Coverage for /usr/local/lib/python3.11/dist-packages/pyrocko/trace.py: 76%
1745 statements
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1# https://pyrocko.org - GPLv3
2#
3# The Pyrocko Developers, 21st Century
4# ---|P------/S----------~Lg----------
6'''
7Basic signal processing for seismic waveforms.
8'''
10import time
11import math
12import copy
13import logging
14import hashlib
15from collections import defaultdict
17import numpy as num
18from scipy import signal
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
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)
35guts_prefix = 'pf'
37logger = logging.getLogger('pyrocko.trace')
40g_tapered_coeffs_cache = {}
41g_one_response = FrequencyResponse()
44@squirrel_content
45class Trace(Object):
47 '''
48 Create new trace object.
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).
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
69 :param meta: additional meta information (not used, but maintained by the
70 library)
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 '''
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')
84 tmin = Timestamp.T(default=Timestamp.D('1970-01-01 00:00:00'))
85 tmax = Timestamp.T()
87 deltat = Float.T(default=1.0)
88 ydata = Array.T(optional=True, shape=(None,), serialize_as='base64+meta')
90 mtime = Timestamp.T(optional=True)
92 cached_frequencies = {}
94 def __init__(self, network='', station='STA', location='', channel='',
95 tmin=0., tmax=None, deltat=1., ydata=None, mtime=None,
96 meta=None, extra=''):
98 Object.__init__(self, init_props=False)
100 time_float = util.get_time_float()
102 if not isinstance(tmin, time_float):
103 tmin = Trace.tmin.regularize_extra(tmin)
105 if tmax is not None and not isinstance(tmax, time_float):
106 tmax = Trace.tmax.regularize_extra(tmax)
108 if mtime is not None and not isinstance(mtime, time_float):
109 mtime = Trace.mtime.regularize_extra(mtime)
111 if ydata is not None and not isinstance(ydata, num.ndarray):
112 ydata = Trace.ydata.regularize_extra(ydata)
114 self._growbuffer = None
116 tmin = time_float(tmin)
117 if tmax is not None:
118 tmax = time_float(tmax)
120 if mtime is None:
121 mtime = time_float(time.time())
123 self.network, self.station, self.location, self.channel, \
124 self.extra = [
125 reuse(x) for x in (
126 network, station, location, channel, extra)]
128 self.tmin = tmin
129 self.deltat = deltat
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
141 self.meta = meta
142 self.ydata = ydata
143 self.mtime = mtime
144 self._update_ids()
145 self.file = None
146 self._pchain = None
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))
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
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)
168 @property
169 def time_span(self):
170 return self.tmin, self.tmax
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))
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()))
188 @property
189 def summary(self):
190 return util.fmt_summary(self.summary_entries, (10, 20, 55, 0))
192 @property
193 def summary_stats(self):
194 return self.summary + ' | ' + util.fmt_summary(
195 self.summary_stats_entries, (12, 12, 12, 12))
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)
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
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
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
220 self.extra = ''
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 = ''
230 self._growbuffer = None
231 self._update_ids()
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())
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:]))
248 return sha1.hexdigest()
250 def name(self):
251 '''
252 Get a short string description.
253 '''
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)))
259 return s
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))
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))
286 def assert_almost_equal(self, other, rtol=1e-5, atol=0.0):
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))
305 assert num.allclose(self.ydata, other.ydata, rtol=rtol, atol=atol), \
306 'trace values differ'
308 def __hash__(self):
309 return id(self)
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()
319 return self.tmin+it*self.deltat, self.ydata[it]
321 def interpolate(self, t, clip=False):
322 '''
323 Value of trace between supporting points through linear interpolation.
325 :param t: time instant
326 :param clip: whether to clip indices to trace ends
327 '''
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)
336 def index_clip(self, i):
337 '''
338 Clip index to valid range.
339 '''
341 return min(max(0, i), self.ydata.size)
343 def add(self, other, interpolate=True, left=0., right=0.):
344 '''
345 Add values of other trace (self += other).
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 '''
357 if interpolate:
358 assert self.deltat <= other.deltat \
359 or same_sampling_rate(self, other)
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]
372 def mult(self, other, interpolate=True):
373 '''
374 Muliply with values of other trace ``(self *= other)``.
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 '''
386 if interpolate:
387 assert self.deltat <= other.deltat or \
388 same_sampling_rate(self, other)
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
401 ibeg1 = self.index_clip(ibeg1)
402 iend1 = self.index_clip(iend1)
403 ibeg2 = self.index_clip(ibeg2)
404 iend2 = self.index_clip(iend2)
406 self.ydata[ibeg1:iend1] *= other.ydata[ibeg2:iend2]
408 def max(self):
409 '''
410 Get time and value of data maximum.
411 '''
413 i = num.argmax(self.ydata)
414 return self.tmin + i*self.deltat, self.ydata[i]
416 def min(self):
417 '''
418 Get time and value of data minimum.
419 '''
421 i = num.argmin(self.ydata)
422 return self.tmin + i*self.deltat, self.ydata[i]
424 def absmax(self):
425 '''
426 Get time and value of maximum of the absolute of data.
427 '''
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)
436 def set_codes(
437 self, network=None, station=None, location=None, channel=None,
438 extra=None):
440 '''
441 Set network, station, location, and channel codes.
442 '''
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
455 self._update_ids()
457 def set_network(self, network):
458 self.network = network
459 self._update_ids()
461 def set_station(self, station):
462 self.station = station
463 self._update_ids()
465 def set_location(self, location):
466 self.location = location
467 self._update_ids()
469 def set_channel(self, channel):
470 self.channel = channel
471 self._update_ids()
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)
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 '''
485 return not (tmax <= self.tmin or self.tmax < tmin) \
486 and (selector is None or selector(self))
488 def _update_ids(self):
489 '''
490 Update dependent ids.
491 '''
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))
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)
505 def set_mtime(self, mtime):
506 '''
507 Set modification time of the trace.
508 '''
510 self.mtime = mtime
512 def get_xdata(self):
513 '''
514 Create array for time axis.
515 '''
517 if self.ydata is None:
518 raise NoData()
520 return self.tmin \
521 + num.arange(len(self.ydata), dtype=num.float64) * self.deltat
523 def get_ydata(self):
524 '''
525 Get data array.
526 '''
528 if self.ydata is None:
529 raise NoData()
531 return self.ydata
533 def set_ydata(self, new_ydata):
534 '''
