2577 

2578 :param n: 

2579 North trace. 

2580 :type n: 

2581 :py:class:`~pyrocko.trace.Trace` 

2582 

2583 :param e: 

2584 East trace. 

2585 :type e: 

2586 :py:class:`~pyrocko.trace.Trace` 

2587 

2588 :param source: 

2589 Source of the recorded signal. 

2590 :type source: 

2591 :py:class:`pyrocko.gf.seismosizer.Source` 

2592 

2593 :param receiver: 

2594 Receiver of the recorded signal. 

2595 :type receiver: 

2596 :py:class:`pyrocko.model.location.Location` 

2597 

2598 :param out_channels: 

2599 Channel codes of the output channels (radial, transversal). 

2600 Default is ('R', 'T'). 

2601 

2602 :type out_channels 

2603 optional, tuple[str, str] 

2604 

2605 :returns: 

2606 Rotated traces (radial, transversal). 

2607 :rtype: 

2608 tuple[ 

2609 :py:class:`~pyrocko.trace.Trace`, 

2610 :py:class:`~pyrocko.trace.Trace`] 

2611 ''' 

2612 azimuth = orthodrome.azimuth(receiver, source) + 180. 

2613 in_channels = n.channel, e.channel 

2614 out = rotate( 

2615 [n, e], azimuth, 

2616 in_channels=in_channels, 

2617 out_channels=out_channels) 

2618 

2619 assert len(out) == 2 

2620 for tr in out: 

2621 if tr.channel == out_channels[0]: 

2622 r = tr 

2623 elif tr.channel == out_channels[1]: 

2624 t = tr 

2625 else: 

2626 assert False 

2627 

2628 return r, t 

2629 

2630 

2631def rotate_to_lqt(traces, backazimuth, incidence, in_channels, 

2632 out_channels=('L', 'Q', 'T')): 

2633 ''' 

2634 Rotate traces from ZNE to LQT system. 

2635 

2636 :param traces: list of traces in arbitrary order 

2637 :param backazimuth: backazimuth in degrees clockwise from north 

2638 :param incidence: incidence angle in degrees from vertical 

2639 :param in_channels: input channel names 

2640 :param out_channels: output channel names (default: ('L', 'Q', 'T')) 

2641 :returns: list of transformed traces 

2642 ''' 

2643 i = incidence/180.*num.pi 

2644 b = backazimuth/180.*num.pi 

2645 

2646 ci = num.cos(i) 

2647 cb = num.cos(b) 

2648 si = num.sin(i) 

2649 sb = num.sin(b) 

2650 

2651 rotmat = num.array( 

2652 [[ci, -cb*si, -sb*si], [si, cb*ci, sb*ci], [0., sb, -cb]]) 

2653 return project(traces, rotmat, in_channels, out_channels) 

2654 

2655 

2656def _decompose(a): 

2657 ''' 

2658 Decompose matrix into independent submatrices. 

2659 ''' 

2660 

2661 def depends(iout, a): 

2662 row = a[iout, :] 

2663 return set(num.arange(row.size).compress(row != 0.0)) 

2664 

2665 def provides(iin, a): 

2666 col = a[:, iin] 

2667 return set(num.arange(col.size).compress(col != 0.0)) 

2668 

2669 a = num.asarray(a) 

2670 outs = set(range(a.shape[0])) 

2671 systems = [] 

2672 while outs: 

2673 iout = outs.pop() 

2674 

2675 gout = set() 

2676 for iin in depends(iout, a): 

2677 gout.update(provides(iin, a)) 

2678 

2679 if not gout: 

2680 continue 

2681 

2682 gin = set() 

2683 for iout2 in gout: 

2684 gin.update(depends(iout2, a)) 

2685 

2686 if not gin: 

2687 continue 

2688 

2689 for iout2 in gout: 

2690 if iout2 in outs: 

2691 outs.remove(iout2) 

2692 

2693 gin = list(gin) 

2694 gin.sort() 

2695 gout = list(gout) 

2696 gout.sort() 

2697 

2698 systems.append((gin, gout, a[gout, :][:, gin])) 

2699 

2700 return systems 

2701 

2702 

2703def _channels_to_names(channels): 

2704 from pyrocko import squirrel 

2705 names = [] 

2706 for ch in channels: 

2707 if isinstance(ch, model.Channel): 

2708 names.append(ch.name) 

2709 elif isinstance(ch, squirrel.Channel): 

2710 names.append(ch.codes.channel) 

2711 else: 

2712 names.append(ch) 

2713 

2714 return names 

2715 

2716 

2717def project(traces, matrix, in_channels, out_channels): 

2718 ''' 

2719 Affine transform of three-component traces. 

2720 

2721 Compute matrix-vector product of three-component traces, to e.g. rotate 

2722 traces into a different basis. The traces are distinguished and ordered by 

2723 their channel attribute. The tranform is applied to overlapping parts of 

2724 any appropriate combinations of the input traces. This should allow this 

2725 function to be robust with data gaps. It also tries to apply the 

2726 tranformation to subsets of the channels, if this is possible, so that, if 

2727 for example a vertical compontent is missing, horizontal components can 

2728 still be rotated. 

2729 

2730 :param traces: list of traces in arbitrary order 

2731 :param matrix: tranformation matrix 

2732 :param in_channels: input channel names 

2733 :param out_channels: output channel names 

2734 :returns: list of transformed traces 

2735 ''' 

2736 

2737 in_channels = tuple(_channels_to_names(in_channels)) 

2738 out_channels = tuple(_channels_to_names(out_channels)) 

2739 systems = _decompose(matrix) 

2740 

2741 # fallback to full matrix if some are not quadratic 

2742 for iins, iouts, submatrix in systems: 

2743 if submatrix.shape[0] != submatrix.shape[1]: 

2744 if len(in_channels) != 3 or len(out_channels) != 3: 

2745 return [] 

2746 else: 

2747 return _project3(traces, matrix, in_channels, out_channels) 

2748 

2749 projected = [] 

2750 for iins, iouts, submatrix in systems: 

2751 in_cha = tuple([in_channels[iin] for iin in iins]) 

2752 out_cha = tuple([out_channels[iout] for iout in iouts]) 

