1# https://pyrocko.org - GPLv3
2#
3# The Pyrocko Developers, 21st Century
4# ---|P------/S----------~Lg----------
6'''
7This module provides basic signal processing for seismic traces.
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 the :py:meth:`Trace.downsample` one or several
756 times. If ``allow_upsample_max`` is set to a value larger than 1,
757 intermediate upsampling steps are allowed, in order to increase the
758 number of 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.downample`
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)
1671 data = self.ydata
1673 data_pad = num.zeros(ntrans, dtype=float)
1674 data_pad[:ndata] = data
1675 if demean:
1676 data_pad[:ndata] -= data.mean()
1678 if tfade != 0.0:
1679 data_pad[:ndata] *= costaper(
1680 0., tfade, self.deltat*(ndata-1)-tfade, self.deltat*ndata,
1681 ndata, self.deltat)
1683 fdata = num.fft.rfft(data_pad)
1684 fdata *= coeffs
1685 ddata = num.fft.irfft(fdata)
1686 output = self.copy()
1687 output.ydata = ddata[:ndata]
1689 if cut_off_fading and tfade != 0.0:
1690 try:
1691 output.chop(output.tmin+tfade, output.tmax-tfade, inplace=True)
1692 except NoData:
1693 raise TraceTooShort(
1694 'Trace %s.%s.%s.%s too short for fading length setting. '
1695 'trace length = %g, fading length = %g'
1696 % (self.nslc_id + (self.tmax-self.tmin, tfade)))
1697 else:
1698 output.ydata = output.ydata.copy()
1700 return output
1702 def differentiate(self, n=1, order=4, inplace=True):
1703 '''
1704 Approximate first or second derivative of the trace.
1706 :param n: 1 for first derivative, 2 for second
1707 :param order: order of the approximation 2 and 4 are supported
1708 :param inplace: if ``True`` the trace is differentiated in place,
1709 otherwise a new trace object with the derivative is returned.
1711 Raises :py:exc:`ValueError` for unsupported `n` or `order`.
1713 See :py:func:`~pyrocko.util.diff_fd` for implementation details.
1714 '''
1716 ddata = util.diff_fd(n, order, self.deltat, self.ydata)
1718 if inplace:
1719 self.ydata = ddata
1720 else:
1721 output = self.copy(data=False)
1722 output.set_ydata(ddata)
1723 return output
1725 def drop_chain_cache(self):
1726 if self._pchain:
1727 self._pchain.clear()
1729 def init_chain(self):
1730 self._pchain = pchain.Chain(
1731 do_downsample,
1732 do_extend,
1733 do_pre_taper,
1734 do_fft,
1735 do_filter,
1736 do_ifft)
1738 def run_chain(self, tmin, tmax, deltat, setup, nocache):
1739 if setup.domain == 'frequency_domain':
1740 _, _, data = self._pchain(
1741 (self, deltat),
1742 (tmin, tmax),
1743 (setup.taper,),
1744 (setup.filter,),
1745 (setup.filter,),
1746 nocache=nocache)
1748 return num.abs(data), num.abs(data)
1750 else:
1751 processed = self._pchain(
1752 (self, deltat),
1753 (tmin, tmax),
1754 (setup.taper,),
1755 (setup.filter,),
1756 (setup.filter,),
1757 (),
1758 nocache=nocache)
1760 if setup.domain == 'time_domain':
1761 data = processed.get_ydata()
1763 elif setup.domain == 'envelope':
1764 processed = processed.envelope(inplace=False)
1766 elif setup.domain == 'absolute':
1767 processed.set_ydata(num.abs(processed.get_ydata()))
1769 return processed.get_ydata(), processed
1771 def misfit(self, candidate, setup, nocache=False, debug=False):
1772 '''
1773 Calculate misfit and normalization factor against candidate trace.
1775 :param candidate: :py:class:`Trace` object
1776 :param setup: :py:class:`MisfitSetup` object
1777 :returns: tuple ``(m, n)``, where m is the misfit value and n is the
1778 normalization divisor
1780 If the sampling rates of ``self`` and ``candidate`` differ, the trace
1781 with the higher sampling rate will be downsampled.
1782 '''
1784 a = self
1785 b = candidate
1787 for tr in (a, b):
1788 if not tr._pchain:
1789 tr.init_chain()
1791 deltat = max(a.deltat, b.deltat)
1792 tmin = min(a.tmin, b.tmin) - deltat
1793 tmax = max(a.tmax, b.tmax) + deltat
1795 adata, aproc = a.run_chain(tmin, tmax, deltat, setup, nocache)
1796 bdata, bproc = b.run_chain(tmin, tmax, deltat, setup, nocache)
1798 if setup.domain != 'cc_max_norm':
1799 m, n = Lx_norm(bdata, adata, norm=setup.norm)
1800 else:
1801 ctr = correlate(aproc, bproc, mode='full', normalization='normal')
1802 ccmax = ctr.max()[1]
1803 m = 0.5 - 0.5 * ccmax
1804 n = 0.5
1806 if debug:
1807 return m, n, aproc, bproc
1808 else:
1809 return m, n
1811 def spectrum(self, pad_to_pow2=False, tfade=None):
1812 '''
1813 Get FFT spectrum of trace.
1815 :param pad_to_pow2: whether to zero-pad the data to next larger
1816 power-of-two length
1817 :param tfade: ``None`` or a time length in seconds, to apply cosine
1818 shaped tapers to both
1820 :returns: a tuple with (frequencies, values)
1821 '''
1823 ndata = self.ydata.size
1825 if pad_to_pow2:
1826 ntrans = nextpow2(ndata)
1827 else:
1828 ntrans = ndata
1830 if tfade is None:
1831 ydata = self.ydata
1832 else:
1833 ydata = self.ydata * costaper(
1834 0., tfade, self.deltat*(ndata-1)-tfade, self.deltat*ndata,
1835 ndata, self.deltat)
1837 fydata = num.fft.rfft(ydata, ntrans)
1838 df = 1./(ntrans*self.deltat)
1839 fxdata = num.arange(len(fydata))*df
1840 return fxdata, fydata
1842 def multi_filter(self, filter_freqs, bandwidth):
1844 class Gauss(FrequencyResponse):
1845 f0 = Float.T()
1846 a = Float.T(default=1.0)
1848 def __init__(self, f0, a=1.0, **kwargs):
1849 FrequencyResponse.__init__(self, f0=f0, a=a, **kwargs)
1851 def evaluate(self, freqs):
1852 omega0 = 2.*math.pi*self.f0
1853 omega = 2.*math.pi*freqs
1854 return num.exp(-((omega-omega0)
1855 / (self.a*omega0))**2)
1857 freqs, coeffs = self.spectrum()
1858 n = self.data_len()
1859 nfilt = len(filter_freqs)
1860 signal_tf = num.zeros((nfilt, n))
1861 centroid_freqs = num.zeros(nfilt)
1862 for ifilt, f0 in enumerate(filter_freqs):
1863 taper = Gauss(f0, a=bandwidth)
1864 weights = taper.evaluate(freqs)
1865 nhalf = freqs.size
1866 analytic_spec = num.zeros(n, dtype=complex)
1867 analytic_spec[:nhalf] = coeffs*weights
1869 enorm = num.abs(analytic_spec[:nhalf])**2
1870 enorm /= num.sum(enorm)
1872 if n % 2 == 0:
1873 analytic_spec[1:nhalf-1] *= 2.
1874 else:
1875 analytic_spec[1:nhalf] *= 2.
