Included rotation of seismograms using Obspys stream.rotation for a more reliable estimation of source spectra.
This commit is contained in:
Ludger Küperkoch
parent
77ad274f8f
commit
d6ae82e070
@ -12,7 +12,7 @@ from obspy.core import Stream, UTCDateTime
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from pylot.core.pick.utils import getsignalwin, crossings_nonzero_all
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from pylot.core.util.utils import getPatternLine
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from scipy.optimize import curve_fit
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from scipy import integrate
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from scipy import integrate, signal
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from pylot.core.read.data import Data
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class Magnitude(object):
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@ -200,7 +200,7 @@ class WApp(Magnitude):
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class M0Mw(Magnitude):
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'''
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Method to calculate seismic moment Mo and moment magnitude Mw.
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Requires results of class w0fc for calculating plateau w0
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Requires results of class calcsourcespec for calculating plateau w0
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and corner frequency fc of source spectrum, respectively. Uses
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subfunction calcMoMw.py. Returns modified dictionary of picks including
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Dc-value, corner frequency fc, seismic moment Mo and
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@ -212,17 +212,12 @@ class M0Mw(Magnitude):
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picks = self.getpicks()
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nllocfile = self.getNLLocfile()
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wfdat = self.getwfstream()
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# get vertical component data only
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zdat = wfdat.select(component="Z")
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if len(zdat) == 0: # check for other components
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zdat = wfdat.select(component="3")
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self.picdic = None
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for key in picks:
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if picks[key]['P']['weight'] < 4:
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# select waveform
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selwf = zdat.select(station=key)
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# get hypocentral distance of station
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# from NLLoc-location file
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selwf = wfdat.select(station=key)
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if len(key) > 4:
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Ppattern = '%s ? ? ? P' % key
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elif len(key) == 4:
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@ -230,15 +225,22 @@ class M0Mw(Magnitude):
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elif len(key) < 4:
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Ppattern = '%s ? ? ? P' % key
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nllocline = getPatternLine(nllocfile, Ppattern)
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# get hypocentral distance, station azimuth and
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# angle of incidence from NLLoc-location file
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delta = float(nllocline.split(None)[21])
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az = float(nllocline.split(None)[22])
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inc = float(nllocline.split(None)[24])
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# call subfunction to estimate source spectrum
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# and to derive w0 and fc
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[w0, fc] = calcsourcespec(selwf, picks[key]['P']['mpp'], \
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self.getiplot(), self.getinvdir())
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self.getinvdir(), az, inc, self.getiplot())
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if w0 is not None:
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# call subfunction to calculate Mo and Mw
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[Mo, Mw] = calcMoMw(selwf, w0, self.getrho(), self.getvp(), \
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zdat = selwf.select(component="Z")
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if len(zdat) == 0: # check for other components
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zdat = selwf.select(component="3")
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[Mo, Mw] = calcMoMw(zdat, w0, self.getrho(), self.getvp(), \
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delta, self.getinvdir())
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else:
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Mo = None
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@ -276,131 +278,180 @@ def calcMoMw(wfstream, w0, rho, vp, delta, inv):
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def calcsourcespec(wfstream, onset, iplot, inventory):
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def calcsourcespec(wfstream, onset, inventory, azimuth, incidence, iplot):
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'''
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Subfunction to calculate the source spectrum and to derive from that the plateau
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(usually called omega0) and the corner frequency assuming Aki's omega-square
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source model. Has to be derived from instrument corrected displacement traces,
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thus restitution and integration necessary!
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thus restitution and integration necessary! Integrated traces have to be rotated
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into ray-coordinate system ZNE => LQT!
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'''
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print ("Calculating source spectrum ....")
