Source code for stacking

"""
Utility module of the EQcorrscan package to allow for different methods of
stacking of seismic signal in one place.

Calum Chamberlain 24/06/2015

Copyright 2015 Calum Chamberlain

This file is part of EQcorrscan.

    EQcorrscan is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    EQcorrscan is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with EQcorrscan.  If not, see <http://www.gnu.org/licenses/>.

"""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from __future__ import unicode_literals
import numpy as np


[docs]def linstack(streams): """ Function to compute the linear stack of a series of seismic streams of \ multiplexed data. :type streams: list of Streams :param stream: List of streams to stack :returns: stack - Stream """ # import matplotlib.pyplot as plt stack = streams[np.argmax([len(stream) for stream in streams])].copy() for tr in stack: tr.data = tr.data / np.sqrt(np.mean(np.square(tr.data))) tr.data = np.nan_to_num(tr.data) for i in range(1, len(streams)): # print("Stacking stream "+str(i)) for tr in stack: # print(tr.stats.station+'.'+tr.stats.channel) matchtr = streams[i].select(station=tr.stats.station, channel=tr.stats.channel) if matchtr: # Normalize the data before stacking norm = matchtr[0].data /\ np.sqrt(np.mean(np.square(matchtr[0].data))) norm = np.nan_to_num(norm) tr.data = np.sum((norm, tr.data), axis=0) return stack
[docs]def PWS_stack(streams, weight=2): """ Function to compute the phase weighted stack of a series of streams. Recommend aligning the traces before stacking. :type streams: list of obspy.Stream :param streams: List of Stream to stack :type weight: float :param weight: Exponent to the phase stack used for weighting. :return: obspy.Stream """ from scipy.signal import hilbert # First get the linear stack which we will weight by the phase stack Linstack = linstack(streams) # Compute the instantaneous phase instaphases = [] print("Computing instantaneous phase") for stream in streams: instaphase = stream.copy() for tr in instaphase: analytic = hilbert(tr.data) envelope = np.sqrt(np.sum((np.square(analytic), np.square(tr.data)), axis=0)) tr.data = analytic / envelope instaphases.append(instaphase) # Compute the phase stack print("Computing the phase stack") Phasestack = linstack(instaphases) # print(type(Phasestack)) # Compute the phase-weighted stack for tr in Phasestack: tr.data = Linstack.select(station=tr.stats.station)[0].data *\ np.abs(tr.data ** weight) return Phasestack
[docs]def align_traces(trace_list, shift_len, master=False): """ Function to allign traces relative to each other based on their \ cross-correlation value. :type trace_list: list of Traces :param trace_list: List of traces to allign :type shift_len: int :param shift_len: Length to allow shifting within in samples :type master: obspy.Trace :param master: Master trace to align to, if set to False will align to \ the largest amplitude trace (default) :returns: list of shifts for best allignment in seconds """ from obspy.signal.cross_correlation import xcorr from copy import deepcopy traces = deepcopy(trace_list) if not master: # Use trace with largest MAD amplitude as master master = traces[0] MAD_master = np.median(np.abs(master.data)) for i in range(1, len(traces)): if np.median(np.abs(traces[i])) > MAD_master: master = traces[i] MAD_master = np.median(np.abs(master.data)) else: print('Using master given by user') shifts = [] ccs = [] for i in range(len(traces)): if not master.stats.sampling_rate == traces[i].stats.sampling_rate: raise ValueError('Sampling rates not the same') shift, cc = xcorr(master, traces[i], shift_len) shifts.append(shift / master.stats.sampling_rate) ccs.append(cc) return shifts, ccs
if __name__ == "__main__": import doctest doctest.testmod()