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pyaftan.py
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# -*- coding: utf-8 -*-
"""
A python module for aftan (Automatic Frequency-Time ANalysis) analysis
This module include two major functions:
1. aftan written in pure python
2. a python wrapper for fortran77 version of aftan
:Dependencies:
numpy >=1.9.1
scipy >=0.18.0
matplotlib >=1.4.3
ObsPy >=1.0.1
pyfftw 0.10.3 (optional)
:Copyright:
Author: Lili Feng
Graduate Research Assistant
CIEI, Department of Physics, University of Colorado Boulder
email: [email protected]
:References:
Levshin, A. L., and M. H. Ritzwoller. Automated detection, extraction, and measurement of regional surface waves.
Monitoring the Comprehensive Nuclear-Test-Ban Treaty: Surface Waves. Birkh?user Basel, 2001. 1531-1545.
Bensen, G. D., et al. Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements.
Geophysical Journal International 169.3 (2007): 1239-1260.
"""
import obspy
import numpy as np
import scipy.interpolate
import matplotlib.pyplot as plt
# import matplotlib.pylab as plb
import os
import warnings
from scipy.signal import argrelmax, argrelmin, argrelextrema
import scipy.interpolate
try:
import pyfftw
useFFTW=True
except:
useFFTW=False
try:
import aftan
isaftanf77=True
except:
isaftanf77=False
def _aftan_gaussian_filter(alpha, omega0, ns, indata, omsArr):
"""Internal Gaussian filter function used for aftan
"""
om2 = -(omsArr-omega0)*(omsArr-omega0)*alpha/omega0/omega0
b = np.exp(om2)
b[np.abs(om2)>=40.] = 0.
filterred_data = indata*b
filterred_data[ns/2:] = 0
filterred_data[0] /= 2
filterred_data[ns/2-1] = filterred_data[ns/2-1].real+0.j
return filterred_data
class ftanParam(object):
""" An object to handle ftan output parameters
===========================================================================
Basic FTAN parameters:
nfout1_1 - output number of frequencies for arr1, (integer*4)
arr1_1 - preliminary results.
Description: real*8 arr1(8,n), n >= nfin)
arr1_1[0,:] - central periods, s
arr1_1[1,:] - observed periods, s
arr1_1[2,:] - group velocities, km/s
arr1_1[3,:] - phase velocities, km/s or phase if nphpr=0, rad
arr1_1[4,:] - amplitudes, Db
arr1_1[5,:] - discrimination function
arr1_1[6,:] - signal/noise ratio, Db
arr1_1[7,:] - maximum half width, s
arr1_1[8,:] - amplitudes
arr2_1 - final results with jump detection
nfout2_1 - output number of frequencies for arr2, (integer*4)
Description: real*8 arr2(7,n), n >= nfin)
If nfout2 == 0, no final result.
arr2_1[0,:] - central periods, s
arr2_1[1,:] - observed periods, s
arr2_1[2,:] - group velocities, km/sor phase if nphpr=0, rad
arr2_1[3,:] - phase velocities, km/s
arr2_1[4,:] - amplitudes, Db
arr2_1[5,:] - signal/noise ratio, Db
arr2_1[6,:] - maximum half width, s
arr2_1[7,:] - amplitudes
tamp_1 - time to the beginning of ampo table, s (real*8)
nrow_1 - number of rows in array ampo, (integer*4)
ncol_1 - number of columns in array ampo, (integer*4)
amp_1 - Ftan amplitude array, Db, (real*8)
ierr_1 - completion status, =0 - O.K., (integer*4)
=1 - some problems occures
=2 - no final results
----------------------------------------------------------------------------
Phase-Matched-Filtered FTAN parameters:
nfout1_2 - output number of frequencies for arr1, (integer*4)
arr1_2 - preliminary results.
Description: real*8 arr1(8,n), n >= nfin)
arr1_2[0,:] - central periods, s (real*8)
arr1_2[1,:] - apparent periods, s (real*8)
arr1_2[2,:] - group velocities, km/s (real*8)
arr1_2[3,:] - phase velocities, km/s (real*8)
arr1_2[4,:] - amplitudes, Db (real*8)
arr1_2[5,:] - discrimination function, (real*8)
arr1_2[6,:] - signal/noise ratio, Db (real*8)
arr1_2[7,:] - maximum half width, s (real*8)
arr1_2[8,:] - amplitudes
arr2_2 - final results with jump detection
nfout2_2 - output number of frequencies for arr2, (integer*4)
Description: real*8 arr2(7,n), n >= nfin)
If nfout2 == 0, no final results.
arr2_2[0,:] - central periods, s (real*8)
arr2_2[1,:] - apparent periods, s (real*8)
arr2_2[2,:] - group velocities, km/s (real*8)
arr2_2[3,:] - phase velocities, km/s (real*8)
arr2_2[4,:] - amplitudes, Db (real*8)
arr2_2[5,:] - signal/noise ratio, Db (real*8)
arr2_2[6,:] - maximum half width, s (real*8)
arr2_2[7,:] - amplitudes
arr2_2[8,:] - signal/noise ratio (optional)
tamp_2 - time to the beginning of ampo table, s (real*8)
nrow_2 - number of rows in array ampo, (integer*4)
ncol_2 - number of columns in array ampo, (integer*4)
amp_2 - Ftan amplitude array, Db, (real*8)
ierr_2 - completion status, =0 - O.K., (integer*4)
=1 - some problems occures
=2 - no final results
===========================================================================
"""
def __init__(self):
# Parameters for first iteration
self.nfout1_1 = 0
self.arr1_1 = np.array([])
self.nfout2_1 = 0
self.arr2_1 = np.array([])
self.tamp_1 = 0.