1877 analytic = num.fft.ifft(analytic_spec)
1878 signal_tf[ifilt, :] = num.abs(analytic)
1880 enorm = num.abs(analytic_spec[:nhalf])**2
1881 enorm /= num.sum(enorm)
1882 centroid_freqs[ifilt] = num.sum(freqs*enorm)
1884 return centroid_freqs, signal_tf
1886 def _get_tapered_coeffs(
1887 self, ntrans, freqlimits, transfer_function, invert=False):
1889 cache_key = (
1890 ntrans, self.deltat, freqlimits, transfer_function.uuid, invert)
1892 if cache_key in g_tapered_coeffs_cache:
1893 return g_tapered_coeffs_cache[cache_key]
1895 deltaf = 1./(self.deltat*ntrans)
1896 nfreqs = ntrans//2 + 1
1897 transfer = num.ones(nfreqs, dtype=complex)
1898 hi = snapper(nfreqs, deltaf)
1899 if freqlimits is not None:
1900 kmin, kmax = hi(freqlimits[0]), hi(freqlimits[3])
1901 freqs = num.arange(kmin, kmax)*deltaf
1902 coeffs = transfer_function.evaluate(freqs)
1903 if invert:
1904 if num.any(coeffs == 0.0):
1905 raise InfiniteResponse('%s.%s.%s.%s' % self.nslc_id)
1907 transfer[kmin:kmax] = 1.0 / coeffs
1908 else:
1909 transfer[kmin:kmax] = coeffs
1911 tapered_transfer = costaper(*freqlimits, nfreqs, deltaf) * transfer
1912 else:
1913 if invert:
1914 raise Exception(
1915 'transfer: `freqlimits` must be given when `invert` is '
1916 'set to `True`')
1918 freqs = num.arange(nfreqs) * deltaf
1919 tapered_transfer = transfer_function.evaluate(freqs)
1921 tapered_transfer[0] = 0.0 # don't introduce static offsets
1923 g_tapered_coeffs_cache[cache_key] = tapered_transfer
1924 return tapered_transfer
1926 def fill_template(self, template, **additional):
1927 '''
1928 Fill string template with trace metadata.
1930 Uses normal python '%(placeholder)s' string templates. The following
1931 placeholders are considered: ``network``, ``station``, ``location``,
1932 ``channel``, ``tmin`` (time of first sample), ``tmax`` (time of last
1933 sample), ``tmin_ms``, ``tmax_ms``, ``tmin_us``, ``tmax_us``,
1934 ``tmin_year``, ``tmax_year``, ``tmin_month``, ``tmax_month``,
1935 ``tmin_day``, ``tmax_day``, ``julianday``. The variants ending with
1936 ``'_ms'`` include milliseconds, those with ``'_us'`` include
1937 microseconds, those with ``'_year'`` contain only the year.
1938 '''
1940 template = template.replace('%n', '%(network)s')\
1941 .replace('%s', '%(station)s')\
1942 .replace('%l', '%(location)s')\
1943 .replace('%c', '%(channel)s')\
1944 .replace('%b', '%(tmin)s')\
1945 .replace('%e', '%(tmax)s')\
1946 .replace('%j', '%(julianday)s')
1948 params = dict(
1949 zip(('network', 'station', 'location', 'channel'), self.nslc_id))
1950 params['tmin'] = util.time_to_str(
1951 self.tmin, format='%Y-%m-%d_%H-%M-%S')
1952 params['tmax'] = util.time_to_str(
1953 self.tmax, format='%Y-%m-%d_%H-%M-%S')
1954 params['tmin_ms'] = util.time_to_str(
1955 self.tmin, format='%Y-%m-%d_%H-%M-%S.3FRAC')
1956 params['tmax_ms'] = util.time_to_str(
1957 self.tmax, format='%Y-%m-%d_%H-%M-%S.3FRAC')
1958 params['tmin_us'] = util.time_to_str(
1959 self.tmin, format='%Y-%m-%d_%H-%M-%S.6FRAC')
1960 params['tmax_us'] = util.time_to_str(
1961 self.tmax, format='%Y-%m-%d_%H-%M-%S.6FRAC')
1962 params['tmin_year'], params['tmin_month'], params['tmin_day'] \
1963 = util.time_to_str(self.tmin, format='%Y-%m-%d').split('-')
1964 params['tmax_year'], params['tmax_month'], params['tmax_day'] \
1965 = util.time_to_str(self.tmax, format='%Y-%m-%d').split('-')
1966 params['julianday'] = util.julian_day_of_year(self.tmin)
1967 params.update(additional)
1968 return template % params
1970 def plot(self):
1971 '''
1972 Show trace with matplotlib.
1974 See also: :py:meth:`Trace.snuffle`.
1975 '''
1977 import pylab
1978 pylab.plot(self.get_xdata(), self.get_ydata())
1979 name = '%s %s %s - %s' % (
1980 self.channel,
1981 self.station,
1982 time.strftime('%d-%m-%y %H:%M:%S', time.gmtime(self.tmin)),
1983 time.strftime('%d-%m-%y %H:%M:%S', time.gmtime(self.tmax)))
1985 pylab.title(name)
1986 pylab.show()
1988 def snuffle(self, **kwargs):
1989 '''
1990 Show trace in a snuffler window.
1992 :param stations: list of :py:class:`pyrocko.model.Station` objects or
1993 ``None``
1994 :param events: list of :py:class:`pyrocko.model.Event` objects or
1995 ``None``
1996 :param markers: list of :py:class:`pyrocko.gui.snuffler.marker.Marker`
1997 objects or ``None``
1998 :param ntracks: float, number of tracks to be shown initially (default:
1999 12)
2000 :param follow: time interval (in seconds) for real time follow mode or
2001 ``None``
2002 :param controls: bool, whether to show the main controls (default:
2003 ``True``)
2004 :param opengl: bool, whether to use opengl (default: ``False``)
2005 '''
2007 return snuffle([self], **kwargs)
2010def snuffle(traces, **kwargs):
2011 '''
2012 Show traces in a snuffler window.
2014 :param stations: list of :py:class:`pyrocko.model.Station` objects or
2015 ``None``
2016 :param events: list of :py:class:`pyrocko.model.Event` objects or ``None``
2017 :param markers: list of :py:class:`pyrocko.gui.snuffler.marker.Marker`
2018 objects or ``None``
2019 :param ntracks: float, number of tracks to be shown initially (default: 12)
2020 :param follow: time interval (in seconds) for real time follow mode or
2021 ``None``
2022 :param controls: bool, whether to show the main controls (default:
2023 ``True``)
2024 :param opengl: bool, whether to use opengl (default: ``False``)
2025 '''
2027 from pyrocko import pile
2028 from pyrocko.gui.snuffler import snuffler
2029 p = pile.Pile()
2030 if traces:
2031 trf = pile.MemTracesFile(None, traces)
2032 p.add_file(trf)
2033 return snuffler.snuffle(p, **kwargs)
2036def downsample_tpad(
2037 deltat_in, deltat_out, allow_upsample_max=1, ftype='fir-remez'):
2038 '''
2039 Get approximate amount of cutoff which will be produced by downsampling.
2041 The :py:meth:`Trace.downsample_to` method removes some samples at the
2042 beginning and end of the trace which is downsampled. This function
2043 estimates the approximate length [s] which will be cut off for a given set
2044 of parameters supplied to :py:meth:`Trace.downsample_to`.
2046 :param deltat_in:
2047 Input sampling interval [s].
2048 :type deltat_in:
2049 float
2051 :param deltat_out:
2052 Output samling interval [s].
2053 :type deltat_out:
2054 float
2056 :returns:
2057 Approximate length [s] which will be cut off.
2059 See :py:meth:`Trace.downsample_to` for details.
2060 '''
2062 upsratio, deci_seq = _configure_downsampling(
2063 deltat_in, deltat_out, allow_upsample_max)
2065 tpad = 0.0
2066 deltat = deltat_in / upsratio
2067 for deci in deci_seq:
2068 b, a, n = util.decimate_coeffs(deci, None, ftype)
2069 # n//2 for the antialiasing
2070 # +deci for possible snap to multiples
2071 # +1 for rounding errors
2072 tpad += (n//2 + deci + 1) * deltat
2073 deltat = deltat * deci
2075 return tpad
2078def _configure_downsampling(deltat_in, deltat_out, allow_upsample_max):
2079 for upsratio in range(1, allow_upsample_max+1):
2080 dratio = (upsratio/deltat_in) / (1./deltat_out)
2081 deci_seq = util.decitab(int(round(dratio)))
2082 if abs(dratio - round(dratio)) / dratio < 0.0001 and deci_seq:
2083 return upsratio, [deci for deci in deci_seq if deci != 1]
2085 raise util.UnavailableDecimation('ratio = %g' % (deltat_out / deltat_in))
2088class InfiniteResponse(Exception):
2089 '''
2090 This exception is raised by :py:class:`Trace` operations when deconvolution
2091 of a frequency response (instrument response transfer function) would
2092 result in a division by zero.
2093 '''
2096class MisalignedTraces(Exception):
2097 '''
2098 This exception is raised by some :py:class:`Trace` operations when tmin,
2099 tmax or number of samples do not match.
2100 '''
2102 pass
2105class NoData(Exception):
2106 '''
2107 This exception is raised by some :py:class:`Trace` operations when no or
2108 not enough data is available.
2109 '''
2111 pass
2114class AboveNyquist(Exception):
2115 '''
2116 This exception is raised by some :py:class:`Trace` operations when given
2117 frequencies are above the Nyquist frequency.
2118 '''
2120 pass
2123class TraceTooShort(Exception):
2124 '''
2125 This exception is raised by some :py:class:`Trace` operations when the
2126 trace is too short.
2127 '''
2129 pass
2132class ResamplingFailed(Exception):
2133 pass
2136def minmax(traces, key=None, mode='minmax', outer_mode='minmax'):
2138 '''
2139 Get data range given traces grouped by selected pattern.
2141 :param key: a callable which takes as single argument a trace and returns a
2142 key for the grouping of the results. If this is ``None``, the default,
2143 ``lambda tr: (tr.network, tr.station, tr.location, tr.channel)`` is
2144 used.