2753 if submatrix.shape[0] == 1: 

2754 projected.extend(_project1(traces, submatrix, in_cha, out_cha)) 

2755 elif submatrix.shape[1] == 2: 

2756 projected.extend(_project2(traces, submatrix, in_cha, out_cha)) 

2757 else: 

2758 projected.extend(_project3(traces, submatrix, in_cha, out_cha)) 

2759 

2760 return projected 

2761 

2762 

2763def project_dependencies(matrix, in_channels, out_channels): 

2764 ''' 

2765 Figure out what dependencies project() would produce. 

2766 ''' 

2767 

2768 in_channels = tuple(_channels_to_names(in_channels)) 

2769 out_channels = tuple(_channels_to_names(out_channels)) 

2770 systems = _decompose(matrix) 

2771 

2772 subpro = [] 

2773 for iins, iouts, submatrix in systems: 

2774 if submatrix.shape[0] != submatrix.shape[1]: 

2775 subpro.append((matrix, in_channels, out_channels)) 

2776 

2777 if not subpro: 

2778 for iins, iouts, submatrix in systems: 

2779 in_cha = tuple([in_channels[iin] for iin in iins]) 

2780 out_cha = tuple([out_channels[iout] for iout in iouts]) 

2781 subpro.append((submatrix, in_cha, out_cha)) 

2782 

2783 deps = {} 

2784 for mat, in_cha, out_cha in subpro: 

2785 for oc in out_cha: 

2786 if oc not in deps: 

2787 deps[oc] = [] 

2788 

2789 for ic in in_cha: 

2790 deps[oc].append(ic) 

2791 

2792 return deps 

2793 

2794 

2795def _project1(traces, matrix, in_channels, out_channels): 

2796 assert len(in_channels) == 1 

2797 assert len(out_channels) == 1 

2798 assert matrix.shape == (1, 1) 

2799 

2800 projected = [] 

2801 for a in traces: 

2802 if not (a.channel,) == in_channels: 

2803 continue 

2804 

2805 ac = a.copy() 

2806 ac.set_ydata(matrix[0, 0]*a.get_ydata()) 

2807 ac.set_codes(channel=out_channels[0]) 

2808 projected.append(ac) 

2809 

2810 return projected 

2811 

2812 

2813def _project2(traces, matrix, in_channels, out_channels): 

2814 assert len(in_channels) == 2 

2815 assert len(out_channels) == 2 

2816 assert matrix.shape == (2, 2) 

2817 projected = [] 

2818 for a in traces: 

2819 for b in traces: 

2820 if not ((a.channel, b.channel) == in_channels and 

2821 a.nslc_id[:3] == b.nslc_id[:3] and 

2822 abs(a.deltat-b.deltat) < a.deltat*0.001): 

2823 continue 

2824 

2825 tmin = max(a.tmin, b.tmin) 

2826 tmax = min(a.tmax, b.tmax) 

2827 

2828 if tmin > tmax: 

2829 continue 

2830 

2831 ac = a.chop(tmin, tmax, inplace=False, include_last=True) 

2832 bc = b.chop(tmin, tmax, inplace=False, include_last=True) 

2833 if abs(ac.tmin - bc.tmin) > ac.deltat*0.01: 

2834 logger.warning( 

2835 'Cannot project traces with displaced sampling ' 

2836 '(%s, %s, %s, %s)' % a.nslc_id) 

2837 continue 

2838 

2839 acydata = num.dot(matrix[0], (ac.get_ydata(), bc.get_ydata())) 

2840 bcydata = num.dot(matrix[1], (ac.get_ydata(), bc.get_ydata())) 

2841 

2842 ac.set_ydata(acydata) 

2843 bc.set_ydata(bcydata) 

2844 

2845 ac.set_codes(channel=out_channels[0]) 

2846 bc.set_codes(channel=out_channels[1]) 

2847 

2848 projected.append(ac) 

2849 projected.append(bc) 

2850 

2851 return projected 

2852 

2853 

2854def _project3(traces, matrix, in_channels, out_channels): 

2855 assert len(in_channels) == 3 

2856 assert len(out_channels) == 3 

2857 assert matrix.shape == (3, 3) 

2858 projected = [] 

2859 for a in traces: 

2860 for b in traces: 

2861 for c in traces: 

2862 if not ((a.channel, b.channel, c.channel) == in_channels 

2863 and a.nslc_id[:3] == b.nslc_id[:3] 

2864 and b.nslc_id[:3] == c.nslc_id[:3] 

2865 and abs(a.deltat-b.deltat) < a.deltat*0.001 

2866 and abs(b.deltat-c.deltat) < b.deltat*0.001): 

2867 

2868 continue 

2869 

2870 tmin = max(a.tmin, b.tmin, c.tmin) 

2871 tmax = min(a.tmax, b.tmax, c.tmax) 

2872 

2873 if tmin >= tmax: 

2874 continue 

2875 

2876 ac = a.chop(tmin, tmax, inplace=False, include_last=True) 

2877 bc = b.chop(tmin, tmax, inplace=False, include_last=True) 

2878 cc = c.chop(tmin, tmax, inplace=False, include_last=True) 

2879 if (abs(ac.tmin - bc.tmin) > ac.deltat*0.01 

2880 or abs(bc.tmin - cc.tmin) > bc.deltat*0.01): 

2881 

2882 logger.warning( 

2883 'Cannot project traces with displaced sampling ' 

2884 '(%s, %s, %s, %s)' % a.nslc_id) 

2885 continue 

2886 

2887 acydata = num.dot( 

2888 matrix[0], 

2889 (ac.get_ydata(), bc.get_ydata(), cc.get_ydata())) 

2890 bcydata = num.dot( 

2891 matrix[1], 

2892 (ac.get_ydata(), bc.get_ydata(), cc.get_ydata())) 

2893 ccydata = num.dot( 

2894 matrix[2], 

2895 (ac.get_ydata(), bc.get_ydata(), cc.get_ydata())) 

2896 

2897 ac.set_ydata(acydata) 

2898 bc.set_ydata(bcydata) 

2899 cc.set_ydata(ccydata) 

2900 

2901 ac.set_codes(channel=out_channels[0]) 

