-
Notifications
You must be signed in to change notification settings - Fork 33
/
Copy pathuncertainties.py
1694 lines (1481 loc) · 87.1 KB
/
uncertainties.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
'''
A fault class dealing with uncertainties in the forward model (fault geometry, crustal elastic properties)
Written by T. Ragon September 2018
'''
# Externals
import numpy as np
import os
from scipy.stats import linregress
# Personals
from .multifaultsolve import multifaultsolve as multiflt
class uncertainties(object):
# ----------------------------------------------------------------------
# Initialize class
def __init__(self, name, faults, datasets, export=None, verbose=True):
'''
Class calculating the covariance matrix of the predictions.
Args:
* name : Name of the object
* faults : Prior fault geometry, can be a list of several faults
* datasets : List of data objects
ex: dataset=[gps]+[insar1,insar2]
* export : None by default
or string with path to directory
'''
self.verbose = verbose
if self.verbose:
print ("---------------------------------")
print ("---------------------------------")
print ("Initializing uncertainties object")
# Store things into self
self.name = name
self.faults = faults
self.datasets = datasets
self.export = export
# check the utm zone
if np.shape(self.faults)!=():
self.utmzone = faults[0].utmzone
for fault in faults:
if fault.utmzone is not self.utmzone:
print("UTM zones are not equivalent, this is a problem")
self.ready = False
return
self.xy2ll = faults[0].xy2ll
self.ll2xy = faults[0].ll2xy
else:
self.utmzone = faults.utmzone
# check that Cd have been assembled prior to initialization
if np.shape(self.faults)!=():
for fault in faults:
# if fault.dassembled is None:
# print("d has not been assembled in fault structure {}".format(fault.name))
if fault.Cd is None:
print("Cd has not been assembled in fault structure {}".format(fault.name))
else:
self.Cd = fault.Cd
else:
if self.faults.Cd is None:
print("Cd has not been assembled in fault structure {}".format(self.faults.name))
else:
self.Cd = self.faults.Cd
# Set the kernels and covariance matrices as empty arrays
self.KDip = []
self.KStrike = []
self.KPosition = []
self.KElastic = []
self.KernelsFull = []
self.CovDip = []
self.CovStrike = []
self.CovPosition = []
self.CovElastic = []
self.CovFull = []
self.CpDip = []
self.CpStrike = []
self.CpPosition = []
self.CpElastic = []
self.CpFull = []
self.CdFull = []
return
# ----------------------------------------------------------------------
# ----------------------------------------------------------------------
# Calculate uncertainties related to the fault dip
def calcCpDip(self, dip_range, sigma, mprior, edks=False, **edks_params):
'''
Calculate the uncertainties of the predictions deriving from uncertainties in the fault dip.
From Ragon et al. (2018) GJI
Args:
* dip_range : array, dip values (in degrees) to test around the prior fault dip (of Fault)
ex: dip_range = [-1,2]
If there are several fault segments (e.g. several faults in fault), len(dip_range) must be equal to len(fault)
ex: dip_range = [[-1,2],[-2,3],[-4,1],[0,5]] for a fault with 4 segments
* sigma : prior uncertainty (standard deviation) in the dip parameter (in degrees)
ex: sigma = 5
If there are several fault segments (e.g. several faults in fault), len(sigma) must be equal to len(fault)
ex: sigma = [5,7,2,3] for a fault with 4 segments
* mprior : initial model used to calculate Cp
length must be equal to two times the number of patches
can be uniform and derived from Mo, ex: meanslip = -Mo*10**(-7)/(3*10**10*length*width)
OR derived from a first inversion without accounting for uncertainties
Kwargs:
* edks : If True, GFs calculated using a layered Earth model calculated with EDKS.
If False, GFs with Okada
If edks is True, please specify in **edks_params:
ex: Cp_dip(fault,datasets,[40,50],sigma,mprior,edks=True,edksdir='path/to/kernels',modelname='CIA',sourceSpacing=0.5)
* edksdir : path of the edks kernels
* modelname : Filename of the EDKS kernels
* sourceSpacing : source spacing to calculate the Green's Functions
OR sourceNumber : Number of sources per patches.
OR sourceArea : Maximum Area of the sources.
Returns:
* CpDip
/!\ To save you from having to recalculate a new fault geometry for each new dip parameter,
each fault patches are rotated along the fault tip. When Equivalent Rectangles are
calculated, fault patches are approximated and it may bias slighly (0 to 5% -?)
the value of Cp. To avoid this effect, you could instead recalculate your fault geometry.