535 Replace data array.
536 '''
538 self.drop_growbuffer()
539 self.ydata = new_ydata
540 self.tmax = self.tmin+(len(self.ydata)-1)*self.deltat
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
548 def drop_data(self):
549 '''
550 Forget data, make dataless trace.
551 '''
553 self.drop_growbuffer()
554 self.ydata = None
556 def drop_growbuffer(self):
557 '''
558 Detach the traces grow buffer.
559 '''
561 self._growbuffer = None
562 self._pchain = None
564 def copy(self, data=True):
565 '''
566 Make a deep copy of the trace.
567 '''
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
576 def crop_zeros(self):
577 '''
578 Remove any zeros at beginning and end.
579 '''
581 indices = num.where(self.ydata != 0.0)[0]
582 if indices.size == 0:
583 raise NoData()
585 ibeg = indices[0]
586 iend = indices[-1]+1
587 if ibeg == 0 and iend == self.ydata.size-1:
588 return
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()
596 def append(self, data):
597 '''
598 Append data to the end of the trace.
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 '''
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
615 def chop(
616 self, tmin, tmax, inplace=True, include_last=False,
617 snap=(round, round), want_incomplete=True):
619 '''
620 Cut the trace to given time span.
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 '''
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()
645 ibeg = max(0, t2ind(tmin-self.tmin, self.deltat, snap[0]))
646 iplus = 0
647 if include_last:
648 iplus = 1
650 iend = min(
651 self.data_len(),
652 t2ind(tmax-self.tmin, self.deltat, snap[1])+iplus)
654 if ibeg >= iend:
655 raise NoData()
657 obj = self
658 if not inplace:
659 obj = self.copy(data=False)
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
667 obj.tmin = obj.tmin+ibeg*obj.deltat
668 obj.tmax = obj.tmin+((iend-ibeg)-1)*obj.deltat
670 obj._update_ids()
672 return obj
674 def downsample(
675 self, ndecimate, snap=False, demean=False, ftype='fir-remez',
676 cut=False):
678 '''
679 Downsample (decimate) trace by a given integer factor.
681 Antialiasing filter details:
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.
690 Comparison of the digital filters:
692 .. figure :: ../../static/downsampling-filter-comparison.png
693 :width: 60%
694 :alt: Comparison of the downsampling filters.
696 See also :py:meth:`Trace.downsample_to`.
698 :param ndecimate:
699 Decimation factor, avoid values larger than 8.
700 :type ndecimate:
701 int
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
709 :param demean:
710 Whether to demean the signal before filtering.
711 :type demean:
712 bool
714 :param ftype:
715 Which FIR filter to use, choose from ``'iir'``, ``'fir'``,
716 ``'fir-remez'``. Default is ``'fir-remez'``.
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)
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
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()
747 def downsample_to(
748 self, deltat, snap=False, allow_upsample_max=1, demean=False,
749 ftype='fir-remez', cut=False):
751 '''
752 Downsample to given sampling rate.
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.
760 If the requested ratio is not supported, an exception of type
761 :py:exc:`pyrocko.util.UnavailableDecimation` is raised.
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`.
770 See also: :meth:`Trace.downsample`.
772 :param deltat:
773 Desired sampling interval in [s].
774 :type deltat:
775 float
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
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
789 :param demean:
790 Whether to demean the signal before filtering.
791 :type demean:
792 bool
794 :param ftype:
795 Which FIR filter to use, choose from ``'iir'``, ``'fir'``,
796 ``'fir-remez'``. Default is ``'fir-remez'``.
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 '''
805 upsratio, deci_seq = _configure_downsampling(
806 self.deltat, deltat, allow_upsample_max)
808 if demean:
809 self.drop_growbuffer()
810 self.ydata = self.ydata.astype(num.float64)
811 self.ydata -= num.mean(self.ydata)
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
825 for i, ndecimate in enumerate(deci_seq):
826 self.downsample(
827 ndecimate, snap=snap, demean=False, ftype=ftype, cut=cut)
829 def resample(self, deltat):
830 '''
831 Resample to given sampling rate ``deltat``.
833 Resampling is performed in the frequency domain.
834 '''
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))
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)
860 def resample_simple(self, deltat):
861 tyear = 3600*24*365.
863 if deltat == self.deltat:
864 return
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
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()
879 delete = False
880 if ninterval < 0:
881 ninterval = - ninterval
882 delete = True
884 tyearbegin = util.year_start(self.tmin)
886 nmin = int(round((self.tmin - tyearbegin)/deltat))
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]
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))
906 data.append(data_split[-1])
908 ydata_new = num.concatenate(data)
910 self.tmin = tyearbegin + nmin * deltat
911 self.deltat = deltat
912 self.set_ydata(ydata_new)
914 def stretch(self, tmin_new, tmax_new):
915 '''
916 Stretch signal while preserving sample rate using sinc interpolation.
918 :param tmin_new: new time of first sample
919 :param tmax_new: new time of last sample
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 '''
927 i_control = num.array([0, self.ydata.size-1], dtype=num.int64)
928 t_control = num.array([tmin_new, tmax_new], dtype=float)
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))
935 assert n_new >= 2
937 tmax_new = tmin_new + (n_new-1) * self.deltat
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)
944 self.tmin = tmin_new
945 self.set_ydata(ydata_new)
946 self._update_ids()
948 def nyquist_check(self, frequency, intro='Corner frequency', warn=True,
949 raise_exception=False):
951 '''
952 Check if a given frequency is above the Nyquist frequency of the trace.
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 '''
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)
969 def lowpass(self, order, corner, nyquist_warn=True,
970 nyquist_exception=False, demean=True):
972 '''
973 Apply Butterworth lowpass to the trace.
975 :param order: order of the filter
976 :param corner: corner frequency of the filter
978 Mean is removed before filtering.
979 '''
981 self.nyquist_check(
982 corner, 'Corner frequency of lowpass', nyquist_warn,
983 nyquist_exception)
985 (b, a) = _get_cached_filter_coeffs(
986 order, [corner*2.0*self.deltat], btype='low')
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.')