2902 bc.set_codes(channel=out_channels[1]) 

2903 cc.set_codes(channel=out_channels[2]) 

2904 

2905 projected.append(ac) 

2906 projected.append(bc) 

2907 projected.append(cc) 

2908 

2909 return projected 

2910 

2911 

2912def correlate(a, b, mode='valid', normalization=None, use_fft=False): 

2913 ''' 

2914 Cross correlation of two traces. 

2915 

2916 :param a,b: input traces 

2917 :param mode: ``'valid'``, ``'full'``, or ``'same'`` 

2918 :param normalization: ``'normal'``, ``'gliding'``, or ``None`` 

2919 :param use_fft: bool, whether to do cross correlation in spectral domain 

2920 

2921 :returns: trace containing cross correlation coefficients 

2922 

2923 This function computes the cross correlation between two traces. It 

2924 evaluates the discrete equivalent of 

2925 

2926 .. math:: 

2927 

2928 c(t) = \\int_{-\\infty}^{\\infty} a^{\\ast}(\\tau) b(t+\\tau) d\\tau 

2929 

2930 where the star denotes complex conjugate. Note, that the arguments here are 

2931 swapped when compared with the :py:func:`numpy.correlate` function, 

2932 which is internally called. This function should be safe even with older 

2933 versions of NumPy, where the correlate function has some problems. 

2934 

2935 A trace containing the cross correlation coefficients is returned. The time 

2936 information of the output trace is set so that the returned cross 

2937 correlation can be viewed directly as a function of time lag. 

2938 

2939 Example:: 

2940 

2941 # align two traces a and b containing a time shifted similar signal: 

2942 c = pyrocko.trace.correlate(a,b) 

2943 t, coef = c.max() # get time and value of maximum 

2944 b.shift(-t) # align b with a 

2945 

2946 ''' 

2947 

2948 assert_same_sampling_rate(a, b) 

2949 

2950 ya, yb = a.ydata, b.ydata 

2951 

2952 # need reversed order here: 

2953 yc = numpy_correlate_fixed(yb, ya, mode=mode, use_fft=use_fft) 

2954 kmin, kmax = numpy_correlate_lag_range(yb, ya, mode=mode, use_fft=use_fft) 

2955 

2956 if normalization == 'normal': 

2957 normfac = num.sqrt(num.sum(ya**2))*num.sqrt(num.sum(yb**2)) 

2958 yc = yc/normfac 

2959 

2960 elif normalization == 'gliding': 

2961 if mode != 'valid': 

2962 assert False, 'gliding normalization currently only available ' \ 

2963 'with "valid" mode.' 

2964 

2965 if ya.size < yb.size: 

2966 yshort, ylong = ya, yb 

2967 else: 

2968 yshort, ylong = yb, ya 

2969 

2970 epsilon = 0.00001 

2971 normfac_short = num.sqrt(num.sum(yshort**2)) 

2972 normfac = normfac_short * num.sqrt( 

2973 moving_sum(ylong**2, yshort.size, mode='valid')) \ 

2974 + normfac_short*epsilon 

2975 

2976 if yb.size <= ya.size: 

2977 normfac = normfac[::-1] 

2978 

2979 yc /= normfac 

2980 

2981 c = a.copy() 

2982 c.set_ydata(yc) 

2983 c.set_codes(*merge_codes(a, b, '~')) 

2984 c.shift(-c.tmin + b.tmin-a.tmin + kmin * c.deltat) 

2985 

2986 return c 

2987 

2988 

2989def deconvolve( 

2990 a, b, waterlevel, 

2991 tshift=0., 

2992 pad=0.5, 

2993 fd_taper=None, 

2994 pad_to_pow2=True): 

2995 

2996 same_sampling_rate(a, b) 

2997 assert abs(a.tmin - b.tmin) < a.deltat * 0.001 

2998 deltat = a.deltat 

2999 npad = int(round(a.data_len()*pad + tshift / deltat)) 

3000 

3001 ndata = max(a.data_len(), b.data_len()) 

3002 ndata_pad = ndata + npad 

3003 

3004 if pad_to_pow2: 

3005 ntrans = nextpow2(ndata_pad) 

3006 else: 

3007 ntrans = ndata 

3008 

3009 aspec = num.fft.rfft(a.ydata, ntrans) 

3010 bspec = num.fft.rfft(b.ydata, ntrans) 

3011 

3012 out = aspec * num.conj(bspec) 

3013 

3014 bautocorr = bspec*num.conj(bspec) 

3015 denom = num.maximum(bautocorr, waterlevel * bautocorr.max()) 

3016 

3017 out /= denom 

3018 df = 1/(ntrans*deltat) 

3019 

3020 if fd_taper is not None: 

3021 fd_taper(out, 0.0, df) 

3022 

3023 ydata = num.roll(num.fft.irfft(out), int(round(tshift/deltat))) 

3024 c = a.copy(data=False) 

3025 c.set_ydata(ydata[:ndata]) 

3026 c.set_codes(*merge_codes(a, b, '/')) 

3027 return c 

3028 

3029 

3030def assert_same_sampling_rate(a, b, eps=1.0e-6): 

3031 assert same_sampling_rate(a, b, eps), \ 

3032 'Sampling rates differ: %g != %g' % (a.deltat, b.deltat) 

3033 

3034 

3035def same_sampling_rate(a, b, eps=1.0e-6): 

3036 ''' 

3037 Check if two traces have the same sampling rate. 

3038 

3039 :param a,b: input traces 

3040 :param eps: relative tolerance 

3041 ''' 

3042 

3043 return abs(a.deltat - b.deltat) < (a.deltat + b.deltat)*eps 

3044 

3045 

3046def fix_deltat_rounding_errors(deltat): 

3047 ''' 

3048 Try to undo sampling rate rounding errors. 

3049 

3050 Fix rounding errors of sampling intervals when these are read from single 

3051 precision floating point values. 

3052 

3053 Assumes that the true sampling rate or sampling interval was an integer 

3054 value. No correction will be applied if this would change the sampling 

3055 rate by more than 0.001%. 

