/
test_rotate.py
478 lines (416 loc) · 19.9 KB
/
test_rotate.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
#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
The Rotate test suite.
"""
import gzip
import itertools
import numpy as np
from obspy.signal.rotate import (rotate_lqt_zne, rotate_ne_rt, rotate_rt_ne,
rotate_zne_lqt, _dip_azimuth2zne_base_vector,
rotate2zne)
import pytest
class TestRotate():
"""
Test cases for Rotate.
"""
def test_rotate_ne_rt_vs_pitsa(self, testdata):
"""
Test horizontal component rotation against PITSA.
"""
# load test files
with gzip.open(testdata['rjob_20051006_n.gz']) as f:
data_n = np.loadtxt(f)
with gzip.open(testdata['rjob_20051006_e.gz']) as f:
data_e = np.loadtxt(f)
# test different angles, one from each sector
for angle in [30, 115, 185, 305]:
# rotate traces
datcorr_r, datcorr_t = rotate_ne_rt(data_n, data_e, angle)
# load pitsa files
with gzip.open(testdata['rjob_20051006_r_%sdeg.gz' % angle]) as f:
data_pitsa_r = np.loadtxt(f)
with gzip.open(testdata['rjob_20051006_t_%sdeg.gz' % angle]) as f:
data_pitsa_t = np.loadtxt(f)
# Assert.
assert np.allclose(datcorr_r, data_pitsa_r, rtol=1E-3, atol=1E-5)
assert np.allclose(datcorr_t, data_pitsa_t, rtol=1E-3, atol=1E-5)
def test_rotate_zne_lqt_vs_pitsa(self, testdata):
"""
Test LQT component rotation against PITSA. Test back-rotation.
"""
# load test files
with gzip.open(testdata['rjob_20051006.gz']) as f:
data_z = np.loadtxt(f)
with gzip.open(testdata['rjob_20051006_n.gz']) as f:
data_n = np.loadtxt(f)
with gzip.open(testdata['rjob_20051006_e.gz']) as f:
data_e = np.loadtxt(f)
# test different backazimuth/incidence combinations
for ba, inci in ((60, 130), (210, 60)):
# rotate traces
data_l, data_q, data_t = \
rotate_zne_lqt(data_z, data_n, data_e, ba, inci)
# rotate traces back to ZNE
data_back_z, data_back_n, data_back_e = \
rotate_lqt_zne(data_l, data_q, data_t, ba, inci)
# load pitsa files
with gzip.open(
testdata[f'rjob_20051006_q_{ba}ba_{inci}inc.gz']) as f:
data_pitsa_q = np.loadtxt(f)
with gzip.open(
testdata[f'rjob_20051006_t_{ba}ba_{inci}inc.gz']) as f:
data_pitsa_t = np.loadtxt(f)
with gzip.open(
testdata[f'rjob_20051006_l_{ba}ba_{inci}inc.gz']) as f:
data_pitsa_l = np.loadtxt(f)
# Assert the output. Has to be to rather low accuracy due to
# rounding error prone rotation and single precision value.
assert np.allclose(data_l, data_pitsa_l, rtol=1E-3, atol=1E-5)
assert np.allclose(data_q, data_pitsa_q, rtol=1E-3, atol=1E-5)
assert np.allclose(data_t, data_pitsa_t, rtol=1E-3, atol=1E-5)
assert np.allclose(data_z, data_back_z, rtol=1E-3, atol=1E-5)
assert np.allclose(data_n, data_back_n, rtol=1E-3, atol=1E-5)
assert np.allclose(data_e, data_back_e, rtol=1E-3, atol=1E-5)
def test_rotate_ne_rt_ne(self, testdata):
"""
Rotating there and back with the same back-azimuth should not change
the data.
"""
# load the data
with gzip.open(testdata['rjob_20051006_n.gz']) as f:
data_n = np.loadtxt(f)
with gzip.open(testdata['rjob_20051006_e.gz']) as f:
data_e = np.loadtxt(f)
# Use double precision to get more accuracy for testing.
data_n = np.require(data_n, np.float64)
data_e = np.require(data_e, np.float64)
ba = 33.3
new_n, new_e = rotate_ne_rt(data_n, data_e, ba)
new_n, new_e = rotate_rt_ne(new_n, new_e, ba)
assert np.allclose(data_n, new_n, rtol=1E-7, atol=1E-12)
assert np.allclose(data_e, new_e, rtol=1E-7, atol=1E-12)
def test_rotate2zne_round_trip(self):
"""
The rotate2zne() function has an inverse argument. Thus round
tripping should work.