self.nrow_1 = 0
self.ncol_1 = 0
self.ampo_1 = np.array([],dtype='float32')
self.ierr_1 = 0
# Parameters for second iteration
self.nfout1_2 = 0
self.arr1_2 = np.array([])
self.nfout2_2 = 0
self.arr2_2 = np.array([])
self.tamp_2 = 0.
self.nrow_2 = 0
self.ncol_2 = 0
self.ampo_2 = np.array([])
self.ierr_2 = 0
# Flag for existence of predicted phase dispersion curve
self.preflag = False
self.station_id = None
def writeDISP(self, fnamePR):
"""
Write FTAN parameters to DISP files given a prefix.
fnamePR: file name prefix
_1_DISP.0: arr1_1
_1_DISP.1: arr2_1
_2_DISP.0: arr1_2
_2_DISP.1: arr2_2
"""
if self.nfout1_1 != 0:
f10 = fnamePR+'_1_DISP.0'
Lf10 = self.nfout1_1
outArrf10 = np.arange(Lf10)
for i in xrange(9): outArrf10 = np.append(outArrf10, self.arr1_1[i,:Lf10])
outArrf10 = outArrf10.reshape((10,Lf10))
outArrf10 = outArrf10.T
np.savetxt(f10, outArrf10, fmt='%4d %10.4lf %10.4lf %12.4lf %12.4lf %12.4lf %12.4lf %8.3lf %12.4lf %12.4lf')
if self.nfout2_1 != 0:
f11 = fnamePR+'_1_DISP.1'
Lf11 = self.nfout2_1
outArrf11 = np.arange(Lf11)
for i in xrange(8): outArrf11 = np.append(outArrf11, self.arr2_1[i,:Lf11])
outArrf11 = outArrf11.reshape((9,Lf11))
outArrf11 = outArrf11.T
np.savetxt(f11, outArrf11, fmt='%4d %10.4lf %10.4lf %12.4lf %12.4lf %12.4lf %8.3lf %12.4lf %12.4lf')
if self.nfout1_2 != 0:
f20 = fnamePR+'_2_DISP.0'
Lf20 = self.nfout1_2
outArrf20 = np.arange(Lf20)
for i in xrange(9):
outArrf20=np.append(outArrf20, self.arr1_2[i,:Lf20])
outArrf20=outArrf20.reshape((10,Lf20))
outArrf20=outArrf20.T
np.savetxt(f20, outArrf20, fmt='%4d %10.4lf %10.4lf %12.4lf %12.4lf %12.4lf %12.4lf %8.3lf %12.4lf %12.4lf')
if self.nfout2_2 != 0:
f21 = fnamePR+'_2_DISP.1'
Lf21 = self.nfout2_2
outArrf21 = np.arange(Lf21)
for i in xrange(9): outArrf21 = np.append(outArrf21, self.arr2_2[i,:Lf21])
outArrf21 = outArrf21.reshape((10,Lf21))
outArrf21 = outArrf21.T
np.savetxt(f21, outArrf21, fmt='%4d %10.4lf %10.4lf %12.4lf %12.4lf %12.4lf %12.4lf %8.3lf %12.4lf %12.4lf')
return
def writeDISPbinary(self, fnamePR):
"""
Write FTAN parameters to DISP files given a prefix.
fnamePR: file name prefix
_1_DISP.0: arr1_1
_1_DISP.1: arr2_1
_2_DISP.0: arr1_2
_2_DISP.1: arr2_2
"""
f10 = fnamePR+'_1_DISP.0'
np.savez(f10, self.arr1_1, np.array([self.nfout1_1]) )
f11 = fnamePR+'_1_DISP.1'
np.savez(f11, self.arr2_1, np.array([self.nfout2_1]) )
f20 = fnamePR+'_2_DISP.0'
np.savez(f20, self.arr1_2, np.array([self.nfout1_2]) )
f21 = fnamePR+'_2_DISP.1'
np.savez(f21, self.arr2_2, np.array([self.nfout2_2]) )
return
def FTANcomp(self, inftanparam, compflag=1):
"""
Compare aftan results for two ftanParam objects.
"""
if not isinstance(inftanparam, ftanParam):
raise ValueError('Input inftanparam is not type of ftanParam!')