3056 ''' 

3057 

3058 if deltat <= 1.0: 

3059 deltat_new = 1.0 / round(1.0 / deltat) 

3060 else: 

3061 deltat_new = round(deltat) 

3062 

3063 if abs(deltat_new - deltat) / deltat > 1e-5: 

3064 deltat_new = deltat 

3065 

3066 return deltat_new 

3067 

3068 

3069def merge_codes(a, b, sep='-'): 

3070 ''' 

3071 Merge network-station-location-channel codes of a pair of traces. 

3072 ''' 

3073 

3074 o = [] 

3075 for xa, xb in zip(a.nslc_id, b.nslc_id): 

3076 if xa == xb: 

3077 o.append(xa) 

3078 else: 

3079 o.append(sep.join((xa, xb))) 

3080 return o 

3081 

3082 

3083class Taper(Object): 

3084 ''' 

3085 Base class for tapers. 

3086 

3087 Does nothing by default. 

3088 ''' 

3089 

3090 def __call__(self, y, x0, dx): 

3091 pass 

3092 

3093 

3094class CosTaper(Taper): 

3095 ''' 

3096 Cosine Taper. 

3097 

3098 :param a: start of fading in 

3099 :param b: end of fading in 

3100 :param c: start of fading out 

3101 :param d: end of fading out 

3102 ''' 

3103 

3104 a = Float.T() 

3105 b = Float.T() 

3106 c = Float.T() 

3107 d = Float.T() 

3108 

3109 def __init__(self, a, b, c, d): 

3110 Taper.__init__(self, a=a, b=b, c=c, d=d) 

3111 

3112 def __call__(self, y, x0, dx): 

3113 

3114 if y.dtype == num.dtype(float): 

3115 _apply_costaper = signal_ext.apply_costaper 

3116 else: 

3117 _apply_costaper = apply_costaper 

3118 

3119 _apply_costaper(self.a, self.b, self.c, self.d, y, x0, dx) 

3120 

3121 def span(self, y, x0, dx): 

3122 return span_costaper(self.a, self.b, self.c, self.d, y, x0, dx) 

3123 

3124 def time_span(self): 

3125 return self.a, self.d 

3126 

3127 

3128class CosFader(Taper): 

3129 ''' 

3130 Cosine Fader. 

3131 

3132 :param xfade: fade in and fade out time in seconds (optional) 

3133 :param xfrac: fade in and fade out as fraction between 0. and 1. (optional) 

3134 

3135 Only one argument can be set. The other should to be ``None``. 

3136 ''' 

3137 

3138 xfade = Float.T(optional=True) 

3139 xfrac = Float.T(optional=True) 

3140 

3141 def __init__(self, xfade=None, xfrac=None): 

3142 Taper.__init__(self, xfade=xfade, xfrac=xfrac) 

3143 assert (xfade is None) != (xfrac is None) 

3144 self._xfade = xfade 

3145 self._xfrac = xfrac 

3146 

3147 def __call__(self, y, x0, dx): 

3148 

3149 xfade = self._xfade 

3150 

3151 xlen = (y.size - 1)*dx 

3152 if xfade is None: 

3153 xfade = xlen * self._xfrac 

3154 

3155 a = x0 

3156 b = x0 + xfade 

3157 c = x0 + xlen - xfade 

3158 d = x0 + xlen 

3159 

3160 apply_costaper(a, b, c, d, y, x0, dx) 

3161 

3162 def span(self, y, x0, dx): 

3163 return 0, y.size 

3164 

3165 def time_span(self): 

3166 return None, None 

3167 

3168 

3169def none_min(li): 

3170 if None in li: 

3171 return None 

3172 else: 

3173 return min(x for x in li if x is not None) 

3174 

3175 

3176def none_max(li): 

3177 if None in li: 

3178 return None 

3179 else: 

3180 return max(x for x in li if x is not None) 

3181 

3182 

3183class MultiplyTaper(Taper): 

3184 ''' 

3185 Multiplication of several tapers. 

3186 ''' 

3187 

3188 tapers = List.T(Taper.T()) 

3189 

3190 def __init__(self, tapers=None): 

3191 if tapers is None: 

3192 tapers = [] 

3193 

3194 Taper.__init__(self, tapers=tapers) 

3195 

3196 def __call__(self, y, x0, dx): 

3197 for taper in self.tapers: 

3198 taper(y, x0, dx) 

3199 

3200 def span(self, y, x0, dx): 

3201 spans = [] 

3202 for taper in self.tapers: 

3203 spans.append(taper.span(y, x0, dx)) 

3204 

3205 mins, maxs = list(zip(*spans)) 

3206 return min(mins), max(maxs) 

3207 

3208 def time_span(self): 

3209 spans = [] 

3210 for taper in self.tapers: 

3211 spans.append(taper.time_span()) 

3212 

3213 mins, maxs = list(zip(*spans)) 

3214 return none_min(mins), none_max(maxs) 

3215 

3216 

3217class GaussTaper(Taper): 

3218 ''' 

3219 Frequency domain Gaussian filter. 

3220 ''' 

3221 

3222 alpha = Float.T() 

3223 

3224 def __init__(self, alpha): 

3225 Taper.__init__(self, alpha=alpha) 

3226 self._alpha = alpha 

3227 

3228 def __call__(self, y, x0, dx): 

3229 f = x0 + num.arange(y.size)*dx 

3230 y *= num.exp(-num.pi**2 / (self._alpha**2) * f**2) 

3231 

3232 

3233cached_coefficients = {} 

3234 

3235 

3236def _get_cached_filter_coeffs(order, corners, btype): 

3237 ck = (order, tuple(corners), btype) 

3238 if ck not in cached_coefficients: 

3239 if len(corners) == 1: 

3240 corners = corners[0] 

3241 

3242 cached_coefficients[ck] = signal.butter( 

3243 order, corners, btype=btype) 

3244 

3245 return cached_coefficients[ck] 

3246 

3247 

3248class _globals(object): 

3249 _numpy_has_correlate_flip_bug = None 

3250 

3251 

3252def _default_key(tr): 

3253 return (tr.network, tr.station, tr.location, tr.channel) 

3254 

3255 

3256def numpy_has_correlate_flip_bug(): 

3257 ''' 

3258 Check if NumPy's correlate function reveals old behaviour. 

3259 ''' 