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)
1000 def highpass(self, order, corner, nyquist_warn=True,
1001 nyquist_exception=False, demean=True):
1003 '''
1004 Apply butterworth highpass to the trace.
1006 :param order: order of the filter
1007 :param corner: corner frequency of the filter
1009 Mean is removed before filtering.
1010 '''
1012 self.nyquist_check(
1013 corner, 'Corner frequency of highpass', nyquist_warn,
1014 nyquist_exception)
1016 (b, a) = _get_cached_filter_coeffs(
1017 order, [corner*2.0*self.deltat], btype='high')
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)
1030 def bandpass(self, order, corner_hp, corner_lp, demean=True):
1031 '''
1032 Apply butterworth bandpass to the trace.
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
1038 Mean is removed before filtering.
1039 '''
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)
1053 def bandstop(self, order, corner_hp, corner_lp, demean=True):
1054 '''
1055 Apply bandstop (attenuates frequencies in band) to the trace.
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
1061 Mean is removed before filtering.
1062 '''
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)
1076 def envelope(self, inplace=True):
1077 '''
1078 Calculate the envelope of the trace.
1080 :param inplace: calculate envelope in place
1082 The calculation follows:
1084 .. math::
1086 Y' = \\sqrt{Y^2+H(Y)^2}
1088 where H is the Hilbert-Transform of the signal Y.
1089 '''
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
1101 def taper(self, taperer, inplace=True, chop=False):
1102 '''
1103 Apply a :py:class:`Taper` to the trace.
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 '''
1111 if not inplace:
1112 tr = self.copy()
1113 else:
1114 tr = self
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])
1121 taperer(tr.ydata, tr.tmin, tr.deltat)
1123 if not inplace:
1124 return tr
1126 def whiten(self, order=6):
1127 '''
1128 Whiten signal in time domain using autoregression and recursive filter.
1130 :param order: order of the autoregression process
1131 '''
1133 b, a = self.whitening_coefficients(order)
1134 self.drop_growbuffer()
1135 self.ydata = signal.lfilter(b, a, self.ydata)
1137 def whitening_coefficients(self, order=6):
1138 ar = yulewalker(self.ydata, order)
1139 b, a = [1.] + ar.tolist(), [1.]
1140 return b, a
1142 def ampspec_whiten(
1143 self,
1144 width,
1145 td_taper='auto',
1146 fd_taper='auto',
1147 pad_to_pow2=True,
1148 demean=True):
1150 '''
1151 Whiten signal via frequency domain using moving average on amplitude
1152 spectra.
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
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.
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 '''
1174 ndata = self.data_len()
1176 if pad_to_pow2:
1177 ntrans = nextpow2(ndata)
1178 else:
1179 ntrans = ndata
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))
1187 if td_taper == 'auto':
1188 td_taper = CosFader(1./width)
1190 if fd_taper == 'auto':
1191 fd_taper = CosFader(width)
1193 if td_taper:
1194 self.taper(td_taper)
1196 ydata = self.get_ydata().astype(float)
1197 if demean:
1198 ydata -= ydata.mean()
1200 spec = num.fft.rfft(ydata, ntrans)
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]
1211 denom = amp_smoothed * amp
1212 numer = amp
1213 eps = num.mean(denom) * 1e-9
1214 if eps == 0.0:
1215 eps = 1e-9
1217 numer += eps
1218 denom += eps
1219 spec *= numer/denom
1221 if fd_taper:
1222 fd_taper(spec, 0., df)
1224 ydata = num.fft.irfft(spec)
1225 self.set_ydata(ydata[:ndata])
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)
1233 return Trace.cached_frequencies[ck]
1235 def bandpass_fft(self, corner_hp, corner_lp):
1236 '''
1237 Apply boxcar bandbpass to trace (in spectral domain).
1238 '''
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]
1252 def shift(self, tshift):
1253 '''
1254 Time shift the trace.
1255 '''
1257 self.tmin += tshift
1258 self.tmax += tshift
1259 self._update_ids()
1261 def snap(self, inplace=True, interpolate=False):
1262 '''
1263 Shift trace samples to nearest even multiples of the sampling rate.
1265 :param inplace: (boolean) snap traces inplace
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 '''
1272 tmin = round(self.tmin/self.deltat)*self.deltat
1273 tmax = tmin + (self.ydata.size-1)*self.deltat
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
1282 xself = self.copy()
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)
1293 signal_ext.antidrift(i_control, t_control,
1294 xself.ydata.astype(float),
1295 float(tmin-tref), xself.deltat, ydata_new)
1297 xself.ydata = ydata_new
1299 xself.tmin = tmin
1300 xself.tmax = tmax
1301 xself._update_ids()
1303 return xself
1305 def fix_deltat_rounding_errors(self):
1306 '''
1307 Try to undo sampling rate rounding errors.
1309 See :py:func:`fix_deltat_rounding_errors`.
1310 '''
1312 self.deltat = fix_deltat_rounding_errors(self.deltat)
1313 self.tmax = self.tmin + (self.data_len() - 1) * self.deltat
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.
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``)
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 ============= ====================================== ===========
1335 '''
1337 nshort = int(round(tshort/self.deltat))
1338 nlong = int(round(tlong/self.deltat))
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))
1346 if quad:
1347 sqrdata = self.ydata**2
1348 else:
1349 sqrdata = self.ydata
1351 mavg_short = moving_avg(sqrdata, nshort)
1352 mavg_long = moving_avg(sqrdata, nlong)
1354 self.drop_growbuffer()
1356 if scalingmethod not in (1, 2, 3):
1357 raise Exception('Invalid argument to scalingrange argument.')
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)
1365 if scalingmethod == 3:
1366 self.ydata = num.maximum(self.ydata, 0.)
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.
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``)
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 ============= ====================================== ===========
1388 With ``scalingmethod=1``, the values produced by this variant of the
1389 STA/LTA are equivalent to
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}
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 '''
1400 n = self.data_len()
1401 tmin = self.tmin
1403 nshort = max(1, int(round(tshort/self.deltat)))
1404 nlong = max(1, int(round(tlong/self.deltat)))
1406 assert nshort < nlong
1408 if nlong > len(self.ydata):
1409 raise TraceTooShort(
1410 'Samples in trace: %s, samples needed: %s'
1411 % (len(self.ydata), nlong))
1413 if quad:
1414 sqrdata = self.ydata**2
1415 else:
1416 sqrdata = self.ydata
1418 nshift = int(math.floor(0.5 * (nlong - nshort)))
1419 if nlong % 2 != 0 and nshort % 2 == 0:
1420 nshift += 1
1422 mavg_short = moving_avg(sqrdata, nshort)[nshift:]
1423 mavg_long = moving_avg(sqrdata, nlong)[:sqrdata.size-nshift]
1425 self.drop_growbuffer()
1427 if scalingmethod not in (1, 2, 3):
1428 raise Exception('Invalid argument to scalingrange argument.')