2145 :param mode: ``'minmax'`` or floating point number. If this is
2146 ``'minmax'``, minimum and maximum of the traces are used, if it is a
2147 number, mean +- standard deviation times ``mode`` is used.
2149 param outer_mode: ``'minmax'`` to use mininum and maximum of the
2150 single-trace ranges, or ``'robust'`` to use the interval to discard 10%
2151 extreme values on either end.
2153 :returns: a dict with the combined data ranges.
2155 Examples::
2157 ranges = minmax(traces, lambda tr: tr.channel)
2158 print ranges['N'] # print min & max of all traces with channel == 'N'
2159 print ranges['E'] # print min & max of all traces with channel == 'E'
2161 ranges = minmax(traces, lambda tr: (tr.network, tr.station))
2162 print ranges['GR', 'HAM3'] # print min & max of all traces with
2163 # network == 'GR' and station == 'HAM3'
2165 ranges = minmax(traces, lambda tr: None)
2166 print ranges[None] # prints min & max of all traces
2167 '''
2169 if key is None:
2170 key = _default_key
2172 ranges = defaultdict(list)
2173 for trace in traces:
2174 if isinstance(mode, str) and mode == 'minmax':
2175 mi, ma = num.nanmin(trace.ydata), num.nanmax(trace.ydata)
2176 else:
2177 mean = trace.ydata.mean()
2178 std = trace.ydata.std()
2179 mi, ma = mean-std*mode, mean+std*mode
2181 k = key(trace)
2182 ranges[k].append((mi, ma))
2184 for k in ranges:
2185 mins, maxs = num.array(ranges[k]).T
2186 if outer_mode == 'minmax':
2187 ranges[k] = num.nanmin(mins), num.nanmax(maxs)
2188 elif outer_mode == 'robust':
2189 ranges[k] = num.percentile(mins, 10.), num.percentile(maxs, 90.)
2191 return ranges
2194def minmaxtime(traces, key=None):
2196 '''
2197 Get time range given traces grouped by selected pattern.
2199 :param key: a callable which takes as single argument a trace and returns a
2200 key for the grouping of the results. If this is ``None``, the default,
2201 ``lambda tr: (tr.network, tr.station, tr.location, tr.channel)`` is
2202 used.
2204 :returns: a dict with the combined data ranges.
2205 '''
2207 if key is None:
2208 key = _default_key
2210 ranges = {}
2211 for trace in traces:
2212 mi, ma = trace.tmin, trace.tmax
2213 k = key(trace)
2214 if k not in ranges:
2215 ranges[k] = mi, ma
2216 else:
2217 tmi, tma = ranges[k]
2218 ranges[k] = min(tmi, mi), max(tma, ma)
2220 return ranges
2223def degapper(
2224 traces,
2225 maxgap=5,
2226 fillmethod='interpolate',
2227 deoverlap='use_second',
2228 maxlap=None):
2230 '''
2231 Try to connect traces and remove gaps.
2233 This method will combine adjacent traces, which match in their network,
2234 station, location and channel attributes. Overlapping parts are handled
2235 according to the ``deoverlap`` argument.
2237 :param traces: input traces, must be sorted by their full_id attribute.
2238 :param maxgap: maximum number of samples to interpolate.
2239 :param fillmethod: what to put into the gaps: 'interpolate' or 'zeros'.
2240 :param deoverlap: how to handle overlaps: 'use_second' to use data from
2241 second trace (default), 'use_first' to use data from first trace,
2242 'crossfade_cos' to crossfade with cosine taper, 'add' to add amplitude
2243 values.
2244 :param maxlap: maximum number of samples of overlap which are removed
2246 :returns: list of traces
2247 '''
2249 in_traces = traces
2250 out_traces = []
2251 if not in_traces:
2252 return out_traces
2253 out_traces.append(in_traces.pop(0))
2254 while in_traces:
2256 a = out_traces[-1]
2257 b = in_traces.pop(0)
2259 avirt, bvirt = a.ydata is None, b.ydata is None
2260 assert avirt == bvirt, \
2261 'traces given to degapper() must either all have data or have ' \
2262 'no data.'
2264 virtual = avirt and bvirt
2266 if (a.nslc_id == b.nslc_id and a.deltat == b.deltat
2267 and a.data_len() >= 1 and b.data_len() >= 1
2268 and (virtual or a.ydata.dtype == b.ydata.dtype)):
2270 dist = (b.tmin-(a.tmin+(a.data_len()-1)*a.deltat))/a.deltat
2271 idist = int(round(dist))
2272 if abs(dist - idist) > 0.05 and idist <= maxgap:
2273 # logger.warning('Cannot degap traces with displaced sampling '
2274 # '(%s, %s, %s, %s)' % a.nslc_id)
2275 pass
2276 else:
2277 if 1 < idist <= maxgap:
2278 if not virtual:
2279 if fillmethod == 'interpolate':
2280 filler = a.ydata[-1] + (
2281 ((1.0 + num.arange(idist-1, dtype=float))
2282 / idist) * (b.ydata[0]-a.ydata[-1])
2283 ).astype(a.ydata.dtype)
2284 elif fillmethod == 'zeros':
2285 filler = num.zeros(idist-1, dtype=a.ydata.dtype)
2286 a.ydata = num.concatenate((a.ydata, filler, b.ydata))
2287 a.tmax = b.tmax
2288 if a.mtime and b.mtime:
2289 a.mtime = max(a.mtime, b.mtime)
2290 continue
2292 elif idist == 1:
2293 if not virtual:
2294 a.ydata = num.concatenate((a.ydata, b.ydata))
2295 a.tmax = b.tmax
2296 if a.mtime and b.mtime:
2297 a.mtime = max(a.mtime, b.mtime)
2298 continue
2300 elif idist <= 0 and (maxlap is None or -maxlap < idist):
2301 if b.tmax > a.tmax:
2302 if not virtual:
2303 na = a.ydata.size
2304 n = -idist+1
2305 if deoverlap == 'use_second':
2306 a.ydata = num.concatenate(
2307 (a.ydata[:-n], b.ydata))
2308 elif deoverlap in ('use_first', 'crossfade_cos'):
2309 a.ydata = num.concatenate(
2310 (a.ydata, b.ydata[n:]))
2311 elif deoverlap == 'add':
2312 a.ydata[-n:] += b.ydata[:n]
2313 a.ydata = num.concatenate(
2314 (a.ydata, b.ydata[n:]))
2315 else:
2316 assert False, 'unknown deoverlap method'
2318 if deoverlap == 'crossfade_cos':
2319 n = -idist+1
2320 taper = 0.5-0.5*num.cos(
2321 (1.+num.arange(n))/(1.+n)*num.pi)
2322 a.ydata[na-n:na] *= 1.-taper
2323 a.ydata[na-n:na] += b.ydata[:n] * taper
2325 a.tmax = b.tmax
2326 if a.mtime and b.mtime:
2327 a.mtime = max(a.mtime, b.mtime)
2328 continue
2329 else:
2330 # make short second trace vanish
2331 continue
2333 if b.data_len() >= 1:
2334 out_traces.append(b)
2336 for tr in out_traces:
2337 tr._update_ids()
2339 return out_traces
2342def rotate(traces, azimuth, in_channels, out_channels):
2343 '''
2344 2D rotation of traces.