3260 

3261 if _globals._numpy_has_correlate_flip_bug is None: 

3262 a = num.array([0, 0, 1, 0, 0, 0, 0]) 

3263 b = num.array([0, 0, 0, 0, 1, 0, 0, 0]) 

3264 ab = num.correlate(a, b, mode='same') 

3265 ba = num.correlate(b, a, mode='same') 

3266 _globals._numpy_has_correlate_flip_bug = num.all(ab == ba) 

3267 

3268 return _globals._numpy_has_correlate_flip_bug 

3269 

3270 

3271def numpy_correlate_fixed(a, b, mode='valid', use_fft=False): 

3272 ''' 

3273 Call :py:func:`numpy.correlate` with fixes. 

3274 

3275 c[k] = sum_i a[i+k] * conj(b[i]) 

3276 

3277 Note that the result produced by newer numpy.correlate is always flipped 

3278 with respect to the formula given in its documentation (if ascending k 

3279 assumed for the output). 

3280 ''' 

3281 

3282 if use_fft: 

3283 if a.size < b.size: 

3284 c = signal.fftconvolve(b[::-1], a, mode=mode) 

3285 else: 

3286 c = signal.fftconvolve(a, b[::-1], mode=mode) 

3287 return c 

3288 

3289 else: 

3290 buggy = numpy_has_correlate_flip_bug() 

3291 

3292 a = num.asarray(a) 

3293 b = num.asarray(b) 

3294 

3295 if buggy: 

3296 b = num.conj(b) 

3297 

3298 c = num.correlate(a, b, mode=mode) 

3299 

3300 if buggy and a.size < b.size: 

3301 return c[::-1] 

3302 else: 

3303 return c 

3304 

3305 

3306def numpy_correlate_emulate(a, b, mode='valid'): 

3307 ''' 

3308 Slow version of :py:func:`numpy.correlate` for comparison. 

3309 ''' 

3310 

3311 a = num.asarray(a) 

3312 b = num.asarray(b) 

3313 kmin = -(b.size-1) 

3314 klen = a.size-kmin 

3315 kmin, kmax = numpy_correlate_lag_range(a, b, mode=mode) 

3316 kmin = int(kmin) 

3317 kmax = int(kmax) 

3318 klen = kmax - kmin + 1 

3319 c = num.zeros(klen, dtype=num.promote_types(b.dtype, a.dtype)) 

3320 for k in range(kmin, kmin+klen): 

3321 imin = max(0, -k) 

3322 ilen = min(b.size, a.size-k) - imin 

3323 c[k-kmin] = num.sum( 

3324 a[imin+k:imin+ilen+k] * num.conj(b[imin:imin+ilen])) 

3325 

3326 return c 

3327 

3328 

3329def numpy_correlate_lag_range(a, b, mode='valid', use_fft=False): 

3330 ''' 

3331 Get range of lags for which :py:func:`numpy.correlate` produces values. 

3332 ''' 

3333 

3334 a = num.asarray(a) 

3335 b = num.asarray(b) 

3336 

3337 kmin = -(b.size-1) 

3338 if mode == 'full': 

3339 klen = a.size-kmin 

3340 elif mode == 'same': 

3341 klen = max(a.size, b.size) 

3342 kmin += (a.size+b.size-1 - max(a.size, b.size)) // 2 + \ 

3343 int(not use_fft and a.size % 2 == 0 and b.size > a.size) 

3344 elif mode == 'valid': 

3345 klen = abs(a.size - b.size) + 1 

3346 kmin += min(a.size, b.size) - 1 

3347 

3348 return kmin, kmin + klen - 1 

3349 

3350 

3351def autocorr(x, nshifts): 

3352 ''' 

3353 Compute biased estimate of the first autocorrelation coefficients. 

3354 

3355 :param x: input array 

3356 :param nshifts: number of coefficients to calculate 

3357 ''' 

3358 

3359 mean = num.mean(x) 

3360 std = num.std(x) 

3361 n = x.size 

3362 xdm = x - mean 

3363 r = num.zeros(nshifts) 

3364 for k in range(nshifts): 

3365 r[k] = 1./((n-num.abs(k))*std) * num.sum(xdm[:n-k] * xdm[k:]) 

3366 

3367 return r 

3368 

3369 

3370def yulewalker(x, order): 

3371 ''' 

3372 Compute autoregression coefficients using Yule-Walker method. 

3373 

3374 :param x: input array 

3375 :param order: number of coefficients to produce 

3376 

3377 A biased estimate of the autocorrelation is used. The Yule-Walker equations 

3378 are solved by :py:func:`numpy.linalg.inv` instead of Levinson-Durbin 

3379 recursion which is normally used. 

3380 ''' 

3381 

3382 gamma = autocorr(x, order+1) 

3383 d = gamma[1:1+order] 

3384 a = num.zeros((order, order)) 

3385 gamma2 = num.concatenate((gamma[::-1], gamma[1:order])) 

3386 for i in range(order): 

3387 ioff = order-i 

3388 a[i, :] = gamma2[ioff:ioff+order] 

3389 

3390 return num.dot(num.linalg.inv(a), -d) 

3391 

3392 

3393def moving_avg(x, n): 

3394 n = int(n) 

3395 cx = x.cumsum() 

3396 nn = len(x) 

3397 y = num.zeros(nn, dtype=cx.dtype) 

3398 y[n//2:n//2+(nn-n)] = (cx[n:]-cx[:-n])/n 

3399 y[:n//2] = y[n//2] 

3400 y[n//2+(nn-n):] = y[n//2+(nn-n)-1] 

3401 return y 

3402 

3403 

3404def moving_sum(x, n, mode='valid'): 

3405 n = int(n) 

3406 cx = x.cumsum() 

3407 nn = len(x) 

3408 

3409 if mode == 'valid': 

3410 if nn-n+1 <= 0: 

3411 return num.zeros(0, dtype=cx.dtype) 

3412 y = num.zeros(nn-n+1, dtype=cx.dtype) 

3413 y[0] = cx[n-1] 

3414 y[1:nn-n+1] = cx[n:nn]-cx[0:nn-n] 

3415 

3416 if mode == 'full': 