fparam1 = self
fparam2 = inftanparam
if compflag == 1:
obper1 = fparam1.arr1_1[1,:fparam1.nfout1_1]
gvel1 = fparam1.arr1_1[2,:fparam1.nfout1_1]
phvel1 = fparam1.arr1_1[3,:fparam1.nfout1_1]
obper2 = fparam2.arr1_1[1,:fparam2.nfout1_1]
gvel2 = fparam2.arr1_1[2,:fparam2.nfout1_1]
phvel2 = fparam2.arr1_1[3,:fparam2.nfout1_1]
elif compflag == 2:
obper1 = fparam1.arr2_1[1,:fparam1.nfout2_1]
gvel1 = fparam1.arr2_1[2,:fparam1.nfout2_1]
phvel1 = fparam1.arr2_1[3,:fparam1.nfout2_1]
obper2 = fparam2.arr2_1[1,:fparam2.nfout2_1]
gvel2 = fparam2.arr2_1[2,:fparam2.nfout2_1]
phvel2 = fparam2.arr2_1[3,:fparam2.nfout2_1]
elif compflag == 3:
obper1 = fparam1.arr1_2[1,:fparam1.nfout1_2]
gvel1 = fparam1.arr1_2[2,:fparam1.nfout1_2]
phvel1 = fparam1.arr1_2[3,:fparam1.nfout1_2]
obper2 = fparam2.arr1_2[1,:fparam2.nfout1_2]
gvel2 = fparam2.arr1_2[2,:fparam2.nfout1_2]
phvel2 = fparam2.arr1_2[3,:fparam2.nfout1_2]
else:
obper1 = fparam1.arr2_2[1,:fparam1.nfout2_2]
gvel1 = fparam1.arr2_2[2,:fparam1.nfout2_2]
phvel1 = fparam1.arr2_2[3,:fparam1.nfout2_2]
obper2 = fparam2.arr2_2[1,:fparam2.nfout2_2]
gvel2 = fparam2.arr2_2[2,:fparam2.nfout2_2]
phvel2 = fparam2.arr2_2[3,:fparam2.nfout2_2]
plt.figure()
ax = plt.subplot()
ax.plot(obper1, gvel1, '--k', lw=3) #
ax.plot(obper2, gvel2, 'bo', markersize=5)
plt.xlabel('Period(s)')
plt.ylabel('Velocity(km/s)')
plt.title('Group Velocity Comparison')
if (fparam1.preflag and fparam2.preflag):
plt.figure()
ax = plt.subplot()
ax.plot(obper1, phvel1, '--k', lw=3) #
ax.plot(obper2, phvel2, 'bo', markersize=5)
plt.xlabel('Period(s)')
plt.ylabel('Velocity(km/s)')
plt.title('Phase Velocity Comparison')
return
class InputFtanParam(object): ###
"""
A subclass to store input parameters for aftan analysis and SNR Analysis
===============================================================================================================
Parameters:
pmf - flag for Phase-Matched-Filtered output (default: Fasle)
piover4 - phase shift = pi/4*piover4, for cross-correlation piover4 should be -1.0
vmin - minimal group velocity, km/s
vmax - maximal group velocity, km/s
tmin - minimal period, s
tmax - maximal period, s
tresh - treshold for jump detection, usualy = 10, need modifications
ffact - factor to automatic filter parameter, usualy =1
taperl - factor for the left end seismogram tapering, taper = taperl*tmax, (real*8)
snr - phase match filter parameter, spectra ratio to determine cutting point for phase matched filter
fmatch - factor to length of phase matching window
fhlen - half length of Gaussian width
nfin - number of initial period points
npoints - number of continuous points in jump correction
perc - output segment
predV - predicted phase velocity curve, period = predV[:, 0], Vph = predV[:, 1]
===============================================================================================================
"""
def __init__(self):
self.pmf = True
self.piover4 = -1.0
self.vmin = 1.5
self.vmax = 5.0
self.tmin = 4.0
self.tmax = 70.0
self.tresh = 20.0
self.ffact = 1.0
self.taperl = 1.0
self.snr = 0.2
self.fmatch = 1.0
self.fhlen = 0.008
self.nfin = 64
self.npoints = 3
self.perc = 50
self.predV = np.array([])
class aftantrace(obspy.core.trace.Trace):
"""
aftantrace:
A derived class inherited from obspy.core.trace.Trace. This derived class have a variety of new member functions
"""
def init_ftanParam(self):
"""Initialize ftan parameters
"""
self.ftanparam = ftanParam()
def reverse(self):
"""Reverse the trace
"""
self.data = self.data[::-1]
return
def makesym(self):
"""Turn the double lagged cross-correlation data to one single lag
"""
if abs(self.stats.sac.b+self.stats.sac.e) > self.stats.delta:
raise ValueError('Error: Not neg-pos trace!')
if self.stats.npts%2 != 1:
raise ValueError('Error: Incompatible begin and end time!')
nhalf = (self.stats.npts-1)/2+1
neg = self.data[:nhalf]
pos = self.data[nhalf-1:self.stats.npts]
neg = neg[::-1]
self.data = (pos+neg)/2
self.stats.npts = nhalf
self.stats.starttime = self.stats.starttime+self.stats.sac.e
self.stats.sac.b = 0.
return
def getneg(self):
"""Get the negative lag of a cross-correlation record
"""
if abs(self.stats.sac.b+self.stats.sac.e) > self.stats.delta:
raise ValueError('Error: Not neg-pos trace!')
negTr = self.copy()
t = self.stats.starttime
L = (int)((self.stats.npts-1)/2)+1
negTr.data = negTr.data[:L]
negTr.data = negTr.data[::-1]
negTr.stats.npts = L
negTr.stats.sac.b = 0.
negTr.stats.starttime = t-self.stats.sac.b
return negTr
def getpos(self):
"""Get the positive lag of a cross-correlation record
"""
if abs(self.stats.sac.b+self.stats.sac.e)>self.stats.delta:
raise ValueError('Error: Not neg-pos trace!')
posTr = self.copy()
t = self.stats.starttime
L = (int)((self.stats.npts-1)/2)+1
posTr.data = posTr.data[L-1:]
posTr.stats.npts = L
posTr.stats.sac.b = 0.