2346 :param traces: list of input traces
2347 :param azimuth: difference of the azimuths of the component directions
2348 (azimuth of out_channels[0]) - (azimuth of in_channels[0])
2349 :param in_channels: names of the input channels (e.g. 'N', 'E')
2350 :param out_channels: names of the output channels (e.g. 'R', 'T')
2351 :returns: list of rotated traces
2352 '''
2354 phi = azimuth/180.*math.pi
2355 cphi = math.cos(phi)
2356 sphi = math.sin(phi)
2357 rotated = []
2358 in_channels = tuple(_channels_to_names(in_channels))
2359 out_channels = tuple(_channels_to_names(out_channels))
2360 for a in traces:
2361 for b in traces:
2362 if ((a.channel, b.channel) == in_channels and
2363 a.nslc_id[:3] == b.nslc_id[:3] and
2364 abs(a.deltat-b.deltat) < a.deltat*0.001):
2365 tmin = max(a.tmin, b.tmin)
2366 tmax = min(a.tmax, b.tmax)
2368 if tmin < tmax:
2369 ac = a.chop(tmin, tmax, inplace=False, include_last=True)
2370 bc = b.chop(tmin, tmax, inplace=False, include_last=True)
2371 if abs(ac.tmin - bc.tmin) > ac.deltat*0.01:
2372 logger.warning(
2373 'Cannot rotate traces with displaced sampling '
2374 '(%s, %s, %s, %s)' % a.nslc_id)
2375 continue
2377 acydata = ac.get_ydata()*cphi+bc.get_ydata()*sphi
2378 bcydata = -ac.get_ydata()*sphi+bc.get_ydata()*cphi
2379 ac.set_ydata(acydata)
2380 bc.set_ydata(bcydata)
2382 ac.set_codes(channel=out_channels[0])
2383 bc.set_codes(channel=out_channels[1])
2384 rotated.append(ac)
2385 rotated.append(bc)
2387 return rotated
2390def rotate_to_rt(n, e, source, receiver, out_channels=('R', 'T')):
2391 '''
2392 Rotate traces from NE to RT system.
2394 :param n:
2395 North trace.
2396 :type n:
2397 :py:class:`~pyrocko.trace.Trace`
2399 :param e:
2400 East trace.
2401 :type e:
2402 :py:class:`~pyrocko.trace.Trace`
2404 :param source:
2405 Source of the recorded signal.
2406 :type source:
2407 :py:class:`pyrocko.gf.seismosizer.Source`
2409 :param receiver:
2410 Receiver of the recorded signal.
2411 :type receiver:
2412 :py:class:`pyrocko.model.location.Location`
2414 :param out_channels:
2415 Channel codes of the output channels (radial, transversal).
2416 Default is ('R', 'T').
2417 .
2418 :type out_channels
2419 optional, tuple[str, str]
2421 :returns:
2422 Rotated traces (radial, transversal).
2423 :rtype:
2424 tuple[
2425 :py:class:`~pyrocko.trace.Trace`,
2426 :py:class:`~pyrocko.trace.Trace`]
2427 '''
2428 azimuth = orthodrome.azimuth(receiver, source) + 180.
2429 in_channels = n.channel, e.channel
2430 out = rotate(
2431 [n, e], azimuth,
2432 in_channels=in_channels,
2433 out_channels=out_channels)
2435 assert len(out) == 2
2436 for tr in out:
2437 if tr.channel == out_channels[0]:
2438 r = tr
2439 elif tr.channel == out_channels[1]:
2440 t = tr
2441 else:
2442 assert False
2444 return r, t
2447def rotate_to_lqt(traces, backazimuth, incidence, in_channels,
2448 out_channels=('L', 'Q', 'T')):
2449 '''
2450 Rotate traces from ZNE to LQT system.
2452 :param traces: list of traces in arbitrary order
2453 :param backazimuth: backazimuth in degrees clockwise from north
2454 :param incidence: incidence angle in degrees from vertical
2455 :param in_channels: input channel names
2456 :param out_channels: output channel names (default: ('L', 'Q', 'T'))
2457 :returns: list of transformed traces
2458 '''
2459 i = incidence/180.*num.pi
2460 b = backazimuth/180.*num.pi
2462 ci = num.cos(i)
2463 cb = num.cos(b)
2464 si = num.sin(i)
2465 sb = num.sin(b)
2467 rotmat = num.array(
2468 [[ci, -cb*si, -sb*si], [si, cb*ci, sb*ci], [0., sb, -cb]])
2469 return project(traces, rotmat, in_channels, out_channels)
2472def _decompose(a):
2473 '''
2474 Decompose matrix into independent submatrices.
2475 '''
2477 def depends(iout, a):
2478 row = a[iout, :]
2479 return set(num.arange(row.size).compress(row != 0.0))
2481 def provides(iin, a):
2482 col = a[:, iin]
2483 return set(num.arange(col.size).compress(col != 0.0))
2485 a = num.asarray(a)
2486 outs = set(range(a.shape[0]))
2487 systems = []
2488 while outs:
2489 iout = outs.pop()
2491 gout = set()
2492 for iin in depends(iout, a):
2493 gout.update(provides(iin, a))
2495 if not gout:
2496 continue
2498 gin = set()
2499 for iout2 in gout:
2500 gin.update(depends(iout2, a))
2502 if not gin:
2503 continue
2505 for iout2 in gout:
2506 if iout2 in outs:
2507 outs.remove(iout2)
2509 gin = list(gin)
2510 gin.sort()
2511 gout = list(gout)
2512 gout.sort()
2514 systems.append((gin, gout, a[gout, :][:, gin]))
2516 return systems
2519def _channels_to_names(channels):
2520 from pyrocko import squirrel
2521 names = []
2522 for ch in channels:
2523 if isinstance(ch, model.Channel):
2524 names.append(ch.name)
2525 elif isinstance(ch, squirrel.Channel):
2526 names.append(ch.codes.channel)
2527 else:
2528 names.append(ch)
2530 return names
2533def project(traces, matrix, in_channels, out_channels):
2534 '''
2535 Affine transform of three-component traces.
2537 Compute matrix-vector product of three-component traces, to e.g. rotate
2538 traces into a different basis. The traces are distinguished and ordered by
2539 their channel attribute. The tranform is applied to overlapping parts of
2540 any appropriate combinations of the input traces. This should allow this
2541 function to be robust with data gaps. It also tries to apply the
2542 tranformation to subsets of the channels, if this is possible, so that, if
2543 for example a vertical compontent is missing, horizontal components can
2544 still be rotated.
2546 :param traces: list of traces in arbitrary order
2547 :param matrix: tranformation matrix
2548 :param in_channels: input channel names
2549 :param out_channels: output channel names
2550 :returns: list of transformed traces
2551 '''
2553 in_channels = tuple(_channels_to_names(in_channels))
2554 out_channels = tuple(_channels_to_names(out_channels))
2555 systems = _decompose(matrix)
2557 # fallback to full matrix if some are not quadratic
2558 for iins, iouts, submatrix in systems:
2559 if submatrix.shape[0] != submatrix.shape[1]:
2560 if len(in_channels) != 3 or len(out_channels) != 3:
2561 return []
2562 else:
2563 return _project3(traces, matrix, in_channels, out_channels)
2565 projected = []
2566 for iins, iouts, submatrix in systems:
2567 in_cha = tuple([in_channels[iin] for iin in iins])
2568 out_cha = tuple([out_channels[iout] for iout in iouts])
2569 if submatrix.shape[0] == 1:
2570 projected.extend(_project1(traces, submatrix, in_cha, out_cha))
2571 elif submatrix.shape[1] == 2:
2572 projected.extend(_project2(traces, submatrix, in_cha, out_cha))
2573 else:
2574 projected.extend(_project3(traces, submatrix, in_cha, out_cha))
2576 return projected
2579def project_dependencies(matrix, in_channels, out_channels):
2580 '''
