pyrocko.trace¶
Basic signal processing for seismic waveforms.
Functions

Calculate the misfit denominator m and the normalization divisor n according to norm. 

Compute biased estimate of the first autocorrelation coefficients. 

Successively downsample broken continuous trace data (coroutine). 

Successively filter broken continuous trace data (coroutine). 

Cross correlation of two traces. 

Try to connect traces and remove gaps. 

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

Equalize sampling rates of two traces (reduce higher sampling rate to lower). 

Try to undo sampling rate rounding errors. 

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

Return the hilbert transform of x of length N. 

Merge networkstationlocationchannel codes of a pair of traces. 

Get data range given traces grouped by selected pattern. 

Get time range given traces grouped by selected pattern. 

Slow version of 

Call 

Get range of lags for which 
Check if NumPy's correlate function reveals old behaviour. 


Affine transform of threecomponent traces. 

Figure out what dependencies project() would produce. 

2D rotation of traces. 

Rotate traces from ZNE to LQT system. 

Rotate traces from NE to RT system. 

Check if two traces have the same sampling rate. 

Show traces in a snuffler window. 

Compute autoregression coefficients using YuleWalker method. 
Classes

Cosine Fader. 

Cosine Taper. 

Any 

Frequency domain Gaussian filter. 

Contains misfit setup to be used in 

Multiplication of several tapers. 

Utility to store channelspecific state in coroutines. 

Base class for tapers. 

