diff --git a/pylot/core/analysis/magnitude.py b/pylot/core/analysis/magnitude.py index 4391d16b..17d3c16f 100644 --- a/pylot/core/analysis/magnitude.py +++ b/pylot/core/analysis/magnitude.py @@ -9,6 +9,7 @@ import matplotlib.pyplot as plt import numpy as np from obspy.core import Stream from pylot.core.pick.utils import getsignalwin +from scipy.optimize import curve_fit class Magnitude(object): ''' @@ -165,21 +166,74 @@ class DCfc(Magnitude): Y = abs(y[: N/2]) L = (N - 1) / tr.stats.sampling_rate f = np.arange(0, fny, 1/L) + + # remove zero-frequency and frequencies above + # corner frequency of seismometer (assumed + # to be 100 Hz) + fi = np.where((f >= 1) & (f < 100)) + F = f[fi] + YY = Y[fi] + # get plateau (DC value) and corner frequency + # initial guess of plateau + DCin = np.mean(YY[0:100]) + # initial guess of corner frequency + # where spectral level reached 50% of flat level + iin = np.where(YY >= 0.5 * DCin) + Fcin = F[iin[0][np.size(iin) - 1]] + fit = synthsourcespec(F, DCin, Fcin) + [optspecfit, pcov] = curve_fit(synthsourcespec, F, YY.real, [DCin, Fcin]) + self.w0 = optspecfit[0] + self.fc = optspecfit[1] + print ("DCfc: Determined DC-value: %f, \n" \ + "Determined corner frequency: %f" % (self.w0, self.fc)) - if self.getiplot() > 1: - f1 = plt.figure(1) + + #if self.getiplot() > 1: + iplot=2 + if iplot > 1: + f1 = plt.figure() plt.subplot(2,1,1) - plt.plot(t, np.multiply(tr, 1000), 'k') # show displacement in mm - plt.plot(t[iwin], np.multiply(xdat, 1000), 'g') # show displacement in mm + # show displacement in mm + plt.plot(t, np.multiply(tr, 1000), 'k') + plt.plot(t[iwin], np.multiply(xdat, 1000), 'g') plt.title('Seismogram and P pulse, station %s' % tr.stats.station) plt.xlabel('Time since %s' % tr.stats.starttime) plt.ylabel('Displacement [mm]') plt.subplot(2,1,2) - plt.semilogy(f, Y.real) - plt.title('Source Spectrum from P Pulse') + plt.semilogy(f, Y.real, 'k') + plt.semilogy(F, YY.real) + plt.semilogy(F, fit, 'g') + plt.title('Source Spectrum from P Pulse, DC=%f m/Hz, fc=%4.1f Hz' \ + % (self.w0, self.fc)) plt.xlabel('Frequency [Hz]') plt.ylabel('Amplitude [m/Hz]') plt.show() raw_input() plt.close(f1) + + +def synthsourcespec(f, omega0, fcorner): + ''' + Calculates synthetic source spectrum from given plateau and corner + frequency assuming Akis omega-square model. + + :param: f, frequencies + :type: array + + :param: omega0, DC-value (plateau) of source spectrum + :type: float + + :param: fcorner, corner frequency of source spectrum + :type: float + ''' + + #ssp = omega0 / (pow(2, (1 + f / fcorner))) + ssp = omega0 / (1 + pow(2, (f / fcorner))) + + #plt.plot(f, ssp) + #plt.show() + #raw_input() + + return ssp +