2581 Figure out what dependencies project() would produce.
2582 '''
2584 in_channels = tuple(_channels_to_names(in_channels))
2585 out_channels = tuple(_channels_to_names(out_channels))
2586 systems = _decompose(matrix)
2588 subpro = []
2589 for iins, iouts, submatrix in systems:
2590 if submatrix.shape[0] != submatrix.shape[1]:
2591 subpro.append((matrix, in_channels, out_channels))
2593 if not subpro:
2594 for iins, iouts, submatrix in systems:
2595 in_cha = tuple([in_channels[iin] for iin in iins])
2596 out_cha = tuple([out_channels[iout] for iout in iouts])
2597 subpro.append((submatrix, in_cha, out_cha))
2599 deps = {}
2600 for mat, in_cha, out_cha in subpro:
2601 for oc in out_cha:
2602 if oc not in deps:
2603 deps[oc] = []
2605 for ic in in_cha:
2606 deps[oc].append(ic)
2608 return deps
2611def _project1(traces, matrix, in_channels, out_channels):
2612 assert len(in_channels) == 1
2613 assert len(out_channels) == 1
2614 assert matrix.shape == (1, 1)
2616 projected = []
2617 for a in traces:
2618 if not (a.channel,) == in_channels:
2619 continue
2621 ac = a.copy()
2622 ac.set_ydata(matrix[0, 0]*a.get_ydata())
2623 ac.set_codes(channel=out_channels[0])
2624 projected.append(ac)
2626 return projected
2629def _project2(traces, matrix, in_channels, out_channels):
2630 assert len(in_channels) == 2
2631 assert len(out_channels) == 2
2632 assert matrix.shape == (2, 2)
2633 projected = []
2634 for a in traces:
2635 for b in traces:
2636 if not ((a.channel, b.channel) == in_channels and
2637 a.nslc_id[:3] == b.nslc_id[:3] and
2638 abs(a.deltat-b.deltat) < a.deltat*0.001):
2639 continue
2641 tmin = max(a.tmin, b.tmin)
2642 tmax = min(a.tmax, b.tmax)
2644 if tmin > tmax:
2645 continue
2647 ac = a.chop(tmin, tmax, inplace=False, include_last=True)
2648 bc = b.chop(tmin, tmax, inplace=False, include_last=True)
2649 if abs(ac.tmin - bc.tmin) > ac.deltat*0.01:
2650 logger.warning(
2651 'Cannot project traces with displaced sampling '
2652 '(%s, %s, %s, %s)' % a.nslc_id)
2653 continue
2655 acydata = num.dot(matrix[0], (ac.get_ydata(), bc.get_ydata()))
2656 bcydata = num.dot(matrix[1], (ac.get_ydata(), bc.get_ydata()))
2658 ac.set_ydata(acydata)
2659 bc.set_ydata(bcydata)
2661 ac.set_codes(channel=out_channels[0])
2662 bc.set_codes(channel=out_channels[1])
2664 projected.append(ac)
2665 projected.append(bc)
2667 return projected
2670def _project3(traces, matrix, in_channels, out_channels):
2671 assert len(in_channels) == 3
2672 assert len(out_channels) == 3
2673 assert matrix.shape == (3, 3)
2674 projected = []
2675 for a in traces:
2676 for b in traces:
2677 for c in traces:
2678 if not ((a.channel, b.channel, c.channel) == in_channels
2679 and a.nslc_id[:3] == b.nslc_id[:3]
2680 and b.nslc_id[:3] == c.nslc_id[:3]
2681 and abs(a.deltat-b.deltat) < a.deltat*0.001
2682 and abs(b.deltat-c.deltat) < b.deltat*0.001):
2684 continue
2686 tmin = max(a.tmin, b.tmin, c.tmin)
2687 tmax = min(a.tmax, b.tmax, c.tmax)
2689 if tmin >= tmax:
2690 continue
2692 ac = a.chop(tmin, tmax, inplace=False, include_last=True)
2693 bc = b.chop(tmin, tmax, inplace=False, include_last=True)
2694 cc = c.chop(tmin, tmax, inplace=False, include_last=True)
2695 if (abs(ac.tmin - bc.tmin) > ac.deltat*0.01
2696 or abs(bc.tmin - cc.tmin) > bc.deltat*0.01):
2698 logger.warning(
2699 'Cannot project traces with displaced sampling '
2700 '(%s, %s, %s, %s)' % a.nslc_id)
2701 continue
2703 acydata = num.dot(
2704 matrix[0],
2705 (ac.get_ydata(), bc.get_ydata(), cc.get_ydata()))
2706 bcydata = num.dot(
2707 matrix[1],
2708 (ac.get_ydata(), bc.get_ydata(), cc.get_ydata()))
2709 ccydata = num.dot(
2710 matrix[2],
2711 (ac.get_ydata(), bc.get_ydata(), cc.get_ydata()))
2713 ac.set_ydata(acydata)
2714 bc.set_ydata(bcydata)
2715 cc.set_ydata(ccydata)
2717 ac.set_codes(channel=out_channels[0])
2718 bc.set_codes(channel=out_channels[1])
2719 cc.set_codes(channel=out_channels[2])
2721 projected.append(ac)
2722 projected.append(bc)
2723 projected.append(cc)
2725 return projected
2728def correlate(a, b, mode='valid', normalization=None, use_fft=False):
2729 '''
2730 Cross correlation of two traces.
2732 :param a,b: input traces
2733 :param mode: ``'valid'``, ``'full'``, or ``'same'``
2734 :param normalization: ``'normal'``, ``'gliding'``, or ``None``
2735 :param use_fft: bool, whether to do cross correlation in spectral domain
2737 :returns: trace containing cross correlation coefficients
2739 This function computes the cross correlation between two traces. It
2740 evaluates the discrete equivalent of
2742 .. math::
2744 c(t) = \\int_{-\\infty}^{\\infty} a^{\\ast}(\\tau) b(t+\\tau) d\\tau
2746 where the star denotes complex conjugate. Note, that the arguments here are
2747 swapped when compared with the :py:func:`numpy.correlate` function,
2748 which is internally called. This function should be safe even with older
2749 versions of NumPy, where the correlate function has some problems.
2751 A trace containing the cross correlation coefficients is returned. The time
2752 information of the output trace is set so that the returned cross
2753 correlation can be viewed directly as a function of time lag.
2755 Example::
2757 # align two traces a and b containing a time shifted similar signal:
2758 c = pyrocko.trace.correlate(a,b)
2759 t, coef = c.max() # get time and value of maximum
2760 b.shift(-t) # align b with a
2762 '''
2764 assert_same_sampling_rate(a, b)
2766 ya, yb = a.ydata, b.ydata
2768 # need reversed order here:
2769 yc = numpy_correlate_fixed(yb, ya, mode=mode, use_fft=use_fft)
2770 kmin, kmax = numpy_correlate_lag_range(yb, ya, mode=mode, use_fft=use_fft)
2772 if normalization == 'normal':
2773 normfac = num.sqrt(num.sum(ya**2))*num.sqrt(num.sum(yb**2))
2774 yc = yc/normfac
2776 elif normalization == 'gliding':
2777 if mode != 'valid':
2778 assert False, 'gliding normalization currently only available ' \
2779 'with "valid" mode.'
2781 if ya.size < yb.size:
2782 yshort, ylong = ya, yb
2783 else:
2784 yshort, ylong = yb, ya
2786 epsilon = 0.00001
2787 normfac_short = num.sqrt(num.sum(yshort**2))
2788 normfac = normfac_short * num.sqrt(
2789 moving_sum(ylong**2, yshort.size, mode='valid')) \
2790 + normfac_short*epsilon
2792 if yb.size <= ya.size:
2793 normfac = normfac[::-1]
2795 yc /= normfac
2797 c = a.copy()
2798 c.set_ydata(yc)
2799 c.set_codes(*merge_codes(a, b, '~'))
2800 c.shift(-c.tmin + b.tmin-a.tmin + kmin * c.deltat)
2802 return c
2805def deconvolve(
2806 a, b, waterlevel,
2807 tshift=0.,
2808 pad=0.5,
2809 fd_taper=None,
2810 pad_to_pow2=True):
2812 same_sampling_rate(a, b)
2813 assert abs(a.tmin - b.tmin) < a.deltat * 0.001
2814 deltat = a.deltat
2815 npad = int(round(a.data_len()*pad + tshift / deltat))
2817 ndata = max(a.data_len(), b.data_len())
2818 ndata_pad = ndata + npad
2820 if pad_to_pow2:
2821 ntrans = nextpow2(ndata_pad)
2822 else:
2823 ntrans = ndata
2825 aspec = num.fft.rfft(a.ydata, ntrans)
2826 bspec = num.fft.rfft(b.ydata, ntrans)
2828 out = aspec * num.conj(bspec)
2830 bautocorr = bspec*num.conj(bspec)
2831 denom = num.maximum(bautocorr, waterlevel * bautocorr.max())
2833 out /= denom
2834 df = 1/(ntrans*deltat)
2836 if fd_taper is not None:
2837 fd_taper(out, 0.0, df)
2839 ydata = num.roll(num.fft.irfft(out), int(round(tshift/deltat)))
2840 c = a.copy(data=False)
2841 c.set_ydata(ydata[:ndata])
2842 c.set_codes(*merge_codes(a, b, '/'))
2843 return c
2846def assert_same_sampling_rate(a, b, eps=1.0e-6):
2847 assert same_sampling_rate(a, b, eps), \
2848 'Sampling rates differ: %g != %g' % (a.deltat, b.deltat)
2851def same_sampling_rate(a, b, eps=1.0e-6):
2852 '''
2853 Check if two traces have the same sampling rate.
2855 :param a,b: input traces
2856 :param eps: relative tolerance
2857 '''
2859 return abs(a.deltat - b.deltat) < (a.deltat + b.deltat)*eps
2862def fix_deltat_rounding_errors(deltat):
2863 '''
2864 Try to undo sampling rate rounding errors.
2866 Fix rounding errors of sampling intervals when these are read from single
2867 precision floating point values.
2869 Assumes that the true sampling rate or sampling interval was an integer
2870 value. No correction will be applied if this would change the sampling
2871 rate by more than 0.001%.