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fc = None
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w0 = None
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data = Data()
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z_copy = wfstream.copy()
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[corzdat, restflag] = data.restituteWFData(inventory, z_copy)
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wf_copy = wfstream.copy()
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[cordat, restflag] = data.restituteWFData(inventory, wf_copy)
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if restflag == 1:
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# integrate to displacment
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corintzdat = integrate.cumtrapz(corzdat[0], None, corzdat[0].stats.delta)
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z_copy[0].data = corintzdat
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tr = z_copy[0]
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# get window after P pulse for
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# calculating source spectrum
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if tr.stats.sampling_rate <= 100:
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winzc = tr.stats.sampling_rate
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elif tr.stats.sampling_rate > 100 and \
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tr.stats.sampling_rate <= 200:
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winzc = 0.5 * tr.stats.sampling_rate
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elif tr.stats.sampling_rate > 200 and \
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tr.stats.sampling_rate <= 400:
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winzc = 0.2 * tr.stats.sampling_rate
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elif tr.stats.sampling_rate > 400:
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winzc = tr.stats.sampling_rate
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tstart = UTCDateTime(tr.stats.starttime)
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tonset = onset.timestamp -tstart.timestamp
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impickP = tonset * tr.stats.sampling_rate
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wfzc = tr.data[impickP : impickP + winzc]
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# get time array
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t = np.arange(0, len(tr) * tr.stats.delta, tr.stats.delta)
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# calculate spectrum using only first cycles of
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# waveform after P onset!
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zc = crossings_nonzero_all(wfzc)
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if np.size(zc) == 0 or len(zc) <= 3:
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print ("Something is wrong with the waveform, "
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"no zero crossings derived!")
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print ("No calculation of source spectrum possible!")
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plotflag = 0
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else:
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plotflag = 1
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index = min([3, len(zc) - 1])
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calcwin = (zc[index] - zc[0]) * z_copy[0].stats.delta
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iwin = getsignalwin(t, tonset, calcwin)
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xdat = tr.data[iwin]
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zdat = cordat.select(component="Z")
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if len(zdat) == 0:
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zdat = cordat.select(component="3")
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cordat_copy = cordat.copy()
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# get equal time stamps and lengths of traces
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# necessary for rotation of traces
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tr0start = cordat_copy[0].stats.starttime
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tr0start = tr0start.timestamp
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tr0end = cordat_copy[0].stats.endtime
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tr0end = tr0end.timestamp
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tr1start = cordat_copy[1].stats.starttime
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tr1start = tr1start.timestamp
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tr1end = cordat_copy[1].stats.endtime
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tr1end = tr1end.timestamp
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tr2start = cordat_copy[2].stats.starttime
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tr2start = tr2start.timestamp
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tr2end = cordat_copy[0].stats.endtime
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tr2end = tr2end.timestamp
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trstart = UTCDateTime(max([tr0start, tr1start, tr2start]))
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trend = UTCDateTime(min([tr0end, tr1end, tr2end]))
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cordat_copy.trim(trstart, trend)
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minlen = min([len(cordat_copy[0]), len(cordat_copy[1]), len(cordat_copy[2])])
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cordat_copy[0].data = cordat_copy[0].data[0:minlen]
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cordat_copy[1].data = cordat_copy[1].data[0:minlen]
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cordat_copy[2].data = cordat_copy[2].data[0:minlen]
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try:
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# rotate into LQT (ray-coordindate-) system using Obspy's rotate
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# L: P-wave direction
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# Q: SV-wave direction
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# T: SH-wave direction
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LQT=cordat_copy.rotate('ZNE->LQT',azimuth, incidence)
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ldat = LQT.select(component="L")
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if len(ldat) == 0:
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# yet Obspy's rotate can not handle channels 3/2/1
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ldat = LQT.select(component="Z")
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# fft
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fny = tr.stats.sampling_rate / 2
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l = len(xdat) / tr.stats.sampling_rate
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n = tr.stats.sampling_rate * l # number of fft bins after Bath
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# find next power of 2 of data length
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m = pow(2, np.ceil(np.log(len(xdat)) / np.log(2)))
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N = int(np.power(m, 2))
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y = tr.stats.delta * np.fft.fft(xdat, N)
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Y = abs(y[: N/2])
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L = (N - 1) / tr.stats.sampling_rate