Create new trace object. 
Exceptions
This exception is raised by some 

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

This exception is raised by 

This exception is raised by some 

This exception is raised by some 

This exception is raised by some 
 class Trace(network='', station='STA', location='', channel='', tmin=0.0, tmax=None, deltat=1.0, ydata=None, mtime=None, meta=None, extra='')[source]¶
Bases:
Object
Create new trace object.
A
Trace
object represents a single continuous strip of evenly sampled time series data. It is built from a 1D NumPy array containing the data samples and some attributes describing its beginning and ending time, its sampling rate and four string identifiers (its network, station, location and channel code). Parameters:
network – network code
station – station code
location – location code
channel – channel code
extra – extra code
tmin – system time of first sample in [s]
tmax – system time of last sample in [s] (if set to
None
it is computed from length ofydata
)deltat – sampling interval in [s]
ydata – 1D numpy array with data samples (can be
None
whentmax
is notNone
)mtime – optional modification time
meta – additional meta information (not used, but maintained by the library)
The length of the network, station, location and channel codes is not resricted by this software, but data formats like SAC, MiniSEED or GSE have different limits on the lengths of these codes. The codes set here are silently truncated when the trace is stored
 ♦ network¶
str
, default:''
Deployment/network code (18)
 ♦ station¶
str
, default:'STA'
Station code (15)
 ♦ location¶
str
, default:''
Location code (02)
 ♦ channel¶
str
, default:''
Channel code (3)
 ♦ extra¶
str
, default:''
Extra/custom code
 ♦ tmin¶
pyrocko.util.get_time_float (
pyrocko.guts.Timestamp
), default:str_to_time('19700101 00:00:00')
 ♦ tmax¶
pyrocko.util.get_time_float (
pyrocko.guts.Timestamp
)
 ♦ deltat¶
float
, default:1.0
 ♦ ydata¶
numpy.ndarray (
pyrocko.guts_array.Array
), optional
 ♦ mtime¶
pyrocko.util.get_time_float (
pyrocko.guts.Timestamp
), optional
 interpolate(t, clip=False)[source]¶
Value of trace between supporting points through linear interpolation.
 Parameters:
t – time instant
clip – whether to clip indices to trace ends
 add(other, interpolate=True, left=0.0, right=0.0)[source]¶
Add values of other trace (self += other).
Add values of
other
trace to the values ofself
, where it intersects withother
. This method does not change the extent ofself
. Ifinterpolate
isTrue
(the default), the values ofother
to be added are interpolated at sampling instants ofself
. Linear interpolation is performed. In this case the sampling rate ofother
must be equal to or lower than that ofself
. Ifinterpolate
isFalse
, the sampling rates of the two traces must match.
 mult(other, interpolate=True)[source]¶
Muliply with values of other trace
(self *= other)
.Multiply values of
other
trace to the values ofself
, where it intersects withother
. This method does not change the extent ofself
. Ifinterpolate
isTrue
(the default), the values ofother
to be multiplied are interpolated at sampling instants ofself
. Linear interpolation is performed. In this case the sampling rate ofother
must be equal to or lower than that ofself
. Ifinterpolate
isFalse
, the sampling rates of the two traces must match.
 set_codes(network=None, station=None, location=None, channel=None, extra=None)[source]¶
Set network, station, location, and channel codes.
 is_relevant(tmin, tmax, selector=None)[source]¶
Check if trace has overlap with a given time span and matches a condition callback. (internal use)
 append(data)[source]¶
Append data to the end of the trace.
To make this method efficient when successively very few or even single samples are appended, a larger grow buffer is allocated upon first invocation. The traces data is then changed to be a view into the currently filled portion of the grow buffer array.
 chop(tmin, tmax, inplace=True, include_last=False, snap=(<builtin function round>, <builtin function round>), want_incomplete=True)[source]¶
Cut the trace to given time span.
If the
inplace
argument is True (the default) the trace is cut in place, otherwise a new trace with the cut part is returned. By default, the indices where to start and end the trace data array are determined by rounding oftmin
andtmax
to sampling instances using Python’sround()
function. This behaviour can be changed with thesnap
argument, which takes a tuple of two functions (one for the lower and one for the upper end) to be used instead ofround()
. The last sample is by default not included unlessinclude_last
is set to True. If the given time span exceeds the available time span of the trace, the available part is returned, unlesswant_incomplete
is set to False  in that case, aNoData
exception is raised. This exception is always raised, when the requested time span does dot overlap with the trace’s time span.
 downsample(ndecimate, snap=False, demean=False, ftype='firremez', cut=False)[source]¶