3417 y = num.zeros(nn+n-1, dtype=cx.dtype) 

3418 if n <= nn: 

3419 y[0:n] = cx[0:n] 

3420 y[n:nn] = cx[n:nn]-cx[0:nn-n] 

3421 y[nn:nn+n-1] = cx[-1]-cx[nn-n:nn-1] 

3422 else: 

3423 y[0:nn] = cx[0:nn] 

3424 y[nn:n] = cx[nn-1] 

3425 y[n:nn+n-1] = cx[nn-1] - cx[0:nn-1] 

3426 

3427 if mode == 'same': 

3428 n1 = (n-1)//2 

3429 y = num.zeros(nn, dtype=cx.dtype) 

3430 if n <= nn: 

3431 y[0:n-n1] = cx[n1:n] 

3432 y[n-n1:nn-n1] = cx[n:nn]-cx[0:nn-n] 

3433 y[nn-n1:nn] = cx[nn-1] - cx[nn-n:nn-n+n1] 

3434 else: 

3435 y[0:max(0, nn-n1)] = cx[min(n1, nn):nn] 

3436 y[max(nn-n1, 0):min(n-n1, nn)] = cx[nn-1] 

3437 y[min(n-n1, nn):nn] = cx[nn-1] - cx[0:max(0, nn-(n-n1))] 

3438 

3439 return y 

3440 

3441 

3442def nextpow2(i): 

3443 return 2**int(math.ceil(math.log(i)/math.log(2.))) 

3444 

3445 

3446def snapper_w_offset(nmax, offset, delta, snapfun=math.ceil): 

3447 def snap(x): 

3448 return max(0, min(int(snapfun((x-offset)/delta)), nmax)) 

3449 return snap 

3450 

3451 

3452def snapper(nmax, delta, snapfun=math.ceil): 

3453 def snap(x): 

3454 return max(0, min(int(snapfun(x/delta)), nmax)) 

3455 return snap 

3456 

3457 

3458def apply_costaper(a, b, c, d, y, x0, dx): 

3459 abcd = num.array((a, b, c, d), dtype=float) 

3460 ja, jb, jc, jd = num.clip(num.ceil((abcd-x0)/dx).astype(int), 0, y.size) 

3461 y[:ja] = 0. 

3462 y[ja:jb] *= 0.5 \ 

3463 - 0.5*num.cos((dx*num.arange(ja, jb)-(a-x0))/(b-a)*num.pi) 

3464 y[jc:jd] *= 0.5 \ 

3465 + 0.5*num.cos((dx*num.arange(jc, jd)-(c-x0))/(d-c)*num.pi) 

3466 y[jd:] = 0. 

3467 

3468 

3469def span_costaper(a, b, c, d, y, x0, dx): 

3470 hi = snapper_w_offset(y.size, x0, dx) 

3471 return hi(a), hi(d) - hi(a) 

3472 

3473 

3474def costaper(a, b, c, d, nfreqs, deltaf): 

3475 hi = snapper(nfreqs, deltaf) 

3476 tap = num.zeros(nfreqs) 

3477 tap[hi(a):hi(b)] = 0.5 \ 

3478 - 0.5*num.cos((deltaf*num.arange(hi(a), hi(b))-a)/(b-a)*num.pi) 

3479 tap[hi(b):hi(c)] = 1. 

3480 tap[hi(c):hi(d)] = 0.5 \ 

3481 + 0.5*num.cos((deltaf*num.arange(hi(c), hi(d))-c)/(d-c)*num.pi) 

3482 

3483 return tap 

3484 

3485 

3486def t2ind(t, tdelta, snap=round): 

3487 return int(snap(t/tdelta)) 

3488 

3489 

3490def hilbert(x, N=None): 

3491 ''' 

3492 Return the hilbert transform of x of length N. 

3493 

3494 (from scipy.signal, but changed to use fft and ifft from numpy.fft) 

3495 ''' 

3496 

3497 x = num.asarray(x) 

3498 if N is None: 

3499 N = len(x) 

3500 if N <= 0: 

3501 raise ValueError('N must be positive.') 

3502 if num.iscomplexobj(x): 

3503 logger.warning('imaginary part of x ignored.') 

3504 x = num.real(x) 

3505 

3506 Xf = num.fft.fft(x, N, axis=0) 

3507 h = num.zeros(N) 

3508 if N % 2 == 0: 

3509 h[0] = h[N//2] = 1 

3510 h[1:N//2] = 2 

3511 else: 

3512 h[0] = 1 

3513 h[1:(N+1)//2] = 2 

3514 

3515 if len(x.shape) > 1: 

3516 h = h[:, num.newaxis] 

3517 x = num.fft.ifft(Xf*h) 

3518 return x 

3519 

3520 

3521def near(a, b, eps): 

3522 return abs(a-b) < eps 

3523 

3524 

3525def coroutine(func): 

3526 def wrapper(*args, **kwargs): 

3527 gen = func(*args, **kwargs) 

3528 next(gen) 

3529 return gen 

3530 

3531 wrapper.__name__ = func.__name__ 

3532 wrapper.__dict__ = func.__dict__ 

3533 wrapper.__doc__ = func.__doc__ 

3534 return wrapper 

3535 

3536 

3537class States(object): 

3538 ''' 

3539 Utility to store channel-specific state in coroutines. 

3540 ''' 

3541 

3542 def __init__(self): 

3543 self._states = {} 

3544 

3545 def get(self, tr): 

3546 k = tr.nslc_id 

3547 if k in self._states: 

3548 tmin, deltat, dtype, value = self._states[k] 

3549 if (near(tmin, tr.tmin, deltat/100.) 

3550 and near(deltat, tr.deltat, deltat/10000.) 

