-
Notifications
You must be signed in to change notification settings - Fork 11
/
hypo.py
2736 lines (2314 loc) · 90 KB
/
hypo.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
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
# -*- coding: utf-8 -*-
"""
HYPOcenter location from arrival time data in PYthon.
There are currently 4 hypocenter location functions in this module
hypoloc : Locate hypocenters for constant velocity model
hypolocPS : Locate hypocenters from P- and S-wave arrival time data for
constant velocity models
jointHypoVel : Joint hypocenter-velocity inversion on a regular grid (cubic
cells)
jointHypoVelPS : Joint hypocenter-velocity inversion of P- and S-wave arrival
time data
See the tutorials for some examples. There is also a notebook about the theory.
Created on Wed Nov 2 10:29:32 2016
@author: giroux
"""
import sys
from multiprocessing import Process, Queue
import numpy as np
import scipy.sparse as sp
import scipy.sparse.linalg as spl
from scipy.linalg import lstsq
import matplotlib.pyplot as plt
from ttcrpy.rgrid import Grid3d
# %% hypoloc
def hypoloc(data, rcv, V, hinit, maxit, convh, tol=1e-6, verbose=False):
"""
Locate hypocenters for constant velocity model.
Parameters
----------
data : array_like, shape (m, 3)
input data
first column is event ID number
second column is arrival time
third column is receiver index
rcv : array_like, shape (n, 3)
coordinates of receivers
first column is easting
second column is northing
third column is elevation
V : float
wave velocity
hinit : array_like, shape (m, 3)
initial hypocenter coordinate. The format is the same as for data
maxit : int
max number of iterations
convh : float
convergence criterion (units of distance)
tol : float
Stopping tolerance
verbose : bool
run in verbose mode
Returns
-------
loc : ndarray of float
hypocenter coordinates
res : ndarray of float
norm of residuals at each iteration for each event (nev x maxit)
"""
if verbose:
print('\n *** Hypocenter inversion ***\n')
evID = np.unique(data[:, 0])
loc = hinit.copy()
res = np.zeros((evID.size, maxit+1))
nev = 0
for eid in evID:
ind = eid == data[:, 0]
ix = data[ind, 2]
x = np.zeros((ix.size, 3))
for i in np.arange(ix.size):
x[i, :] = rcv[int(1.e-6 + ix[i]), :]
t = data[ind, 1]
inh = eid == loc[:, 0]
if verbose:
print('Locating hypocenters no ' + str(int(1.e-6 + eid)))
sys.stdout.flush()
xinit = loc[inh, 2:]
tinit = loc[inh, 1]
dx = x[:, 0] - xinit[0, 0]
dy = x[:, 1] - xinit[0, 1]
dz = x[:, 2] - xinit[0, 2]
ds = np.sqrt(dx * dx + dy * dy + dz * dz)
tcalc = tinit + ds / V
r = t - tcalc
res[nev, 0] = np.linalg.norm(r)
for it in range(maxit):
H = np.ones((x.shape[0], 4))
H[:, 1] = -1.0 / V * dx / ds
H[:, 2] = -1.0 / V * dy / ds
H[:, 3] = -1.0 / V * dz / ds
# dh,residuals,rank, s = np.linalg.H.T.dot((H, r)
dh = np.linalg.solve(H.T.dot(H), H.T.dot(r))