Downsample (decimate) trace by a given integer factor.
Antialiasing filter details:
iir
: A Chebyshev type I digital filter of order 8 with maximum ripple of 0.05 dB in the passband.fir
: A FIR filter using a Hamming window and 31 taps and a wellbehaved phase response.firremez
: A FIR filter based on the Remez exchange algorithm with45*ndecimate
taps and a cutoff at 75% Nyquist frequency.
Comparison of the digital filters:
See also
Trace.downsample_to()
. Parameters:
ndecimate (int) – Decimation factor, avoid values larger than 8.
snap (bool) – Whether to put the new sampling instants closest to multiples of the sampling rate (according to absolute time).
demean (bool) – Whether to demean the signal before filtering.
ftype – Which FIR filter to use, choose from
'iir'
,'fir'
,'firremez'
. Default is'firremez'
.cut (bool) – Whether to cut off samples in the beginning of the trace which are polluted by artifacts of the antialiasing filter.
 downsample_to(deltat, snap=False, allow_upsample_max=1, demean=False, ftype='firremez', cut=False)[source]¶
Downsample to given sampling rate.
Tries to downsample the trace to a target sampling interval of
deltat
. This runsdownsample()
one or several times. Ifallow_upsample_max
is set to a value larger than 1, intermediate upsampling steps are allowed, in order to increase the number of possible downsampling ratios.If the requested ratio is not supported, an exception of type
pyrocko.util.UnavailableDecimation
is raised.The downsampled trace will be shorter than the input trace because the antialiasing filter introduces edge effects. If cut is selected, additionally, polluted samples in the beginning of the trace are removed. The approximate amount of cutoff which will be produced by a given downsampling configuration can be estimated with
downsample_tpad()
.See also:
Trace.downsample()
. Parameters:
deltat (float) – Desired sampling interval in [s].
allow_upsample_max (int) – Maximum allowed upsampling factor of the signal to achieve the desired sampling interval. Default is
1
.snap (bool) – Whether to put the new sampling instants closest to multiples of the sampling rate (according to absolute time).
demean (bool) – Whether to demean the signal before filtering.
ftype – Which FIR filter to use, choose from
'iir'
,'fir'
,'firremez'
. Default is'firremez'
.cut – Whether to cut off samples in the beginning of the trace which are polluted by artifacts of the antialiasing filter.
 resample(deltat)[source]¶
Resample to given sampling rate
deltat
.Resampling is performed in the frequency domain.
 stretch(tmin_new, tmax_new)[source]¶
Stretch signal while preserving sample rate using sinc interpolation.
 Parameters:
tmin_new – new time of first sample
tmax_new – new time of last sample
This method can be used to correct for a small linear time drift or to introduce subsample time shifts. The amount of stretching is limited to 10% by the implementation and is expected to be much smaller than that by the approximations used.
 nyquist_check(frequency, intro='Corner frequency', warn=True, raise_exception=False)[source]¶
Check if a given frequency is above the Nyquist frequency of the trace.
 Parameters:
intro – string used to introduce the warning/error message
warn – whether to emit a warning
raise_exception – whether to raise an
AboveNyquist
exception.
 lowpass(order, corner, nyquist_warn=True, nyquist_exception=False, demean=True)[source]¶
Apply Butterworth lowpass to the trace.
 Parameters:
order – order of the filter
corner – corner frequency of the filter
Mean is removed before filtering.
 highpass(order, corner, nyquist_warn=True, nyquist_exception=False, demean=True)[source]¶
Apply butterworth highpass to the trace.
 Parameters:
order – order of the filter
corner – corner frequency of the filter
Mean is removed before filtering.
 bandpass(order, corner_hp, corner_lp, demean=True)[source]¶
Apply butterworth bandpass to the trace.
 Parameters:
order – order of the filter
corner_hp – lower corner frequency of the filter
corner_lp – upper corner frequency of the filter
Mean is removed before filtering.
 bandstop(order, corner_hp, corner_lp, demean=True)[source]¶
Apply bandstop (attenuates frequencies in band) to the trace.
 Parameters:
order – order of the filter
corner_hp – lower corner frequency of the filter
corner_lp – upper corner frequency of the filter
Mean is removed before filtering.
 envelope(inplace=True)[source]¶
Calculate the envelope of the trace.
 Parameters:
inplace – calculate envelope in place
The calculation follows:
where H is the HilbertTransform of the signal Y.
 taper(taperer, inplace=True, chop=False)[source]¶
Apply a
Taper
to the trace. Parameters:
taperer – instance of
Taper
subclassinplace – apply taper inplace
chop – if
True
: exclude tapered parts from the resulting trace
 whiten(order=6)[source]¶
Whiten signal in time domain using autoregression and recursive filter.
 Parameters:
order – order of the autoregression process