posTr.stats.starttime = t-self.stats.sac.b
return posTr
def aftan(self, pmf=True, piover4=-1.0, vmin=1.5, vmax=5.0, tmin=4.0, tmax=30.0, tresh=20.0, ffact=1.0,
taperl=1.0, snr=0.2, fmatch=1.0, nfin=64, npoints=3, perc=50., phvelname='', predV=np.array([])):
""" (Automatic Frequency-Time ANalysis) aftan analysis:
===========================================================================================================
Input Parameters:
pmf - flag for Phase-Matched-Filtered output (default: True)
piover4 - phase shift = pi/4*piover4, for cross-correlation piover4 should be -1.0
vmin - minimal group velocity, km/s
vmax - maximal group velocity, km/s
tmin - minimal period, s
tmax - maximal period, s
tresh - treshold for jump detection, usualy = 10, need modifications
ffact - factor to automatic filter parameter, usualy =1
taperl - factor for the left end seismogram tapering, taper = taperl*tmax, (real*8)
snr - phase match filter parameter, spectra ratio to determine cutting point for phase matched filter
fmatch - factor to length of phase matching window
nfin - number of initial period points
npoints - number of continuous points in jump correction
perc - output segment
phvelname - predicted phase velocity file name
predV - predicted phase velocity curve, period = predV[:, 0], Vph = predV[:, 1]
Output:
self.ftanparam, a object of ftanParam class, to store output aftan results
===========================================================================================================
"""
# preparing for data
try:
self.ftanparam
except:
self.init_ftanParam()
try:
dist = self.stats.sac.dist
except:
dist, az, baz = obspy.geodetics.base.gps2dist_azimuth(self.stats.sac.evla, self.stats.sac.evlo,
self.stats.sac.stla, self.stats.sac.stlo) # distance is in m
self.stats.sac.dist = dist/1000.
dist = dist/1000.
if predV.size != 0:
self.ftanparam.preflag = True
elif os.path.isfile(phvelname):
predV = np.loadtxt(phvelname)
self.ftanparam.preflag = True
else:
warnings.warn('No predicted dispersion curve for:'+self.stats.network+'.'+self.stats.station, UserWarning, stacklevel=1)
# basic aftan
self._aftanpg(piover4=piover4, vmin=vmin, vmax=vmax, tmin=tmin, tmax=tmax, tresh=tresh, ffact=ffact, taperl=taperl,
nfin=nfin, npoints=npoints, perc=perc, predV=predV)
# phase matched filter aftan
if pmf:
self._aftanipg(piover4=piover4, vmin=vmin, vmax=vmax, tresh=tresh, ffact=ffact, taperl=taperl,
snr=snr, fmatch=fmatch, nfin=nfin, npoints=npoints, perc=perc, predV=predV)
return
def _aftanpg(self, piover4, vmin, vmax, tmin, tmax, tresh, ffact, taperl, nfin, npoints, perc, predV):
""" Basic aftan analysis, internal function
===========================================================================================================
Input Parameters:
piover4 - phase shift = pi/4*piover4, for cross-correlation piover4 should be -1.0
vmin - minimal group velocity, km/s
vmax - maximal group velocity, km/s
tmin - minimal period, s
tmax - maximal period, s
tresh - treshold for jump detection, usualy = 10, need modifications
ffact - factor to automatic filter parameter, usualy =1
taperl - factor for the left end seismogram tapering, taper = taperl*tmax, (real*8)
nfin - number of initial period points
npoints - number of continuous points in jump correction
perc - output segment
predV - predicted phase velocity curve, period = predV[:, 0], Vph = predV[:, 1]
===========================================================================================================
Output:
self.ftanparam, a object of ftanParam class, to store output aftan results
"""
if self.ftanparam.preflag:
phprper = predV[:,0]
phprvel = predV[:,1]
nprpv = predV[:,0].size
else:
nprpv = 0
phprper = np.array([])
phprvel = np.array([])
dt = self.stats.delta
tb = self.stats.sac.b
nsam = self.stats.npts
dist = self.stats.sac.dist
# alpha=ffact*20.*np.sqrt(dist/1000.)
alpha = ffact*20.
# number of samples for tapering, left and right end
ntapb = int(round(taperl*tmax/dt))
ntape = int(round(tmax/dt))
omb = 2.0*np.pi/tmax
ome = 2.0*np.pi/tmin
# tapering seismogram
nb = int(max(2, round((dist/vmax-tb)/dt)))
tamp = (nb-1)*dt+tb
ne = int(min(nsam, round((dist/vmin-tb)/dt)))
nrow = nfin
ncol = ne-nb+1
tArr = np.arange(ne-nb+1)*dt+tb
tArr[tArr==0.] = -1.
vArr = dist/tArr
tdata, ncorr = self.taper( max(nb, ntapb+1), min(ne, self.stats.npts-ntape), ntapb, ntape)
# prepare for FFT
ns = max(1<<(ncorr-1).bit_length(), 2**12) # different !!!
domega = 2.*np.pi/ns/dt
step = (np.log(omb)-np.log(ome))/(nfin -1)
omegaArr = np.exp(np.log(ome)+np.arange(nfin)*step)
perArr = 2.*np.pi/omegaArr
# FFT
if useFFTW:
fftdata = pyfftw.interfaces.numpy_fft.fft(tdata, ns)
else:
fftdata = np.fft.fft(tdata, ns)
omsArr = np.arange(ns)*domega
phaArr = np.zeros((ne+3-nb, nfin))
ampo = np.zeros((ne+3-nb, nfin))
amp = np.zeros((ne+3-nb, nfin))
# main loop by frequency
for k in range(nfin):
# Gaussian filter
filterS = _aftan_gaussian_filter(alpha=alpha, omega0=omegaArr[k], ns=ns, indata=fftdata, omsArr=omsArr)
# return fs, filterS
if useFFTW:
filterT = pyfftw.interfaces.numpy_fft.ifft(filterS, ns)
else:
filterT = np.fft.ifft(filterS, ns)
# need to multiply by 2 due to zero padding of negative frequencies
# but NO NEED to divide by ns due to the difference of numpy style and FFTW style
filterT = 2.*filterT
phaArr[:,k] = np.arctan2(np.imag(filterT[nb-2:ne+1]), np.real(filterT[nb-2:ne+1]))
ampo[:,k] = np.abs(filterT[nb-2:ne+1])
amp[:,k] = 20.*np.log10(ampo[:,k])
# normalization amp diagram to 100 Db with three decade cutting
amax = amp.max()
amp = amp+100.-amax
amp[amp<40.]= 40.
