Included AR prediction on all 3 components
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Ludger Küperkoch
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2a385512ee
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8fa9ec74c0
@ -17,7 +17,6 @@ autoregressive prediction: application ot local and regional distances, Geophys.
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"""
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import numpy as np
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from obspy.core import Stream
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import scipy
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class CharacteristicFunction(object):
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'''
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@ -125,7 +124,10 @@ class CharacteristicFunction(object):
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start = self.cut[0] / self.dt
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stop = self.cut[1] / self.dt
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if len(self.orig_data) == 1:
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data = self.orig_data[0].data[start:stop]
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zz = self.orig_data.copy()
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z1 = zz[0].copy()
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zz[0].data = z1.data[start:stop]
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data = zz
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return data
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elif len(self.orig_data) == 2:
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hh = self.orig_data.copy()
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@ -135,13 +137,19 @@ class CharacteristicFunction(object):
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hh[1].data = h2.data[start:stop]
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data = hh
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return data
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elif len(self.orig_data) == 3:
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hh = self.orig_data.copy()
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h1 = hh[0].copy()
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h2 = hh[1].copy()
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h3 = hh[2].copy()
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hh[0].data = h1.data[start:stop]
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hh[1].data = h2.data[start:stop]
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hh[2].data = h3.data[start:stop]
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data = hh
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return data
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else:
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if len(self.orig_data) == 1:
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data = self.orig_data[0]
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return data
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elif len(self.orig_data) == 2:
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data = self.orig_data
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return data
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data = self.orig_data
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return data
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def calcCF(self, data=None):
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self.cf = data
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@ -160,7 +168,8 @@ class AICcf(CharacteristicFunction):
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def calcCF(self, data):
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print 'Calculating AIC ...'
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xnp = self.getDataArray()
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x = self.getDataArray()
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xnp = x[0].data
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datlen = len(xnp)
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k = np.arange(1, datlen)
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cf = np.zeros(datlen)
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@ -188,7 +197,8 @@ class HOScf(CharacteristicFunction):
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def calcCF(self, data):
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xnp = self.getDataArray(self.getCut())
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x = self.getDataArray(self.getCut())
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xnp =x[0].data
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if self.getOrder() == 3: # this is skewness
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print 'Calculating skewness ...'
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y = np.power(xnp, 3)
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@ -206,8 +216,10 @@ class HOScf(CharacteristicFunction):
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#moving windows
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LTA = np.zeros(len(xnp))
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for j in range(3, len(xnp)):
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if j <= ilta:
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for j in range(0, len(xnp)):
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if j < 4:
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LTA[j] = 0
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elif j <= ilta:
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lta = (y[j] + lta * (j-1)) / j
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lta1 = (y1[j] + lta1 * (j-1)) / j
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else:
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@ -218,9 +230,7 @@ class HOScf(CharacteristicFunction):
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LTA[j] = lta / np.power(lta1, 1.5)
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elif self.getOrder() == 4:
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LTA[j] = lta / np.power(lta1, 2)
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LTA[0:3] = 0
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self.cf = LTA
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@ -229,7 +239,8 @@ class ARZcf(CharacteristicFunction):
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def calcCF(self, data):
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print 'Calculating AR-prediction error from single trace ...'
