trace
¶
This module provides basic signal processing for seismic traces.

class
Trace
(network='', station='STA', location='', channel='', tmin=0.0, tmax=None, deltat=1.0, ydata=None, mtime=None, meta=None)[source]¶ 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
 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:''

♦
station
¶ str
, default:'STA'

♦
location
¶ str
, default:''

♦
channel
¶ str
, default:''

♦
tmin
¶ builtins.float
(pyrocko.guts.Timestamp
), default:0.0

♦
tmax
¶ builtins.float
(pyrocko.guts.Timestamp
)

♦
deltat
¶ float
, default:1.0

♦
ydata
¶ numpy.ndarray
(pyrocko.guts_array.Array
), optional

♦
mtime
¶ builtins.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)[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, initials=None, demean=False)[source]¶ Downsample trace by a given integer factor.
Parameters:  ndecimate – decimation factor, avoid values larger than 8
 snap – whether to put the new sampling instances closest to multiples of the sampling rate.
 initials –
None
,True
, or initial conditions for the antialiasing filter, obtained from a previous run. In the latter two cases the final state of the filter is returned instead ofNone
.  demean – whether to demean the signal before filtering.

downsample_to
(deltat, snap=False, allow_upsample_max=1, initials=None, demean=False)[source]¶ Downsample to given sampling rate.
Tries to downsample the trace to a target sampling interval of
deltat
. This runs theTrace.downsample()
one or several times. If allow_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.

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
subclass  inplace – apply taper inplace
 chop – if
True
: exclude tapered parts from the resulting trace
 taperer – instance of

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* Tl/Ts [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* Tl/Ts [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
object  setup –
MisfitSetup
object
Returns: tuple
(m, n)
, where m is the misfit value and n is the normalization divisorIf the sampling rates of
self
andcandidate
differ, the trace with the higher sampling rate will be downsampled. candidate –

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
,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 objects or
None
 events – list of pyrocko.model.Event objects or
None
 markers – list of pyrocko.gui.util.Marker objects or
None
 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
)
 stations – list of pyrocko.model.Station objects or

snuffle
(traces, **kwargs)[source]¶ Show traces in a snuffler window.
Parameters:  stations – list of pyrocko.model.Station objects or
None
 events – list of pyrocko.model.Event objects or
None
 markers – list of pyrocko.gui.util.Marker objects or
None
 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
)
 stations – list of pyrocko.model.Station objects or

exception
InfiniteResponse
[source]¶ 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]¶ This exception is raised by some
Trace
operations when tmin, tmax or number of samples do not match.

exception
NoData
[source]¶ This exception is raised by some
Trace
operations when no or not enough data is available.

exception
AboveNyquist
[source]¶ This exception is raised by some
Trace
operations when given frequencies are above the Nyquist frequency.

exception
TraceTooShort
[source]¶ This exception is raised by some
Trace
operations when the trace is too short.

minmax
(traces, key=None, 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 times
mode
is used.
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
 key – a callable which takes as single argument a trace and returns a
key for the grouping of the results. If this is

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_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]¶ 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]¶ 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

class
Evalresp
(respfile, trace=None, target='dis', nslc_id=None, time=None)[source]¶ Calls evalresp and generates values of the instrument response transfer function.
Parameters:  respfile – response file in evalresp format
 trace – trace for which the response is to be extracted from the file
 target –
'dis'
for displacement or'vel'
for velocity

♦
respfile
¶ str

♦
nslc_id
¶ tuple
of 4str
objects, default:(None, None, None, None)

♦
target
¶ str
, default:'dis'

♦
instant
¶ float

class
InverseEvalresp
(respfile, trace, target='dis')[source]¶ Calls evalresp and generates values of the inverse instrument response for deconvolution of instrument response.
Parameters:  respfile – response file in evalresp format
 trace – trace for which the response is to be extracted from the file
 target –
'dis'
for displacement or'vel'
for velocity

♦
respfile
¶ str

♦
nslc_id
¶ tuple
of 4str
objects, default:(None, None, None, None)

♦
target
¶ str
, default:'dis'

♦
instant
¶ float

class
PoleZeroResponse
(zeros=None, poles=None, constant=(1+0j))[source]¶ Evaluates frequency response from polezero representation.
Parameters:  zeros –
numpy.array
containing complex positions of zeros  poles –
numpy.array
containing complex positions of poles  constant – gain as floating point number
(j*2*pi*f  zeros[0]) * (j*2*pi*f  zeros[1]) * ... T(f) = constant *  (j*2*pi*f  poles[0]) * (j*2*pi*f  poles[1]) * ...
The poles and zeros should be given as angular frequencies, not in Hz.

♦
zeros
¶ list
ofcomplex
objects, default:[]

♦
poles
¶ list
ofcomplex
objects, default:[]

♦
constant
¶ complex
, default:(1+0j)
 zeros –

class
ButterworthResponse
(**kwargs)[source]¶ Butterworth frequency response.
Parameters:  corner – corner frequency of the response
 order – order of the response
 type – either
high
orlow

♦
corner
¶ float
, default:1.0

♦
order
¶ int
, default:4

♦
type
¶ builtins.str
(pyrocko.guts.StringChoice
), default:'low'

class
SampledResponse
(frequencies, values, left=None, right=None)[source]¶ Interpolates frequency response given at a set of sampled frequencies.
Parameters:  frequencies,values – frequencies and values of the sampled response function.
 left,right – values to return when input is out of range. If set to
None
(the default) the endpoints are returned.

♦
frequencies
¶ numpy.ndarray
(pyrocko.guts_array.Array
)

♦
values
¶ numpy.ndarray
(pyrocko.guts_array.Array
)

♦
left
¶ complex
, optional

♦
right
¶ complex
, optional

inverse
()[source]¶ Get inverse as a new
SampledResponse
object.

class
IntegrationResponse
(n=1, gain=1.0)[source]¶ The integration response, optionally multiplied by a constant gain.
Parameters:  n – exponent (integer)
 gain – gain factor (float)
gain T(f) =  (j*2*pi * f)^n

♦
n
¶ int
, optional, default:1

♦
gain
¶ float
, optional, default:1.0

class
DifferentiationResponse
(n=1, gain=1.0)[source]¶ The differentiation response, optionally multiplied by a constant gain.
Parameters:  n – exponent (integer)
 gain – gain factor (float)
T(f) = gain * (j*2*pi * f)^n

♦
n
¶ int
, optional, default:1

♦
gain
¶ float
, optional, default:1.0

class
AnalogFilterResponse
(b, a)[source]¶ Frequency response of an analog filter.
(see
scipy.signal.freqs()
).
♦
b
¶ list
offloat
objects, default:[]

♦
a
¶ list
offloat
objects, default:[]

♦

class
MultiplyResponse
(responses=None)[source]¶ Multiplication of several
FrequencyResponse
objects.
♦
responses
¶ list
ofFrequencyResponse
objects, default:[]

♦

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
(dummy) → str[source]¶ Any
str
out of['time_domain', 'frequency_domain', 'envelope', 'absolute', 'cc_max_norm']
.

class
MisfitSetup
(**kwargs)[source]¶ 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
¶ FrequencyResponse
, optional

♦
domain
¶ builtins.str
(DomainChoice
), default:'time_domain'