tim1 = np.zeros(nfin)
tvis1 = np.zeros(nfin)
ampgr1 = np.zeros(nfin)
grvel1 = np.zeros(nfin)
snr1 = np.zeros(nfin)
wdth1 = np.zeros(nfin)
phgr1 = np.zeros(nfin)
ind_all = []
ipar_all = []
for k in xrange(nfin):
ampk = amp[:,k]
ampok = ampo[:,k]
ind_localmax = argrelmax(ampk)[0]
omega = omegaArr[k]
if ind_localmax.size == 0:
ind_localmax= np.append(ind_localmax, ne+1-nb)
ind_all.append(ind_localmax)
dph, tm, ph, t = self._fmax(amp=ampk, pha=phaArr[:,k], ind=ind_localmax, om=omega, piover4=piover4)
imax = tm.argmax()
ipar = np.zeros((6, ind_localmax.size))
ipar[0, :] = (nb+ind_localmax-2.+t)*dt # note the difference with aftanf77, due to ind_localmax
ipar[1, :] = 2*np.pi*dt/dph
ipar[2, :] = tm
ipar[5, :] = ph
if ind_localmax.size == 1:
lmindex = (ampok[:ind_localmax[0]]).argmin()
rmindex = (ampok[ind_localmax[0]:]).argmin()
lm = (ampok[:ind_localmax[0]])[lmindex]
rm = (ampok[ind_localmax[0]:])[rmindex]
else:
splitArr = np.split(ampok, ind_localmax)
minArr = np.array([])
minindexArr = np.array([])
for tempArr in splitArr:
temp_ind_min = tempArr.argmin()
minArr = np.append(minArr, tempArr[temp_ind_min])
minindexArr = np.append(minindexArr, temp_ind_min)
lm = minArr[:-1]
rm = minArr[1:]
minindexArr[1:] = minindexArr[1:]+ind_localmax
lmindex = minindexArr[:-1]
rmindex = minindexArr[1:]
ipar[3,:] = 20.*np.log10(ampok[ind_localmax]/np.sqrt(lm*rm))
ipar[4,:] = (np.abs(ind_localmax-lmindex)+np.abs(ind_localmax-rmindex))/2.*dt
tim1[k] = ipar[0,imax]
tvis1[k] = ipar[1,imax]
ampgr1[k] = ipar[2,imax]
grvel1[k] = dist/(tim1[k] +tb)
snr1[k] = ipar[3,imax]
wdth1[k] = ipar[4,imax] ### Note half width is not completely the same as ftanf77, need further check!!!
phgr1[k] = ipar[5,imax]
ipar_all.append(ipar)
nfout1 = nfin
per1 = perArr
################################################
# Check jumps in dispersion curve
################################################
grvel2 = grvel1.copy()
tvis2 = tvis1.copy()
ampgr2 = ampgr1.copy()
phgr2 = phgr1.copy()
snr2 = snr1.copy()
wdth2 = wdth1.copy()
ftrig1, trig, ierr = self._trigger(grvel=grvel1, om=omegaArr, tresh=tresh)
if ierr !=0:
deltrig = trig[1:]-trig[:-1]
ijmp = np.where(np.abs(deltrig)>1.5)[0]
if ijmp.size > 1: ### need check
delijmp = ijmp[1:]-ijmp[:-1]
ii = np.where(delijmp<npoints)[0]
##########################################################################
# Try to correct jumps by finding another local maximum as group arrival
##########################################################################
if ii.size != 0:
grvelt = grvel2.copy()
tvist = tvis2.copy()
ampgrt = ampgr2.copy()
phgrt = phgr2.copy()
snrt = snr2.copy()
wdtht = wdth2.copy()
for kk in ii:
istrt = ijmp[kk]
ibeg = istrt+1
iend = ijmp[kk+1]
### nested loop, need further improvements
for i in xrange(iend-ibeg+1):
k = ibeg+i
ind_localmax= ind_all[k]
ipar = ipar_all[k]
wor = np.abs(dist/(ipar[0,:]+tb)-grvel2[k-1])
ima = wor.argmin() # find group arrivals that has smallest
grvel2[k] = dist/(ipar[0,ima]+tb)
tvis2[k] = ipar[1,ima]
ampgr2[k] = ipar[2,ima]
phgr2[k] = ipar[5,ima]
snr2[k] = ipar[3,ima]
wdth2[k] = ipar[4,ima]
ftrig2, trig, ierr = self._trigger(grvel=grvel2, om=omegaArr, tresh=tresh)
temptrig = trig[istrt:iend+2]
if (np.where(temptrig>0.5)[0]).size==0:
grvelt = grvel2.copy()
tvist = tvis2.copy()
ampgrt = ampgr2.copy()
phgrt = phgr2.copy()
snrt = snr2.copy()
wdtht = wdth2.copy()
grvel2 = grvelt.copy()
tvis2 = tvist.copy()
ampgr2 = ampgrt.copy()
phgr2 = phgrt.copy()
snr2 = snrt.copy()
wdth2 = wdtht.copy()
ftrig2, trig, ierr = self._trigger(grvel=grvel2, om=omegaArr, tresh=tresh)
################################################
# after correcting possible jumps, we cut frequency range to single
# segment with maximum length
################################################
if ierr != 0:
indx = np.where(np.abs(trig)>0.5)[0]
indx = np.append(indx, nfin-1)
iimax = indx[1:]-indx[:-1]
ipos = iimax.argmax()
ist = max(indx[ipos], 0)
ibe = min(indx[ipos+1], nfin-1)
nfout2 = ibe-ist+1
per2 = perArr[ist:ibe+1]
grvel2 = grvel2[ist:ibe+1]
tvis2 = tvis2[ist:ibe+1]
ampgr2 = ampgr2[ist:ibe+1]
phgr2 = phgr2[ist:ibe+1]
snr2 = snr2[ist:ibe+1]
wdth2 = wdth2[ist:ibe+1]
else:
nfout2 = nfin
per2 = perArr.copy()
else:
nfout2 = nfin
per2 = perArr.copy()
################################################
# fill out output data arrays
################################################
if nprpv != 0:
phV1 = self._phtovel(per=tvis1, U=grvel1, pha=phgr1, npr=nprpv, prper=phprper, prvel=phprvel)
amp1 = 10.**( (ampgr1-100.+amax) /20.)