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)
1436 if scalingmethod == 3:
1437 ydata = num.maximum(self.ydata, 0.)
1439 self.set_ydata(ydata)
1441 self.shift((math.ceil(0.5*nlong) - nshort + 1) * self.deltat)
1443 self.chop(
1444 tmin + (nlong - nshort) * self.deltat,
1445 tmin + (n - nshort) * self.deltat)
1447 def peaks(self, threshold, tsearch,
1448 deadtime=False,
1449 nblock_duration_detection=100):
1451 '''
1452 Detect peaks above a given threshold (method 1).
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 '''
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
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]
1480 if tpeak < tzero:
1481 continue
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
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
1510 tpeaks.append(tpeak)
1511 apeaks.append(apeak)
1512 tzeros.append(tzero)
1514 if deadtime:
1515 return tpeaks, apeaks, tzeros
1516 else:
1517 return tpeaks, apeaks
1519 def peaks2(self, threshold, tsearch):
1521 '''
1522 Detect peaks above a given threshold (method 2).
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 '''
1534 a = num.copy(self.ydata)
1536 amin = num.min(a)
1538 a[0] = amin
1539 a[1: -1][num.diff(a, 2) <= 0.] = amin
1540 a[-1] = amin
1542 data = []
1543 while True:
1544 imax = num.argmax(a)
1545 amax = a[imax]
1547 if amax < threshold or amax == amin:
1548 break
1550 data.append((self.tmin + imax * self.deltat, amax))
1552 ntsearch = int(round(tsearch / self.deltat))
1553 a[max(imax-ntsearch//2, 0):min(imax+ntsearch//2, a.size)] = amin
1555 if data:
1556 data.sort()
1557 tpeaks, apeaks = list(zip(*data))
1558 else:
1559 tpeaks, apeaks = [], []
1561 return tpeaks, apeaks
1563 def extend(self, tmin=None, tmax=None, fillmethod='zeros'):
1564 '''
1565 Extend trace to given span.
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 '''
1573 nold = self.ydata.size
1575 if tmin is not None:
1576 nl = min(0, int(round((tmin-self.tmin)/self.deltat)))
1577 else:
1578 nl = 0
1580 if tmax is not None:
1581 nh = max(nold - 1, int(round((tmax-self.tmin)/self.deltat)))
1582 else:
1583 nh = nold - 1
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
1601 self.drop_growbuffer()
1602 self.ydata = data
1604 self.tmin += nl * self.deltat
1605 self.tmax = self.tmin + (self.ydata.size - 1) * self.deltat
1607 self._update_ids()
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):
1617 '''
1618 Return new trace with transfer function applied (convolution).
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 '''
1632 if transfer_function is None:
1633 transfer_function = g_one_response
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)))
1641 if freqlimits is None and (
1642 transfer_function is None or transfer_function.is_scalar()):
1644 # special case for flat responses
1646 output = self.copy()
1647 data = self.ydata
1648 ndata = data.size
1650 if transfer_function is not None:
1651 c = num.abs(transfer_function.evaluate(num.ones(1))[0])
1653 if invert:
1654 c = 1.0/c
1656 data *= c
1658 if tfade != 0.0:
1659 data *= costaper(
1660 0., tfade, self.deltat*(ndata-1)-tfade, self.deltat*ndata,
1661 ndata, self.deltat)
1663 output.ydata = data
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)
1672 data = self.ydata
1674 data_pad = num.zeros(ntrans, dtype=float)
1675 data_pad[:ndata] = data
1676 if demean:
1677 data_pad[:ndata] -= data.mean()
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)
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]
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()
1701 return output
1703 def differentiate(self, n=1, order=4, inplace=True):
1704 '''
1705 Approximate first or second derivative of the trace.
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.
1712 Raises :py:exc:`ValueError` for unsupported `n` or `order`.
1714 See :py:func:`~pyrocko.util.diff_fd` for implementation details.
1715 '''
1717 ddata = util.diff_fd(n, order, self.deltat, self.ydata)
1719 if inplace:
1720 self.ydata = ddata
1721 else:
1722 output = self.copy(data=False)
1723 output.set_ydata(ddata)
1724 return output
1726 def drop_chain_cache(self):
1727 if self._pchain:
1728 self._pchain.clear()
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)
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)
1749 return num.abs(data), num.abs(data)
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)
1761 if setup.domain == 'time_domain':
1762 data = processed.get_ydata()
1764 elif setup.domain == 'envelope':
1765 processed = processed.envelope(inplace=False)
1767 elif setup.domain == 'absolute':
1768 processed.set_ydata(num.abs(processed.get_ydata()))
1770 return processed.get_ydata(), processed
1772 def misfit(self, candidate, setup, nocache=False, debug=False):
1773 '''
1774 Calculate misfit and normalization factor against candidate trace.
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
1781 If the sampling rates of ``self`` and ``candidate`` differ, the trace
1782 with the higher sampling rate will be downsampled.
1783 '''
1785 a = self
1786 b = candidate
1788 for tr in (a, b):
1789 if not tr._pchain:
1790 tr.init_chain()
1792 deltat = max(a.deltat, b.deltat)
1793 tmin = min(a.tmin, b.tmin) - deltat
1794 tmax = max(a.tmax, b.tmax) + deltat
1796 adata, aproc = a.run_chain(tmin, tmax, deltat, setup, nocache)
1797 bdata, bproc = b.run_chain(tmin, tmax, deltat, setup, nocache)
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
1807 if debug:
1808 return m, n, aproc, bproc
1809 else:
1810 return m, n
1812 def spectrum(self, pad_to_pow2=False, tfade=None):
1813 '''
1814 Get FFT spectrum of trace.
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
1821 :returns: a tuple with (frequencies, values)
1822 '''
1824 ndata = self.ydata.size
1826 if pad_to_pow2:
1827 ntrans = nextpow2(ndata)
1828 else:
1829 ntrans = ndata
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)
1838 fydata = num.fft.rfft(ydata, ntrans)
1839 df = 1./(ntrans*self.deltat)
1840 fxdata = num.arange(len(fydata))*df
1841 return fxdata, fydata
1843 def multi_filter(self, filter_freqs, bandwidth):
1845 class Gauss(FrequencyResponse):
1846 f0 = Float.T()
1847 a = Float.T(default=1.0)
1849 def __init__(self, f0, a=1.0, **kwargs):
1850 FrequencyResponse.__init__(self, f0=f0, a=a, **kwargs)
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)
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
1870 enorm = num.abs(analytic_spec[:nhalf])**2
1871 enorm /= num.sum(enorm)
1873 if n % 2 == 0:
1874 analytic_spec[1:nhalf-1] *= 2.