2872 '''
2874 if deltat <= 1.0:
2875 deltat_new = 1.0 / round(1.0 / deltat)
2876 else:
2877 deltat_new = round(deltat)
2879 if abs(deltat_new - deltat) / deltat > 1e-5:
2880 deltat_new = deltat
2882 return deltat_new
2885def merge_codes(a, b, sep='-'):
2886 '''
2887 Merge network-station-location-channel codes of a pair of traces.
2888 '''
2890 o = []
2891 for xa, xb in zip(a.nslc_id, b.nslc_id):
2892 if xa == xb:
2893 o.append(xa)
2894 else:
2895 o.append(sep.join((xa, xb)))
2896 return o
2899class Taper(Object):
2900 '''
2901 Base class for tapers.
2903 Does nothing by default.
2904 '''
2906 def __call__(self, y, x0, dx):
2907 pass
2910class CosTaper(Taper):
2911 '''
2912 Cosine Taper.
2914 :param a: start of fading in
2915 :param b: end of fading in
2916 :param c: start of fading out
2917 :param d: end of fading out
2918 '''
2920 a = Float.T()
2921 b = Float.T()
2922 c = Float.T()
2923 d = Float.T()
2925 def __init__(self, a, b, c, d):
2926 Taper.__init__(self, a=a, b=b, c=c, d=d)
2928 def __call__(self, y, x0, dx):
2930 if y.dtype == num.dtype(float):
2931 _apply_costaper = signal_ext.apply_costaper
2932 else:
2933 _apply_costaper = apply_costaper
2935 _apply_costaper(self.a, self.b, self.c, self.d, y, x0, dx)
2937 def span(self, y, x0, dx):
2938 return span_costaper(self.a, self.b, self.c, self.d, y, x0, dx)
2940 def time_span(self):
2941 return self.a, self.d
2944class CosFader(Taper):
2945 '''
2946 Cosine Fader.
2948 :param xfade: fade in and fade out time in seconds (optional)
2949 :param xfrac: fade in and fade out as fraction between 0. and 1. (optional)
2951 Only one argument can be set. The other should to be ``None``.
2952 '''
2954 xfade = Float.T(optional=True)
2955 xfrac = Float.T(optional=True)
2957 def __init__(self, xfade=None, xfrac=None):
2958 Taper.__init__(self, xfade=xfade, xfrac=xfrac)
2959 assert (xfade is None) != (xfrac is None)
2960 self._xfade = xfade
2961 self._xfrac = xfrac
2963 def __call__(self, y, x0, dx):
2965 xfade = self._xfade
2967 xlen = (y.size - 1)*dx
2968 if xfade is None:
2969 xfade = xlen * self._xfrac
2971 a = x0
2972 b = x0 + xfade
2973 c = x0 + xlen - xfade
2974 d = x0 + xlen
2976 apply_costaper(a, b, c, d, y, x0, dx)
2978 def span(self, y, x0, dx):
2979 return 0, y.size
2981 def time_span(self):
2982 return None, None
2985def none_min(li):
2986 if None in li:
2987 return None
2988 else:
2989 return min(x for x in li if x is not None)
2992def none_max(li):
2993 if None in li:
2994 return None
2995 else:
2996 return max(x for x in li if x is not None)
2999class MultiplyTaper(Taper):
3000 '''
3001 Multiplication of several tapers.
3002 '''
3004 tapers = List.T(Taper.T())
3006 def __init__(self, tapers=None):
3007 if tapers is None:
3008 tapers = []
3010 Taper.__init__(self, tapers=tapers)
3012 def __call__(self, y, x0, dx):
3013 for taper in self.tapers:
3014 taper(y, x0, dx)
3016 def span(self, y, x0, dx):
3017 spans = []
3018 for taper in self.tapers:
3019 spans.append(taper.span(y, x0, dx))
3021 mins, maxs = list(zip(*spans))
3022 return min(mins), max(maxs)
3024 def time_span(self):
3025 spans = []
3026 for taper in self.tapers:
3027 spans.append(taper.time_span())
3029 mins, maxs = list(zip(*spans))
3030 return none_min(mins), none_max(maxs)
3033class GaussTaper(Taper):
3034 '''
3035 Frequency domain Gaussian filter.
3036 '''
3038 alpha = Float.T()
3040 def __init__(self, alpha):
3041 Taper.__init__(self, alpha=alpha)
3042 self._alpha = alpha
3044 def __call__(self, y, x0, dx):
3045 f = x0 + num.arange(y.size)*dx
3046 y *= num.exp(-num.pi**2 / (self._alpha**2) * f**2)
3049cached_coefficients = {}
3052def _get_cached_filter_coeffs(order, corners, btype):
3053 ck = (order, tuple(corners), btype)
3054 if ck not in cached_coefficients:
3055 if len(corners) == 0:
3056 cached_coefficients[ck] = signal.butter(
3057 order, corners[0], btype=btype)
3058 else:
3059 cached_coefficients[ck] = signal.butter(
3060 order, corners, btype=btype)
3062 return cached_coefficients[ck]
3065class _globals(object):
3066 _numpy_has_correlate_flip_bug = None
3069def _default_key(tr):
3070 return (tr.network, tr.station, tr.location, tr.channel)
3073def numpy_has_correlate_flip_bug():
3074 '''
3075 Check if NumPy's correlate function reveals old behaviour.
3076 '''
3078 if _globals._numpy_has_correlate_flip_bug is None:
3079 a = num.array([0, 0, 1, 0, 0, 0, 0])
3080 b = num.array([0, 0, 0, 0, 1, 0, 0, 0])
3081 ab = num.correlate(a, b, mode='same')
3082 ba = num.correlate(b, a, mode='same')
3083 _globals._numpy_has_correlate_flip_bug = num.all(ab == ba)
3085 return _globals._numpy_has_correlate_flip_bug
3088def numpy_correlate_fixed(a, b, mode='valid', use_fft=False):
3089 '''
3090 Call :py:func:`numpy.correlate` with fixes.
3092 c[k] = sum_i a[i+k] * conj(b[i])
3094 Note that the result produced by newer numpy.correlate is always flipped
3095 with respect to the formula given in its documentation (if ascending k
3096 assumed for the output).
3097 '''
3099 if use_fft:
3100 if a.size < b.size:
3101 c = signal.fftconvolve(b[::-1], a, mode=mode)
3102 else:
3103 c = signal.fftconvolve(a, b[::-1], mode=mode)
3104 return c
3106 else:
3107 buggy = numpy_has_correlate_flip_bug()
3109 a = num.asarray(a)
3110 b = num.asarray(b)
3112 if buggy:
3113 b = num.conj(b)
3115 c = num.correlate(a, b, mode=mode)
3117 if buggy and a.size < b.size:
3118 return c[::-1]
3119 else:
3120 return c
3123def numpy_correlate_emulate(a, b, mode='valid'):
3124 '''
3125 Slow version of :py:func:`numpy.correlate` for comparison.
3126 '''
3128 a = num.asarray(a)
3129 b = num.asarray(b)
3130 kmin = -(b.size-1)
3131 klen = a.size-kmin
3132 kmin, kmax = numpy_correlate_lag_range(a, b, mode=mode)
3133 kmin = int(kmin)
3134 kmax = int(kmax)
3135 klen = kmax - kmin + 1
3136 c = num.zeros(klen, dtype=num.find_common_type((b.dtype, a.dtype), ()))
3137 for k in range(kmin, kmin+klen):
3138 imin = max(0, -k)
3139 ilen = min(b.size, a.size-k) - imin
3140 c[k-kmin] = num.sum(
3141 a[imin+k:imin+ilen+k] * num.conj(b[imin:imin+ilen]))
3143 return c
3146def numpy_correlate_lag_range(a, b, mode='valid', use_fft=False):
3147 '''
3148 Get range of lags for which :py:func:`numpy.correlate` produces values.
3149 '''
3151 a = num.asarray(a)
3152 b = num.asarray(b)
3154 kmin = -(b.size-1)
3155 if mode == 'full':
3156 klen = a.size-kmin
3157 elif mode == 'same':
3158 klen = max(a.size, b.size)
3159 kmin += (a.size+b.size-1 - max(a.size, b.size)) // 2 + \
3160 int(not use_fft and a.size % 2 == 0 and b.size > a.size)
3161 elif mode == 'valid':
3162 klen = abs(a.size - b.size) + 1
3163 kmin += min(a.size, b.size) - 1
3165 return kmin, kmin + klen - 1
3168def autocorr(x, nshifts):
3169 '''
3170 Compute biased estimate of the first autocorrelation coefficients.
3172 :param x: input array
3173 :param nshifts: number of coefficients to calculate
3174 '''
3176 mean = num.mean(x)
3177 std = num.std(x)
3178 n = x.size
3179 xdm = x - mean
3180 r = num.zeros(nshifts)
3181 for k in range(nshifts):
3182 r[k] = 1./((n-num.abs(k))*std) * num.sum(xdm[:n-k] * xdm[k:])
3184 return r
3187def yulewalker(x, order):
3188 '''
3189 Compute autoregression coefficients using Yule-Walker method.
3191 :param x: input array
3192 :param order: number of coefficients to produce
3194 A biased estimate of the autocorrelation is used. The Yule-Walker equations
3195 are solved by :py:func:`numpy.linalg.inv` instead of Levinson-Durbin
3196 recursion which is normally used.