self.ftanparam.nfout1_1 = nfout1
arr1_1 = np.concatenate((per1, tvis1, grvel1, phV1, ampgr1, ftrig1, snr1, wdth1, amp1))
self.ftanparam.arr1_1 = arr1_1.reshape(9, per1.size)
if nfout2 != 0:
phV2 = self._phtovel(per=tvis2, U=grvel2, pha=phgr2, npr=nprpv, prper=phprper, prvel=phprvel)
amp2 = 10.**( (ampgr2-100.+amax) /20.)
self.ftanparam.nfout2_1 = nfout2
arr2_1 = np.concatenate((per2, tvis2, grvel2, phV2, ampgr2, snr2, wdth2, amp2))
self.ftanparam.arr2_1 = arr2_1.reshape(8, per2.size)
else:
amp1 = 10.**( (ampgr1-100.+amax) /20.)
self.ftanparam.nfout1_1 = nfout1
arr1_1 = np.concatenate((per1, tvis1, grvel1, phgr1, ampgr1, ftrig1, snr1, wdth1, amp1))
self.ftanparam.arr1_1 = arr1_1.reshape(9, per1.size)
if nfout2 != 0:
amp2 = 10.**( (ampgr2-100.+amax) /20.)
self.ftanparam.nfout2_1 = nfout2
arr2_1 = np.concatenate((per2, tvis2, grvel2, phgr2, ampgr2, snr2, wdth2, amp2))
self.ftanparam.arr2_1 = arr2_1.reshape(8, per2.size)
self.ftanparam.ampo_1 = amp
self.ftanparam.ncol_1, self.ftanparam.nrow_1= amp.shape
if nfout2 < perc*nfin/100:
self.ftanparam.ierr_1 = 2
else:
self.ftanparam.ierr_1 = ierr
self.ftanparam.tamp_1 = (nb-1)*dt+tb
return
def _aftanipg(self, piover4, vmin, vmax, tresh, ffact, taperl, snr, fmatch, nfin, npoints, perc, predV):
""" (Automatic Frequency-Time ANalysis) aftan analysis:
===========================================================================================================
Input Parameters:
piover4 - phase shift = pi/4*piover4, for cross-correlation piover4 should be -1.0
vmin - minimal group velocity, km/s
vmax - maximal group velocity, km/s
tmin - minimal period, s
tmax - maximal period, s
tresh - treshold for jump detection, usualy = 10, need modifications
ffact - factor to automatic filter parameter, usualy =1
taperl - factor for the left end seismogram tapering, taper = taperl*tmax, (real*8)
snr - phase match filter parameter, spectra ratio to determine cutting point for phase matched filter
fmatch - factor to length of phase matching window
nfin - number of initial period points
npoints - number of continuous points in jump correction
perc - output segment
predV - predicted phase velocity curve, period = predV[:, 0], Vph = predV[:, 1]
===========================================================================================================
Output:
self.ftanparam, a object of ftanParam class, to store output aftan results
"""
if self.ftanparam.preflag:
phprper = predV[:,0]
phprvel = predV[:,1]
nprpv = predV[:,0].size
else:
nprpv = 0
phprper = np.array([])
phprvel = np.array([])
tmin = self.ftanparam.arr2_1[1, 0]
tmax = self.ftanparam.arr2_1[1, -1]
dt = self.stats.delta
tb = self.stats.sac.b
nsam = self.stats.npts
dist = self.stats.sac.dist
# end of preparing data
# alpha=ffact*20.*np.sqrt(dist/1000.)
alpha = ffact*20.
# number of samples for tapering, left and right end
ntapb = int(round(taperl*tmax/dt))
ntape = int(round(tmax/dt))
omb = 2.0*np.pi/tmax
ome = 2.0*np.pi/tmin
tg0, cubicspline = self._pred_cur(np.sqrt(omb*ome))
# tapering seismogram
nb = int(max(2, round((dist/vmax-tb)/dt)))
tamp = (nb-1)*dt+tb
ne = int(min(nsam, round((dist/vmin-tb)/dt)))
nrow = nfin
ncol = ne-nb+1
tArr = np.arange(ne-nb+1)*dt+tb
tArr[tArr==0.] = -1.
vArr = dist/tArr
tdata, ncorr = self.taper( max(nb, ntapb+1), min(ne, self.stats.npts-ntape), ntapb, ntape)
ns = max(1<<(ncorr-1).bit_length(), 2**12) # different !!!
domega = 2.*np.pi/ns/dt
step = (np.log(omb)-np.log(ome))/(nfin -1)
omegaArr = np.exp(np.log(ome)+np.arange(nfin)*step)
perArr = 2.*np.pi/omegaArr
################################################
# Phase Matched Filtering
################################################
# FFT
if useFFTW:
fftdata = pyfftw.interfaces.numpy_fft.fft(tdata, ns)
else:
fftdata = np.fft.fft(tdata, ns)
# spectral taperring
omstart, inds, inde, omdom, ampdom = self._tapers(omb=omb, ome=ome, dom=domega, alpha=alpha, ns=ns )
omstart = float(round(omstart/domega))*domega
inde = min(inde, ns/2+2)
pha_cor = np.zeros(ns, dtype='complex64')
for i in xrange(ns):
pha_cor.real[i] = cubicspline.integrate(a=np.sqrt(omb*ome), b=omdom[i])
pha_cor.real[:inds-1] = 0.