if not np.all(np.isfinite(dh)):
try:
U, S, VVh = np.linalg.svd(H.T.dot(H) + 1e-9 * np.eye(4))
VV = VVh.T
dh = np.dot(VV, np.dot(U.T, H.T.dot(r)) / S)
except np.linalg.linalg.LinAlgError:
print(
' Event could not be relocated (iteration no ' +
str(it) +
'), skipping')
sys.stdout.flush()
break
loc[inh, 1:] += dh
xinit = loc[inh, 2:]
tinit = loc[inh, 1]
dx = x[:, 0] - xinit[0, 0]
dy = x[:, 1] - xinit[0, 1]
dz = x[:, 2] - xinit[0, 2]
ds = np.sqrt(dx * dx + dy * dy + dz * dz)
tcalc = tinit + ds / V
r = t - tcalc
res[nev, it+1] = np.linalg.norm(r)
if np.sum(np.abs(dh[1:]) < convh) == 3 or res[nev, it+1] < tol:
if verbose:
print(' Converged at iteration ' + str(it + 1))
sys.stdout.flush()
break
else:
if verbose:
print(' Reached max number of iteration (' +
str(maxit) + ')')
sys.stdout.flush()
nev += 1
if verbose:
print('\n ** Inversion complete **\n', flush=True)
return loc, res
def hypolocPS(data, rcv, V, hinit, maxit, convh, tol=1e-6, verbose=False):
"""
Locate hypocenters for constant velocity model
Parameters
----------
data : array_like, shape (m, 6)
input data
first column is event ID number
second column is arrival time
third column is receiver index
fourth column is code for wave type: 0 for P-wave and 1 for S-wave
rcv : array_like, shape (n, 3)
coordinates of receivers
first column is easting
second column is northing
third column is elevation
V : tuple of float
wave velocities, 1st value is for P-wave, 2nd for S-wave
hinit : array_like, shape (m, 6)
initial hypocenter coordinate. The format is the same as for data
maxit : int
max number of iterations
convh : float
convergence criterion (units of distance)
tol : float
Stopping tolerance
verbose : bool
run in verbose mode
Returns
-------
loc : ndarray of float
hypocenter coordinates
res : ndarray of float, shape (nev, maxit)
norm of residuals at each iteration for each event
"""
if verbose:
print('\n *** Hypocenter inversion -- P and S-wave data ***\n')
evID = np.unique(data[:, 0])
loc = hinit.copy()
res = np.zeros((evID.size, maxit+1))
nev = 0
# set origin time to 0 and offset data accordingly
data = data.copy()
hyp0_dt = {}
for n in range(loc.shape[0]):
hyp0_dt[loc[n, 0]] = loc[n, 1]
loc[n, 1] -= hyp0_dt[loc[n, 0]]
for n in range(data.shape[0]):
try:
dt = hyp0_dt[data[n, 0]]
data[n, 1] -= dt
except KeyError():
raise ValueError('Event ' +
str(data[n, 0]) +
' not found in hinit')
for eid in evID:
ind = eid == data[:, 0]
ix = data[ind, 2]
x = np.zeros((ix.size, 3))
for i in np.arange(ix.size):
x[i, :] = rcv[int(1.e-6 + ix[i]), :]
t = data[ind, 1]
ph = data[ind, 3]
vel = np.zeros((len(ph),))
for n in range(len(ph)):
vel[n] = V[int(1.e-6 + ph[n])]
inh = eid == loc[:, 0]
if verbose:
print('Locating hypocenters no ' + str(int(1.e-6 + eid)))
sys.stdout.flush()
xinit = loc[inh, 2:]
tinit = loc[inh, 1]
dx = x[:, 0] - xinit[0, 0]
dy = x[:, 1] - xinit[0, 1]
