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Extended class MoMw for calculating source spectrum. New functions calcsourcespec, calcMoMw and run_calcMoMw implemented.

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Ludger Küperkoch 2015-12-02 10:12:37 +01:00
parent 40f38ebf84
commit 46cbe96a43
1 changed files with 147 additions and 76 deletions
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223
pylot/core/analysis/magnitude.py
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@ -8,10 +8,12 @@ Created August/September 2015.
import matplotlib.pyplot as plt import matplotlib.pyplot as plt
import numpy as np import numpy as np
from obspy.core import Stream from obspy.core import Stream, UTCDateTime
from pylot.core.pick.utils import getsignalwin from pylot.core.pick.utils import getsignalwin, crossings_nonzero_all
from pylot.core.util.utils import getPatternLine from pylot.core.util.utils import getPatternLine
from scipy.optimize import curve_fit from scipy.optimize import curve_fit
from scipy import integrate
from pylot.core.read.data import Data
class Magnitude(object): class Magnitude(object):
''' '''
@ -20,7 +22,8 @@ class Magnitude(object):
and moment magnitudes. and moment magnitudes.
''' '''
def __init__(self, wfstream, To, pwin, iplot, NLLocfile=None, picks=None, rho=None, vp=None): def __init__(self, wfstream, To, pwin, iplot, NLLocfile=None, \
picks=None, rho=None, vp=None, invdir=None):
''' '''
:param: wfstream :param: wfstream
:type: `~obspy.core.stream.Stream :type: `~obspy.core.stream.Stream
@ -30,7 +33,7 @@ class Magnitude(object):
:param: pwin, pick window [To To+pwin] to get maximum :param: pwin, pick window [To To+pwin] to get maximum
peak-to-peak amplitude (WApp) or to calculate peak-to-peak amplitude (WApp) or to calculate
source spectrum (DCfc) source spectrum (DCfc) around P onset
:type: float :type: float
:param: iplot, no. of figure window for plotting interims results :param: iplot, no. of figure window for plotting interims results
@ -48,6 +51,9 @@ class Magnitude(object):
:param: vp [m/s], P-velocity :param: vp [m/s], P-velocity
:param: integer :param: integer
:param: invdir, path to inventory or dataless-SEED file
:type: string
''' '''
assert isinstance(wfstream, Stream), "%s is not a stream object" % str(wfstream) assert isinstance(wfstream, Stream), "%s is not a stream object" % str(wfstream)
@ -60,6 +66,7 @@ class Magnitude(object):
self.setrho(rho) self.setrho(rho)
self.setpicks(picks) self.setpicks(picks)
self.setvp(vp) self.setvp(vp)
self.setinvdir(invdir)
self.calcwapp() self.calcwapp()
self.calcsourcespec() self.calcsourcespec()
self.run_calcMoMw() self.run_calcMoMw()
@ -122,6 +129,12 @@ class Magnitude(object):
def getfc(self): def getfc(self):
return self.fc return self.fc
def setinvdir(self, invdir):
self.invdir = invdir
def getinvdir(self):
return self.invdir
def getpicdic(self): def getpicdic(self):
return self.picdic return self.picdic
@ -190,7 +203,8 @@ class M0Mw(Magnitude):
Requires results of class w0fc for calculating plateau w0 Requires results of class w0fc for calculating plateau w0
and corner frequency fc of source spectrum, respectively. Uses and corner frequency fc of source spectrum, respectively. Uses
subfunction calcMoMw.py. Returns modified dictionary of picks including subfunction calcMoMw.py. Returns modified dictionary of picks including
seismic moment Mo and corresponding moment magntiude Mw. Dc-value, corner frequency fc, seismic moment Mo and
corresponding moment magntiude Mw.