pha_cor.real[inde:] = 0.
dci = 0+1j
pha_cor = np.exp(dci*pha_cor)
fftdata = fftdata*pha_cor*ampdom
if useFFTW:
env = pyfftw.interfaces.numpy_fft.ifft(fftdata, ns)
else:
env = np.fft.ifft(fftdata, ns)
env = 2.*env
dw = omegaArr[0]-omegaArr[-1]
t_env = self._tgauss(fsnr=snr, gt0=tg0, dw=dw, n=ns, fmatch=fmatch, seis=env)
#################################
# End of phase matched filter
#################################
if useFFTW:
fftdata = pyfftw.interfaces.numpy_fft.fft(t_env, ns)
else:
fftdata = np.fft.fft(t_env, ns)
fftdata = fftdata/pha_cor
omsArr = np.arange(ns)*domega
phaArr = np.zeros((ne+3-nb, nfin))
ampo = np.zeros((ne+3-nb, nfin))
amp = np.zeros((ne+3-nb, nfin))
# main loop by frequency
for k in xrange(nfin):
# Gaussian filter
filterS = _aftan_gaussian_filter(alpha=alpha, omega0=omegaArr[k], ns=ns, indata=fftdata, omsArr=omsArr)
if useFFTW:
filterT = pyfftw.interfaces.numpy_fft.ifft(filterS, ns)
else:
filterT = np.fft.ifft(filterS, ns)
# need to multiply by 2 due to zero padding of negative frequencies
# but NO NEED to divide by ns due to the difference of numpy style and FFTW style
filterT = 2.*filterT
phaArr[:,k] = np.arctan2(np.imag(filterT[nb-2:ne+1]), np.real(filterT[nb-2:ne+1]))
ampo[:,k] = np.abs(filterT[nb-2:ne+1])
amp[:,k] = 20.*np.log10(ampo[:,k])
# normalization amp diagram to 100 Db with three decade cutting
amax = amp.max()
amp = amp+100.-amax
amp[amp<40.]= 40.
tim1 = np.zeros(nfin)
tvis1 = np.zeros(nfin)
ampgr1 = np.zeros(nfin)
grvel1 = np.zeros(nfin)
snr1 = np.zeros(nfin)
wdth1 = np.zeros(nfin)
phgr1 = np.zeros(nfin)
ind_all = []
ipar_all = []
for k in xrange(nfin):
ampk = amp[:,k]
ampok = ampo[:,k]
ind_localmax= argrelmax(ampk)[0]
omega = omegaArr[k]
if ind_localmax.size == 0:
ind_localmax = np.append(ind_localmax, ne+1-nb)
ind_all.append(ind_localmax)
dph, tm, ph, t = self._fmax(amp=ampk, pha=phaArr[:,k], ind=ind_localmax, om=omega, piover4=piover4)
imax = tm.argmax()
ipar = np.zeros((6, ind_localmax.size))
ipar[0, :] = (nb+ind_localmax-2.+t)*dt # note the difference with aftanf77, due to ind_localmax
ipar[1, :] = 2*np.pi*dt/dph
ipar[2, :] = tm
ipar[5, :] = ph
if ind_localmax.size==1:
lmindex = (ampok[:ind_localmax[0]]).argmin()
rmindex = (ampok[ind_localmax[0]:]).argmin()
lm = (ampok[:ind_localmax[0]])[lmindex]
rm = (ampok[ind_localmax[0]:])[rmindex]
else:
splitArr = np.split(ampok, ind_localmax)
minArr = np.array([])
minindexArr = np.array([])
for tempArr in splitArr:
temp_ind_min = tempArr.argmin()
minArr = np.append(minArr, tempArr[temp_ind_min])
minindexArr = np.append(minindexArr, temp_ind_min)
lm = minArr[:-1]
rm = minArr[1:]
minindexArr[1:] = minindexArr[1:]+ind_localmax
lmindex = minindexArr[:-1]
rmindex = minindexArr[1:]
ipar[3,:] = 20.*np.log10(ampok[ind_localmax]/np.sqrt(lm*rm))
ipar[4,:] = (np.abs(ind_localmax-lmindex)+np.abs(ind_localmax-rmindex))/2.*dt
tim1[k] = ipar[0,imax]
tvis1[k] = ipar[1,imax]
ampgr1[k] = ipar[2,imax]
grvel1[k] = dist/(tim1[k] +tb)
snr1[k] = ipar[3,imax]
wdth1[k] = ipar[4,imax] ### Note half width is not completely the same as ftanf77, need further check!!!
