-
Notifications
You must be signed in to change notification settings - Fork 0
/
mtm_obj.py
272 lines (227 loc) · 7.06 KB
/
mtm_obj.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
from scipy import signal
import numpy as np
import math
import matplotlib.pyplot as plt
from ricker import ricker
from shift import shift
from obspy import read
# 1 - Read/synthetize data
tmax = 12
dt = 0.002
nt = math.floor(tmax/dt) + 1
t = np.arange(0,nt)*dt
f = 1.0
wavelet = ricker(f, dt)
d = np.zeros(nt)
d[round(nt/2)] = 1.0
d = np.convolve(d,wavelet,'same') #observed data
misfit = np.zeros(21)
for id in range(-10,11):
#td = 0.1 #time delay (if td > 0, syn arrive after obs)
td = id * 0.1
print(td)
s = shift(d, dt, td) #synthetic data
#st = read('trival_data.sac',debug_headers=True)
#d = st[0].data
#st = read('trival_syn.sac',debug_headers=True)
#s = st[0].data
#dt = st[0].stats.delta
#nt = st[0].stats.npts
#t = np.arange(0,nt)*dt
#plt.plot(t,d,'b')
#plt.plot(t,s,'r')
#plt.xlabel('Time (s)')
#plt.ylabel('Amplitude')
#plt.title('Observed (blue) and synthetic data (red)')
#plt.show()
#print(np.argmax(d))
# print(np.argmax(s))
#plt.magnitude_spectrum(d,Fs=1/dt)
#plt.show()
# 2 - Butterwoth bandpass filter data (optional)
# 3 - Windowing
n1 = 0
n2 = nt
d = d[n1:n2] # d[n1] -> d[n2-1]
s = s[n1:n2] # s[n1] -> s[n2-1]
t = np.arange(n1,n2)*dt # n1*dt -> (n2-1)*dt
nt = len(t)
#plt.plot(t,d,'r')
#plt.plot(t,s,'b')
#plt.xlabel('Time (s)')
#plt.ylabel('Amplitude')
#plt.title('Windowed observed and synthetic data')
#plt.show()
# 4 - pre-process/time domain taper applied to windowed data
alpha = 10
nlen = len(s)
it_axis = np.arange(0,nlen)
cos_taper = 1.0 - np.cos(math.pi * it_axis / (nlen - 1)) ** alpha
d = d * cos_taper
s = s * cos_taper
#plt.plot(t, cos_taper)
#plt.title('Cosine taper')
#plt.show()
#plt.plot(t,d,'r')
#plt.plot(t,s,'b')
#plt.xlabel('Time (s)')
#plt.ylabel('Amplitude')
#plt.title('Tapered observed and synthetic data')
#plt.show()
# 5 - compute_cc
cc = np.correlate(d, s, "same")
ishift = np.argmax(cc) - int(nlen/2)
tshift = ishift*dt
dlnA = 0.5 * math.log(sum(d*d) / sum(s*s) )
#print('Time shift measured by cc:', tshift, 's')
#print('Amplitude difference measured by cc:', dlnA)
# 6 - deconstruct_dat_cc (Apply CC -\delta T and -\delta A to the observed data prior to MTM)
# Why?
d_dec = np.zeros(nlen)
for i in range(0, nlen):
if (i + ishift) > 0 and (i + ishift) < nlen - 1:
d_dec[i] = d[i + ishift]
if ishift < 0:
d_dec[0:-ishift] = d_dec[-ishift+1]
if ishift > 0:
d_dec[nlen-ishift-1:nlen-1] = d_dec[nlen-ishift-2]
d_dec = d_dec * math.exp(-dlnA)
#plt.plot(t,s,'r')
#plt.plot(t,d_dec,'b')
#plt.xlabel('Time (s)')
#plt.ylabel('Amplitude')
#plt.title('Synthetic data and Deconstruct data')
#plt.show()
# 7 - compute_average_error (sigma_t)
#function
# compute_average_error
# 8 - FFT parameters
nextpow2 = math.ceil(math.log2(nt))
nfft = 2 * int(math.pow(2, nextpow2))
f0 = 0.0
df = 1.0/(nfft * dt)
dw = 2*math.pi * df
fnum = int(nfft/2) + 1
w = np.zeros(nfft) # angular frequency vector
w[0:fnum] = dw * np.arange(0,fnum) # positive frequency
w[fnum:nfft] = dw * np.arange(-fnum + 2, 0) # negative frequency
#Spectrum of synthetic data
S = np.fft.fft(s,nfft)
spectrum = np.abs(S)
#plt.plot(spectrum)
#plt.title('Spectrum of synthetic data')