 ampspec_whiten(width, td_taper='auto', fd_taper='auto', pad_to_pow2=True, demean=True)[source]¶
Whiten signal via frequency domain using moving average on amplitude spectra.
 Parameters:
width – width of smoothing kernel [Hz]
td_taper – time domain taper, object of type
Taper
orNone
or'auto'
.fd_taper – frequency domain taper, object of type
Taper
orNone
or'auto'
.pad_to_pow2 – whether to pad the signal with zeros up to a length of 2^n
demean – whether to demean the signal before tapering
The signal is first demeaned and then tapered using
td_taper
. Then, the spectrum is calculated and inversely weighted with a smoothed version of its amplitude spectrum. A moving average is used for the smoothing. The smoothed spectrum is then tapered usingfd_taper
. Finally, the smoothed and tapered spectrum is backtransformed into the time domain.If
td_taper
is set to'auto'
,CosFader(1.0/width)
is used. Iffd_taper
is set to'auto'
,CosFader(width)
is used.
 snap(inplace=True, interpolate=False)[source]¶
Shift trace samples to nearest even multiples of the sampling rate.
 Parameters:
inplace – (boolean) snap traces inplace
If
inplace
isFalse
and the difference of tmin and tmax of both, the snapped and the original trace is smaller than 0.01 x deltat,snap()
returns the unsnapped instance of the original trace.
 sta_lta_centered(tshort, tlong, quad=True, scalingmethod=1)[source]¶
Run special STA/LTA filter where the short time window is centered on the long time window.
 Parameters:
tshort – length of short time window in [s]
tlong – length of long time window in [s]
quad – whether to square the data prior to applying the STA/LTA filter
scalingmethod – integer key to select how output values are scaled / normalized (
1
,2
, or3
)
Scalingmethod
Implementation
Range
1
As/Al* Ts/Tl
[0,1]
2
(As/Al  1) / (Tl/Ts  1)
[Ts/Tl,1]
3
Like
2
but clipping range at zero[0,1]
 sta_lta_right(tshort, tlong, quad=True, scalingmethod=1)[source]¶
Run special STA/LTA filter where the short time window is overlapping with the last part of the long time window.
 Parameters:
tshort – length of short time window in [s]
tlong – length of long time window in [s]
quad – whether to square the data prior to applying the STA/LTA filter
scalingmethod – integer key to select how output values are scaled / normalized (
1
,2
, or3
)
Scalingmethod
Implementation
Range
1
As/Al* Ts/Tl
[0,1]
2
(As/Al  1) / (Tl/Ts  1)
[Ts/Tl,1]
3
Like
2
but clipping range at zero[0,1]
With
scalingmethod=1
, the values produced by this variant of the STA/LTA are equivalent towhere are the input samples, are the number of samples in the short time window and are the number of samples in the long time window.
 peaks(threshold, tsearch, deadtime=False, nblock_duration_detection=100)[source]¶
Detect peaks above a given threshold (method 1).
From every instant, where the signal rises above
threshold
, a time length oftsearch
seconds is searched for a maximum. A list with tuples (time, value) for each detected peak is returned. Thedeadtime
argument turns on a special deadtime duration detection algorithm useful in combination with recursive STA/LTA filters.
 peaks2(threshold, tsearch)[source]¶
Detect peaks above a given threshold (method 2).
This variant of peak detection is a bit more robust (and slower) than the one implemented in
Trace.peaks()
. First all samples witha[i1] < a[i] > a[i+1]
are masked as potential peaks. From these, iteratively the one with the maximum amplitudea[j]
and timet[j]
is choosen and potential peaks withint[j]  tsearch, t[j] + tsearch
are discarded. The algorithm stops, whena[j] < threshold
or when no more potential peaks are left.
 extend(tmin=None, tmax=None, fillmethod='zeros')[source]¶
Extend trace to given span.
 Parameters:
tmin – begin time of new span
tmax – end time of new span
fillmethod –
'zeros'
,'repeat'
,'mean'
, or'median'
 transfer(tfade=0.0, freqlimits=None, transfer_function=None, cut_off_fading=True, demean=True, invert=False)[source]¶
Return new trace with transfer function applied (convolution).
 Parameters:
tfade – rise/fall time in seconds of taper applied in timedomain at both ends of trace.
freqlimits – 4tuple with corner frequencies in Hz.
transfer_function – FrequencyResponse object; must provide a method ‘evaluate(freqs)’, which returns the transfer function coefficients at the frequencies ‘freqs’.
cut_off_fading – whether to cut off rise/fall interval in output trace.
demean – remove mean before applying transfer function
invert – set to True to do a deconvolution
 differentiate(n=1, order=4, inplace=True)[source]¶
Approximate first or second derivative of the trace.
 Parameters:
n – 1 for first derivative, 2 for second
order – order of the approximation 2 and 4 are supported
inplace – if
True
the trace is differentiated in place, otherwise a new trace object with the derivative is returned.
Raises
ValueError
for unsupported n or order.See
diff_fd()
for implementation details.
 misfit(candidate, setup, nocache=False, debug=False)[source]¶
Calculate misfit and normalization factor against candidate trace.