dz = x[:, 2] - xinit[0, 2]
ds = np.sqrt(dx * dx + dy * dy + dz * dz)
tcalc = tinit + ds / vel
r = t - tcalc
res[nev, 0] = np.linalg.norm(r)
for it in range(maxit):
H = np.ones((x.shape[0], 4))
H[:, 1] = -1.0 / vel * dx / ds
H[:, 2] = -1.0 / vel * dy / ds
H[:, 3] = -1.0 / vel * dz / ds
# dh,residuals,rank, s = lsqsq(H, r)
try:
dh = np.linalg.solve(H.T.dot(H), H.T.dot(r))
except np.linalg.linalg.LinAlgError:
try:
U, S, VVh = np.linalg.svd(H.T.dot(H) + 1e-9 * np.eye(4))
VV = VVh.T
dh = np.dot(VV, np.dot(U.T, H.T.dot(r)) / S)
except np.linalg.linalg.LinAlgError:
print(
' Event could not be relocated (iteration no ' +
str(it) +
'), skipping')
sys.stdout.flush()
break
loc[inh, 1:] += dh
xinit = loc[inh, 2:]
tinit = loc[inh, 1]
dx = x[:, 0] - xinit[0, 0]
dy = x[:, 1] - xinit[0, 1]
dz = x[:, 2] - xinit[0, 2]
ds = np.sqrt(dx * dx + dy * dy + dz * dz)
tcalc = tinit + ds / vel
r = t - tcalc
res[nev, it+1] = np.linalg.norm(r)
if np.sum(np.abs(dh[1:]) < convh) == 3 or res[nev, it+1] < tol:
if verbose:
print(' Converged at iteration ' + str(it + 1))
sys.stdout.flush()
break
else:
if verbose:
print(' Reached max number of iteration (' +
str(maxit) + ')')
sys.stdout.flush()
nev += 1
# add time offset
for n in range(loc.shape[0]):
loc[n, 1] += hyp0_dt[loc[n, 0]]
if verbose:
print('\n ** Inversion complete **\n', flush=True)
return loc, res
# %% InvParams
class InvParams():
def __init__(self, maxit, maxit_hypo, conv_hypo, Vlim, dmax, lagrangians,
invert_vel=True, invert_VsVp=True, hypo_2step=False,
use_sc=True, constr_sc=True, show_plots=False, save_V=False,
save_rp=False, verbose=True):
"""
Parameters
----------
maxit : max number of iterations
maxit_hypo :
conv_hypo : convergence criterion (units of distance)
Vlim : tuple holding (Vpmin, Vpmax, PAp, Vsmin, Vsmax, PAs) for
velocity penalties
PA is slope of penalty function
dmax : tuple holding max admissible corrections, i.e.
dVp_max
dx_max
dt_max
dVs_max
lagrangians : tuple holding 4 values
λ : weight of smoothing constraint
γ : weight of penalty constraint
α : weight of velocity data point constraint
wzK : weight for vertical smoothing (w.r. to
horizontal smoothing)
invert_vel : perform velocity inversion if True (True by default)
invert_VsVp : find Vs/Vp ratio rather that Vs (True by default)
hypo_2step : Hypocenter relocation done in 2 steps (False by default)
Step 1: longitude and latitude only allowed to vary
Step 2: all 4 parameters allowed to vary
use_sc : Use static corrections
constr_sc : Constrain sum of P-wave static corrections to zero
show_plots : show various plots during inversion (True by default)
save_V : save intermediate velocity models (False by default)
save in vtk format if VTK module can be found
save_rp : save ray paths (False by default)
VTK module must be installed
verbose : print information message about inversion progression