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f = np.arange(0, fny, 1/L)
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# integrate to displacement
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# unrotated vertical component (for copmarison)
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inttrz = signal.detrend(integrate.cumtrapz(zdat[0].data, None, \
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zdat[0].stats.delta))
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# rotated component Z => L
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Ldat = signal.detrend(integrate.cumtrapz(ldat[0].data, None, \
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ldat[0].stats.delta))
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# remove zero-frequency and frequencies above
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# corner frequency of seismometer (assumed
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# to be 100 Hz)
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fi = np.where((f >= 1) & (f < 100))
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F = f[fi]
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YY = Y[fi]
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# get plateau (DC value) and corner frequency
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# initial guess of plateau
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w0in = np.mean(YY[0:100])
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# initial guess of corner frequency
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# where spectral level reached 50% of flat level
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iin = np.where(YY >= 0.5 * w0in)
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Fcin = F[iin[0][np.size(iin) - 1]]
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# get window after P pulse for
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# calculating source spectrum
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if zdat[0].stats.sampling_rate <= 100:
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winzc = zdat[0].stats.sampling_rate
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elif zdat[0].stats.sampling_rate > 100 and \
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zdat[0].stats.sampling_rate <= 200:
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winzc = 0.5 * zdat[0].stats.sampling_rate
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elif zdat[0].stats.sampling_rate > 200 and \
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zdat[0].stats.sampling_rate <= 400:
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winzc = 0.2 * zdat[0].stats.sampling_rate
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elif zdat[0].stats.sampling_rate > 400:
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winzc = zdat[0].stats.sampling_rate
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tstart = UTCDateTime(zdat[0].stats.starttime)
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tonset = onset.timestamp -tstart.timestamp
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impickP = tonset * zdat[0].stats.sampling_rate
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wfzc = Ldat[impickP : impickP + winzc]
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# get time array
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t = np.arange(0, len(inttrz) * zdat[0].stats.delta, \
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zdat[0].stats.delta)
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# calculate spectrum using only first cycles of
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# waveform after P onset!
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zc = crossings_nonzero_all(wfzc)
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if np.size(zc) == 0 or len(zc) <= 3:
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print ("calcsourcespec: Something is wrong with the waveform, "
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"no zero crossings derived!")
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print ("No calculation of source spectrum possible!")
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plotflag = 0
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else:
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plotflag = 1
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index = min([3, len(zc) - 1])
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calcwin = (zc[index] - zc[0]) * zdat[0].stats.delta
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iwin = getsignalwin(t, tonset, calcwin)
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xdat = Ldat[iwin]
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# use of implicit scipy otimization function
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fit = synthsourcespec(F, w0in, Fcin)
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[optspecfit, pcov] = curve_fit(synthsourcespec, F, YY.real, [w0in, Fcin])
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w01 = optspecfit[0]
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fc1 = optspecfit[1]
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print ("w0fc: Determined w0-value: %e m/Hz, \n"
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"Determined corner frequency: %f Hz" % (w01, fc1))
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# fft
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fny = zdat[0].stats.sampling_rate / 2
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l = len(xdat) / zdat[0].stats.sampling_rate
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# number of fft bins after Bath
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n = zdat[0].stats.sampling_rate * l
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# find next power of 2 of data length
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m = pow(2, np.ceil(np.log(len(xdat)) / np.log(2)))
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N = int(np.power(m, 2))
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y = zdat[0].stats.delta * np.fft.fft(xdat, N)
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Y = abs(y[: N/2])
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L = (N - 1) / zdat[0].stats.sampling_rate
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f = np.arange(0, fny, 1/L)
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# remove zero-frequency and frequencies above
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# corner frequency of seismometer (assumed
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# to be 100 Hz)
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fi = np.where((f >= 1) & (f < 100))
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F = f[fi]
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YY = Y[fi]
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# get plateau (DC value) and corner frequency
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# initial guess of plateau
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w0in = np.mean(YY[0:100])
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# initial guess of corner frequency
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# where spectral level reached 50% of flat level
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iin = np.where(YY >= 0.5 * w0in)
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Fcin = F[iin[0][np.size(iin) - 1]]
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# use of implicit scipy otimization function
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fit = synthsourcespec(F, w0in, Fcin)