''' '''
def run_calcMoMw(self): def run_calcMoMw(self):
@ -198,12 +212,15 @@ class M0Mw(Magnitude):
picks = self.getpicks() picks = self.getpicks()
nllocfile = self.getNLLocfile() nllocfile = self.getNLLocfile()
wfdat = self.getwfstream() wfdat = self.getwfstream()
# get vertical component data only
zdat = wfdat.select(component="Z")
if len(zdat) == 0: # check for other components
zdat = wfdat.select(component="3")
for key in picks: for key in picks:
if picks[key]['P']['weight'] < 4 and picks[key]['P']['w0'] is not None: if picks[key]['P']['weight'] < 4:
# select waveform # select waveform
selwf = wfdat.select(station=key) selwf = zdat.select(station=key)
# get corresponding height of source spectrum plateau w0
w0 = picks[key]['P']['w0']
# get hypocentral distance of station # get hypocentral distance of station
# from NLLoc-location file # from NLLoc-location file
if len(key) > 4: if len(key) > 4:
@ -214,14 +231,27 @@ class M0Mw(Magnitude):
Ppattern = '%s ? ? ? P' % key Ppattern = '%s ? ? ? P' % key
nllocline = getPatternLine(nllocfile, Ppattern) nllocline = getPatternLine(nllocfile, Ppattern)
delta = float(nllocline.split(None)[21]) delta = float(nllocline.split(None)[21])
# call subfunction # call subfunction to estimate source spectrum
[Mo, Mw] = calcMoMw(selwf, w0, self.getrho(), self.getvp(), delta) # and to derive w0 and fc
# add Mo and Mw to dictionary [w0, fc] = calcsourcespec(selwf, picks[key]['P']['mpp'], \
self.getiplot(), self.getinvdir())
if w0 is not None:
# call subfunction to calculate Mo and Mw
[Mo, Mw] = calcMoMw(selwf, w0, self.getrho(), self.getvp(), \
delta, self.getinvdir())
else:
Mo = None
Mw = None
# add w0, fc, Mo and Mw to dictionary
picks[key]['P']['w0'] = w0
picks[key]['P']['fc'] = fc
picks[key]['P']['Mo'] = Mo picks[key]['P']['Mo'] = Mo
picks[key]['P']['Mw'] = Mw picks[key]['P']['Mw'] = Mw
self.picdic = picks self.picdic = picks
def calcMoMw(wfstream, w0, rho, vp, delta): def calcMoMw(wfstream, w0, rho, vp, delta, inv):
''' '''
Subfunction of run_calcMoMw to calculate individual Subfunction of run_calcMoMw to calculate individual
seismic moments and corresponding moment magnitudes. seismic moments and corresponding moment magnitudes.
@ -245,94 +275,135 @@ def calcMoMw(wfstream, w0, rho, vp, delta):
return Mo, Mw return Mo, Mw
class w0fc(Magnitude):
def calcsourcespec(wfstream, onset, iplot, inventory):
''' '''
Method to calculate the source spectrum and to derive from that the plateau Subfunction to calculate the source spectrum and to derive from that the plateau
(usually called omega0) and the corner frequency assuming Aki's omega-square (usually called omega0) and the corner frequency assuming Aki's omega-square
source model. Has to be derived from instrument corrected displacement traces! source model. Has to be derived from instrument corrected displacement traces,
thus restitution and integration necessary!
''' '''
print ("Calculating source spectrum ....")
def calcsourcespec(self): fc = None
print ("Calculating source spectrum ....") w0 = None
data = Data()
z_copy = wfstream.copy()
self.w0 = None # DC-value [corzdat, restflag] = data.restituteWFData(inventory, z_copy)
self.fc = None # corner frequency
stream = self.getwfstream()
tr = stream[0]
if restflag == 1:
# integrate to displacment
corintzdat = integrate.cumtrapz(corzdat[0], None, corzdat[0].stats.delta)
z_copy[0].data = corintzdat
tr = z_copy[0]
# get window after P pulse for
# calculating source spectrum
if tr.stats.sampling_rate <= 100:
winzc = tr.stats.sampling_rate
elif tr.stats.sampling_rate > 100 and \
tr.stats.sampling_rate <= 200:
winzc = 0.5 * tr.stats.sampling_rate
elif tr.stats.sampling_rate > 200 and \
tr.stats.sampling_rate <= 400:
winzc = 0.2 * tr.stats.sampling_rate
elif tr.stats.sampling_rate > 400:
winzc = tr.stats.sampling_rate
tstart = UTCDateTime(tr.stats.starttime)
tonset = onset.timestamp -tstart.timestamp
impickP = tonset * tr.stats.sampling_rate
wfzc = tr.data[impickP : impickP + winzc]
# get time array # get time array
t = np.arange(0, len(tr) * tr.stats.delta, tr.stats.delta) t = np.arange(0, len(tr) * tr.stats.delta, tr.stats.delta)
iwin = getsignalwin(t, self.getTo(), self.getpwin()) # calculate spectrum using only first cycles of
xdat = tr.data[iwin] # waveform after P onset!
zc = crossings_nonzero_all(wfzc)
if np.size(zc) == 0 or len(zc) <= 3:
print ("Something is wrong with the waveform, "
"no zero crossings derived!")
print ("No calculation of source spectrum possible!")