"""
np.random.seed(45645623)
z = np.random.random(10)
n = np.random.random(10)
e = np.random.random(10)
for _ in range(100):
# The risk of producing linear dependent directions is very
# small (the seed value should also prevent it across machines).
dip_1, dip_2, dip_3 = np.random.random(3) * 180.0 - 90.0
azi_1, azi_2, azi_3 = np.random.random(3) * 360.0
a, b, c = rotate2zne(z, azi_1, dip_1,
n, azi_2, dip_2,
e, azi_3, dip_3)
z_new, n_new, e_new = rotate2zne(a, azi_1, dip_1,
b, azi_2, dip_2,
c, azi_3, dip_3,
inverse=True)
np.testing.assert_allclose(z, z_new, rtol=1E-7, atol=1e-7)
np.testing.assert_allclose(n, n_new, rtol=1E-7, atol=1e-7)
np.testing.assert_allclose(e, e_new, rtol=1E-7, atol=1e-7)
def test_rotate2zne_raise(self):
"""
Check that rotate2zne() raises on unequal lengths of data.
"""
z = np.ones(3, dtype=np.float64)
n = np.ones(5, dtype=np.float64)
e = np.ones(3, dtype=np.float64)
# Random values.
dip_1, dip_2, dip_3 = 0.0, 30.0, 60.0
azi_1, azi_2, azi_3 = 0.0, 170.0, 35.0
with pytest.raises(
ValueError,
match='All three data arrays must be of same length.'):
rotate2zne(z, azi_1, dip_1, n, azi_2, dip_2, e, azi_3, dip_3)
def test_base_vector_calculation_simple_cases(self):
"""
Tests the _dip_azimuth2zne_base_vector() with some simple cases.
"""
# Up and down.
np.testing.assert_allclose(_dip_azimuth2zne_base_vector(-90, 0),
[1.0, 0.0, 0.0], atol=1E-10)
np.testing.assert_allclose(_dip_azimuth2zne_base_vector(90, 0),
[-1.0, 0.0, 0.0], atol=1E-10)
# North and South.
np.testing.assert_allclose(_dip_azimuth2zne_base_vector(0, 0),
[0.0, 1.0, 0.0], atol=1E-10)
np.testing.assert_allclose(_dip_azimuth2zne_base_vector(0, 180),
[0.0, -1.0, 0.0], atol=1E-10)
# East and West.
np.testing.assert_allclose(_dip_azimuth2zne_base_vector(0, 90),
[0.0, 0.0, 1.0], atol=1E-10)
np.testing.assert_allclose(_dip_azimuth2zne_base_vector(0, 270),
[0.0, 0.0, -1.0], atol=1E-10)
# Normalizing helper.
def _n(v):
return np.array(v) / np.linalg.norm(np.array(v))
# 4 corners in the plain.
np.testing.assert_allclose(_dip_azimuth2zne_base_vector(0, 45),
_n([0.0, 1.0, 1.0]), atol=1E-10)
np.testing.assert_allclose(_dip_azimuth2zne_base_vector(0, 135),
_n([0.0, -1.0, 1.0]), atol=1E-10)
np.testing.assert_allclose(_dip_azimuth2zne_base_vector(0, 225),
_n([0.0, -1.0, -1.0]), atol=1E-10)
np.testing.assert_allclose(_dip_azimuth2zne_base_vector(0, 315),
_n([0.0, 1.0, -1.0]), atol=1E-10)
