Extended class MoMw for calculating source spectrum. New functions calcsourcespec, calcMoMw and run_calcMoMw implemented.
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@ -8,10 +8,12 @@ Created August/September 2015.
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import matplotlib.pyplot as plt
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import numpy as np
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from obspy.core import Stream
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from pylot.core.pick.utils import getsignalwin
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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 pylot.core.read.data import Data
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class Magnitude(object):
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'''
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@ -20,7 +22,8 @@ class Magnitude(object):
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and moment magnitudes.
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'''
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def __init__(self, wfstream, To, pwin, iplot, NLLocfile=None, picks=None, rho=None, vp=None):
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def __init__(self, wfstream, To, pwin, iplot, NLLocfile=None, \
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picks=None, rho=None, vp=None, invdir=None):
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'''
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:param: wfstream
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:type: `~obspy.core.stream.Stream
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@ -30,7 +33,7 @@ class Magnitude(object):
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:param: pwin, pick window [To To+pwin] to get maximum
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peak-to-peak amplitude (WApp) or to calculate
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source spectrum (DCfc)
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source spectrum (DCfc) around P onset
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:type: float
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:param: iplot, no. of figure window for plotting interims results
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@ -48,6 +51,9 @@ class Magnitude(object):
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:param: vp [m/s], P-velocity
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:param: integer
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:param: invdir, path to inventory or dataless-SEED file
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:type: string
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'''
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assert isinstance(wfstream, Stream), "%s is not a stream object" % str(wfstream)
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@ -60,6 +66,7 @@ class Magnitude(object):
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self.setrho(rho)
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self.setpicks(picks)
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self.setvp(vp)
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self.setinvdir(invdir)
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self.calcwapp()
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self.calcsourcespec()
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self.run_calcMoMw()
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@ -122,6 +129,12 @@ class Magnitude(object):
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def getfc(self):
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return self.fc
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def setinvdir(self, invdir):
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self.invdir = invdir
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def getinvdir(self):
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return self.invdir
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def getpicdic(self):
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return self.picdic
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@ -190,7 +203,8 @@ class M0Mw(Magnitude):
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Requires results of class w0fc 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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seismic moment Mo and corresponding moment magntiude Mw.
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Dc-value, corner frequency fc, seismic moment Mo and
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corresponding moment magntiude Mw.
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'''
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def run_calcMoMw(self):
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@ -198,12 +212,15 @@ 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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for key in picks:
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if picks[key]['P']['weight'] < 4 and picks[key]['P']['w0'] is not None:
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if picks[key]['P']['weight'] < 4:
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# select waveform
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selwf = wfdat.select(station=key)
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# get corresponding height of source spectrum plateau w0
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w0 = picks[key]['P']['w0']
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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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if len(key) > 4:
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@ -214,14 +231,27 @@ class M0Mw(Magnitude):
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Ppattern = '%s ? ? ? P' % key
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nllocline = getPatternLine(nllocfile, Ppattern)
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delta = float(nllocline.split(None)[21])
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# call subfunction
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[Mo, Mw] = calcMoMw(selwf, w0, self.getrho(), self.getvp(), delta)
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# add Mo and Mw to dictionary
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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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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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delta, self.getinvdir())
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else:
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Mo = None
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Mw = None
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# add w0, fc, Mo and Mw to dictionary
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picks[key]['P']['w0'] = w0
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picks[key]['P']['fc'] = fc
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picks[key]['P']['Mo'] = Mo
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picks[key]['P']['Mw'] = Mw
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self.picdic = picks
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def calcMoMw(wfstream, w0, rho, vp, delta):
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def calcMoMw(wfstream, w0, rho, vp, delta, inv):
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'''
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Subfunction of run_calcMoMw to calculate individual
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seismic moments and corresponding moment magnitudes.
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@ -245,94 +275,135 @@ def calcMoMw(wfstream, w0, rho, vp, delta):
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return Mo, Mw
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class w0fc(Magnitude):
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def calcsourcespec(wfstream, onset, iplot, inventory):
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'''
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Method to calculate the source spectrum and to derive from that the plateau
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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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source model. Has to be derived from instrument corrected displacement traces,
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thus restitution and integration necessary!
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'''
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print ("Calculating source spectrum ....")
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def calcsourcespec(self):
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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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self.w0 = None # DC-value
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self.fc = None # corner frequency
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stream = self.getwfstream()
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tr = stream[0]
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[corzdat, restflag] = data.restituteWFData(inventory, z_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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iwin = getsignalwin(t, self.getTo(), self.getpwin())
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xdat = tr.data[iwin]
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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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# 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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# 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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# 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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# 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 ("w0fc: Determined w0-value: %e m/Hz, \n"
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"Determined corner frequency: %f Hz" % (w01, fc1))
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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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# use of conventional fitting
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[w02, fc2] = fitSourceModel(F, YY.real, Fcin, self.getiplot())
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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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self.w0 = np.median([w01, w02])
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self.fc = np.median([fc1, fc2])
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print("w0fc: Using w0-value = %e m/Hz and fc = %f Hz" % (self.w0, self.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("w0fc: Using w0-value = %e m/Hz and fc = %f Hz" % (w0, fc))
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if self.getiplot() > 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 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' % tr.stats.station)
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plt.xlabel('Time since %s' % tr.stats.starttime)
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plt.ylabel('Displacement [mm]')
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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 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([self.fc, self.fc], [self.w0/100, self.w0], '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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% (self.w0, self.fc))
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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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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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def synthsourcespec(f, omega0, fcorner):
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'''
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