 Parameters:
candidate –
Trace
objectsetup –
MisfitSetup
object
 Returns:
tuple
(m, n)
, where m is the misfit value and n is the normalization divisor
If the sampling rates of
self
andcandidate
differ, the trace with the higher sampling rate will be downsampled.
 spectrum(pad_to_pow2=False, tfade=None)[source]¶
Get FFT spectrum of trace.
 Parameters:
pad_to_pow2 – whether to zeropad the data to next larger poweroftwo length
tfade –
None
or a time length in seconds, to apply cosine shaped tapers to both
 Returns:
a tuple with (frequencies, values)
 fill_template(template, **additional)[source]¶
Fill string template with trace metadata.
Uses normal python ‘%(placeholder)s’ string templates. The following placeholders are considered:
network
,station
,location
,channel
,tmin
(time of first sample),tmax
(time of last sample),tmin_ms
,tmax_ms
,tmin_us
,tmax_us
,tmin_year
,tmax_year
,tmin_month
,tmax_month
,tmin_day
,tmax_day
,julianday
. The variants ending with'_ms'
include milliseconds, those with'_us'
include microseconds, those with'_year'
contain only the year.
 plot()[source]¶
Show trace with matplotlib.
See also:
Trace.snuffle()
.
 snuffle(**kwargs)[source]¶
Show trace in a snuffler window.
 Parameters:
stations – list of
pyrocko.model.station.Station
objects orNone
events – list of
pyrocko.model.event.Event
objects orNone
markers – list of
pyrocko.gui.snuffler.marker.Marker
objects orNone
ntracks – float, number of tracks to be shown initially (default: 12)
follow – time interval (in seconds) for real time follow mode or
None
controls – bool, whether to show the main controls (default:
True
)opengl – bool, whether to use opengl (default:
False
)
 snuffle(traces, **kwargs)[source]¶
Show traces in a snuffler window.
 Parameters:
stations – list of
pyrocko.model.station.Station
objects orNone
events – list of
pyrocko.model.event.Event
objects orNone
markers – list of
pyrocko.gui.snuffler.marker.Marker
objects orNone
ntracks – int, number of tracks to be shown initially (default: 12)
follow – time interval (in seconds) for real time follow mode or
None
controls – bool, whether to show the main controls (default:
True
)opengl – bool, whether to use opengl (default:
False
)
 downsample_tpad(deltat_in, deltat_out, allow_upsample_max=1, ftype='firremez')[source]¶
Get approximate amount of cutoff which will be produced by downsampling.
The
Trace.downsample_to()
method removes some samples at the beginning and end of the trace which is downsampled. This function estimates the approximate length [s] which will be cut off for a given set of parameters supplied toTrace.downsample_to()
. Parameters:
 Returns:
Approximate length [s] which will be cut off.
See
Trace.downsample_to()
for details.
 get_traces_data_as_array(traces)[source]¶
Merge data samples from multiple traces into a 2D array.
 Parameters:
traces (list of
pyrocko.Trace
objects) – Input waveforms. Raises:
IncompatibleTraces
if traces have different time span, sample rate or data type, or if traces is an empty list. Returns:
2D array as
data[itrace, isample]
. Return type:
 exception IncompatibleTraces[source]¶
Bases:
Exception
Raised when traces have incompatible sampling rate, time span or data type.
 exception InfiniteResponse[source]¶
Bases:
Exception
This exception is raised by
Trace
operations when deconvolution of a frequency response (instrument response transfer function) would result in a division by zero.
 exception MisalignedTraces[source]¶
Bases:
Exception
This exception is raised by some
Trace
operations when tmin, tmax or number of samples do not match.
 exception NoData[source]¶
Bases:
Exception
This exception is raised by some
Trace
operations when no or not enough data is available.
 exception AboveNyquist[source]¶
Bases:
Exception
This exception is raised by some
Trace
operations when given frequencies are above the Nyquist frequency.
 exception TraceTooShort[source]¶
Bases:
Exception
This exception is raised by some
Trace
operations when the trace is too short.
 minmax(traces, key=None, mode='minmax', outer_mode='minmax')[source]¶
Get data range given traces grouped by selected pattern.
 Parameters:
key – a callable which takes as single argument a trace and returns a key for the grouping of the results. If this is
None
, the default,lambda tr: (tr.network, tr.station, tr.location, tr.channel)
is used.mode –
'minmax'
or floating point number. If this is'minmax'
, minimum and maximum of the traces are used, if it is a number, mean + standard deviation timesmode
is used.
 param outer_mode:
'minmax'
to use mininum and maximum of the singletrace ranges, or
'robust'
to use the interval to discard 10% extreme values on either end.
 Returns:
a dict with the combined data ranges.
Examples:
ranges = minmax(traces, lambda tr: tr.channel) print ranges['N'] # print min & max of all traces with channel == 'N' print ranges['E'] # print min & max of all traces with channel == 'E' ranges = minmax(traces, lambda tr: (tr.network, tr.station)) print ranges['GR', 'HAM3'] # print min & max of all traces with # network == 'GR' and station == 'HAM3' ranges = minmax(traces, lambda tr: None) print ranges[None] # prints min & max of all traces