(True by default)
"""
self.maxit = maxit
self.maxit_hypo = maxit_hypo
self.conv_hypo = conv_hypo
self.Vpmin = Vlim[0]
self.Vpmax = Vlim[1]
self.PAp = Vlim[2]
if len(Vlim) > 3:
self.Vsmin = Vlim[3]
self.Vsmax = Vlim[4]
self.PAs = Vlim[5]
self.dVp_max = dmax[0]
self.dx_max = dmax[1]
self.dt_max = dmax[2]
if len(dmax) > 3:
self.dVs_max = dmax[3]
self.λ = lagrangians[0]
self.γ = lagrangians[1]
self.α = lagrangians[2]
self.wzK = lagrangians[3]
self.invert_vel = invert_vel
self.invert_VsVp = invert_VsVp
self.hypo_2step = hypo_2step
self.use_sc = use_sc
self.constr_sc = constr_sc
self.show_plots = show_plots
self.save_V = save_V
self.save_rp = save_rp
self.verbose = verbose
self._final_iteration = False
# %% joint hypocenter - velocity
def jointHypoVel(par, grid, data, rcv, Vinit, hinit, caldata=np.array([]),
Vpts=np.array([])):
"""
Joint hypocenter-velocity inversion on a regular grid
Parameters
----------
par : instance of InvParams
grid : instance of Grid3d
data : a numpy array with 5 columns
1st column is event ID number
2nd column is arrival time
3rd column is receiver index
*** important ***
data should sorted by event ID first, then by receiver index
rcv: : coordinates of receivers
1st column is receiver easting
2nd column is receiver northing
3rd column is receiver elevation
Vinit : initial velocity model
hinit : initial hypocenter coordinate
1st column is event ID number
2nd column is origin time
3rd column is event easting
4th column is event northing
5th column is event elevation
*** important ***
for efficiency reason when computing matrix M, initial
hypocenters should _not_ be equal for any two event, e.g. they
shoud all be different
caldata : calibration shot data, numpy array with 8 columns
1st column is cal shot ID number
2nd column is arrival time
3rd column is receiver index
4th column is source easting
5th column is source northing
6th column is source elevation
*** important ***
cal shot data should sorted by cal shot ID first, then by
receiver index
Vpts : known velocity points, numpy array with 4 columns
1st column is velocity
2nd column is easting
3rd column is northing
4th column is elevation
Returns
-------
loc : hypocenter coordinates
V : velocity model
sc : static corrections
res : residuals
"""
evID = np.unique(data[:, 0])
nev = evID.size
if par.use_sc:
nsta = rcv.shape[0]
else:
nsta = 0
sc = np.zeros(nsta)
hyp0 = hinit.copy()
nslowness = grid.nparams
rcv_data = np.empty((data.shape[0], 3))
for ne in np.arange(nev):
indr = np.nonzero(data[:, 0] == evID[ne])[0]
for i in indr:
rcv_data[i, :] = rcv[int(1.e-6 + data[i, 2])]
if data.shape[0] > 0:
tobs = data[:, 1]
else:
tobs = np.array([])
if caldata.shape[0] > 0:
calID = np.unique(caldata[:, 0])
ncal = calID.size
hcal = np.column_stack(
(caldata[:, 0], np.zeros(caldata.shape[0]), caldata[:, 3:6]))
tcal = caldata[:, 1]