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xnp = self.getDataArray(self.getCut())
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x = self.getDataArray(self.getCut())
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xnp = x[0].data
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#some parameters needed
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#add noise to time series
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xnoise = xnp + np.random.normal(0.0, 1.0, len(xnp)) * self.getFnoise() * max(abs(xnp))
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@ -240,17 +251,9 @@ class ARZcf(CharacteristicFunction):
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lpred = int(np.ceil(self.getTime2() / self.getIncrement())) #length of AR-prediction window [samples]
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cf = []
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step = ldet + self.getOrder() - 1
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for i in range(ldet + self.getOrder() - 1, tend - lpred + 1):
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if i == step:
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'''
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In order to speed up the algorithm AR parameters are kept for time
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intervals of length ldet
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'''
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#determination of AR coefficients
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self.arDetZ(xnoise, self.getOrder(), i-ldet, i)
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step = step + ldet
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for i in range(ldet + self.getOrder() - 1, tend - lpred + 1, lpred / 16):
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#determination of AR coefficients
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self.arDetZ(xnoise, self.getOrder(), i-ldet, i)
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#AR prediction of waveform using calculated AR coefficients
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self.arPredZ(xnp, self.arpara, i + 1, lpred)
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#prediction error = CF
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@ -298,7 +301,7 @@ class ARZcf(CharacteristicFunction):
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A[ji,ki] = A[ki,ji]
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#apply Moore-Penrose pseudo inverse for SVD yielding the AR-parameters
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#apply Moore-Penrose inverse for SVD yielding the AR-parameters
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self.arpara = np.dot(np.linalg.pinv(A), rhs)
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def arPredZ(self, data, arpara, rind, lpred):
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@ -359,17 +362,8 @@ class ARHcf(CharacteristicFunction):
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lpred = int(np.ceil(self.getTime2() / self.getIncrement())) #length of AR-prediction window [samples]
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cf = []
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arstep = ldet + self.getOrder() - 3
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for i in range(ldet + self.getOrder() - 3, tend - lpred + 1):
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if i == arstep:
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'''
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In order to speed up the algorithm AR parameters are kept for time
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intervals of length ldet
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'''
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#determination of AR coefficients
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self.arDetH(Xnoise, self.getOrder(), i-ldet, i)
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arstep = arstep + ldet
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for i in range(ldet + self.getOrder() - 3, tend - lpred + 1, lpred / 4):
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self.arDetH(Xnoise, self.getOrder(), i-ldet, i)
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#AR prediction of waveform using calculated AR coefficients
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self.arPredH(xnp, self.arpara, i + 1, lpred)
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#prediction error = CF
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@ -420,14 +414,8 @@ class ARHcf(CharacteristicFunction):
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A[ji,ki] = A[ki,ji]
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#apply Moore-Penrose pseudo inverse for SVD yielding the AR-parameters
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#self.arpara = np.dot(np.linalg.pinv(A), rhs)
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#self.arpara = np.linalg.solve(A, rhs)
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#arpara = scipy.linalg.lstsq(A, rhs)
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#arpara = np.linalg.lstsq(A, rhs)
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#self.arpara = arpara[0]
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self.arpara = np.dot(scipy.linalg.pinv(A), rhs)
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#apply Moore-Penrose inverse for SVD yielding the AR-parameters
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self.arpara = np.dot(np.linalg.pinv(A), rhs)
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def arPredH(self, data, arpara, rind, lpred):
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'''
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@ -472,4 +460,122 @@ class ARHcf(CharacteristicFunction):
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class AR3Ccf(CharacteristicFunction):
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pass
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def calcCF(self, data):
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print 'Calculating AR-prediction error from all 3 components ...'
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xnp = self.getDataArray(self.getCut())
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#some parameters needed
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#add noise to time series
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xenoise = xnp[0].data + np.random.normal(0.0, 1.0, len(xnp[0].data)) * self.getFnoise() * max(abs(xnp[0].data))
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xnnoise = xnp[1].data + np.random.normal(0.0, 1.0, len(xnp[1].data)) * self.getFnoise() * max(abs(xnp[1].data))
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xznoise = xnp[2].data + np.random.normal(0.0, 1.0, len(xnp[2].data)) * self.getFnoise() * max(abs(xnp[2].data))
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Xnoise = np.array( [xenoise.tolist(), xnnoise.tolist(), xznoise.tolist()] )
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tend = len(xnp[0].data)
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#Time1: length of AR-determination window [sec]
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#Time2: length of AR-prediction window [sec]
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ldet = int(round(self.getTime1() / self.getIncrement())) #length of AR-determination window [samples]
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lpred = int(np.ceil(self.getTime2() / self.getIncrement())) #length of AR-prediction window [samples]
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cf = []
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for i in range(ldet + self.getOrder() - 3, tend - lpred + 1, lpred / 4):
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self.arDet3C(Xnoise, self.getOrder(), i-ldet, i)
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#AR prediction of waveform using calculated AR coefficients
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self.arPred3C(xnp, self.arpara, i + 1, lpred)
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#prediction error = CF
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err = np.sqrt(np.sum(np.power(self.xpred[0][i:i + lpred] - xnp[0][i:i + lpred], 2) \
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+ np.power(self.xpred[1][i:i + lpred] - xnp[1][i:i + lpred], 2) \
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+ np.power(self.xpred[2][i:i + lpred] - xnp[2][i:i + lpred], 2)) / (3 * lpred))
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cf.append(err)
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#convert list to numpy array
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cf = np.asarray(cf)
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self.cf = cf
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def arDet3C(self, data, order, rind, ldet):
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'''
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Function to calculate AR parameters arpara after Thomas Meier (CAU), published
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in Kueperkoch et al. (2012). This function solves SLE using the Moore-
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Penrose inverse, i.e. the least-squares approach. "data" is a structured array.