1875 else:
1876 analytic_spec[1:nhalf] *= 2.
1878 analytic = num.fft.ifft(analytic_spec)
1879 signal_tf[ifilt, :] = num.abs(analytic)
1881 enorm = num.abs(analytic_spec[:nhalf])**2
1882 enorm /= num.sum(enorm)
1883 centroid_freqs[ifilt] = num.sum(freqs*enorm)
1885 return centroid_freqs, signal_tf
1887 def _get_tapered_coeffs(
1888 self, ntrans, freqlimits, transfer_function, invert=False,
1889 demean=True):
1891 cache_key = (
1892 ntrans, self.deltat, freqlimits, transfer_function.uuid, invert,
1893 demean)
1895 if cache_key in g_tapered_coeffs_cache:
1896 return g_tapered_coeffs_cache[cache_key]
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)
1910 transfer[kmin:kmax] = 1.0 / coeffs
1911 else:
1912 transfer[kmin:kmax] = coeffs
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`')
1921 freqs = num.arange(nfreqs) * deltaf
1922 tapered_transfer = transfer_function.evaluate(freqs)
1924 g_tapered_coeffs_cache[cache_key] = tapered_transfer
1926 if demean:
1927 tapered_transfer[0] = 0.0 # don't introduce static offsets
1929 return tapered_transfer
1931 def fill_template(self, template, **additional):
1932 '''
1933 Fill string template with trace metadata.
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 '''
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')
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
1975 def plot(self):
1976 '''
1977 Show trace with matplotlib.
1979 See also: :py:meth:`Trace.snuffle`.
1980 '''
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)))
1990 pylab.title(name)
1991 pylab.show()
1993 def snuffle(self, **kwargs):
1994 '''
1995 Show trace in a snuffler window.
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 '''
2012 return snuffle([self], **kwargs)
2015def snuffle(traces, **kwargs):
2016 '''
2017 Show traces in a snuffler window.
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 '''
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)
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.
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`.
2052 :param deltat_in:
2053 Input sampling interval [s].
2054 :type deltat_in:
2055 float
2057 :param deltat_out:
2058 Output samling interval [s].
2059 :type deltat_out:
2060 float
2062 :returns:
2063 Approximate length [s] which will be cut off.
2065 See :py:meth:`Trace.downsample_to` for details.
2066 '''
2068 upsratio, deci_seq = _configure_downsampling(
2069 deltat_in, deltat_out, allow_upsample_max)
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
2081 return tpad
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]
2091 raise util.UnavailableDecimation('ratio = %g' % (deltat_out / deltat_in))
2094def _all_same(xs):
2095 return all(x == xs[0] for x in xs)
2098def _incompatibilities(traces):
2099 if not traces:
2100 return None
2102 params = [
2103 (tr.ydata.size, tr.ydata.dtype, tr.deltat, tr.tmin)
2104 for tr in traces]
2106 if not _all_same(params):
2107 return params
2108 else:
2109 return None
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)))
2124def _ensure_compatible(traces):
2125 params = _incompatibilities(traces)
2126 if params:
2127 _raise_incompatible_traces(params)
2130def _almost_equal(a, b, atol):
2131 return abs(a-b) < atol
2134def get_traces_data_as_array(traces):
2135 '''
2136 Merge data samples from multiple traces into a 2D array.
2138 :param traces:
2139 Input waveforms.
2140 :type traces:
2141 list of :py:class:`pyrocko.Trace <pyrocko.trace.Trace>` objects
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.
2147 :returns:
2148 2D array as ``data[itrace, isample]``.
2149 :rtype:
2150 :py:class:`numpy.ndarray`
2151 '''
2153 if not traces:
2154 raise IncompatibleTraces('Need at least one trace.')
2156 _ensure_compatible(traces)
2158 return num.vstack([tr.ydata for tr in traces])
2161def make_traces_compatible(
2162 traces,
2163 dtype=None,
2164 deltat=None,
2165 enforce_global_snap=True,
2166 warn_snap=False):
2168 eps_snap = 1e-3
2170 if not traces:
2171 return []
2173 traces = list(traces)
2175 dtypes = [tr.ydata.dtype for tr in traces]
2176 if not _all_same(dtypes) or dtype is not None:
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))
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
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))
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
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
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)
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.')
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)
2228 tr_copy.snap(interpolate=True)
2229 if tref != 0.0:
2230 tr_copy.shift(tref)
2232 traces[itr] = tr_copy
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
2238 tmin = num.max(tmins)
2239 tmax = num.min(tmaxs)
2241 if tmin > tmax:
2242 raise IncompatibleTraces('Traces do not overlap.')
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)):
2249 traces[itr] = tr.chop(
2250 tmin, tmax,
2251 inplace=False,
2252 want_incomplete=False,
2253 include_last=True)
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()
2263 return traces
2266class IncompatibleTraces(Exception):
2267 '''
2268 Raised when traces have incompatible sampling rate, time span or data type.
2269 '''
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 '''
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 '''
2286 pass
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 '''
2295 pass
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 '''
2304 pass
2307class TraceTooShort(Exception):
2308 '''
2309 This exception is raised by some :py:class:`Trace` operations when the
2310 trace is too short.
2311 '''
2313 pass
2316class ResamplingFailed(Exception):
2317 pass
2320def minmax(traces, key=None, mode='minmax', outer_mode='minmax'):
2322 '''
2323 Get data range given traces grouped by selected pattern.
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.
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.
2337 :returns: a dict with the combined data ranges.
2339 Examples::
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'
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'
2349 ranges = minmax(traces, lambda tr: None)
2350 print ranges[None] # prints min & max of all traces
2351 '''
2353 if key is None:
2354 key = _default_key
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
2365 k = key(trace)
2366 ranges[k].append((mi, ma))
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.)