3197 '''
3199 gamma = autocorr(x, order+1)
3200 d = gamma[1:1+order]
3201 a = num.zeros((order, order))
3202 gamma2 = num.concatenate((gamma[::-1], gamma[1:order]))
3203 for i in range(order):
3204 ioff = order-i
3205 a[i, :] = gamma2[ioff:ioff+order]
3207 return num.dot(num.linalg.inv(a), -d)
3210def moving_avg(x, n):
3211 n = int(n)
3212 cx = x.cumsum()
3213 nn = len(x)
3214 y = num.zeros(nn, dtype=cx.dtype)
3215 y[n//2:n//2+(nn-n)] = (cx[n:]-cx[:-n])/n
3216 y[:n//2] = y[n//2]
3217 y[n//2+(nn-n):] = y[n//2+(nn-n)-1]
3218 return y
3221def moving_sum(x, n, mode='valid'):
3222 n = int(n)
3223 cx = x.cumsum()
3224 nn = len(x)
3226 if mode == 'valid':
3227 if nn-n+1 <= 0:
3228 return num.zeros(0, dtype=cx.dtype)
3229 y = num.zeros(nn-n+1, dtype=cx.dtype)
3230 y[0] = cx[n-1]
3231 y[1:nn-n+1] = cx[n:nn]-cx[0:nn-n]
3233 if mode == 'full':
3234 y = num.zeros(nn+n-1, dtype=cx.dtype)
3235 if n <= nn:
3236 y[0:n] = cx[0:n]
3237 y[n:nn] = cx[n:nn]-cx[0:nn-n]
3238 y[nn:nn+n-1] = cx[-1]-cx[nn-n:nn-1]
3239 else:
3240 y[0:nn] = cx[0:nn]
3241 y[nn:n] = cx[nn-1]
3242 y[n:nn+n-1] = cx[nn-1] - cx[0:nn-1]
3244 if mode == 'same':
3245 n1 = (n-1)//2
3246 y = num.zeros(nn, dtype=cx.dtype)
3247 if n <= nn:
3248 y[0:n-n1] = cx[n1:n]
3249 y[n-n1:nn-n1] = cx[n:nn]-cx[0:nn-n]
3250 y[nn-n1:nn] = cx[nn-1] - cx[nn-n:nn-n+n1]
3251 else:
3252 y[0:max(0, nn-n1)] = cx[min(n1, nn):nn]
3253 y[max(nn-n1, 0):min(n-n1, nn)] = cx[nn-1]
3254 y[min(n-n1, nn):nn] = cx[nn-1] - cx[0:max(0, nn-(n-n1))]
3256 return y
3259def nextpow2(i):
3260 return 2**int(math.ceil(math.log(i)/math.log(2.)))
3263def snapper_w_offset(nmax, offset, delta, snapfun=math.ceil):
3264 def snap(x):
3265 return max(0, min(int(snapfun((x-offset)/delta)), nmax))
3266 return snap
3269def snapper(nmax, delta, snapfun=math.ceil):
3270 def snap(x):
3271 return max(0, min(int(snapfun(x/delta)), nmax))
3272 return snap
3275def apply_costaper(a, b, c, d, y, x0, dx):
3276 abcd = num.array((a, b, c, d), dtype=float)
3277 ja, jb, jc, jd = num.clip(num.ceil((abcd-x0)/dx).astype(int), 0, y.size)
3278 y[:ja] = 0.
3279 y[ja:jb] *= 0.5 \
3280 - 0.5*num.cos((dx*num.arange(ja, jb)-(a-x0))/(b-a)*num.pi)
3281 y[jc:jd] *= 0.5 \
3282 + 0.5*num.cos((dx*num.arange(jc, jd)-(c-x0))/(d-c)*num.pi)
3283 y[jd:] = 0.
3286def span_costaper(a, b, c, d, y, x0, dx):
3287 hi = snapper_w_offset(y.size, x0, dx)
3288 return hi(a), hi(d) - hi(a)
3291def costaper(a, b, c, d, nfreqs, deltaf):
3292 hi = snapper(nfreqs, deltaf)
3293 tap = num.zeros(nfreqs)
3294 tap[hi(a):hi(b)] = 0.5 \
3295 - 0.5*num.cos((deltaf*num.arange(hi(a), hi(b))-a)/(b-a)*num.pi)
3296 tap[hi(b):hi(c)] = 1.
3297 tap[hi(c):hi(d)] = 0.5 \
3298 + 0.5*num.cos((deltaf*num.arange(hi(c), hi(d))-c)/(d-c)*num.pi)
3300 return tap
3303def t2ind(t, tdelta, snap=round):
3304 return int(snap(t/tdelta))
3307def hilbert(x, N=None):
3308 '''
3309 Return the hilbert transform of x of length N.
3311 (from scipy.signal, but changed to use fft and ifft from numpy.fft)
3312 '''
3314 x = num.asarray(x)
3315 if N is None:
3316 N = len(x)
3317 if N <= 0:
3318 raise ValueError('N must be positive.')
3319 if num.iscomplexobj(x):
3320 logger.warning('imaginary part of x ignored.')
3321 x = num.real(x)
3323 Xf = num.fft.fft(x, N, axis=0)
3324 h = num.zeros(N)
3325 if N % 2 == 0:
3326 h[0] = h[N//2] = 1
3327 h[1:N//2] = 2
3328 else:
3329 h[0] = 1
3330 h[1:(N+1)//2] = 2
3332 if len(x.shape) > 1:
3333 h = h[:, num.newaxis]
3334 x = num.fft.ifft(Xf*h)
3335 return x
3338def near(a, b, eps):
3339 return abs(a-b) < eps
3342def coroutine(func):
3343 def wrapper(*args, **kwargs):
3344 gen = func(*args, **kwargs)
3345 next(gen)
3346 return gen
3348 wrapper.__name__ = func.__name__
3349 wrapper.__dict__ = func.__dict__
3350 wrapper.__doc__ = func.__doc__
3351 return wrapper
3354class States(object):
3355 '''
3356 Utility to store channel-specific state in coroutines.
3357 '''
3359 def __init__(self):
3360 self._states = {}
3362 def get(self, tr):
3363 k = tr.nslc_id
3364 if k in self._states:
3365 tmin, deltat, dtype, value = self._states[k]
3366 if (near(tmin, tr.tmin, deltat/100.)
3367 and near(deltat, tr.deltat, deltat/10000.)
3368 and dtype == tr.ydata.dtype):
3370 return value
3372 return None
3374 def set(self, tr, value):
3375 k = tr.nslc_id
3376 if k in self._states and self._states[k][-1] is not value:
3377 self.free(self._states[k][-1])
3379 self._states[k] = (tr.tmax+tr.deltat, tr.deltat, tr.ydata.dtype, value)
3381 def free(self, value):
3382 pass
3385@coroutine
3386def co_list_append(list):
3387 while True:
3388 list.append((yield))
3391class ScipyBug(Exception):
3392 pass
3395@coroutine
3396def co_lfilter(target, b, a):
3397 '''
3398 Successively filter broken continuous trace data (coroutine).
3400 Create coroutine which takes :py:class:`Trace` objects, filters their data
3401 through :py:func:`scipy.signal.lfilter` and sends new :py:class:`Trace`
3402 objects containing the filtered data to target. This is useful, if one
3403 wants to filter a long continuous time series, which is split into many
3404 successive traces without producing filter artifacts at trace boundaries.
3406 Filter states are kept *per channel*, specifically, for each (network,
3407 station, location, channel) combination occuring in the input traces, a
3408 separate state is created and maintained. This makes it possible to filter
3409 multichannel or multistation data with only one :py:func:`co_lfilter`
3410 instance.
3412 Filter state is reset, when gaps occur.
3414 Use it like this::
3416 from pyrocko.trace import co_lfilter, co_list_append
3418 filtered_traces = []
3419 pipe = co_lfilter(co_list_append(filtered_traces), a, b)
3420 for trace in traces:
3421 pipe.send(trace)
3423 pipe.close()
3425 '''
3427 try:
3428 states = States()
3429 output = None
3430 while True:
3431 input = (yield)
3433 zi = states.get(input)
3434 if zi is None:
3435 zi = num.zeros(max(len(a), len(b))-1, dtype=float)
3437 output = input.copy(data=False)
3438 try:
3439 ydata, zf = signal.lfilter(b, a, input.get_ydata(), zi=zi)
3440 except ValueError:
3441 raise ScipyBug(
3442 'signal.lfilter failed: could be related to a bug '
3443 'in some older scipy versions, e.g. on opensuse42.1')
3445 output.set_ydata(ydata)
3446 states.set(input, zf)
3447 target.send(output)
3449 except GeneratorExit:
3450 target.close()
3453def co_antialias(target, q, n=None, ftype='fir'):
3454 b, a, n = util.decimate_coeffs(q, n, ftype)
3455 anti = co_lfilter(target, b, a)
3456 return anti
3459@coroutine
3460def co_dropsamples(target, q, nfir):
3461 try:
3462 states = States()
3463 while True:
3464 tr = (yield)
3465 newdeltat = q * tr.deltat
3466 ioffset = states.get(tr)
3467 if ioffset is None:
3468 # for fir filter, the first nfir samples are pulluted by
3469 # boundary effects; cut it off.