rcv_cal = np.empty((caldata.shape[0], 3))
Lsc_cal = []
for nc in range(ncal):
indr = np.nonzero(caldata[:, 0] == calID[nc])[0]
nst = np.sum(indr.size)
for i in indr:
rcv_cal[i, :] = rcv[int(1.e-6 + caldata[i, 2])]
if par.use_sc:
tmp = np.zeros((nst, nsta))
for n in range(nst):
tmp[n, int(1.e-6 + caldata[indr[n], 2])] = 1.0
Lsc_cal.append(sp.csr_matrix(tmp))
else:
ncal = 0
tcal = np.array([])
if np.isscalar(Vinit):
V = Vinit + np.zeros(nslowness)
s = np.ones(nslowness) / Vinit
else:
V = Vinit
s = 1. / Vinit
if Vpts.size > 0:
if Vpts.shape[1] > 4: # check if we have Vs data in array
itmp = Vpts[:, 4] == 0
Vpts = Vpts[itmp, :4] # keep only Vp data
if par.verbose:
print('\n *** Joint hypocenter-velocity inversion ***\n')
if par.invert_vel:
resV = np.zeros(par.maxit + 1)
resAxb = np.zeros(par.maxit)
P = np.ones(nslowness)
dP = sp.csr_matrix(
(np.ones(nslowness), (np.arange(
nslowness, dtype=np.int64), np.arange(
nslowness, dtype=np.int64))), shape=(
nslowness, nslowness))
Spmax = 1. / par.Vpmin
Spmin = 1. / par.Vpmax
deltam = np.zeros(nslowness + nsta)
if par.constr_sc and par.use_sc:
u1 = np.ones(nslowness + nsta)
u1[:nslowness] = 0.0
i = np.arange(nslowness, nslowness + nsta)
j = np.arange(nslowness, nslowness + nsta)
nn = i.size
i = np.kron(i, np.ones((nn,)))
j = np.kron(np.ones((nn,)), j)
u1Tu1 = sp.csr_matrix((np.ones((i.size,)), (i, j)),
shape=(nslowness + nsta, nslowness + nsta))
else:
u1 = np.zeros(nslowness + nsta)
u1Tu1 = sp.csr_matrix((nslowness + nsta, nslowness + nsta))
if Vpts.size > 0:
if par.verbose:
print('Building velocity data point matrix D')
sys.stdout.flush()
D = grid.compute_D(Vpts[:, 1:])
D1 = sp.hstack((D, sp.coo_matrix((Vpts.shape[0], nsta)))).tocsr()
Spts = 1. / Vpts[:, 0]
else:
D = 0.0
if par.verbose:
print('Building regularization matrix K')
sys.stdout.flush()
Kx, Ky, Kz = grid.compute_K()
Kx1 = sp.hstack((Kx, sp.coo_matrix((nslowness, nsta)))).tocsr()
KtK = Kx1.T * Kx1
Ky1 = sp.hstack((Ky, sp.coo_matrix((nslowness, nsta)))).tocsr()
KtK += Ky1.T * Ky1
Kz1 = sp.hstack((Kz, sp.coo_matrix((nslowness, nsta)))).tocsr()
KtK += par.wzK * Kz1.T * Kz1
nK = spl.norm(KtK)
Kx = Kx.tocsr()
Ky = Ky.tocsr()
Kz = Kz.tocsr()
else:
resV = None
resAxb = None
if par.verbose:
print('\nStarting iterations')
for it in np.arange(par.maxit):
par._final_iteration = it == par.maxit - 1
if par.invert_vel:
if par.verbose:
print(
'\nIteration {0:d} - Updating velocity model'.format(it+1))
print(' Updating penalty vector')
sys.stdout.flush()
# compute vector C
cx = Kx * s
cy = Ky * s
cz = Kz * s
# compute dP/dV, matrix of penalties derivatives
for n in np.arange(nslowness):
if s[n] < Spmin:
P[n] = par.PAp * (Spmin - s[n])
dP[n, n] = -par.PAp
elif s[n] > Spmax:
P[n] = par.PAp * (s[n] - Spmax)
dP[n, n] = par.PAp
else:
P[n] = 0.0
dP[n, n] = 0.0
if par.verbose:
npel = np.sum(P != 0.0)
if npel > 0:
print(' Penalties applied at {0:d} nodes'.format(npel))
if par.verbose:
print(' Raytracing')
sys.stdout.flush()
if nev > 0:
hyp = np.empty((data.shape[0], 5))
for ne in np.arange(nev):
indh = np.nonzero(hyp0[:, 0] == evID[ne])[0]
indr = np.nonzero(data[:, 0] == evID[ne])[0]
for i in indr:
hyp[i, :] = hyp0[indh[0], :]
tcalc, rays, Lev = grid.raytrace(hyp, rcv_data, s,
return_rays=True,
compute_L=True)
s0 = grid.get_s0(hyp)
else:
tcalc = np.array([])
if ncal > 0:
tcalc_cal, Lcal = grid.raytrace(hcal, rcv_cal, s,
compute_L=True)
else:
tcalc_cal = np.array([])
r1a = tobs - tcalc
r1 = tcal - tcalc_cal
if r1a.size > 0:
r1 = np.hstack((np.zeros(data.shape[0] - 4 * nev), r1))
if par.show_plots:
plt.figure(1)
plt.cla()
plt.plot(r1a, 'o')
plt.title('Residuals - Iteration {0:d}'.format(it + 1))
plt.show(block=False)
plt.pause(0.0001)
resV[it] = np.linalg.norm(np.hstack((r1a, r1)))
# initializing matrix M; matrix of partial derivatives of velocity
# dt/dV
if par.verbose:
print(' Building matrix L')
sys.stdout.flush()
L1 = None
ir1 = 0
for ne in range(nev):
if par.verbose:
print(' Event ID ' + str(int(1.e-6 + evID[ne])))
sys.stdout.flush()
indh = np.nonzero(hyp0[:, 0] == evID[ne])[0]
indr = np.nonzero(data[:, 0] == evID[ne])[0]
nst = np.sum(indr.size)
nst2 = nst - 4
H = np.ones((nst, 4))
for ns in range(nst):
raysi = rays[indr[ns]]
S0 = s0[indr[ns]]
d = (raysi[1, :] - hyp0[indh, 2:]).flatten()
ds = np.sqrt(np.sum(d * d))
H[ns, 1] = -S0 * d[0] / ds
H[ns, 2] = -S0 * d[1] / ds
H[ns, 3] = -S0 * d[2] / ds
Q, _ = np.linalg.qr(H, mode='complete')
T = sp.csr_matrix(Q[:, 4:]).T
L = sp.csr_matrix(Lev[ne], shape=(nst, nslowness))
if par.use_sc:
Lsc = np.zeros((nst, nsta))
for ns in range(nst):
Lsc[ns, int(1.e-6 + data[indr[ns], 2])] = 1.
L = sp.hstack((L, sp.csr_matrix(Lsc)))
L = T * L
if L1 is None:
L1 = L
else:
L1 = sp.vstack((L1, L))
r1[ir1 + np.arange(nst2, dtype=np.int64)] = T.dot(r1a[indr])
ir1 += nst2
for nc in range(ncal):
L = Lcal[nc]
if par.use_sc:
L = sp.hstack((L, Lsc_cal[nc]))
if L1 is None:
L1 = L
else:
L1 = sp.vstack((L1, L))
if par.verbose:
print(' Assembling matrices and solving system')
sys.stdout.flush()
ssc = -np.sum(sc) # u1.T * deltam
dP1 = sp.hstack(
(dP, sp.csr_matrix(
np.zeros(
(nslowness, nsta))))).tocsr() # dP prime
# compute A & h for inversion
L1 = L1.tocsr()
A = L1.T * L1
nM = spl.norm(A)
λ = par.λ * nM / nK
A += λ * KtK
tmp = dP1.T * dP1
nP = spl.norm(tmp)
if nP != 0.0:
γ = par.γ * nM / nP
else:
γ = par.γ
A += γ * tmp
A += u1Tu1
b = L1.T * r1
tmp2x = Kx1.T * cx
tmp2y = Ky1.T * cy
tmp2z = Kz1.T * cz
tmp3 = dP1.T * P
tmp = u1 * ssc
b += - λ * tmp2x - λ * tmp2y - par.wzK * λ * tmp2z - γ * tmp3 - tmp
if Vpts.shape[0] > 0:
tmp = D1.T * D1
nD = spl.norm(tmp)
α = par.α * nM / nD
A += α * tmp
b += α * D1.T * (Spts - D * s)
if par.verbose:
print(' calling minres with system of '