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[optspecfit, pcov] = curve_fit(synthsourcespec, F, YY.real, [w0in, Fcin])
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w01 = optspecfit[0]
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fc1 = optspecfit[1]
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print ("calcsourcespec: Determined w0-value: %e m/Hz, \n"
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"Determined corner frequency: %f Hz" % (w01, fc1))
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# use of conventional fitting
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[w02, fc2] = fitSourceModel(F, YY.real, Fcin, iplot)
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# use of conventional fitting
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[w02, fc2] = fitSourceModel(F, YY.real, Fcin, iplot)
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# get w0 and fc as median
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w0 = np.median([w01, w02])
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fc = np.median([fc1, fc2])
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print("w0fc: Using w0-value = %e m/Hz and fc = %f Hz" % (w0, fc))
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# get w0 and fc as median
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w0 = np.median([w01, w02])
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fc = np.median([fc1, fc2])
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print("calcsourcespec: Using w0-value = %e m/Hz and fc = %f Hz" % (w0, fc))
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except TypeError as er:
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raise TypeError('''{0}'''.format(er))
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if iplot > 1:
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f1 = plt.figure()
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plt.subplot(2,1,1)
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# show displacement in mm
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plt.plot(t, np.multiply(tr, 1000), 'k')
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if plotflag == 1:
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plt.plot(t[iwin], np.multiply(xdat, 1000), 'g')
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plt.title('Seismogram and P Pulse, Station %s-%s' \
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% (tr.stats.station, tr.stats.channel))
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else:
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plt.title('Seismogram, Station %s-%s' \
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% (tr.stats.station, tr.stats.channel))
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plt.xlabel('Time since %s' % tr.stats.starttime)
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plt.ylabel('Displacement [mm]')
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if iplot > 1:
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f1 = plt.figure()
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tLdat = np.arange(0, len(Ldat) * zdat[0].stats.delta, \
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zdat[0].stats.delta)
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plt.subplot(2,1,1)
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# show displacement in mm
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p1, = plt.plot(t, np.multiply(inttrz, 1000), 'k')
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p2, = plt.plot(tLdat, np.multiply(Ldat, 1000))
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plt.legend([p1, p2], ['Displacement', 'Rotated Displacement'])
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if plotflag == 1:
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plt.plot(t[iwin], np.multiply(xdat, 1000), 'g')
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plt.title('Seismogram and P Pulse, Station %s-%s' \
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% (zdat[0].stats.station, zdat[0].stats.channel))
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else:
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plt.title('Seismogram, Station %s-%s' \
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% (zdat[0].stats.station, zdat[0].stats.channel))
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plt.xlabel('Time since %s' % zdat[0].stats.starttime)
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plt.ylabel('Displacement [mm]')
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if plotflag == 1:
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plt.subplot(2,1,2)
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plt.loglog(f, Y.real, 'k')
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plt.loglog(F, YY.real)
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plt.loglog(F, fit, 'g')
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plt.loglog([fc, fc], [w0/100, w0], 'g')
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plt.title('Source Spectrum from P Pulse, w0=%e m/Hz, fc=%6.2f Hz' \
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% (w0, fc))
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plt.xlabel('Frequency [Hz]')
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plt.ylabel('Amplitude [m/Hz]')
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plt.grid()
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plt.show()
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raw_input()
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plt.close(f1)
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if plotflag == 1:
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plt.subplot(2,1,2)
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plt.loglog(f, Y.real, 'k')
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plt.loglog(F, YY.real)
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plt.loglog(F, fit, 'g')
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plt.loglog([fc, fc], [w0/100, w0], 'g')
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plt.title('Source Spectrum from P Pulse, w0=%e m/Hz, fc=%6.2f Hz' \
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% (w0, fc))
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plt.xlabel('Frequency [Hz]')
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plt.ylabel('Amplitude [m/Hz]')
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plt.grid()
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plt.show()
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raw_input()
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plt.close(f1)
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return w0, fc
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@ -474,8 +525,13 @@ def fitSourceModel(f, S, fc0, iplot):
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STD.append(stddc + stdFC)
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# get best found w0 anf fc from minimum
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fc = fc[np.argmin(STD)]
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w0 = w0[np.argmin(STD)]
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if len(STD) > 0:
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fc = fc[np.argmin(STD)]
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w0 = w0[np.argmin(STD)]
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elif len(STD) == 0:
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fc = fc0
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w0 = max(S)
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print("fitSourceModel: best fc: %fHz, best w0: %e m/Hz" \
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% (fc, w0))
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