/
test_rotate.py
497 lines (434 loc) · 21 KB
/
test_rotate.py
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#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
The Rotate test suite.
"""
import gzip
import itertools
import os
import unittest
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)
class RotateTestCase(unittest.TestCase):
"""
Test cases for Rotate.
"""
def setUp(self):
# directory where the test files are located
self.path = os.path.join(os.path.dirname(__file__), 'data')
def test_rotate_ne_rt_vs_pitsa(self):
"""
Test horizontal component rotation against PITSA.
"""
# load test files
with gzip.open(os.path.join(self.path, 'rjob_20051006_n.gz')) as f:
data_n = np.loadtxt(f)
with gzip.open(os.path.join(self.path, '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(os.path.join(self.path,
'rjob_20051006_r_%sdeg.gz' %
angle)) as f:
data_pitsa_r = np.loadtxt(f)
with gzip.open(os.path.join(self.path,
'rjob_20051006_t_%sdeg.gz' %
angle)) as f:
data_pitsa_t = np.loadtxt(f)
# Assert.
self.assertTrue(np.allclose(datcorr_r, data_pitsa_r, rtol=1E-3,
atol=1E-5))
self.assertTrue(np.allclose(datcorr_t, data_pitsa_t, rtol=1E-3,
atol=1E-5))
def test_rotate_zne_lqt_vs_pitsa(self):
"""
Test LQT component rotation against PITSA. Test back-rotation.
"""
# load test files
with gzip.open(os.path.join(self.path, 'rjob_20051006.gz')) as f:
data_z = np.loadtxt(f)
with gzip.open(os.path.join(self.path, 'rjob_20051006_n.gz')) as f:
data_n = np.loadtxt(f)
with gzip.open(os.path.join(self.path, '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(os.path.join(self.path,
'rjob_20051006_q_%sba_%sinc.gz' %
(ba, inci))) as f:
data_pitsa_q = np.loadtxt(f)
with gzip.open(os.path.join(self.path,
'rjob_20051006_t_%sba_%sinc.gz' %
(ba, inci))) as f:
data_pitsa_t = np.loadtxt(f)
with gzip.open(os.path.join(self.path,
'rjob_20051006_l_%sba_%sinc.gz' %
(ba, inci))) 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.
self.assertTrue(
np.allclose(data_l, data_pitsa_l, rtol=1E-3, atol=1E-5))
self.assertTrue(
np.allclose(data_q, data_pitsa_q, rtol=1E-3, atol=1E-5))
self.assertTrue(
np.allclose(data_t, data_pitsa_t, rtol=1E-3, atol=1E-5))
self.assertTrue(
np.allclose(data_z, data_back_z, rtol=1E-3, atol=1E-5))
self.assertTrue(
np.allclose(data_n, data_back_n, rtol=1E-3, atol=1E-5))
self.assertTrue(
np.allclose(data_e, data_back_e, rtol=1E-3, atol=1E-5))
def test_rotate_ne_rt_ne(self):
"""
Rotating there and back with the same back-azimuth should not change
the data.
"""
# load the data
with gzip.open(os.path.join(self.path, 'rjob_20051006_n.gz')) as f:
data_n = np.loadtxt(f)
with gzip.open(os.path.join(self.path, '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)
self.assertTrue(np.allclose(data_n, new_n, rtol=1E-7, atol=1E-12))
self.assertTrue(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
self.assertRaisesRegex(
ValueError, '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)
self.assertTrue(np.allclose(v1, v1_ref, rtol=1E-7, atol=1E-7))
self.assertTrue(np.allclose(v2, v2_ref, rtol=1E-7, atol=1E-7))
self.assertTrue(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])
self.assertTrue(np.allclose(z, z_ref, rtol=1E-7, atol=1E-7))
self.assertTrue(np.allclose(n, n_ref, rtol=1E-7, atol=1E-7))
self.assertTrue(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"]):
with self.assertRaises(ValueError) as err:
rotate2zne(a[0], a[1], a[2],
b[0], b[1], b[2],
c[0], c[1], c[2])
self.assertTrue(err.exception.args[0].startswith(
"The given directions are not linearly independent, "
"at least within numerical precision. Determinant of "
"the base change matrix:"))
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.
self.assertEqual(success_count, 3888)
# Also the linearly dependent variants.
self.assertEqual(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 self.assertRaises(AssertionError):
np.testing.assert_allclose(z_new, z[0], rtol=1E-5)
self.assertEqual(success_count, 12)
self.assertEqual(failure_count, 12)