'''
# For a fault with one segment
if np.shape(self.faults)==() or np.shape(self.faults)[0]==1 :
if np.shape(self.faults)==():
fault = self.faults
else:
fault = self.faults[0]
# Define the range on which calculate Kernels
dip_rg = np.linspace(dip_range[0],dip_range[1],6)
# Calculate the Green's functions for the various dips in dip_rg
gfs = []
for d in dip_rg:
print('---------------------------------')
print('---------------------------------')
print('Calculating new Fault Geometry and Greens Functions')
print('For dip = dip_prior + %.2f degrees' % (d))
# Modify the fault geometry
p_axis1 = np.array([fault.xf[-1],fault.yf[-1],fault.top])
p_axis2 = np.array([fault.xf[0],fault.yf[0],fault.top])
# Copy the fault
Fg = fault.duplicateFault()
# Rotate the patches
for p in range(len(fault.patch)):
Fg.rotatePatch(p,d, p_axis1, p_axis2)
Fg.computeEquivRectangle()
if edks is True:
os.chdir(modelname=edks_params['edksdir'])
if 'Spacing' in str(edks_params.items()[1][0]):
gfs.append(Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceSpacing=edks_params.items()[1][1]))
elif 'Number' in str(edks_params.items()[1][0]):
gfs.append(Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceNumber=edks_params.items()[1][1]))
else:
gfs.append(Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceArea=edks_params.items()[1][1]))
else:
gfs.append(Fg.calcGFsCp(self.datasets, edks=False))
# Calculate the sensitivity Kernels of the Green's Functions (the derivatives) by linearizing their variation
slope = np.empty(gfs[0].shape)
rvalue = np.empty(gfs[0].shape)
pvalue = np.empty(gfs[0].shape)
stderr = np.empty(gfs[0].shape)
inter = np.empty(gfs[0].shape)
for i in range(gfs[0].shape[0]):
for j in range(gfs[0].shape[1]):
# Do a linear regression for each couple parameter/data, along the dip range
slope[i,j], inter[i,j], rvalue[i,j], pvalue[i,j], stderr[i,j] = linregress(dip_rg,[gfs[k][i,j] for k in range(len(dip_rg))])
Kdip= slope
K = []
K.append(Kdip)
kernels = np.asarray(K)
k = np.transpose(np.matmul(kernels, mprior))
C1 = np.matmul(k, [[float(sigma)**2]])
CpDip = np.matmul(C1, np.transpose(k))
self.KDip = kernels
self.CovDip = np.array([[float(sigma)**2]])
if self.KernelsFull==[]:
self.KernelsFull = self.KDip
else:
self.KernelsFull = np.concatenate((self.KernelsFull,self.KDip))
if self.CovFull==[]:
self.CovFull = self.CovDip
else:
Z = np.zeros((np.shape(self.CovFull)[0],np.shape(self.CovDip)[0]),dtype=int)
self.CovFull = np.asarray(np.bmat([[self.CovFull, Z], [Z, self.CovDip]]))
self.CpDip = CpDip
if self.CpFull==[]:
self.CpFull = self.CpDip
else:
self.CpFull = np.add(self.CpFull, self.CpDip)
self.CdFull = np.add(self.Cd, self.CpFull)
if self.export is not None:
self.CdFull.astype('f').tofile(os.path.join(self.export,self.name+'CdFull.bin'))
self.KernelsFull.astype('f').tofile(os.path.join(self.export,self.name+'KernelsFull.bin'))
self.CovFull.astype('f').tofile(os.path.join(self.export,self.name+'CovFull.bin'))
self.KDip.astype('f').tofile(os.path.join(self.export,self.name+'KDip.bin'))
self.CovDip.astype('f').tofile(os.path.join(self.export,self.name+'CovDip.bin'))
print('---------------------------------')
print('---------------------------------')
print('CdFull successfully updated with CpDip')
# For a multi-segmented fault
else:
Kdip = []
# Initialize the faults
Faults = []
for f in range(len(self.faults)):
fault = self.faults[f]
dip = dip_range[f][0]
p_axis1 = np.array([fault.xf[0],fault.yf[0],fault.top])
p_axis2 = np.array([fault.xf[-1],fault.yf[-1],fault.top])
Fg = fault.duplicateFault()
for p in range(len(fault.patch)):
Fg.rotatePatch(p,dip, p_axis1, p_axis2)
Fg.computeEquivRectangle()
# Calculate GFs
if edks is True:
os.chdir(modelname=edks_params['edksdir'])
if 'Spacing' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceSpacing=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