2375 return ranges
2378def minmaxtime(traces, key=None):
2380 '''
2381 Get time range given traces grouped by selected pattern.
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.
2388 :returns: a dict with the combined data ranges.
2389 '''
2391 if key is None:
2392 key = _default_key
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)
2404 return ranges
2407def degapper(
2408 traces,
2409 maxgap=5,
2410 fillmethod='interpolate',
2411 deoverlap='use_second',
2412 maxlap=None):
2414 '''
2415 Try to connect traces and remove gaps.
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.
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
2430 :returns: list of traces
2431 '''
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:
2440 a = out_traces[-1]
2441 b = in_traces.pop(0)
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.'
2448 virtual = avirt and bvirt
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)):
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
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
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'
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
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
2517 if b.data_len() >= 1:
2518 out_traces.append(b)
2520 for tr in out_traces:
2521 tr._update_ids()
2523 return out_traces
2526def rotate(traces, azimuth, in_channels, out_channels):
2527 '''
2528 2D rotation of traces.
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 '''
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)
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
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)
2566 ac.set_codes(channel=out_channels[0])
2567 bc.set_codes(channel=out_channels[1])
2568 rotated.append(ac)
2569 rotated.append(bc)
2571 return rotated
2574def rotate_to_rt(n, e, source, receiver, out_channels=('R', 'T')):
2575 '''
2576 Rotate traces from NE to RT system.
2578 :param n:
2579 North trace.
2580 :type n:
2581 :py:class:`~pyrocko.trace.Trace`
2583 :param e:
2584 East trace.
2585 :type e:
2586 :py:class:`~pyrocko.trace.Trace`
2588 :param source:
2589 Source of the recorded signal.
2590 :type source:
2591 :py:class:`pyrocko.gf.seismosizer.Source`
2593 :param receiver:
2594 Receiver of the recorded signal.
2595 :type receiver:
2596 :py:class:`pyrocko.model.location.Location`
2598 :param out_channels:
2599 Channel codes of the output channels (radial, transversal).
2600 Default is ('R', 'T').
2602 :type out_channels
2603 optional, tuple[str, str]
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)
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
2628 return r, t
2631def rotate_to_lqt(traces, backazimuth, incidence, in_channels,
2632 out_channels=('L', 'Q', 'T')):
2633 '''
2634 Rotate traces from ZNE to LQT system.
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
2646 ci = num.cos(i)
2647 cb = num.cos(b)
2648 si = num.sin(i)
2649 sb = num.sin(b)
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)
2656def _decompose(a):
2657 '''
2658 Decompose matrix into independent submatrices.
2659 '''
2661 def depends(iout, a):
2662 row = a[iout, :]
2663 return set(num.arange(row.size).compress(row != 0.0))
2665 def provides(iin, a):
2666 col = a[:, iin]
2667 return set(num.arange(col.size).compress(col != 0.0))
2669 a = num.asarray(a)
2670 outs = set(range(a.shape[0]))
2671 systems = []
2672 while outs:
2673 iout = outs.pop()
2675 gout = set()
2676 for iin in depends(iout, a):
2677 gout.update(provides(iin, a))
2679 if not gout:
2680 continue
2682 gin = set()
2683 for iout2 in gout:
2684 gin.update(depends(iout2, a))
2686 if not gin:
2687 continue
2689 for iout2 in gout:
2690 if iout2 in outs:
2691 outs.remove(iout2)
2693 gin = list(gin)
2694 gin.sort()
2695 gout = list(gout)
2696 gout.sort()
2698 systems.append((gin, gout, a[gout, :][:, gin]))
2700 return systems
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)
2714 return names
2717def project(traces, matrix, in_channels, out_channels):
2718 '''
2719 Affine transform of three-component traces.
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.
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 '''
2737 in_channels = tuple(_channels_to_names(in_channels))
2738 out_channels = tuple(_channels_to_names(out_channels))
2739 systems = _decompose(matrix)
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)
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))
2760 return projected
2763def project_dependencies(matrix, in_channels, out_channels):
2764 '''
2765 Figure out what dependencies project() would produce.
2766 '''
2768 in_channels = tuple(_channels_to_names(in_channels))
2769 out_channels = tuple(_channels_to_names(out_channels))
2770 systems = _decompose(matrix)
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))
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))
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] = []
2789 for ic in in_cha:
2790 deps[oc].append(ic)
2792 return deps
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)
2800 projected = []
2801 for a in traces:
2802 if not (a.channel,) == in_channels:
2803 continue
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)
2810 return projected
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
2825 tmin = max(a.tmin, b.tmin)
2826 tmax = min(a.tmax, b.tmax)
2828 if tmin > tmax:
2829 continue
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
2839 acydata = num.dot(matrix[0], (ac.get_ydata(), bc.get_ydata()))
2840 bcydata = num.dot(matrix[1], (ac.get_ydata(), bc.get_ydata()))
2842 ac.set_ydata(acydata)
2843 bc.set_ydata(bcydata)
2845 ac.set_codes(channel=out_channels[0])
2846 bc.set_codes(channel=out_channels[1])
2848 projected.append(ac)
2849 projected.append(bc)
2851 return projected
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):
2868 continue
2870 tmin = max(a.tmin, b.tmin, c.tmin)
2871 tmax = min(a.tmax, b.tmax, c.tmax)
2873 if tmin >= tmax:
2874 continue
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):
2882 logger.warning(
2883 'Cannot project traces with displaced sampling '
2884 '(%s, %s, %s, %s)' % a.nslc_id)
2885 continue
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()))
2897 ac.set_ydata(acydata)
2898 bc.set_ydata(bcydata)
2899 cc.set_ydata(ccydata)
2901 ac.set_codes(channel=out_channels[0])
2902 bc.set_codes(channel=out_channels[1])
2903 cc.set_codes(channel=out_channels[2])
2905 projected.append(ac)
2906 projected.append(bc)
2907 projected.append(cc)
2909 return projected
2912def correlate(a, b, mode='valid', normalization=None, use_fft=False):
2913 '''
2914 Cross correlation of two traces.
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
2921 :returns: trace containing cross correlation coefficients
2923 This function computes the cross correlation between two traces. It
2924 evaluates the discrete equivalent of
2926 .. math::
2928 c(t) = \\int_{-\\infty}^{\\infty} a^{\\ast}(\\tau) b(t+\\tau) d\\tau
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.