3470 # for iir this may be (much) more, we do not correct for that.
3471 # put sample instances to a time which is a multiple of the
3472 # new sampling interval.
3473 newtmin_want = math.ceil(
3474 (tr.tmin+(nfir+1)*tr.deltat) / newdeltat) * newdeltat \
3475 - (nfir/2*tr.deltat)
3476 ioffset = int(round((newtmin_want - tr.tmin)/tr.deltat))
3477 if ioffset < 0:
3478 ioffset = ioffset % q
3480 newtmin_have = tr.tmin + ioffset * tr.deltat
3481 newtr = tr.copy(data=False)
3482 newtr.deltat = newdeltat
3483 # because the fir kernel shifts data by nfir/2 samples:
3484 newtr.tmin = newtmin_have - (nfir/2*tr.deltat)
3485 newtr.set_ydata(tr.get_ydata()[ioffset::q].copy())
3486 states.set(tr, (ioffset % q - tr.data_len() % q) % q)
3487 target.send(newtr)
3489 except GeneratorExit:
3490 target.close()
3493def co_downsample(target, q, n=None, ftype='fir'):
3494 '''
3495 Successively downsample broken continuous trace data (coroutine).
3497 Create coroutine which takes :py:class:`Trace` objects, downsamples their
3498 data and sends new :py:class:`Trace` objects containing the downsampled
3499 data to target. This is useful, if one wants to downsample a long
3500 continuous time series, which is split into many successive traces without
3501 producing filter artifacts and gaps at trace boundaries.
3503 Filter states are kept *per channel*, specifically, for each (network,
3504 station, location, channel) combination occuring in the input traces, a
3505 separate state is created and maintained. This makes it possible to filter
3506 multichannel or multistation data with only one :py:func:`co_lfilter`
3507 instance.
3509 Filter state is reset, when gaps occur. The sampling instances are choosen
3510 so that they occur at (or as close as possible) to even multiples of the
3511 sampling interval of the downsampled trace (based on system time).
3512 '''
3514 b, a, n = util.decimate_coeffs(q, n, ftype)
3515 return co_antialias(co_dropsamples(target, q, n), q, n, ftype)
3518@coroutine
3519def co_downsample_to(target, deltat):
3521 decimators = {}
3522 try:
3523 while True:
3524 tr = (yield)
3525 ratio = deltat / tr.deltat
3526 rratio = round(ratio)
3527 if abs(rratio - ratio)/ratio > 0.0001:
3528 raise util.UnavailableDecimation('ratio = %g' % ratio)
3530 deci_seq = tuple(x for x in util.decitab(int(rratio)) if x != 1)
3531 if deci_seq not in decimators:
3532 pipe = target
3533 for q in deci_seq[::-1]:
3534 pipe = co_downsample(pipe, q)
3536 decimators[deci_seq] = pipe
3538 decimators[deci_seq].send(tr)
3540 except GeneratorExit:
3541 for g in decimators.values():
3542 g.close()
3545class DomainChoice(StringChoice):
3546 choices = [
3547 'time_domain',
3548 'frequency_domain',
3549 'envelope',
3550 'absolute',
3551 'cc_max_norm']
3554class MisfitSetup(Object):
3555 '''
3556 Contains misfit setup to be used in :py:func:`trace.misfit`
3558 :param description: Description of the setup
3559 :param norm: L-norm classifier
3560 :param taper: Object of :py:class:`Taper`
3561 :param filter: Object of :py:class:`FrequencyResponse`
3562 :param domain: ['time_domain', 'frequency_domain', 'envelope', 'absolute',
3563 'cc_max_norm']
3565 Can be dumped to a yaml file.
3566 '''
3568 xmltagname = 'misfitsetup'
3569 description = String.T(optional=True)
3570 norm = Int.T(optional=False)
3571 taper = Taper.T(optional=False)
3572 filter = FrequencyResponse.T(optional=True)
3573 domain = DomainChoice.T(default='time_domain')
3576def equalize_sampling_rates(trace_1, trace_2):
3577 '''
3578 Equalize sampling rates of two traces (reduce higher sampling rate to
3579 lower).
3581 :param trace_1: :py:class:`Trace` object
3582 :param trace_2: :py:class:`Trace` object
3584 Returns a copy of the resampled trace if resampling is needed.
3585 '''
3587 if same_sampling_rate(trace_1, trace_2):
3588 return trace_1, trace_2
3590 if trace_1.deltat < trace_2.deltat:
3591 t1_out = trace_1.copy()
3592 t1_out.downsample_to(deltat=trace_2.deltat, snap=True)
3593 logger.debug('Trace downsampled (return copy of trace): %s'
3594 % '.'.join(t1_out.nslc_id))
3595 return t1_out, trace_2
3597 elif trace_1.deltat > trace_2.deltat:
3598 t2_out = trace_2.copy()
3599 t2_out.downsample_to(deltat=trace_1.deltat, snap=True)
3600 logger.debug('Trace downsampled (return copy of trace): %s'
3601 % '.'.join(t2_out.nslc_id))
3602 return trace_1, t2_out
3605def Lx_norm(u, v, norm=2):
3606 '''
3607 Calculate the misfit denominator *m* and the normalization devisor *n*
3608 according to norm.
3610 The normalization divisor *n* is calculated from ``v``.
3612 :param u: :py:class:`numpy.array`
3613 :param v: :py:class:`numpy.array`
3614 :param norm: (default = 2)
3616 ``u`` and ``v`` must be of same size.
3617 '''
3619 if norm == 1:
3620 return (
3621 num.sum(num.abs(v-u)),
3622 num.sum(num.abs(v)))
3624 elif norm == 2:
3625 return (
3626 num.sqrt(num.sum((v-u)**2)),
3627 num.sqrt(num.sum(v**2)))
3629 else:
3630 return (
3631 num.power(num.sum(num.abs(num.power(v - u, norm))), 1./norm),
3632 num.power(num.sum(num.abs(num.power(v, norm))), 1./norm))
3635def do_downsample(tr, deltat):
3636 if abs(tr.deltat - deltat) / tr.deltat > 1e-6:
3637 tr = tr.copy()
3638 tr.downsample_to(deltat, snap=True, demean=False)
3639 else:
3640 if tr.tmin/tr.deltat > 1e-6 or tr.tmax/tr.deltat > 1e-6:
3641 tr = tr.copy()
3642 tr.snap()
3643 return tr
3646def do_extend(tr, tmin, tmax):
3647 if tmin < tr.tmin or tmax > tr.tmax:
3648 tr = tr.copy()
3649 tr.extend(tmin=tmin, tmax=tmax, fillmethod='repeat')
3651 return tr
3654def do_pre_taper(tr, taper):
3655 return tr.taper(taper, inplace=False, chop=True)
3658def do_fft(tr, filter):
3659 if filter is None:
3660 return tr
3661 else:
3662 ndata = tr.ydata.size
3663 nfft = nextpow2(ndata)
3664 padded = num.zeros(nfft, dtype=float)
3665 padded[:ndata] = tr.ydata
3666 spectrum = num.fft.rfft(padded)
3667 df = 1.0 / (tr.deltat * nfft)
3668 frequencies = num.arange(spectrum.size)*df
3669 return [tr, frequencies, spectrum]
3672def do_filter(inp, filter):
3673 if filter is None:
3674 return inp
3675 else:
3676 tr, frequencies, spectrum = inp
3677 spectrum *= filter.evaluate(frequencies)
3678 return [tr, frequencies, spectrum]
3681def do_ifft(inp):
3682 if isinstance(inp, Trace):
3683 return inp
3684 else:
3685 tr, _, spectrum = inp
3686 ndata = tr.ydata.size
3687 tr = tr.copy(data=False)
3688 tr.set_ydata(num.fft.irfft(spectrum)[:ndata])
3689 return tr
3692def check_alignment(t1, t2):
3693 if abs(t1.tmin-t2.tmin) > t1.deltat * 1e-4 or \
3694 abs(t1.tmax - t2.tmax) > t1.deltat * 1e-4 or \
3695 t1.ydata.shape != t2.ydata.shape:
3696 raise MisalignedTraces(
3697 'Cannot calculate misfit of %s and %s due to misaligned '
3698 'traces.' % ('.'.join(t1.nslc_id), '.'.join(t2.nslc_id)))