elif 'Number' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceNumber=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceArea=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=False)
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
Faults.append(Fg)
for f in range(len(self.faults)):
Faults_cp = Faults
fault = self.faults[f]
gfs = []
# Define the range on which calculate Kernels
dip_rg = np.linspace(dip_range[f][0],dip_range[f][1],6)
p_axis1 = np.array([fault.xf[0],fault.yf[0],fault.top])
p_axis2 = np.array([fault.xf[-1],fault.yf[-1],fault.top])
# Calculate the Green's functions for the various dips in dip_rg
for d in dip_rg:
print('---------------------------------')
print('---------------------------------')
print('Calculating new Fault Geometry and Greens Functions')
print('For dip = dip_prior + %.2f degrees' % (d))
# Modify the fault geometry
Fg = fault.duplicateFault()
for p in range(len(fault.patch)):
Fg.rotatePatch(p,d, p_axis1, p_axis2)
Fg.computeEquivRectangle()
# Calculate GFs for each different fault geometry
if edks is True:
os.chdir(modelname=edks_params['edksdir'])
if 'Spacing' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceSpacing=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
elif 'Number' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceNumber=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceArea=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=False)
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
Faults_cp[f] = Fg
slv = multiflt('Multi-seg fault', Faults_cp)
slv.assembleGFs()
gfs.append(slv.G)
# Calculate the sensitivity Kernels of the Green's Functions (the derivatives) by linearizing their variation
slope = np.empty(gfs[0].shape)
rvalue = np.empty(gfs[0].shape)
pvalue = np.empty(gfs[0].shape)
stderr = np.empty(gfs[0].shape)
inter = np.empty(gfs[0].shape)
for i in range(gfs[0].shape[0]):
for j in range(gfs[0].shape[1]):
# Do a linear regression for each couple parameter/data, along the dip range
slope[i,j], inter[i,j], rvalue[i,j], pvalue[i,j], stderr[i,j] = linregress(dip_rg,[gfs[k][i,j] for k in range(len(dip_rg))])
Kdip.append(slope)
kernels = np.asarray(Kdip)
k = np.transpose(np.matmul(kernels, mprior))
Covdip = np.zeros((len(self.faults),len(self.faults)))
for f in range(len(self.faults)):
Covdip[f,f] = sigma[f]**2
C1 = np.matmul(k, Covdip)
CpDip = np.matmul(C1, np.transpose(k))
self.KDip = kernels
self.CovDip = Covdip
if self.KernelsFull==[]:
self.KernelsFull = self.KDip
else:
self.KernelsFull = np.concatenate((self.KernelsFull,self.KDip))
if self.CovFull==[]:
self.CovFull = self.CovDip
else:
Z = np.zeros((np.shape(self.CovFull)[0],np.shape(self.CovDip)[0]),dtype=int)
self.CovFull = np.asarray(np.bmat([[self.CovFull, Z], [Z, self.CovDip]]))
self.CpDip = CpDip
if self.CpFull==[]:
self.CpFull = self.CpDip
else:
self.CpFull = np.add(self.CpFull, self.CpDip)
self.CdFull = np.add(self.Cd, self.CpFull)
if self.export is not None:
self.CdFull.astype('f').tofile(os.path.join(self.export,self.name+'CdFull.bin'))
self.KernelsFull.astype('f').tofile(os.path.join(self.export,self.name+'KernelsFull.bin'))
self.CovFull.astype('f').tofile(os.path.join(self.export,self.name+'CovFull.bin'))
self.KDip.astype('f').tofile(os.path.join(self.export,self.name+'KDip.bin'))
self.CovDip.astype('f').tofile(os.path.join(self.export,self.name+'CovDip.bin'))
print('---------------------------------')
print('---------------------------------')
print('CdFull successfully updated with CpDip')
return
# ----------------------------------------------------------------------
# ----------------------------------------------------------------------
# Calculate uncertainties related to the fault strike
def calcCpStrike(self, strike_range, rotation_axis, sigma, mprior, whole_fault=True, edks=False, **edks_params):
'''
Calculate the uncertainties of the predictions deriving from uncertainties in the fault strike.