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.
2939 Example::
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
2946 '''
2948 assert_same_sampling_rate(a, b)
2950 ya, yb = a.ydata, b.ydata
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)
2956 if normalization == 'normal':
2957 normfac = num.sqrt(num.sum(ya**2))*num.sqrt(num.sum(yb**2))
2958 yc = yc/normfac
2960 elif normalization == 'gliding':
2961 if mode != 'valid':
2962 assert False, 'gliding normalization currently only available ' \
2963 'with "valid" mode.'
2965 if ya.size < yb.size:
2966 yshort, ylong = ya, yb
2967 else:
2968 yshort, ylong = yb, ya
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
2976 if yb.size <= ya.size:
2977 normfac = normfac[::-1]
2979 yc /= normfac
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)
2986 return c
2989def deconvolve(
2990 a, b, waterlevel,
2991 tshift=0.,
2992 pad=0.5,
2993 fd_taper=None,
2994 pad_to_pow2=True):
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))
3001 ndata = max(a.data_len(), b.data_len())
3002 ndata_pad = ndata + npad
3004 if pad_to_pow2:
3005 ntrans = nextpow2(ndata_pad)
3006 else:
3007 ntrans = ndata
3009 aspec = num.fft.rfft(a.ydata, ntrans)
3010 bspec = num.fft.rfft(b.ydata, ntrans)
3012 out = aspec * num.conj(bspec)
3014 bautocorr = bspec*num.conj(bspec)
3015 denom = num.maximum(bautocorr, waterlevel * bautocorr.max())
3017 out /= denom
3018 df = 1/(ntrans*deltat)
3020 if fd_taper is not None:
3021 fd_taper(out, 0.0, df)
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
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)
3035def same_sampling_rate(a, b, eps=1.0e-6):
3036 '''
3037 Check if two traces have the same sampling rate.
3039 :param a,b: input traces
3040 :param eps: relative tolerance
3041 '''
3043 return abs(a.deltat - b.deltat) < (a.deltat + b.deltat)*eps
3046def fix_deltat_rounding_errors(deltat):
3047 '''
3048 Try to undo sampling rate rounding errors.
3050 Fix rounding errors of sampling intervals when these are read from single
3051 precision floating point values.
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 '''
3058 if deltat <= 1.0:
3059 deltat_new = 1.0 / round(1.0 / deltat)
3060 else:
3061 deltat_new = round(deltat)
3063 if abs(deltat_new - deltat) / deltat > 1e-5:
3064 deltat_new = deltat
3066 return deltat_new
3069def merge_codes(a, b, sep='-'):
3070 '''
3071 Merge network-station-location-channel codes of a pair of traces.
3072 '''
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
3083class Taper(Object):
3084 '''
3085 Base class for tapers.
3087 Does nothing by default.
3088 '''
3090 def __call__(self, y, x0, dx):
3091 pass
3094class CosTaper(Taper):
3095 '''
3096 Cosine Taper.
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 '''
3104 a = Float.T()
3105 b = Float.T()
3106 c = Float.T()
3107 d = Float.T()
3109 def __init__(self, a, b, c, d):
3110 Taper.__init__(self, a=a, b=b, c=c, d=d)
3112 def __call__(self, y, x0, dx):
3114 if y.dtype == num.dtype(float):
3115 _apply_costaper = signal_ext.apply_costaper
3116 else:
3117 _apply_costaper = apply_costaper
3119 _apply_costaper(self.a, self.b, self.c, self.d, y, x0, dx)
3121 def span(self, y, x0, dx):
3122 return span_costaper(self.a, self.b, self.c, self.d, y, x0, dx)
3124 def time_span(self):
3125 return self.a, self.d
3128class CosFader(Taper):
3129 '''
3130 Cosine Fader.
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)
3135 Only one argument can be set. The other should to be ``None``.
3136 '''
3138 xfade = Float.T(optional=True)
3139 xfrac = Float.T(optional=True)
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
3147 def __call__(self, y, x0, dx):
3149 xfade = self._xfade
3151 xlen = (y.size - 1)*dx
3152 if xfade is None:
3153 xfade = xlen * self._xfrac
3155 a = x0
3156 b = x0 + xfade
3157 c = x0 + xlen - xfade
3158 d = x0 + xlen
3160 apply_costaper(a, b, c, d, y, x0, dx)
3162 def span(self, y, x0, dx):
3163 return 0, y.size
3165 def time_span(self):
3166 return None, None
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)
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)
3183class MultiplyTaper(Taper):
3184 '''
3185 Multiplication of several tapers.
3186 '''
3188 tapers = List.T(Taper.T())
3190 def __init__(self, tapers=None):
3191 if tapers is None:
3192 tapers = []
3194 Taper.__init__(self, tapers=tapers)
3196 def __call__(self, y, x0, dx):
3197 for taper in self.tapers:
3198 taper(y, x0, dx)
3200 def span(self, y, x0, dx):
3201 spans = []
3202 for taper in self.tapers:
3203 spans.append(taper.span(y, x0, dx))
3205 mins, maxs = list(zip(*spans))
3206 return min(mins), max(maxs)
3208 def time_span(self):
3209 spans = []
3210 for taper in self.tapers:
3211 spans.append(taper.time_span())
3213 mins, maxs = list(zip(*spans))
3214 return none_min(mins), none_max(maxs)
3217class GaussTaper(Taper):
3218 '''
3219 Frequency domain Gaussian filter.
3220 '''
3222 alpha = Float.T()
3224 def __init__(self, alpha):
3225 Taper.__init__(self, alpha=alpha)
3226 self._alpha = alpha
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)
3233cached_coefficients = {}
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]
3242 cached_coefficients[ck] = signal.butter(
3243 order, corners, btype=btype)
3245 return cached_coefficients[ck]
3248class _globals(object):
3249 _numpy_has_correlate_flip_bug = None
3252def _default_key(tr):
3253 return (tr.network, tr.station, tr.location, tr.channel)
3256def numpy_has_correlate_flip_bug():
3257 '''
3258 Check if NumPy's correlate function reveals old behaviour.
3259 '''
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)
3268 return _globals._numpy_has_correlate_flip_bug
3271def numpy_correlate_fixed(a, b, mode='valid', use_fft=False):
3272 '''