plotflag = 0
else:
plotflag = 1
index = min([3, len(zc) - 1])
calcwin = (zc[index] - zc[0]) * z_copy[0].stats.delta
iwin = getsignalwin(t, tonset, calcwin)
xdat = tr.data[iwin]
# fft # fft
fny = tr.stats.sampling_rate / 2 fny = tr.stats.sampling_rate / 2
l = len(xdat) / tr.stats.sampling_rate l = len(xdat) / tr.stats.sampling_rate
n = tr.stats.sampling_rate * l # number of fft bins after Bath n = tr.stats.sampling_rate * l # number of fft bins after Bath
# find next power of 2 of data length # find next power of 2 of data length
m = pow(2, np.ceil(np.log(len(xdat)) / np.log(2))) m = pow(2, np.ceil(np.log(len(xdat)) / np.log(2)))
N = int(np.power(m, 2)) N = int(np.power(m, 2))
y = tr.stats.delta * np.fft.fft(xdat, N) y = tr.stats.delta * np.fft.fft(xdat, N)
Y = abs(y[: N/2]) Y = abs(y[: N/2])
L = (N - 1) / tr.stats.sampling_rate L = (N - 1) / tr.stats.sampling_rate
f = np.arange(0, fny, 1/L) f = np.arange(0, fny, 1/L)
# remove zero-frequency and frequencies above # remove zero-frequency and frequencies above
# corner frequency of seismometer (assumed # corner frequency of seismometer (assumed
# to be 100 Hz) # to be 100 Hz)
fi = np.where((f >= 1) & (f < 100)) fi = np.where((f >= 1) & (f < 100))
F = f[fi] F = f[fi]
YY = Y[fi] YY = Y[fi]
# get plateau (DC value) and corner frequency # get plateau (DC value) and corner frequency
# initial guess of plateau # initial guess of plateau
w0in = np.mean(YY[0:100]) w0in = np.mean(YY[0:100])
# initial guess of corner frequency # initial guess of corner frequency
# where spectral level reached 50% of flat level # where spectral level reached 50% of flat level
iin = np.where(YY >= 0.5 * w0in) iin = np.where(YY >= 0.5 * w0in)
Fcin = F[iin[0][np.size(iin) - 1]] Fcin = F[iin[0][np.size(iin) - 1]]
# use of implicit scipy otimization function # use of implicit scipy otimization function
fit = synthsourcespec(F, w0in, Fcin) fit = synthsourcespec(F, w0in, Fcin)
[optspecfit, pcov] = curve_fit(synthsourcespec, F, YY.real, [w0in, Fcin]) [optspecfit, pcov] = curve_fit(synthsourcespec, F, YY.real, [w0in, Fcin])
w01 = optspecfit[0] w01 = optspecfit[0]
fc1 = optspecfit[1] fc1 = optspecfit[1]
print ("w0fc: Determined w0-value: %e m/Hz, \n" print ("w0fc: Determined w0-value: %e m/Hz, \n"
"Determined corner frequency: %f Hz" % (w01, fc1)) "Determined corner frequency: %f Hz" % (w01, fc1))
# use of conventional fitting # use of conventional fitting
[w02, fc2] = fitSourceModel(F, YY.real, Fcin, self.getiplot()) [w02, fc2] = fitSourceModel(F, YY.real, Fcin, iplot)
# get w0 and fc as median # get w0 and fc as median
self.w0 = np.median([w01, w02]) w0 = np.median([w01, w02])
self.fc = np.median([fc1, fc2]) fc = np.median([fc1, fc2])
print("w0fc: Using w0-value = %e m/Hz and fc = %f Hz" % (self.w0, self.fc)) print("w0fc: Using w0-value = %e m/Hz and fc = %f Hz" % (w0, fc))
if self.getiplot() > 1: if iplot > 1:
f1 = plt.figure() f1 = plt.figure()
plt.subplot(2,1,1) plt.subplot(2,1,1)
# show displacement in mm # show displacement in mm
plt.plot(t, np.multiply(tr, 1000), 'k') plt.plot(t, np.multiply(tr, 1000), 'k')
if plotflag == 1:
plt.plot(t[iwin], np.multiply(xdat, 1000), 'g') plt.plot(t[iwin], np.multiply(xdat, 1000), 'g')
plt.title('Seismogram and P pulse, station %s' % tr.stats.station) plt.title('Seismogram and P Pulse, Station %s-%s' \
plt.xlabel('Time since %s' % tr.stats.starttime) % (tr.stats.station, tr.stats.channel))
plt.ylabel('Displacement [mm]') else:
plt.title('Seismogram, Station %s-%s' \
% (tr.stats.station, tr.stats.channel))
plt.xlabel('Time since %s' % tr.stats.starttime)
plt.ylabel('Displacement [mm]')
if plotflag == 1:
plt.subplot(2,1,2) plt.subplot(2,1,2)
plt.loglog(f, Y.real, 'k') plt.loglog(f, Y.real, 'k')
plt.loglog(F, YY.real) plt.loglog(F, YY.real)
plt.loglog(F, fit, 'g') plt.loglog(F, fit, 'g')
plt.loglog([self.fc, self.fc], [self.w0/100, self.w0], 'g') plt.loglog([fc, fc], [w0/100, w0], 'g')
plt.title('Source Spectrum from P Pulse, w0=%e m/Hz, fc=%6.2f Hz' \ plt.title('Source Spectrum from P Pulse, w0=%e m/Hz, fc=%6.2f Hz' \
% (self.w0, self.fc)) % (w0, fc))
plt.xlabel('Frequency [Hz]') plt.xlabel('Frequency [Hz]')
plt.ylabel('Amplitude [m/Hz]') plt.ylabel('Amplitude [m/Hz]')
plt.grid() plt.grid()
plt.show() plt.show()
raw_input() raw_input()
plt.close(f1) plt.close(f1)
return w0, fc
def synthsourcespec(f, omega0, fcorner): def synthsourcespec(f, omega0, fcorner):
''' '''