If the fault is multi-segmented, you have two options:
- investigate the variation of strike for each segment independently
option whole_fault = False
- investigate the variation of strike for the whole fault (whole_fault is True by default)
From Ragon et al. (2018) GJI
Args:
* strike_range : array, strike values (in degrees) to test around the prior fault strike (of Fault)
Positive angles are counter-clockwise looking toward the center of the Earth
ex: strike_range = [-1,2]
If whole_fault is False (multi-segmented fault), len(strike_range) must be equal to len(fault)
ex: strike_range = [[-1,2],[-2,3],[-4,1],[0,5]] for a fault with 4 segments
* rotation_axis : can be 'center', 'first', 'second' or an had-oc position [X,Y]
define the axis around which the fault will rotate
'center' : the center of the fault
'first' : the first point of the fault trace (Fault.xf[0],Fault.yf[0])
'last' : the last point of the fault trace (Fault.xf[-1],Fault.yf[-1])
[X,Y] : ad-hoc coordinates
* sigma : prior uncertainty (standard deviation) in the strike parameter (in degrees)
ex: sigma = 5
If whole_fault is False (multi-segmented fault), len(sigma) must be equal to len(fault)
ex: sigma = [5,7,2,3] for a fault with 4 segments
* mprior : initial model used to calculate Cp
length must be equal to two times the number of patches
can be uniform and derived from Mo, ex: meanslip = -Mo*10**(-7)/(3*10**10*length*width)
OR derived from a first inversion without accounting for uncertainties
* whole_fault : True by default.
if True for a multi-segmented fault, the strike variation for the whole fault will be investigated
the first strike_range value (strike_range[0]) will be assumed as rotation angles for the whole fault
around the center or the whole fault, the first point of the first segment or the last point of the last segment
if False for a multi-segmented fault, the strike variation of each segment will be investigated independently
for either the center, first or last point of each fault segment
Kwargs:
* edks : If True, GFs calculated using a layered Earth model calculated with EDKS.
If False, GFs with Okada
If edks is True, please specify in **edks_params:
ex: Cp_strike(fault,datasets,[40,50],'center',sigma,mprior,edks=True,edksdir='path/to/kernels',modelname='CIA',sourceSpacing=0.5)
* edksdir : path of the edks kernels
* modelname : Filename of the EDKS kernels
* sourceSpacing : source spacing to calculate the Green's Functions
OR sourceNumber : Number of sources per patches.
OR sourceArea : Maximum Area of the sources.
Returns:
* CpStrike
'''
# For a fault with one segment
if np.shape(self.faults)==() or np.shape(self.faults)[0]==1 :
if np.shape(self.faults)==():
fault = self.faults
else:
fault = self.faults[0]
# Define the range on which calculate Kernels
stk_rg = np.linspace(strike_range[0],strike_range[1],6)
# Calculate the Green's functions for the various strike values in stk_rg
gfs = []
# Define the rotation axis
if rotation_axis == 'center':
p_axis1 = np.array([(fault.xf[0]+fault.xf[-1])/2,(fault.yf[0]+fault.yf[-1])/2,fault.top])
p_axis2 = np.array([(fault.xf[0]+fault.xf[-1])/2,(fault.yf[0]+fault.yf[-1])/2,fault.top+10])
elif rotation_axis == 'first':
p_axis1 = np.array([fault.xf[0],fault.yf[0],fault.top])
p_axis2 = np.array([fault.xf[0],fault.yf[0],fault.top+10])
elif rotation_axis == 'last':
p_axis1 = np.array([fault.xf[-1],fault.yf[-1],fault.top])
p_axis2 = np.array([fault.xf[-1],fault.yf[-1],fault.top+10])
else:
p_axis1 = np.array([rotation_axis[0],rotation_axis[1],fault.top])
p_axis2 = np.array([rotation_axis[0],rotation_axis[1],fault.top+10])
for s in stk_rg:
print('---------------------------------')
print('---------------------------------')
print('Calculating new Fault Geometry and Greens Functions')
print('For strike = strike_prior + %.2f degrees' % (s))
# Modify the fault geometry
Fg = fault.duplicateFault()
# rotate the patches
for p in range(len(fault.patch)):
Fg.rotatePatch(p,s, p_axis1, p_axis2)
Fg.computeEquivRectangle()
if edks is True:
os.chdir(modelname=edks_params['edksdir'])
if 'Spacing' in str(edks_params.items()[1][0]):
gfs.append(Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceSpacing=edks_params.items()[1][1]))
elif 'Number' in str(edks_params.items()[1][0]):