'size {0:d} x {1:d}'.format(A.shape[0], A.shape[1]))
sys.stdout.flush()
x = spl.minres(A, b)
deltam = x[0]
resAxb[it] = np.linalg.norm(A * deltam - b)
dmean = np.mean(np.abs(deltam[:nslowness]))
if dmean > par.dVp_max:
if par.verbose:
print(' Scaling Slowness perturbations by {0:e}'.format(
1. / (par.dVp_max * dmean)))
deltam[:nslowness] = deltam[:nslowness] / (par.dVp_max * dmean)
s += deltam[:nslowness]
V = 1. / s
sc += deltam[nslowness:]
if par.save_V:
if par.verbose:
print(' Saving Velocity model')
if 'vtk' in sys.modules:
grid.to_vtk({'Vp': V}, 'Vp{0:02d}'.format(it + 1))
grid.set_slowness(s)
if nev > 0:
if par.verbose:
print('Iteration {0:d} - Relocating events'.format(it + 1))
sys.stdout.flush()
if grid.n_threads == 1 or nev < grid.n_threads:
for ne in range(nev):
_reloc(ne, par, grid, evID, hyp0, data, rcv, tobs)
else:
# run in parallel
blk_size = np.zeros((grid.n_threads,), dtype=np.int64)
nj = nev
while nj > 0:
for n in range(grid.n_threads):
blk_size[n] += 1
nj -= 1
if nj == 0:
break
processes = []
blk_start = 0
h_queue = Queue()
for n in range(grid.n_threads):
blk_end = blk_start + blk_size[n]
p = Process(
target=_rl_worker,
args=(
n,
blk_start,
blk_end,
par,
grid,
evID,
hyp0,
data,
rcv,
tobs,
h_queue),
daemon=True)
processes.append(p)
p.start()
blk_start += blk_size[n]
for ne in range(nev):
h, indh = h_queue.get()
hyp0[indh, :] = h
if par.invert_vel:
if nev > 0:
hyp = np.empty((data.shape[0], 5))
for ne in np.arange(nev):
indh = np.nonzero(hyp0[:, 0] == evID[ne])[0]
indr = np.nonzero(data[:, 0] == evID[ne])[0]
for i in indr:
hyp[i, :] = hyp0[indh[0], :]
tcalc = grid.raytrace(hyp, rcv_data, s)
else:
tcalc = np.array([])
if ncal > 0:
tcalc_cal = grid.raytrace(hcal, rcv_cal, s)
else:
tcalc_cal = np.array([])
r1a = tobs - tcalc
r1 = tcal - tcalc_cal
if r1a.size > 0:
r1 = np.hstack((np.zeros(data.shape[0] - 4 * nev), r1))
if par.show_plots:
plt.figure(1)
plt.cla()
plt.plot(r1a, 'o')
plt.title('Residuals - Final step')
plt.show(block=False)
plt.pause(0.0001)
resV[-1] = np.linalg.norm(np.hstack((r1a, r1)))
r1 = r1.reshape(-1, 1)
r1a = r1a.reshape(-1, 1)
if par.verbose:
print('\n ** Inversion complete **\n', flush=True)
return hyp0, V, sc, (resV, resAxb)
def _rl_worker(
thread_no,
istart,
iend,
par,
grid,
evID,
hyp0,
data,
rcv,
tobs,
h_queue):
for ne in range(istart, iend):
h, indh = _reloc(ne, par, grid, evID, hyp0, data, rcv, tobs, thread_no)
h_queue.put((h, indh))
h_queue.close()
def _reloc(ne, par, grid, evID, hyp0, data, rcv, tobs, thread_no=None):
if par.verbose:
print(' Updating event ID {0:d} ({1:d}/{2:d})'.format(
int(1.e-6 + evID[ne]), ne + 1, evID.size))
sys.stdout.flush()
indh = np.nonzero(hyp0[:, 0] == evID[ne])[0][0]
indr = np.nonzero(data[:, 0] == evID[ne])[0]
hyp_save = hyp0[indh, :].copy()
nst = np.sum(indr.size)
hyp = np.empty((nst, 5))
stn = np.empty((nst, 3))
for i in range(nst):