# 4 corners in the top.
dip = np.rad2deg(np.arctan2(1, np.sqrt(2)))
np.testing.assert_allclose(_dip_azimuth2zne_base_vector(-dip, 45),
_n([1.0, 1.0, 1.0]), atol=1E-10)
np.testing.assert_allclose(_dip_azimuth2zne_base_vector(-dip, 135),
_n([1.0, -1.0, 1.0]), atol=1E-10)
np.testing.assert_allclose(_dip_azimuth2zne_base_vector(-dip, 225),
_n([1.0, -1.0, -1.0]), atol=1E-10)
np.testing.assert_allclose(_dip_azimuth2zne_base_vector(-dip, 315),
_n([1.0, 1.0, -1.0]), atol=1E-10)
# And in the bottom
np.testing.assert_allclose(_dip_azimuth2zne_base_vector(dip, 45),
_n([-1.0, 1.0, 1.0]), atol=1E-10)
np.testing.assert_allclose(_dip_azimuth2zne_base_vector(dip, 135),
_n([-1.0, -1.0, 1.0]), atol=1E-10)
np.testing.assert_allclose(_dip_azimuth2zne_base_vector(dip, 225),
_n([-1.0, -1.0, -1.0]), atol=1E-10)
np.testing.assert_allclose(_dip_azimuth2zne_base_vector(dip, 315),
_n([-1.0, 1.0, -1.0]), atol=1E-10)
def test_base_vector_from_azimuth_and_dip_calculation(self):
"""
Tests the _dip_azimuth2zne_base_vector() method against a solution
from the Wieland book.
"""
dip = - (90.0 - np.rad2deg(np.arctan(np.sqrt(2.0))))
v1 = _dip_azimuth2zne_base_vector(dip, -90.0)
v2 = _dip_azimuth2zne_base_vector(dip, 30.0)
v3 = _dip_azimuth2zne_base_vector(dip, 150.0)
v1_ref = np.array([np.sqrt(2.0), 0.0, -2.0]) / np.sqrt(6.0)
v2_ref = np.array([np.sqrt(2.0), np.sqrt(3.0), 1.0]) / np.sqrt(6.0)
v3_ref = np.array([np.sqrt(2.0), -np.sqrt(3.0), 1.0]) / np.sqrt(6.0)
assert np.allclose(v1, v1_ref, rtol=1E-7, atol=1E-7)
assert np.allclose(v2, v2_ref, rtol=1E-7, atol=1E-7)
assert np.allclose(v3, v3_ref, rtol=1E-7, atol=1E-7)
def test_galperin_configuration(self):
"""
Equal arrays on a Galperin configuration should result in only the
vertical component remaining.
"""
dip = - (90.0 - np.rad2deg(np.arctan(np.sqrt(2.0))))
u = np.array([1.0, 0.0, 1.0])
v = np.array([1.0, 1.0, -1.0])
w = np.array([1.0, -1.0, -1.0])
z, n, e = rotate2zne(
u, -90, dip,
v, 30, dip,
w, 150, dip)
fac = 1.0 / np.sqrt(6.0)
z_ref = np.array([fac * 3.0 * np.sqrt(2.0), 0.0, -fac * np.sqrt(2.0)])
n_ref = np.array([0.0, fac * 2.0 * np.sqrt(3.0), 0.0])
e_ref = np.array([0.0, 0.0, -4.0 * fac])
assert np.allclose(z, z_ref, rtol=1E-7, atol=1E-7)
assert np.allclose(n, n_ref, rtol=1E-7, atol=1E-7)
assert np.allclose(e, e_ref, rtol=1E-7, atol=1E-7)
def test_rotate2zne_against_rotate_ne_rt(self):
np.random.seed(123)
z = np.random.random(10)
n = np.random.random(10)
e = np.random.random(10)
for ba in [0.0, 14.325, 38.234, 78.1, 90.0, 136.3435, 265.4, 351.35]:
r, t = rotate_ne_rt(n=n, e=e, ba=ba)
# Unrotate with rotate2zne() - this should make sure the azimuth is
# interpreted correctly.
z_new, n_new, e_new = rotate2zne(z, 0, -90,
r, ba + 180, 0,
t, ba + 270, 0)
np.testing.assert_allclose(z_new, z)
np.testing.assert_allclose(n_new, n)
np.testing.assert_allclose(e_new, e)
def test_rotate2zne_against_ne_rt_picking_any_two_horizontal_comps(self):
"""
This also tests non-orthogonal configurations to some degree.
"""
np.random.seed(456)
z = np.random.random(10)
n = np.random.random(10)
e = np.random.random(10)
# Careful to not pick any coordinate axes.
for ba in [14.325, 38.234, 78.1, 136.3435, 265.4, 351.35]:
r, t = rotate_ne_rt(n=n, e=e, ba=ba)
_r = [r, ba + 180, 0]
_t = [t, ba + 270, 0]
_n = [n, 0, 0]
_e = [e, 90, 0]
# Picking any two should be enough to reconstruct n and e.
for a, b in itertools.permutations([_r, _t, _n, _e], 2):
z_new, n_new, e_new = rotate2zne(z, 0, -90,
a[0], a[1], a[2],
b[0], b[1], b[2])
np.testing.assert_allclose(z_new, z)
np.testing.assert_allclose(n_new, n)
np.testing.assert_allclose(e_new, e)
def test_rotate2zne_against_lqt(self):
np.random.seed(789)
z = np.random.random(10)
n = np.random.random(10)
e = np.random.random(10)
bas = [0.0, 14.325, 38.234, 78.1, 90.0, 136.3435, 265.4, 180.0,
351.35, 360.0]
incs = [0.0, 10.325, 32.23, 88.1, 90.0, 132.3435, 245.4, 180.0,
341.35, 360.0]
for ba, inc in itertools.product(bas, incs):
l, q, t = rotate_zne_lqt(z=z, n=n, e=e, ba=ba, inc=inc)
dip_l = (inc % 180.0) - 90.0
if 180 <= inc < 360:
dip_l *= -1.0
dip_q = ((inc + 90) % 180) - 90
if 0 < inc < 90 or 270 <= inc < 360:
dip_q *= -1.0
az_l = ba + 180.0
az_q = ba
# Azimuths flip depending on the incidence angle.
if inc > 180:
az_l += 180
if 90 < inc <= 270:
az_q += 180
z_new, n_new, e_new = rotate2zne(l, az_l, dip_l,
q, az_q, dip_q,
t, ba + 270, 0)
np.testing.assert_allclose(z_new, z)
np.testing.assert_allclose(n_new, n)
np.testing.assert_allclose(e_new, e)
def test_rotate2zne_against_lqt_different_combinations(self):
np.random.seed(101112)
z = np.random.random(10)
n = np.random.random(10)
e = np.random.random(10)
# Exclude coordinate axis.
bas = [14.325, 38.234, 78.1, 136.3435, 265.4, 351.35]
incs = [10.325, 32.23, 88.1, 132.3435, 245.4, 341.35]
success_count = 0
failure_count = 0
for ba, inc in itertools.product(bas, incs):
l, q, t = rotate_zne_lqt(z=z, n=n, e=e, ba=ba, inc=inc)
dip_l = (inc % 180.0) - 90.0
if 180 <= inc < 360:
dip_l *= -1.0
dip_q = ((inc + 90) % 180) - 90
if 0 < inc < 90 or 270 <= inc < 360:
dip_q *= -1.0
az_l = ba + 180.0
az_q = ba
# Azimuths flip depending on the incidence angle.
if inc > 180:
az_l += 180
if 90 < inc <= 270:
az_q += 180
_z = [z, 0, -90, "Z"]
_n = [n, 0, 0, "N"]
_e = [e, 90, 0, "E"]
_l = [l, az_l, dip_l, "L"]
_q = [q, az_q, dip_q, "Q"]
_t = [t, ba + 270, 0, "T"]
# Any three of them (except three horizontal ones) should be
# able to reconstruct ZNE.
for a, b, c in itertools.permutations([_l, _q, _t, _z, _n, _e], 3):
# Three horizontal components are linearly dependent, as are
# Z, Q, and L.
if a[2] == b[2] == c[2] == 0 or \
set([_i[3] for _i in (a, b, c)]) == \
set(["Z", "Q", "L"]):
msg = (
"The given directions are not linearly independent, "
"at least within numerical precision. Determinant of "
"the base change matrix:")
with pytest.raises(ValueError, match=msg):
rotate2zne(a[0], a[1], a[2],
b[0], b[1], b[2],
c[0], c[1], c[2])
failure_count += 1
continue
z_new, n_new, e_new = rotate2zne(a[0], a[1], a[2],
b[0], b[1], b[2],
c[0], c[1], c[2])
np.testing.assert_allclose(z_new, z)
np.testing.assert_allclose(n_new, n)
np.testing.assert_allclose(e_new, e)
success_count += 1
# Make sure it actually tested all combinations.
assert success_count == 3888
# Also the linearly dependent variants.
assert failure_count == 432
def test_with_real_data(self):
# Filtered and downsampled test data with two co-located
# seismometers on a step table. One (UVW) in Galperin configuration,
# the other (XYZ) oriented 25 degree towards counter-clockwise from
# North.
#
# Original data can be found here:
# http://examples.obspy.org/step_table_galperin_and_xyz.mseed
#
# Picture of setup:
# http://examples.obspy.org/step_table_galperin_and_xyz.jpg
u = np.array([
-887.77005805, 7126.9690531, 48436.17065483, 138585.24660557,
220190.69362083, 179040.5715419, -21365.23030094,
-253885.25529288, -344888.20815164, -259362.36082208,
-117476.30748613, - 42988.81966958, -45995.43307308,
-57130.87444412, -30545.75344533, 16298.87665025])
v = np.array([
2.33308511e+02, 8.16259596e+03, 5.11074487e+04, 1.48229541e+05,
2.41322335e+05, 2.08201013e+05, 4.93732289e+03, -2.39867750e+05,
-3.44167596e+05, -2.66558032e+05, -1.27714987e+05, -5.54712804e+04,
-6.19973652e+04, -7.66740787e+04, -5.17925310e+04,
-4.71673443e+03])
w = np.array([
1692.48532892, 9875.6136413, 53089.61423663, 149373.52749023,
240009.30157128, 204362.69005767, 1212.47406863, -239380.57384624,
-336783.01040666, -252884.65411222, -110766.44577398,
-38182.18142102, -45729.92956198, -61691.87092415,
-38434.81993441, 6224.73096858])
x = np.array([
-1844.85832046, -1778.44974024, -2145.6117388, -4325.27560474,
-8278.1836905, -10842.53378841, -8565.12113951, -2024.53838011,
4439.22322848, 7340.96354878, 7081.65449722, 6303.91640198,
6549.98692684, 7223.59663617, 7133.72073748, 6068.56702479])
y = np.array([
-242.70568894, -458.3864756, -351.75925077, 2142.51669733,
8287.98182002, 15822.24351111, 20151.78532927, 18511.90136103,
12430.22438956, 5837.66044337, 1274.9580289, -1597.06115226,
-4331.40686142, -7529.87533286, -10544.34374306, -12656.77586305])
z = np.array([
5.79050980e+02, 1.45190734e+04, 8.85582128e+04, 2.53690907e+05,
4.08578800e+05, 3.45046937e+05, -8.15914926e+03, -4.26449298e+05,
-5.97207861e+05, -4.53464470e+05, -2.07176498e+05, -7.94526512e+04,
-8.95206215e+04, -1.14008287e+05, -7.05797830e+04, 1.01175730e+04])
# Component orientations.
u = (u, 90.0, -(90.0 - 54.7), "U")
v = (v, 330.0, -(90.0 - 54.7), "V")
w = (w, 210.0, -(90.0 - 54.7), "W")
x = (x, 65.0, 0.0, "X")
y = (y, 335.0, 0.0, "Y")
z = (z, 0.0, -90.0, "Z")
# Any three should result in the same ZNE.
success_count = 0
failure_count = 0
for a, b, c in itertools.permutations([x, y, z, u], 3):
# Except if "X" and "Y" are both part of it because they don't
# really contain any data (vertical step table).
if set(["X", "Y"]).issubset(set([a[-1], b[-1], c[-1]])):
failure_count += 1
continue
z_new, _, _ = rotate2zne(
a[0], a[1], a[2], b[0], b[1], b[2], c[0], c[1], c[2])
np.testing.assert_allclose(z_new, z[0], rtol=1E-5)
success_count += 1
# Sanity check that it fails for slightly different rotations.
z_new, _, _ = rotate2zne(
a[0], a[1] + 1.5, a[2] - 1.5,
b[0], b[1] - 0.7, b[2] + 1.2,
c[0], c[1] + 1.0, c[2] - 0.4)
with pytest.raises(AssertionError):
np.testing.assert_allclose(z_new, z[0], rtol=1E-5)
assert success_count == 12
assert failure_count == 12