gfs.append(Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceNumber=edks_params.items()[1][1]))
else:
gfs.append(Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceArea=edks_params.items()[1][1]))
else:
gfs.append(Fg.calcGFsCp(self.datasets,edks=False))
# Calculate the sensitivity Kernels of the Green's Functions (the derivatives) by linearizing their variation
slope = np.empty(gfs[0].shape)
rvalue = np.empty(gfs[0].shape)
pvalue = np.empty(gfs[0].shape)
stderr = np.empty(gfs[0].shape)
inter = np.empty(gfs[0].shape)
for i in range(gfs[0].shape[0]):
for j in range(gfs[0].shape[1]):
# Do a linear regression for each couple parameter/data, along the range of strike values
slope[i,j], inter[i,j], rvalue[i,j], pvalue[i,j], stderr[i,j] = linregress(stk_rg,[gfs[k][i,j] for k in range(len(stk_rg))])
Kstk= slope
K = []
K.append(Kstk)
kernels = np.asarray(K)
k = np.transpose(np.matmul(kernels, mprior))
C1 = np.matmul(k, [[float(sigma)**2]])
CpStrike = np.matmul(C1, np.transpose(k))
self.KStrike = kernels
self.CovStrike = np.array([[float(sigma)**2]])
if self.KernelsFull==[]:
self.KernelsFull = self.KStrike
else:
self.KernelsFull = np.concatenate((self.KernelsFull,self.KStrike))
if self.CovFull==[]:
self.CovFull = self.CovStrike
else:
Z = np.zeros((np.shape(self.CovFull)[0],np.shape(self.CovStrike)[0]),dtype=int)
self.CovFull = np.asarray(np.bmat([[self.CovFull, Z], [Z, self.CovStrike]]))
self.CpStrike = CpStrike
if self.CpFull==[]:
self.CpFull = self.CpStrike
else:
self.CpFull = np.add(self.CpFull, self.CpStrike)
self.CdFull = np.add(self.Cd, self.CpFull)
if self.export is not None:
self.CdFull.astype('f').tofile(os.path.join(self.export,self.name+'CdFull.bin'))
self.KernelsFull.astype('f').tofile(os.path.join(self.export,self.name+'KernelsFull.bin'))
self.CovFull.astype('f').tofile(os.path.join(self.export,self.name+'CovFull.bin'))
self.KStrike.astype('f').tofile(os.path.join(self.export,self.name+'KStrike.bin'))
self.CovStrike.astype('f').tofile(os.path.join(self.export,self.name+'CovStrike.bin'))
print('---------------------------------')
print('---------------------------------')
print('CdFull successfully updated with Cpstrike')
# For a multi-segmented fault
elif np.shape(self.faults)!=() and whole_fault==False:
Kstk = []
# Initialize the faults
Faults = []
for f in range(len(self.faults)):
fault = self.faults[f]
strike = strike_range[f][0]
# Define the rotation axis
if rotation_axis == 'center':
p_axis1 = np.array([(fault.xf[0]+fault.xf[-1])/2,(fault.yf[0]+fault.yf[-1])/2,fault.top])
p_axis2 = np.array([(fault.xf[0]+fault.xf[-1])/2,(fault.yf[0]+fault.yf[-1])/2,fault.top+10])
elif rotation_axis == 'first':
p_axis1 = np.array([fault.xf[0],fault.yf[0],fault.top])
p_axis2 = np.array([fault.xf[0],fault.yf[0],fault.top+10])
elif rotation_axis == 'last':
p_axis1 = np.array([fault.xf[-1],fault.yf[-1],fault.top])
p_axis2 = np.array([fault.xf[-1],fault.yf[-1],fault.top+10])
else:
p_axis1 = np.array([rotation_axis[0],rotation_axis[1],fault.top])
p_axis2 = np.array([rotation_axis[0],rotation_axis[1],fault.top+10])
Fg = fault.duplicateFault()
for p in range(len(fault.patch)):
Fg.rotatePatch(p,strike, p_axis1, p_axis2)
Fg.computeEquivRectangle()
# Calculate GFs
if edks is True:
os.chdir(modelname=edks_params['edksdir'])
if 'Spacing' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceSpacing=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
elif 'Number' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceNumber=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceArea=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=False)
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
Faults.append(Fg)
for f in range(len(self.faults)):
Faults_cp = Faults
fault = self.faults[f]
gfs = []
# Define the range on which calculate Kernels
stk_rg = np.linspace(strike_range[f][0],strike_range[f][1],6)
# Define the rotation axis
if rotation_axis == 'center':
p_axis1 = np.array([(fault.xf[0]+fault.xf[-1])/2,(fault.yf[0]+fault.yf[-1])/2,fault.top])
p_axis2 = np.array([(fault.xf[0]+fault.xf[-1])/2,(fault.yf[0]+fault.yf[-1])/2,fault.top+10])
elif rotation_axis == 'first':
p_axis1 = np.array([fault.xf[0],fault.yf[0],fault.top])
p_axis2 = np.array([fault.xf[0],fault.yf[0],fault.top+10])
elif rotation_axis == 'last':