 minmaxtime(traces, key=None)[source]¶
Get time range given traces grouped by selected pattern.
 Parameters:
key – a callable which takes as single argument a trace and returns a key for the grouping of the results. If this is
None
, the default,lambda tr: (tr.network, tr.station, tr.location, tr.channel)
is used. Returns:
a dict with the combined data ranges.
 degapper(traces, maxgap=5, fillmethod='interpolate', deoverlap='use_second', maxlap=None)[source]¶
Try to connect traces and remove gaps.
This method will combine adjacent traces, which match in their network, station, location and channel attributes. Overlapping parts are handled according to the
deoverlap
argument. Parameters:
traces – input traces, must be sorted by their full_id attribute.
maxgap – maximum number of samples to interpolate.
fillmethod – what to put into the gaps: ‘interpolate’ or ‘zeros’.
deoverlap – how to handle overlaps: ‘use_second’ to use data from second trace (default), ‘use_first’ to use data from first trace, ‘crossfade_cos’ to crossfade with cosine taper, ‘add’ to add amplitude values.
maxlap – maximum number of samples of overlap which are removed
 Returns:
list of traces
 rotate(traces, azimuth, in_channels, out_channels)[source]¶
2D rotation of traces.
 Parameters:
traces – list of input traces
azimuth – difference of the azimuths of the component directions (azimuth of out_channels[0])  (azimuth of in_channels[0])
in_channels – names of the input channels (e.g. ‘N’, ‘E’)
out_channels – names of the output channels (e.g. ‘R’, ‘T’)
 Returns:
list of rotated traces
 rotate_to_rt(n, e, source, receiver, out_channels=('R', 'T'))[source]¶
Rotate traces from NE to RT system.
 Parameters:
n (
Trace
) – North trace.e (
Trace
) – East trace.source (
pyrocko.gf.seismosizer.Source
) – Source of the recorded signal.receiver (
pyrocko.model.location.Location
) – Receiver of the recorded signal.out_channels – Channel codes of the output channels (radial, transversal). Default is (‘R’, ‘T’).
 :type out_channels
optional, tuple[str, str]
 rotate_to_lqt(traces, backazimuth, incidence, in_channels, out_channels=('L', 'Q', 'T'))[source]¶
Rotate traces from ZNE to LQT system.
 Parameters:
traces – list of traces in arbitrary order
backazimuth – backazimuth in degrees clockwise from north
incidence – incidence angle in degrees from vertical
in_channels – input channel names
out_channels – output channel names (default: (‘L’, ‘Q’, ‘T’))
 Returns:
list of transformed traces
 project(traces, matrix, in_channels, out_channels)[source]¶
Affine transform of threecomponent traces.
Compute matrixvector product of threecomponent traces, to e.g. rotate traces into a different basis. The traces are distinguished and ordered by their channel attribute. The tranform is applied to overlapping parts of any appropriate combinations of the input traces. This should allow this function to be robust with data gaps. It also tries to apply the tranformation to subsets of the channels, if this is possible, so that, if for example a vertical compontent is missing, horizontal components can still be rotated.
 Parameters:
traces – list of traces in arbitrary order
matrix – tranformation matrix
in_channels – input channel names
out_channels – output channel names
 Returns:
list of transformed traces
 project_dependencies(matrix, in_channels, out_channels)[source]¶
Figure out what dependencies project() would produce.
 correlate(a, b, mode='valid', normalization=None, use_fft=False)[source]¶
Cross correlation of two traces.
 Parameters:
a,b – input traces
mode –
'valid'
,'full'
, or'same'
normalization –
'normal'
,'gliding'
, orNone
use_fft – bool, whether to do cross correlation in spectral domain
 Returns:
trace containing cross correlation coefficients
This function computes the cross correlation between two traces. It evaluates the discrete equivalent of
where the star denotes complex conjugate. Note, that the arguments here are swapped when compared with the
numpy.correlate()
function, which is internally called. This function should be safe even with older versions of NumPy, where the correlate function has some problems.A trace containing the cross correlation coefficients is returned. The time information of the output trace is set so that the returned cross correlation can be viewed directly as a function of time lag.
Example:
# align two traces a and b containing a time shifted similar signal: c = pyrocko.trace.correlate(a,b) t, coef = c.max() # get time and value of maximum b.shift(t) # align b with a
 same_sampling_rate(a, b, eps=1e06)[source]¶
Check if two traces have the same sampling rate.
 Parameters:
a,b – input traces
eps – relative tolerance
 fix_deltat_rounding_errors(deltat)[source]¶
Try to undo sampling rate rounding errors.
Fix rounding errors of sampling intervals when these are read from single precision floating point values.