phgr1[k] = ipar[5,imax]
ipar_all.append(ipar)
nfout1 = nfin
per1 = perArr
################################################
# Check jumps in dispersion curve
################################################
grvel2 = grvel1.copy()
tvis2 = tvis1.copy()
ampgr2 = ampgr1.copy()
phgr2 = phgr1.copy()
snr2 = snr1.copy()
wdth2 = wdth1.copy()
ftrig1, trig, ierr = self._trigger(grvel=grvel1, om=omegaArr, tresh=tresh)
if ierr != 0:
deltrig = trig[1:]-trig[:-1]
ijmp = np.where(np.abs(deltrig)>1.5)[0]
if ijmp.size > 1: ### need check
delijmp = ijmp[1:]-ijmp[:-1]
ii = np.where(delijmp<npoints)[0]
##########################################################################
# Try to correct jumps by finding another local maximum as group arrival
##########################################################################
if ii.size != 0:
grvelt = grvel2.copy()
tvist = tvis2.copy()
ampgrt = ampgr2.copy()
phgrt = phgr2.copy()
snrt = snr2.copy()
wdtht = wdth2.copy()
for kk in ii:
istrt = ijmp[kk]
ibeg = istrt+1
iend = ijmp[kk+1]
### nested loop, need further improvements
for i in xrange(iend-ibeg+1):
k = ibeg+i
ind_localmax= ind_all[k]
ipar = ipar_all[k]
wor = np.abs(dist/(ipar[0,:]+tb)-grvel2[k-1])
ima = wor.argmin() # find group arrivals that has smallest
grvel2[k] = dist/(ipar[0,ima]+tb)
tvis2[k] = ipar[1,ima]
ampgr2[k] = ipar[2,ima]
phgr2[k] = ipar[5,ima]
snr2[k] = ipar[3,ima]
wdth2[k] = ipar[4,ima]
ftrig2, trig, ierr = self._trigger(grvel=grvel2, om=omegaArr, tresh=tresh)
temptrig = trig[istrt:iend+2]
if (np.where(temptrig>0.5)[0]).size == 0:
grvelt = grvel2.copy()
tvist = tvis2.copy()
ampgrt = ampgr2.copy()
phgrt = phgr2.copy()
snrt = snr2.copy()
wdtht = wdth2.copy()
grvel2 = grvelt.copy()
tvis2 = tvist.copy()
ampgr2 = ampgrt.copy()
phgr2 = phgrt.copy()
snr2 = snrt.copy()
wdth2 = wdtht.copy()
ftrig2, trig, ierr = self._trigger(grvel=grvel2, om=omegaArr, tresh=tresh)
################################################
# after correcting possible jumps, we cut frequency range to single
# segment with maximum length
################################################
if ierr != 0:
indx = np.where(np.abs(trig)>0.5)[0]
indx = np.append(indx, nfin-1)
iimax = indx[1:]-indx[:-1]
ipos = iimax.argmax()
ist = max(indx[ipos], 0)
ibe = min(indx[ipos+1], nfin-1)
nfout2 = ibe-ist+1
per2 = perArr[ist:ibe+1]
grvel2 = grvel2[ist:ibe+1]
tvis2 = tvis2[ist:ibe+1]
ampgr2 = ampgr2[ist:ibe+1]
phgr2 = phgr2[ist:ibe+1]
snr2 = snr2[ist:ibe+1]
wdth2 = wdth2[ist:ibe+1]
else:
nfout2 = nfin
per2 = perArr.copy()
else:
nfout2 = nfin
per2 = perArr.copy()
################################################
# fill out output data arrays
################################################
if nprpv != 0:
phV1 = self._phtovel(per=tvis1, U=grvel1, pha=phgr1, npr=nprpv, prper=phprper, prvel=phprvel)
amp1 = 10.**( (ampgr1-100.+amax) /20.)
self.ftanparam.nfout1_2 = nfout1
arr1_2 = np.concatenate((per1, tvis1, grvel1, phV1, ampgr1, ftrig1, snr1, wdth1, amp1))
self.ftanparam.arr1_2 = arr1_2.reshape(9, per1.size)
if nfout2 != 0:
phV2 = self._phtovel(per=tvis2, U=grvel2, pha=phgr2, npr=nprpv, prper=phprper, prvel=phprvel)
amp2 = 10.**( (ampgr2-100.+amax) /20.)
self.ftanparam.nfout2_2 = nfout2
arr2_2 = np.concatenate((per2, tvis2, grvel2, phV2, ampgr2, snr2, wdth2, amp2))
self.ftanparam.arr2_2 = arr2_2.reshape(8, per2.size)
else:
amp1 = 10.**( (ampgr1-100.+amax) /20.)
self.ftanparam.nfout1_2 = nfout1
arr1_2 = np.concatenate((per1, tvis1, grvel1, phgr1, ampgr1, ftrig1, snr1, wdth1, amp1))
self.ftanparam.arr1_2 = arr1_2.reshape(9, per1.size)
if nfout2 != 0:
amp2 = 10.**( (ampgr2-100.+amax) /20.)
self.ftanparam.nfout2_2 = nfout2
arr2_2 = np.concatenate((per2, tvis2, grvel2, phgr2, ampgr2, snr2, wdth2, amp2))
self.ftanparam.arr2_2 = arr2_2.reshape(8, per2.size)
self.ftanparam.ampo_2 = amp
self.ftanparam.ncol_2, self.ftanparam.nrow_2= amp.shape
if nfout2 < perc*nfin/100:
self.ftanparam.ierr_2 = 2
else:
self.ftanparam.ierr_2 = ierr
self.ftanparam.tamp_2 = (nb-1)*dt+tb
return
def _compare_arr(self, data1, data2):
plt.plot(data1-data2, '-y')
plt.plot(data1, '^r')
plt.plot(data2, '*b')
plt.show()
return
def _compare_arr2(self, d1, d2, number):
data1 = d1[:, number]
data2 = d2[:data1.size, number]
plt.plot(data1-data2, '-y')
plt.plot(data1, '^r')
plt.plot(data2, '*b')
plt.show()
return
def taper(self, nb, ne, ntapb, ntape):
omb = np.pi/ntapb
ome = np.pi/ntape
ncorr = int(ne+ntape)
npts = self.stats.npts
if ncorr > npts:
ncorr = npts
dataTapered = np.append(self.data[:ncorr], np.zeros( npts-ncorr ) )
##################################