Included autoregressive prediction on horizontal components
This commit is contained in:
Ludger Küperkoch
parent
fbce83293d
commit
03033f57a1
@ -17,6 +17,7 @@ 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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@ -46,10 +47,10 @@ class CharacteristicFunction(object):
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:type: float (optional, only for AR)
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'''
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assert isinstance(data, Stream), "%s is not a Stream object" % str(data)
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assert isinstance(data, Stream), "%s is not a stream object" % str(data)
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self.orig_data = data[0]
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self.dt = self.orig_data.stats.delta
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self.orig_data = data
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self.dt = self.orig_data[0].stats.delta
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self.setCut(cut)
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self.setTime1(t1)
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self.setTime2(t2)
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@ -118,26 +119,33 @@ class CharacteristicFunction(object):
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cutting window
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'''
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if cut is not None:
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if self.cut[0] == 0:
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start = 0
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else:
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start = self.cut[0] / self.dt
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stop = self.cut[1] / self.dt
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data = self.orig_data.data[start:stop]
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return data
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return self.orig_data.data
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if self.cut[0] == 0:
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start = 0
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else:
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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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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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h1 = hh[0].copy()
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h2 = hh[1].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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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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def calcCF(self, data=None):
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self.cf = data
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def arDet(self, data, order, rind, ldet):
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pass
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def arPred(self, data, arpara, rind, lpred):
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pass
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class AICcf(CharacteristicFunction):
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'''
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@ -150,6 +158,7 @@ class AICcf(CharacteristicFunction):
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'''
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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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datlen = len(xnp)
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@ -158,8 +167,8 @@ class AICcf(CharacteristicFunction):
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cumsumcf = np.cumsum(np.power(xnp, 2))
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i = np.where(cumsumcf == 0)
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cumsumcf[i] = np.finfo(np.float64).eps
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cf[k] = ((k - 1) * np.log(cumsumcf[k] / k) + (datlen - k + 1) *
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np.log((cumsumcf[datlen - 1] -
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cf[k] = ((k - 1) * np.log(cumsumcf[k] / k) + (datlen - k + 1) *
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np.log((cumsumcf[datlen - 1] -
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cumsumcf[k - 1]) / (datlen - k + 1)))
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cf[0] = cf[1]
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inf = np.isinf(cf)
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@ -180,7 +189,6 @@ class HOScf(CharacteristicFunction):
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def calcCF(self, data):
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xnp = self.getDataArray(self.getCut())
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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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@ -190,22 +198,22 @@ class HOScf(CharacteristicFunction):
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y = np.power(xnp, 4)
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y1 = np.power(xnp, 2)
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# Initialisation
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# t2: long term moving window
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#Initialisation
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#t2: long term moving window
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ilta = round(self.getTime2() / self.getIncrement())
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lta = y[0]
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lta1 = y1[0]
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# moving windows
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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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lta = (y[j] + lta * (j - 1)) / j
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lta1 = (y1[j] + lta1 * (j - 1)) / j
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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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lta = (y[j] - y[j - ilta]) / ilta + lta
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lta1 = (y1[j] - y1[j - ilta]) / ilta + lta1
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# define LTA
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#define LTA
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if self.getOrder() == 3:
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LTA[j] = lta / np.power(lta1, 1.5)
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elif self.getOrder() == 4:
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@ -222,39 +230,38 @@ class ARZcf(CharacteristicFunction):
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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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# some parameters needed
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# add noise to time series
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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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tend = len(xnp)
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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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#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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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 lpred
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'''
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# determination of AR coefficients
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self.arDet(xnoise, self.getOrder(), i - ldet, i)
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step = step + lpred
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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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# AR prediction of waveform using calculated AR coefficients
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self.arPred(xnp, self.arpara, i + 1, lpred)
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# prediction error = CF
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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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err = np.sqrt(np.sum(np.power(self.xpred[i:i + lpred] - xnp[i:i + lpred], 2)) / lpred)
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cf.append(err)
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# convert list to numpy array
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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 arDet(self, data, order, rind, ldet):
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def arDetZ(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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@ -274,27 +281,27 @@ class ARZcf(CharacteristicFunction):
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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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#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[i] * data[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.array([[0, 0], [0, 0]])
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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((2,2))
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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[i - ji] * data[i - ki]
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A[ki,ji] = A[ki,ji] + data[i - ji] * data[i - ki]
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A[ji, ki] = A[ki, ji]
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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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#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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def arPred(self, data, arpara, rind, lpred):
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def arPredZ(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 arDet. After
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@ -313,7 +320,7 @@ class ARZcf(CharacteristicFunction):
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Output: predicted waveform z
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'''
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# be sure of the summation indeces
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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) - lpred + 1:
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@ -334,8 +341,134 @@ class ARZcf(CharacteristicFunction):
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class ARHcf(CharacteristicFunction):
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pass
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def calcCF(self, data):
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print 'Calculating AR-prediction error from both horizontal traces ...'
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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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Xnoise = np.array( [xenoise.tolist(), xnnoise.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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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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#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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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)) / (2 * 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 arDetH(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 in order
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to account for polarization.
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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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#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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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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def arPredH(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 arDet. After
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Thomas Meier (CAU), published in Kueperkoch et al. (2012).
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:param: data, horizontal 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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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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z = np.array( [z1.tolist(), z2.tolist()] )
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self.xpred = z
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class AR3Ccf(CharacteristicFunction):
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