p_axis1 = np.array([fault.xf[-1],fault.yf[-1],fault.top])
p_axis2 = np.array([fault.xf[-1],fault.yf[-1],fault.top+10])
else:
p_axis1 = np.array([rotation_axis[0],rotation_axis[1],fault.top])
p_axis2 = np.array([rotation_axis[0],rotation_axis[1],fault.top+10])
# Calculate the Green's functions for the various strike values in stk_rg
for s in stk_rg:
print('---------------------------------')
print('---------------------------------')
print('Calculating new Fault Geometry and Greens Functions')
print('For strike = strike_prior + %.2f degrees' % (s))
# Modify the fault geometry
Fg = fault.duplicateFault()
for p in range(len(fault.patch)):
Fg.rotatePatch(p,s, p_axis1, p_axis2)
Fg.computeEquivRectangle()
# Calculate GFs for each different fault geometry
if edks is True:
os.chdir(modelname=edks_params['edksdir'])
if 'Spacing' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceSpacing=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
elif 'Number' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceNumber=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceArea=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=False)
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
Faults_cp[f] = Fg
slv = multiflt('Multi-seg fault', Faults_cp)
slv.assembleGFs()
gfs.append(slv.G)
# Calculate the sensitivity Kernels of the Green's Functions (the derivatives) by linearizing their variation
slope = np.empty(gfs[0].shape)
rvalue = np.empty(gfs[0].shape)
pvalue = np.empty(gfs[0].shape)
stderr = np.empty(gfs[0].shape)
inter = np.empty(gfs[0].shape)
for i in range(gfs[0].shape[0]):
for j in range(gfs[0].shape[1]):
# Do a linear regression for each couple parameter/data, along the range of strike values
slope[i,j], inter[i,j], rvalue[i,j], pvalue[i,j], stderr[i,j] = linregress(stk_rg,[gfs[k][i,j] for k in range(len(stk_rg))])
Kstk.append(slope)
kernels = np.asarray(Kstk)
k = np.transpose(np.matmul(kernels, mprior))
Covstk = np.zeros((len(self.faults),len(self.faults)))
for f in range(len(self.faults)):
Covstk[f,f] = sigma[f]**2
C1 = np.matmul(k, Covstk)
CpStrike = np.matmul(C1, np.transpose(k))
self.KStrike = kernels
self.CovStrike = Covstk
if self.KernelsFull==[]:
self.KernelsFull = self.KStrike
else:
self.KernelsFull = np.concatenate((self.KernelsFull,self.KStrike))
if self.CovFull==[]:
self.CovFull = self.CovStrike
else:
Z = np.zeros((np.shape(self.CovFull)[0],np.shape(self.CovStrike)[0]),dtype=int)
self.CovFull = np.asarray(np.bmat([[self.CovFull, Z], [Z, self.CovStrike]]))
self.CpStrike = CpStrike
if self.CpFull==[]:
self.CpFull = self.CpStrike
else:
self.CpFull = np.add(self.CpFull, self.CpStrike)
self.CdFull = np.add(self.Cd, self.CpFull)
if self.export is not None:
self.CdFull.astype('f').tofile(os.path.join(self.export,self.name+'CdFull.bin'))
self.KernelsFull.astype('f').tofile(os.path.join(self.export,self.name+'KernelsFull.bin'))
self.CovFull.astype('f').tofile(os.path.join(self.export,self.name+'CovFull.bin'))
self.KStrike.astype('f').tofile(os.path.join(self.export,self.name+'KStrike.bin'))
self.CovStrike.astype('f').tofile(os.path.join(self.export,self.name+'CovStrike.bin'))
print('---------------------------------')
print('---------------------------------')
print('CdFull successfully updated with CpStrike')
else:
# Define the range on which calculate Kernels
stk_rg = np.linspace(strike_range[0][0],strike_range[0][1],6)
# Define the rotation axis
if rotation_axis == 'center':
p_axis1 = np.array([(self.faults[0].xf[0]+self.faults[-1].xf[-1])/2,(self.faults[0].yf[0]+self.faults[-1].yf[-1])/2,self.faults[0].top])
p_axis2 = np.array([(self.faults[0].xf[0]+self.faults[-1].xf[-1])/2,(self.faults[0].yf[0]+self.faults[-1].yf[-1])/2,self.faults[0].top+10])
elif rotation_axis == 'first':
p_axis1 = np.array([self.faults[0].xf[0],self.faults[0].yf[0],self.faults[0].top])
p_axis2 = np.array([self.faults[0].xf[0],self.faults[0].yf[0],self.faults[0].top+10])
elif rotation_axis == 'last':
p_axis1 = np.array([self.faults[-1].xf[-1],self.faults[-1].yf[-1],self.faults[-1].top])
p_axis2 = np.array([self.faults[-1].xf[-1],self.faults[-1].yf[-1],self.faults[-1].top+10])
else:
p_axis1 = np.array([rotation_axis[0],rotation_axis[1],self.faults.top[0]])
p_axis2 = np.array([rotation_axis[0],rotation_axis[1],self.faults.top[0]+10])