3273 Call :py:func:`numpy.correlate` with fixes.
3275 c[k] = sum_i a[i+k] * conj(b[i])
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 '''
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
3289 else:
3290 buggy = numpy_has_correlate_flip_bug()
3292 a = num.asarray(a)
3293 b = num.asarray(b)
3295 if buggy:
3296 b = num.conj(b)
3298 c = num.correlate(a, b, mode=mode)
3300 if buggy and a.size < b.size:
3301 return c[::-1]
3302 else:
3303 return c
3306def numpy_correlate_emulate(a, b, mode='valid'):
3307 '''
3308 Slow version of :py:func:`numpy.correlate` for comparison.
3309 '''
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]))
3326 return c
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 '''
3334 a = num.asarray(a)
3335 b = num.asarray(b)
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
3348 return kmin, kmin + klen - 1
3351def autocorr(x, nshifts):
3352 '''
3353 Compute biased estimate of the first autocorrelation coefficients.
3355 :param x: input array
3356 :param nshifts: number of coefficients to calculate
3357 '''
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:])
3367 return r
3370def yulewalker(x, order):
3371 '''
3372 Compute autoregression coefficients using Yule-Walker method.
3374 :param x: input array
3375 :param order: number of coefficients to produce
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 '''
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]
3390 return num.dot(num.linalg.inv(a), -d)
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
3404def moving_sum(x, n, mode='valid'):
3405 n = int(n)
3406 cx = x.cumsum()
3407 nn = len(x)
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]
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]
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))]
3439 return y
3442def nextpow2(i):
3443 return 2**int(math.ceil(math.log(i)/math.log(2.)))
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
3452def snapper(nmax, delta, snapfun=math.ceil):
3453 def snap(x):
3454 return max(0, min(int(snapfun(x/delta)), nmax))
3455 return snap
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.
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)
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)
3483 return tap
3486def t2ind(t, tdelta, snap=round):
3487 return int(snap(t/tdelta))
3490def hilbert(x, N=None):
3491 '''
3492 Return the hilbert transform of x of length N.
3494 (from scipy.signal, but changed to use fft and ifft from numpy.fft)
3495 '''
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)
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
3515 if len(x.shape) > 1:
3516 h = h[:, num.newaxis]
3517 x = num.fft.ifft(Xf*h)
3518 return x
3521def near(a, b, eps):
3522 return abs(a-b) < eps
3525def coroutine(func):
3526 def wrapper(*args, **kwargs):
3527 gen = func(*args, **kwargs)
3528 next(gen)
3529 return gen
3531 wrapper.__name__ = func.__name__
3532 wrapper.__dict__ = func.__dict__
3533 wrapper.__doc__ = func.__doc__
3534 return wrapper
3537class States(object):
3538 '''
3539 Utility to store channel-specific state in coroutines.
3540 '''
3542 def __init__(self):
3543 self._states = {}
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):
3553 return value
3555 return None
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])
3562 self._states[k] = (tr.tmax+tr.deltat, tr.deltat, tr.ydata.dtype, value)
3564 def free(self, value):
3565 pass
3568@coroutine
3569def co_list_append(list):
3570 while True:
3571 list.append((yield))
3574class ScipyBug(Exception):
3575 pass
3578@coroutine
3579def co_lfilter(target, b, a):
3580 '''
3581 Successively filter broken continuous trace data (coroutine).
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.
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.
3595 Filter state is reset, when gaps occur.
3597 Use it like this::
3599 from pyrocko.trace import co_lfilter, co_list_append
3601 filtered_traces = []
3602 pipe = co_lfilter(co_list_append(filtered_traces), a, b)
3603 for trace in traces:
3604 pipe.send(trace)
3606 pipe.close()
3608 '''
3610 try:
3611 states = States()
3612 output = None
3613 while True:
3614 input = (yield)
3616 zi = states.get(input)
3617 if zi is None:
3618 zi = num.zeros(max(len(a), len(b))-1, dtype=float)
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')
3628 output.set_ydata(ydata)
3629 states.set(input, zf)
3630 target.send(output)
3632 except GeneratorExit:
3633 target.close()
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
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
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)
3672 except GeneratorExit:
3673 target.close()
3676def co_downsample(target, q, n=None, ftype='fir'):
3677 '''
3678 Successively downsample broken continuous trace data (coroutine).
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.
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.
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 '''
3697 b, a, n = util.decimate_coeffs(q, n, ftype)
3698 return co_antialias(co_dropsamples(target, q, n), q, n, ftype)
3701@coroutine
3702def co_downsample_to(target, deltat):
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)
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)
3719 decimators[deci_seq] = pipe
3721 decimators[deci_seq].send(tr)
3723 except GeneratorExit:
3724 for g in decimators.values():
3725 g.close()
3728class DomainChoice(StringChoice):
3729 choices = [
3730 'time_domain',
3731 'frequency_domain',
3732 'envelope',
3733 'absolute',
3734 'cc_max_norm']
3737class MisfitSetup(Object):
3738 '''
3739 Contains misfit setup to be used in :py:meth:`Trace.misfit`
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']
3748 Can be dumped to a yaml file.
3749 '''
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')
3759def equalize_sampling_rates(trace_1, trace_2):
3760 '''
3761 Equalize sampling rates of two traces (reduce higher sampling rate to
3762 lower).
3764 :param trace_1: :py:class:`Trace` object
3765 :param trace_2: :py:class:`Trace` object
3767 Returns a copy of the resampled trace if resampling is needed.
3768 '''
3770 if same_sampling_rate(trace_1, trace_2):
3771 return trace_1, trace_2
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
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
3788def Lx_norm(u, v, norm=2):
3789 '''
3790 Calculate the misfit denominator *m* and the normalization divisor *n*
3791 according to norm.
3793 The normalization divisor *n* is calculated from ``v``.
3795 :param u: :py:class:`numpy.ndarray`
3796 :param v: :py:class:`numpy.ndarray`
3797 :param norm: (default = 2)
3799 ``u`` and ``v`` must be of same size.
3800 '''
3802 if norm == 1:
3803 return (
3804 num.sum(num.abs(v-u)),
3805 num.sum(num.abs(v)))
3807 elif norm == 2:
3808 return (
3809 num.sqrt(num.sum((v-u)**2)),
3810 num.sqrt(num.sum(v**2)))
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))
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
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')
3834 return tr
3837def do_pre_taper(tr, taper):
3838 return tr.taper(taper, inplace=False, chop=True)
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]
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]
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
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)))