3551 and dtype == tr.ydata.dtype): 

3552 

3553 return value 

3554 

3555 return None 

3556 

3557 def set(self, tr, value): 

3558 k = tr.nslc_id 

3559 if k in self._states and self._states[k][-1] is not value: 

3560 self.free(self._states[k][-1]) 

3561 

3562 self._states[k] = (tr.tmax+tr.deltat, tr.deltat, tr.ydata.dtype, value) 

3563 

3564 def free(self, value): 

3565 pass 

3566 

3567 

3568@coroutine 

3569def co_list_append(list): 

3570 while True: 

3571 list.append((yield)) 

3572 

3573 

3574class ScipyBug(Exception): 

3575 pass 

3576 

3577 

3578@coroutine 

3579def co_lfilter(target, b, a): 

3580 ''' 

3581 Successively filter broken continuous trace data (coroutine). 

3582 

3583 Create coroutine which takes :py:class:`Trace` objects, filters their data 

3584 through :py:func:`scipy.signal.lfilter` and sends new :py:class:`Trace` 

3585 objects containing the filtered data to target. This is useful, if one 

3586 wants to filter a long continuous time series, which is split into many 

3587 successive traces without producing filter artifacts at trace boundaries. 

3588 

3589 Filter states are kept *per channel*, specifically, for each (network, 

3590 station, location, channel) combination occuring in the input traces, a 

3591 separate state is created and maintained. This makes it possible to filter 

3592 multichannel or multistation data with only one :py:func:`co_lfilter` 

3593 instance. 

3594 

3595 Filter state is reset, when gaps occur. 

3596 

3597 Use it like this:: 

3598 

3599 from pyrocko.trace import co_lfilter, co_list_append 

3600 

3601 filtered_traces = [] 

3602 pipe = co_lfilter(co_list_append(filtered_traces), a, b) 

3603 for trace in traces: 

3604 pipe.send(trace) 

3605 

3606 pipe.close() 

3607 

3608 ''' 

3609 

3610 try: 

3611 states = States() 

3612 output = None 

3613 while True: 

3614 input = (yield) 

3615 

3616 zi = states.get(input) 

3617 if zi is None: 

3618 zi = num.zeros(max(len(a), len(b))-1, dtype=float) 

3619 

3620 output = input.copy(data=False) 

3621 try: 

3622 ydata, zf = signal.lfilter(b, a, input.get_ydata(), zi=zi) 

3623 except ValueError: 

3624 raise ScipyBug( 

3625 'signal.lfilter failed: could be related to a bug ' 

3626 'in some older scipy versions, e.g. on opensuse42.1') 

3627 

3628 output.set_ydata(ydata) 

3629 states.set(input, zf) 

3630 target.send(output) 

3631 

3632 except GeneratorExit: 

3633 target.close() 

3634 

3635 

3636def co_antialias(target, q, n=None, ftype='fir'): 

3637 b, a, n = util.decimate_coeffs(q, n, ftype) 

3638 anti = co_lfilter(target, b, a) 

3639 return anti 

3640 

3641 

3642@coroutine 

3643def co_dropsamples(target, q, nfir): 

3644 try: 

3645 states = States() 

3646 while True: 

3647 tr = (yield) 

3648 newdeltat = q * tr.deltat 

3649 ioffset = states.get(tr) 

3650 if ioffset is None: 

3651 # for fir filter, the first nfir samples are pulluted by 

3652 # boundary effects; cut it off. 

3653 # for iir this may be (much) more, we do not correct for that. 

3654 # put sample instances to a time which is a multiple of the 

3655 # new sampling interval. 

3656 newtmin_want = math.ceil( 

3657 (tr.tmin+(nfir+1)*tr.deltat) / newdeltat) * newdeltat \ 

3658 - (nfir/2*tr.deltat) 

3659 ioffset = int(round((newtmin_want - tr.tmin)/tr.deltat)) 

3660 if ioffset < 0: 

3661 ioffset = ioffset % q 

3662 

3663 newtmin_have = tr.tmin + ioffset * tr.deltat 

3664 newtr = tr.copy(data=False) 

3665 newtr.deltat = newdeltat 

3666 # because the fir kernel shifts data by nfir/2 samples: 

3667 newtr.tmin = newtmin_have - (nfir/2*tr.deltat) 

3668 newtr.set_ydata(tr.get_ydata()[ioffset::q].copy()) 

3669 states.set(tr, (ioffset % q - tr.data_len() % q) % q) 

3670 target.send(newtr) 

3671 

3672 except GeneratorExit: 

3673 target.close() 

3674 

3675 

3676def co_downsample(target, q, n=None, ftype='fir'): 

3677 ''' 

3678 Successively downsample broken continuous trace data (coroutine). 

3679 

3680 Create coroutine which takes :py:class:`Trace` objects, downsamples their 

3681 data and sends new :py:class:`Trace` objects containing the downsampled 

3682 data to target. This is useful, if one wants to downsample a long 

3683 continuous time series, which is split into many successive traces without 

3684 producing filter artifacts and gaps at trace boundaries. 

3685 

3686 Filter states are kept *per channel*, specifically, for each (network, 

3687 station, location, channel) combination occuring in the input traces, a 

3688 separate state is created and maintained. This makes it possible to filter 

3689 multichannel or multistation data with only one :py:func:`co_lfilter` 

3690 instance. 

3691 

3692 Filter state is reset, when gaps occur. The sampling instances are choosen 

3693 so that they occur at (or as close as possible) to even multiples of the 

3694 sampling interval of the downsampled trace (based on system time). 

3695 ''' 

3696 

3697 b, a, n = util.decimate_coeffs(q, n, ftype) 

3698 return co_antialias(co_dropsamples(target, q, n), q, n, ftype) 

3699 

3700 

3701@coroutine 

3702def co_downsample_to(target, deltat): 

3703 

3704 decimators = {} 

3705 try: 

3706 while True: 

3707 tr = (yield) 

3708 ratio = deltat / tr.deltat 

3709 rratio = round(ratio) 

3710 if abs(rratio - ratio)/ratio > 0.0001: 

3711 raise util.UnavailableDecimation('ratio = %g' % ratio) 

3712 

3713 deci_seq = tuple(x for x in util.decitab(int(rratio)) if x != 1) 

3714 if deci_seq not in decimators: 

3715 pipe = target 

3716 for q in deci_seq[::-1]: 

3717 pipe = co_downsample(pipe, q) 

3718 

3719 decimators[deci_seq] = pipe 

3720 

3721 decimators[deci_seq].send(tr) 

3722 

3723 except GeneratorExit: 

3724 for g in decimators.values(): 

3725 g.close() 

3726 

3727 

3728class DomainChoice(StringChoice): 

3729 choices = [ 

3730 'time_domain', 

3731 'frequency_domain', 

3732 'envelope', 

3733 'absolute', 

3734 'cc_max_norm'] 

3735 

3736 

3737class MisfitSetup(Object): 

3738 ''' 

3739 Contains misfit setup to be used in :py:meth:`Trace.misfit` 

3740 

3741 :param description: Description of the setup 

3742 :param norm: L-norm classifier 

3743 :param taper: Object of :py:class:`Taper` 

3744 :param filter: Object of :py:class:`~pyrocko.response.FrequencyResponse` 

3745 :param domain: ['time_domain', 'frequency_domain', 'envelope', 'absolute', 

3746 'cc_max_norm'] 

3747 

3748 Can be dumped to a yaml file. 

3749 ''' 

3750 

3751 xmltagname = 'misfitsetup' 

3752 description = String.T(optional=True) 

3753 norm = Int.T(optional=False) 

3754 taper = Taper.T(optional=False) 

3755 filter = FrequencyResponse.T(optional=True) 

3756 domain = DomainChoice.T(default='time_domain') 

3757 

3758 

3759def equalize_sampling_rates(trace_1, trace_2): 

3760 ''' 

3761 Equalize sampling rates of two traces (reduce higher sampling rate to 

3762 lower). 

3763 

3764 :param trace_1: :py:class:`Trace` object 

3765 :param trace_2: :py:class:`Trace` object 

3766 

3767 Returns a copy of the resampled trace if resampling is needed. 

3768 ''' 

3769 

3770 if same_sampling_rate(trace_1, trace_2): 

3771 return trace_1, trace_2 

3772 

3773 if trace_1.deltat < trace_2.deltat: 

3774 t1_out = trace_1.copy() 

3775 t1_out.downsample_to(deltat=trace_2.deltat, snap=True) 

3776 logger.debug('Trace downsampled (return copy of trace): %s' 

3777 % '.'.join(t1_out.nslc_id)) 

3778 return t1_out, trace_2 

3779 

3780 elif trace_1.deltat > trace_2.deltat: 

3781 t2_out = trace_2.copy() 

3782 t2_out.downsample_to(deltat=trace_1.deltat, snap=True) 

3783 logger.debug('Trace downsampled (return copy of trace): %s' 

3784 % '.'.join(t2_out.nslc_id)) 

3785 return trace_1, t2_out 

3786 

3787 

3788def Lx_norm(u, v, norm=2): 

3789 ''' 

3790 Calculate the misfit denominator *m* and the normalization divisor *n* 

3791 according to norm. 

3792 

3793 The normalization divisor *n* is calculated from ``v``. 

3794 

3795 :param u: :py:class:`numpy.ndarray` 

3796 :param v: :py:class:`numpy.ndarray` 

3797 :param norm: (default = 2) 

3798 

3799 ``u`` and ``v`` must be of same size. 

3800 ''' 

3801 

3802 if norm == 1: 

3803 return ( 

3804 num.sum(num.abs(v-u)), 

3805 num.sum(num.abs(v))) 

3806 

3807 elif norm == 2: 

3808 return ( 

3809 num.sqrt(num.sum((v-u)**2)), 

3810 num.sqrt(num.sum(v**2))) 

3811 

3812 else: 

3813 return ( 

3814 num.power(num.sum(num.abs(num.power(v - u, norm))), 1./norm), 

3815 num.power(num.sum(num.abs(num.power(v, norm))), 1./norm)) 

3816 

3817 

3818def do_downsample(tr, deltat): 

3819 if abs(tr.deltat - deltat) / tr.deltat > 1e-6: 

3820 tr = tr.copy() 

3821 tr.downsample_to(deltat, snap=True, demean=False) 

3822 else: 

3823 if tr.tmin/tr.deltat > 1e-6 or tr.tmax/tr.deltat > 1e-6: 

3824 tr = tr.copy() 

3825 tr.snap() 

3826 return tr 

3827 

3828 

3829def do_extend(tr, tmin, tmax): 

3830 if tmin < tr.tmin or tmax > tr.tmax: 

3831 tr = tr.copy() 

3832 tr.extend(tmin=tmin, tmax=tmax, fillmethod='repeat') 

3833 

3834 return tr 

3835 

3836 

3837def do_pre_taper(tr, taper): 

3838 return tr.taper(taper, inplace=False, chop=True) 

3839 

3840 

3841def do_fft(tr, filter): 

3842 if filter is None: 

3843 return tr 

3844 else: 

3845 ndata = tr.ydata.size 

3846 nfft = nextpow2(ndata) 

3847 padded = num.zeros(nfft, dtype=float) 

3848 padded[:ndata] = tr.ydata 

3849 spectrum = num.fft.rfft(padded) 

3850 df = 1.0 / (tr.deltat * nfft) 

3851 frequencies = num.arange(spectrum.size)*df 

3852 return [tr, frequencies, spectrum] 

3853 

3854 

3855def do_filter(inp, filter): 

3856 if filter is None: 

3857 return inp 

3858 else: 

3859 tr, frequencies, spectrum = inp 

3860 spectrum *= filter.evaluate(frequencies) 

3861 return [tr, frequencies, spectrum] 

3862 

3863 

3864def do_ifft(inp): 

3865 if isinstance(inp, Trace): 

3866 return inp 

3867 else: 

3868 tr, _, spectrum = inp 

3869 ndata = tr.ydata.size 

3870 tr = tr.copy(data=False) 

3871 tr.set_ydata(num.fft.irfft(spectrum)[:ndata]) 

3872 return tr 

3873 

3874 

3875def check_alignment(t1, t2): 

3876 if abs(t1.tmin-t2.tmin) > t1.deltat * 1e-4 or \ 

3877 abs(t1.tmax - t2.tmax) > t1.deltat * 1e-4 or \ 

3878 t1.ydata.shape != t2.ydata.shape: 

3879 raise MisalignedTraces( 

3880 'Cannot calculate misfit of %s and %s due to misaligned ' 

3881 'traces.' % ('.'.join(t1.nslc_id), '.'.join(t2.nslc_id)))