Kstk = []
# Initialize the faults
Faults = []
for f in range(len(self.faults)):
fault = self.faults[f]
strike = stk_rg[0]
Fg = fault.duplicateFault()
for p in range(len(fault.patch)):
Fg.rotatePatch(p,strike, p_axis1, p_axis2)
Fg.computeEquivRectangle()
# Calculate GFs
if edks is True:
os.chdir(modelname=edks_params['edksdir'])
if 'Spacing' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceSpacing=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
elif 'Number' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceNumber=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceArea=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=False)
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
Faults.append(Fg)
for f in range(len(self.faults)):
Faults_cp = Faults
fault = self.faults[f]
gfs = []
# Calculate the Green's functions for the various strike values in stk_rg
for s in stk_rg:
print('---------------------------------')
print('---------------------------------')
print('Calculating new Fault Geometry and Greens Functions')
print('For strike = strike_prior + %.2f degrees' % (s))
# Modify the fault geometry
Fg = fault.duplicateFault()
for p in range(len(fault.patch)):
Fg.rotatePatch(p,s, p_axis1, p_axis2)
Fg.computeEquivRectangle()
# Calculate GFs for each different fault geometry
if edks is True:
os.chdir(modelname=edks_params['edksdir'])
if 'Spacing' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceSpacing=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
elif 'Number' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceNumber=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceArea=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=False)
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
Faults_cp[f] = Fg
slv = multiflt('Multi-seg fault', Faults_cp)
slv.assembleGFs()
gfs.append(slv.G)
# Calculate the sensitivity Kernels of the Green's Functions (the derivatives) by linearizing their variation
slope = np.empty(gfs[0].shape)
rvalue = np.empty(gfs[0].shape)
pvalue = np.empty(gfs[0].shape)
stderr = np.empty(gfs[0].shape)
inter = np.empty(gfs[0].shape)
for i in range(gfs[0].shape[0]):
for j in range(gfs[0].shape[1]):
# Do a linear regression for each couple parameter/data, along the range of strike values
slope[i,j], inter[i,j], rvalue[i,j], pvalue[i,j], stderr[i,j] = linregress(stk_rg,[gfs[k][i,j] for k in range(len(stk_rg))])
Kstk.append(slope)
kernels = np.asarray(Kstk)
k = np.transpose(np.matmul(kernels, mprior))
Covstk = np.zeros((len(self.faults),len(self.faults)))
for f in range(len(self.faults)):
Covstk[f,f] = sigma[f]**2
C1 = np.matmul(k, Covstk)
CpStrike = np.matmul(C1, np.transpose(k))
self.KStrike = kernels
self.CovStrike = Covstk
if self.KernelsFull==[]:
self.KernelsFull = self.KStrike
else:
self.KernelsFull = np.concatenate((self.KernelsFull,self.KStrike))
if self.CovFull==[]:
self.CovFull = self.CovStrike
else:
Z = np.zeros((np.shape(self.CovFull)[0],np.shape(self.CovStrike)[0]),dtype=int)
self.CovFull = np.asarray(np.bmat([[self.CovFull, Z], [Z, self.CovStrike]]))
self.CpStrike = CpStrike
if self.CpFull==[]:
self.CpFull = self.CpStrike
else:
self.CpFull = np.add(self.CpFull, self.CpStrike)
self.CdFull = np.add(self.Cd, self.CpFull)
if self.export is not None:
self.CdFull.astype('f').tofile(os.path.join(self.export,self.name+'CdFull.bin'))
self.KernelsFull.astype('f').tofile(os.path.join(self.export,self.name+'KernelsFull.bin'))
self.CovFull.astype('f').tofile(os.path.join(self.export,self.name+'CovFull.bin'))
self.KStrike.astype('f').tofile(os.path.join(self.export,self.name+'KStrike.bin'))
self.CovStrike.astype('f').tofile(os.path.join(self.export,self.name+'CovStrike.bin'))
print('---------------------------------')
print('---------------------------------')
print('CdFull successfully updated with CpStrike')
return CpStrike
# ----------------------------------------------------------------------
# ----------------------------------------------------------------------
# Calculate uncertainties related to the fault position
def calcCpPosition(self, position_range, sigma, mprior, whole_fault=True, edks=False, **edks_params):
'''
Calculate the uncertainties of the predictions deriving from uncertainties in the fault position.