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AR parameters are calculated based on both horizontal components and vertical
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componant.
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:param: data, horizontal component seismograms to calculate AR parameters from
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:type: structured array
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:param: order, order of AR process
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:type: int
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:param: rind, first running summation index
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:type: int
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:param: ldet, length of AR-determination window (=end of summation index)
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:type: int
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Output: AR parameters arpara
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'''
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#recursive calculation of data vector (right part of eq. 6.5 in Kueperkoch et al. (2012)
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rhs = np.zeros(self.getOrder())
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for k in range(0, self.getOrder()):
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for i in range(rind, ldet):
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rhs[k] = rhs[k] + data[0,i] * data[0,i - k] + data[1,i] * data[1,i - k] \
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+ data[2,i] * data[2,i - k]
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#recursive calculation of data array (second sum at left part of eq. 6.5 in Kueperkoch et al. 2012)
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A = np.zeros((4,4))
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for k in range(1, self.getOrder() + 1):
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for j in range(1, k + 1):
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for i in range(rind, ldet):
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ki = k - 1
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ji = j - 1
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A[ki,ji] = A[ki,ji] + data[0,i - ji] * data[0,i - ki] + data[1,i - ji] *data[1,i - ki] \
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+ data[2,i - ji] *data[2,i - ki]
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A[ji,ki] = A[ki,ji]
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#apply Moore-Penrose inverse for SVD yielding the AR-parameters
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self.arpara = np.dot(np.linalg.pinv(A), rhs)
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def arPred3C(self, data, arpara, rind, lpred):
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'''
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Function to predict waveform, assuming an autoregressive process of order
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p (=size(arpara)), with AR parameters arpara calculated in arDet3C. After
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Thomas Meier (CAU), published in Kueperkoch et al. (2012).
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:param: data, horizontal and vertical component seismograms to be predicted
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:type: structured array
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:param: arpara, AR parameters
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:type: float
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:param: rind, first running summation index
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:type: int
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:param: lpred, length of prediction window (=end of summation index)
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:type: int
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Output: predicted waveform z
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:type: structured array
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'''
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#be sure of the summation indeces
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if rind < len(arpara) + 1:
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rind = len(arpara) + 1
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if rind > len(data[0]) - lpred + 1:
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rind = len(data[0]) - lpred + 1
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if lpred < 1:
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lpred = 1
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if lpred > len(data[0]) - 1:
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lpred = len(data[0]) - 1
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z1 = np.append(data[0][0:rind], np.zeros(lpred))
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z2 = np.append(data[1][0:rind], np.zeros(lpred))
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z3 = np.append(data[2][0:rind], np.zeros(lpred))
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for i in range(rind, rind + lpred):
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for j in range(1, len(arpara) + 1):
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ji = j - 1
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z1[i] = z1[i] + arpara[ji] * z1[i - ji]
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z2[i] = z2[i] + arpara[ji] * z2[i - ji]
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z3[i] = z3[i] + arpara[ji] * z3[i - ji]
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z = np.array( [z1.tolist(), z2.tolist(), z3.tolist()] )
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self.xpred = z
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