Assumes that the true sampling rate or sampling interval was an integer value. No correction will be applied if this would change the sampling rate by more than 0.001%.
 merge_codes(a, b, sep='')[source]¶
Merge networkstationlocationchannel codes of a pair of traces.
 class CosTaper(a, b, c, d)[source]¶
Bases:
Taper
Cosine Taper.
 Parameters:
a – start of fading in
b – end of fading in
c – start of fading out
d – end of fading out
 ♦ a¶
float
 ♦ b¶
float
 ♦ c¶
float
 ♦ d¶
float
 class CosFader(xfade=None, xfrac=None)[source]¶
Bases:
Taper
Cosine Fader.
 Parameters:
xfade – fade in and fade out time in seconds (optional)
xfrac – fade in and fade out as fraction between 0. and 1. (optional)
Only one argument can be set. The other should to be
None
. ♦ xfade¶
float
, optional
 ♦ xfrac¶
float
, optional
 numpy_correlate_fixed(a, b, mode='valid', use_fft=False)[source]¶
Call
numpy.correlate()
with fixes.c[k] = sum_i a[i+k] * conj(b[i])
Note that the result produced by newer numpy.correlate is always flipped with respect to the formula given in its documentation (if ascending k assumed for the output).
 numpy_correlate_emulate(a, b, mode='valid')[source]¶
Slow version of
numpy.correlate()
for comparison.
 numpy_correlate_lag_range(a, b, mode='valid', use_fft=False)[source]¶
Get range of lags for which
numpy.correlate()
produces values.
 autocorr(x, nshifts)[source]¶
Compute biased estimate of the first autocorrelation coefficients.
 Parameters:
x – input array
nshifts – number of coefficients to calculate
 yulewalker(x, order)[source]¶
Compute autoregression coefficients using YuleWalker method.
 Parameters:
x – input array
order – number of coefficients to produce
A biased estimate of the autocorrelation is used. The YuleWalker equations are solved by
numpy.linalg.inv()
instead of LevinsonDurbin recursion which is normally used.
 hilbert(x, N=None)[source]¶
Return the hilbert transform of x of length N.
(from scipy.signal, but changed to use fft and ifft from numpy.fft)
 co_lfilter(*args, **kwargs)[source]¶
Successively filter broken continuous trace data (coroutine).
Create coroutine which takes
Trace
objects, filters their data throughscipy.signal.lfilter()
and sends newTrace
objects containing the filtered data to target. This is useful, if one wants to filter a long continuous time series, which is split into many successive traces without producing filter artifacts at trace boundaries.Filter states are kept per channel, specifically, for each (network, station, location, channel) combination occuring in the input traces, a separate state is created and maintained. This makes it possible to filter multichannel or multistation data with only one
co_lfilter()
instance.Filter state is reset, when gaps occur.
Use it like this:
from pyrocko.trace import co_lfilter, co_list_append filtered_traces = [] pipe = co_lfilter(co_list_append(filtered_traces), a, b) for trace in traces: pipe.send(trace) pipe.close()
 co_downsample(target, q, n=None, ftype='fir')[source]¶
Successively downsample broken continuous trace data (coroutine).
Create coroutine which takes
Trace
objects, downsamples their data and sends newTrace
objects containing the downsampled data to target. This is useful, if one wants to downsample a long continuous time series, which is split into many successive traces without producing filter artifacts and gaps at trace boundaries.Filter states are kept per channel, specifically, for each (network, station, location, channel) combination occuring in the input traces, a separate state is created and maintained. This makes it possible to filter multichannel or multistation data with only one
co_lfilter()
instance.Filter state is reset, when gaps occur. The sampling instances are choosen so that they occur at (or as close as possible) to even multiples of the sampling interval of the downsampled trace (based on system time).
 class DomainChoice(...) str [source]¶
Bases:
StringChoice
Any
str
out of['time_domain', 'frequency_domain', 'envelope', 'absolute', 'cc_max_norm']
.
 class MisfitSetup(**kwargs)[source]¶
Bases:
Object
Contains misfit setup to be used in
Trace.misfit()
 Parameters:
description – Description of the setup
norm – Lnorm classifier
taper – Object of
Taper
filter – Object of
FrequencyResponse
domain – [‘time_domain’, ‘frequency_domain’, ‘envelope’, ‘absolute’, ‘cc_max_norm’]
Can be dumped to a yaml file.
 ♦ description¶
str
, optional
 ♦ norm¶
int
 ♦ filter¶
pyrocko.response.FrequencyResponse
, optional
 ♦ domain¶
str
(DomainChoice
), default:'time_domain'
 equalize_sampling_rates(trace_1, trace_2)[source]¶
Equalize sampling rates of two traces (reduce higher sampling rate to lower).
Returns a copy of the resampled trace if resampling is needed.
 Lx_norm(u, v, norm=2)[source]¶
Calculate the misfit denominator m and the normalization divisor n according to norm.
The normalization divisor n is calculated from
v
. Parameters:
u –
numpy.ndarray
v –
numpy.ndarray
norm – (default = 2)
u
andv
must be of same size.