hyp[i, :] = hyp0[indh, :]
stn[i, :] = rcv[int(1.e-6 + data[indr[i], 2]), :]
if par.hypo_2step:
if par.verbose:
print(' Updating latitude & longitude', end='')
sys.stdout.flush()
H = np.ones((nst, 2))
for itt in range(par.maxit_hypo):
for i in range(nst):
hyp[i, :] = hyp0[indh, :]
tcalc, rays = grid.raytrace(hyp, stn, thread_no=thread_no,
return_rays=True)
s0 = grid.get_s0(hyp)
for ns in range(nst):
raysi = rays[ns]
S0 = s0[ns]
d = (raysi[1, :] - hyp0[indh, 2:]).flatten()
ds = np.sqrt(np.sum(d * d))
H[ns, 0] = -S0 * d[0] / ds
H[ns, 1] = -S0 * d[1] / ds
r = tobs[indr] - tcalc
x = lstsq(H, r)
deltah = x[0]
if np.sum(np.isfinite(deltah)) != deltah.size:
try:
U, S, VVh = np.linalg.svd(H.T.dot(H) + 1e-9 * np.eye(2))
VV = VVh.T
deltah = np.dot(VV, np.dot(U.T, H.T.dot(r)) / S)
except np.linalg.linalg.LinAlgError:
print(' - Event could not be relocated, '
'resetting and exiting')
hyp0[indh, :] = hyp_save
return hyp_save, indh
for n in range(2):
if np.abs(deltah[n]) > par.dx_max:
deltah[n] = par.dx_max * np.sign(deltah[n])
new_hyp = hyp0[indh, :].copy()
new_hyp[2:4] += deltah
if grid.is_outside(new_hyp[2:].reshape((1, 3))):
print(' Event could not be relocated inside the grid'
' ({0:f}, {1:f}, {2:f}), resetting and exiting'.format(
new_hyp[2],
new_hyp[3],
new_hyp[4]))
hyp0[indh, :] = hyp_save
return hyp_save, indh
hyp0[indh, 2:4] += deltah
if np.sum(np.abs(deltah) < par.conv_hypo) == 2:
if par.verbose:
print(' - converged at iteration ' + str(itt + 1))
sys.stdout.flush()
break
else:
if par.verbose:
print(' - reached max number of iterations')
sys.stdout.flush()
if par.verbose:
print(' Updating all hypocenter params', end='')
sys.stdout.flush()
H = np.ones((nst, 4))
for itt in range(par.maxit_hypo):
for i in range(nst):
hyp[i, :] = hyp0[indh, :]
tcalc, rays = grid.raytrace(hyp, stn, thread_no=thread_no,
return_rays=True)
s0 = grid.get_s0(hyp)
for ns in range(nst):
raysi = rays[ns]
S0 = s0[ns]
d = (raysi[1, :] - hyp0[indh, 2:]).flatten()
ds = np.sqrt(np.sum(d * d))
H[ns, 1] = -S0 * d[0] / ds
H[ns, 2] = -S0 * d[1] / ds
H[ns, 3] = -S0 * d[2] / ds
r = tobs[indr] - tcalc
x = lstsq(H, r)
deltah = x[0]
if np.sum(np.isfinite(deltah)) != deltah.size:
try:
U, S, VVh = np.linalg.svd(H.T.dot(H) + 1e-9 * np.eye(4))
VV = VVh.T
deltah = np.dot(VV, np.dot(U.T, H.T.dot(r)) / S)
except np.linalg.linalg.LinAlgError:
print(' Event could not be relocated, resetting and exiting')
hyp0[indh, :] = hyp_save
return hyp_save, indh
if np.abs(deltah[0]) > par.dt_max:
deltah[0] = par.dt_max * np.sign(deltah[0])
for n in range(1, 4):
if np.abs(deltah[n]) > par.dx_max:
deltah[n] = par.dx_max * np.sign(deltah[n])
new_hyp = hyp0[indh, 1:] + deltah
if grid.is_outside(new_hyp[1:].reshape((1, 3))):
print(' Event could not be relocated inside the grid'
' ({0:f}, {1:f}, {2:f}), resetting and exiting'.format(
new_hyp[1],
new_hyp[2],
new_hyp[3]))