For a one-segment fault, will vary the position perpendicularly to the strike
For a multi-segmented fault, you have two options:
- investigate the variation of the position for each segment independently (may have offset between segments)
the position will vary perpendicularly to the strike of each segment
option whole_fault = False
- investigate the variation of the position for the whole fault (whole_fault is True by default)
the position will vary perpendicularly to the global strike of the fault
From Ragon et al. (2018) GJI
Args:
* position_range : array, position values (in km) to test around the prior fault position (of Fault)
Positive values are +90 degrees from the prior strike
ex: position_range = [-1,2]
If there are several fault segments (e.g. several faults in fault), len(position_range) must be equal to len(fault)
ex: position_range = [[-1,2],[-2,1],[-0.5,0.2],[0,0.5]] for a fault with 4 segments
* sigma : prior uncertainty (standard deviation) in the fault position (in km)
ex: sigma = 5
If there are several fault segments (e.g. several faults in fault), len(sigma) must be equal to len(fault)
ex: sigma = [1,0.5,1,0.5] for a fault with 4 segments
* mprior : initial model used to calculate Cp
length must be equal to two times the number of patches
can be uniform and derived from Mo, ex: meanslip = -Mo*10**(-7)/(3*10**10*length*width)
OR derived from a first inversion without accounting for uncertainties
* whole_fault : True by default.
if True for a multi-segmented fault, the position of the whole fault will be investigated
if False for a multi-segmented fault, the position of each segment will be investigated independently
Kwargs:
* edks : If True, GFs calculated using a layered Earth model calculated with EDKS.
If False, GFs with Okada
If edks is True, please specify in **edks_params:
ex: Cp_strike(fault,datasets,[40,50],'center',sigma,mprior,edks=True,edksdir='path/to/kernels',modelname='CIA',sourceSpacing=0.5)
* edksdir : path of the edks kernels
* modelname : Filename of the EDKS kernels
* sourceSpacing : source spacing to calculate the Green's Functions
OR sourceNumber : Number of sources per patches.
OR sourceArea : Maximum Area of the sources.
Returns:
* CpPosition
'''
# For a fault with one segment
if np.shape(self.faults)==() or np.shape(self.faults)[0]==1 :
if np.shape(self.faults)==():
fault = self.faults
else:
fault = self.faults[0]
# Define the range on which calculate Kernels
pos_rg = np.linspace(position_range[0],position_range[1],6)
# Calculate the Green's functions for the various strike values in stk_rg
gfs = []
for r in pos_rg:
print('---------------------------------')
print('---------------------------------')
print('Calculating new Fault Geometry and Greens Functions')
print('For position = position_prior + %.2f km' % (r))
# Get the fault strike (in radians)
strike = np.arccos( (fault.yf[-1]-fault.yf[0]) /
np.sqrt( (fault.xf[-1]-fault.xf[0])**2
+ (fault.yf[-1]-fault.yf[0])**2 ))
# Calculate the translation vector
x_translation = np.sin(np.pi/2 - strike)* r
y_translation = np.cos(np.pi/2 - strike)* r
z_translation = 0
vector = [x_translation, y_translation, z_translation]
# Modify the fault geometry
Fg = fault.duplicateFault()
for p in range(len(fault.patch)):
Fg.translatePatch(p,vector)
Fg.computeEquivRectangle()
if edks is True:
os.chdir(modelname=edks_params['edksdir'])
if 'Spacing' in str(edks_params.items()[1][0]):
gfs.append(Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceSpacing=edks_params.items()[1][1]))
elif 'Number' in str(edks_params.items()[1][0]):
gfs.append(Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceNumber=edks_params.items()[1][1]))
else: