# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# LICENSE
#
# Copyright (C) 2010-2023 GEM Foundation, G. Weatherill, M. Pagani,
# D. Monelli.
#
# The Hazard Modeller's Toolkit is free software: you can redistribute
# it and/or modify it under the terms of the GNU Affero General Public
# License as published by the Free Software Foundation, either version
# 3 of the License, or (at your option) any later version.
#
# You should have received a copy of the GNU Affero General Public License
# along with OpenQuake. If not, see <http://www.gnu.org/licenses/>
#
# DISCLAIMER
#
# The software Hazard Modeller's Toolkit (openquake.hmtk) provided herein
# is released as a prototype implementation on behalf of
# scientists and engineers working within the GEM Foundation (Global
# Earthquake Model).
#
# It is distributed for the purpose of open collaboration and in the
# hope that it will be useful to the scientific, engineering, disaster
# risk and software design communities.
#
# The software is NOT distributed as part of GEM’s OpenQuake suite
# (https://www.globalquakemodel.org/tools-products) and must be considered as a
# separate entity. The software provided herein is designed and implemented
# by scientific staff. It is not developed to the design standards, nor
# subject to same level of critical review by professional software
# developers, as GEM’s OpenQuake software suite.
#
# Feedback and contribution to the software is welcome, and can be
# directed to the hazard scientific staff of the GEM Model Facility
# (hazard@globalquakemodel.org).
#
# The Hazard Modeller's Toolkit (openquake.hmtk) is therefore distributed WITHOUT
# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
# FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
# for more details.
#
# The GEM Foundation, and the authors of the software, assume no
# liability for use of the software.
"""
Set of moment tensor utility functions
"""
import numpy as np
from math import fabs, log10, sqrt, acos, atan2, pi
[docs]def tensor_components_to_use(mrr, mtt, mpp, mrt, mrp, mtp):
"""
Converts components to Up, South, East definition::
USE = [[mrr, mrt, mrp],
[mtt, mtt, mtp],
[mrp, mtp, mpp]]
"""
return np.array([[mrr, mrt, mrp], [mrt, mtt, mtp], [mrp, mtp, mpp]])
[docs]def tensor_components_to_ned(mrr, mtt, mpp, mrt, mrp, mtp):
"""
Converts components to North, East, Down definition::
NED = [[mtt, -mtp, mrt],
[-mtp, mpp, -mrp],
[mrt, -mtp, mrr]]
"""
return np.array([[mtt, -mtp, mrt], [-mtp, mpp, -mrp], [mrt, -mtp, mrr]])
[docs]def get_azimuth_plunge(vect, degrees=True):
"""
For a given vector in USE format, retrieve the azimuth and plunge
"""
if vect[0] > 0:
vect = -1.0 * np.copy(vect)
vect_hor = sqrt(vect[1] ** 2.0 + vect[2] ** 2.0)
plunge = atan2(-vect[0], vect_hor)
azimuth = atan2(vect[2], -vect[1])
if degrees:
icr = 180.0 / pi
return icr * azimuth % 360.0, icr * plunge
else:
return azimuth % (2.0 * pi), plunge
COORD_SYSTEM = {
"USE": tensor_components_to_use,
"NED": tensor_components_to_ned,
}
ROT_NED_USE = np.array([[0.0, 0.0, -1.0], [-1.0, 0.0, 0.0], [0.0, 1.0, 0.0]])
[docs]def use_to_ned(tensor):
"""
Converts a tensor in USE coordinate sytem to NED
"""
return np.array(ROT_NED_USE.T @ tensor @ ROT_NED_USE)
[docs]def ned_to_use(tensor):
"""
Converts a tensor in NED coordinate sytem to USE
"""
return np.array(ROT_NED_USE @ tensor @ ROT_NED_USE.T)
[docs]def tensor_to_6component(tensor, frame="USE"):
"""
Returns a tensor to six component vector [Mrr, Mtt, Mpp, Mrt, Mrp, Mtp]
"""
if "NED" in frame:
tensor = ned_to_use(tensor)
return [
tensor[0, 0],
tensor[1, 1],
tensor[2, 2],
tensor[0, 1],
tensor[0, 2],
tensor[1, 2],
]
[docs]def normalise_tensor(tensor):
"""
Normalise the tensor by dividing it by its norm, defined such that
np.sqrt(X:X)
"""
tensor_norm = np.linalg.norm(tensor)
return tensor / tensor_norm, tensor_norm
[docs]def eigendecompose(tensor, normalise=False):
"""
Performs and eigendecomposition of the tensor and orders into
descending eigenvalues
"""
if normalise:
tensor, tensor_norm = normalise_tensor(tensor)
else:
tensor_norm = 1.0
eigvals, eigvects = np.linalg.eigh(tensor, UPLO="U")
isrt = np.argsort(eigvals)
eigenvalues = eigvals[isrt] * tensor_norm
eigenvectors = eigvects[:, isrt]
return eigenvalues, eigenvectors
[docs]def matrix_to_euler(rotmat):
"""Inverse of euler_to_matrix()."""
def cvec(x, y, z):
return np.array([[x, y, z]]).T
ex = cvec(1.0, 0.0, 0.0)
ez = cvec(0.0, 0.0, 1.0)
exs = rotmat.T @ ex
ezs = rotmat.T @ ez
enodes = np.cross(ez.T, ezs.T).T
if np.linalg.norm(enodes) < 1e-10:
enodes = exs
enodess = rotmat * enodes
cos_alpha = float((ez.T @ ezs))
if cos_alpha > 1.0:
cos_alpha = 1.0
if cos_alpha < -1.0:
cos_alpha = -1.0
alpha = acos(cos_alpha)
beta = np.mod(atan2(enodes[1, 0], enodes[0, 0]), pi * 2.0)
gamma = np.mod(-atan2(enodess[1, 0], enodess[0, 0]), pi * 2.0)
return unique_euler(alpha, beta, gamma)
[docs]def unique_euler(alpha, beta, gamma):
"""
Uniquify euler angle triplet.
Put euler angles into ranges compatible with (dip,strike,-rake)
in seismology:
alpha (dip) : [0, pi/2]
beta (strike) : [0, 2*pi)
gamma (-rake) : [-pi, pi)
If alpha is near to zero, beta is replaced by beta+gamma and gamma is set
to zero, to prevent that additional ambiguity.
If alpha is near to pi/2, beta is put into the range [0,pi).
"""
alpha = np.mod(alpha, 2.0 * pi)
if 0.5 * pi < alpha and alpha <= pi:
alpha = pi - alpha
beta = beta + pi
gamma = 2.0 * pi - gamma
elif pi < alpha and alpha <= 1.5 * pi:
alpha = alpha - pi
gamma = pi - gamma
elif 1.5 * pi < alpha and alpha <= 2.0 * pi:
alpha = 2.0 * pi - alpha
beta = beta + pi
gamma = pi + gamma
alpha = np.mod(alpha, 2.0 * pi)
beta = np.mod(beta, 2.0 * pi)
gamma = np.mod(gamma + pi, 2.0 * pi) - pi
# If dip is exactly 90 degrees, one is still
# free to choose between looking at the plane from either side.
# Choose to look at such that beta is in the range [0,180)
# This should prevent some problems, when dip is close to 90 degrees:
if fabs(alpha - 0.5 * pi) < 1e-10:
alpha = 0.5 * pi
if fabs(beta - pi) < 1e-10:
beta = pi
if fabs(beta - 2.0 * pi) < 1e-10:
beta = 0.0
if fabs(beta) < 1e-10:
beta = 0.0
if alpha == 0.5 * pi and beta >= pi:
gamma = -gamma
beta = np.mod(beta - pi, 2.0 * pi)
gamma = np.mod(gamma + pi, 2.0 * pi) - pi
assert 0.0 <= beta < pi
assert -pi <= gamma < pi
if alpha < 1e-7:
beta = np.mod(beta + gamma, 2.0 * pi)
gamma = 0.0
return (alpha, beta, gamma)
[docs]def moment_magnitude_scalar(moment):
"""
Uses Hanks & Kanamori formula for calculating moment magnitude from
a scalar moment (Nm)
"""
if isinstance(moment, np.ndarray):
return (2.0 / 3.0) * (np.log10(moment) - 9.05)
else:
return (2.0 / 3.0) * (log10(moment) - 9.05)