#plt.show()
# Estimate stopping frequency
WTR = 0.02
ampmax = 0.0
k_amp_max = 0
for k in range(0, fnum):
if abs(S[k]) > ampmax:
ampmax = abs(S[k])
k_amp_max = k
wtr_level = ampmax * WTR # water level value to stablize
fmax = fnum
fmax_stop = 0
for k in range(0, fnum):
if abs(S[k]) <= wtr_level and fmax_stop == 0 and k > k_amp_max:
fmax_stop = 1
fmax = k
if abs(S[k]) >= 10.0 * wtr_level and fmax_stop == 1 and k > k_amp_max:
fmax_step = 0
fmax = k
#print('Stopping frequency index',fmax)
#print('Stopping frequency',fmax*df, 'Hz')
# 9 - DPSS
M = len(d)
NW = 2.5
Kmax = int(2.0 * NW)
ntaper = Kmax
dpss = signal.windows.dpss(M, NW, Kmax)
#for i in range(0, Kmax):
#plt.plot(t,dpss[i,:])
#plt.xlabel('Time (s)')
#plt.ylabel('Amplitude')
#plt.title('DPSS')
#plt.show()
# 10 - Transfer function
T = np.zeros(fnum, dtype=complex)
A = np.zeros(fnum, dtype=complex)
B = np.zeros(fnum, dtype=complex)
for i in range(0, ntaper):
#apply time domain taper
dtp = d * dpss[i,:]
stp = s * dpss[i,:]
#apply FFT
DTP = np.fft.fft(dtp,nfft)
STP = np.fft.fft(stp,nfft)
#
for k in range(0,fnum): # sum over taper
A[k] = A[k] + DTP[k] * np.conjugate(STP[k])
B[k] = B[k] + STP[k] * np.conjugate(STP[k])
#plt.plot(t,dtp)
# plt.xlabel('Time (s)')
# plt.ylabel('Amplitude')
# plt.title('DPSS tapered observed data')
#plt.show()
# water level
wtr = 1e-2 #water level
ampmax = 0.0
i_amp_max = 1
for k in range(0, fnum):
if abs(B[k]) > ampmax:
ampmax = abs(B[k])
i_amp_max = k
epsilon = ampmax * wtr**2 # water level value to stablize
#print(epsilon)
for k in range(0, fnum):
if abs(B[k]) > epsilon:
T[k] = A[k] / B[k]
else:
T[k] = A[k] / (B[k] + epsilon)
#calculate phase
phase = np.zeros(fmax)
dtau = np.zeros(fmax)
for k in range(0,fmax):
phase[k] = math.atan2(T[k].imag, T[k].real)
waxis = np.arange(0,fmax)*dw
#plt.plot(waxis,phase)
#plt.title('Phase')
#plt.xlabel('Angular frequency')
#plt.show()
# phase correction
# phase correction parameters, between (PI, 2PI), use a higher value for conservative phase wrapping
PHASE_STEP = 1.5 * math.pi
#dtau[0] = tshift
for k in range(0, fmax):
if k > 0 and k < fmax - 1 :
smth = phase[k + 1] + phase[k - 1] - 2.0 * phase[k]
smth1 = (phase[k + 1] + 2.0*math.pi) + phase[k - 1] - 2.0 * phase[k]
smth2 = (phase[k + 1] - 2.0*math.pi) + phase[k - 1] - 2.0 * phase[k]
if abs(smth1) < abs(smth) and abs(smth1) < abs(smth2) and abs(phase[k] - phase[k+1]) > PHASE_STEP:
for j in range(k+1, fmax):
phase[j] = phase[j] + 2.0*math.pi
if abs(smth2) < abs(smth) and abs(smth2) < abs(smth1) and abs(phase[k] - phase[k+1]) > PHASE_STEP:
for j in range(k+1, fmax):
phase[j] = phase[j] - 2.0*math.pi
if k > 0:
dtau[k] = (-1.0/w[k]) * phase[k] # + tshift
waxis = np.arange(0,fmax)*dw
#plt.plot(waxis,phase)
#plt.xlabel('Angular Frequency')
#plt.ylabel('Phase')
#plt.title('Frequency-dependent Phase')
#plt.show()
#plt.plot(waxis,-dtau)
#plt.xlabel('Angular Frequency')
#plt.ylabel('Time delay')
#plt.title('Time delay')
#plt.show()
# estimate error using CC
# misfit function
w_taper = np.zeros(fnum, dtype=complex)
for k in range(0, fmax):
w_taper[k] = 1.0 - math.cos(math.pi * k/(fmax - 1))**alpha
misfit[id] = float(0.5 * 2.0 * df * np.sum((dtau[0:fmax])**2 * w_taper[0:fmax]))
print('misfit:',misfit)
plt.plot(misfit)
plt.show()