Source code for openquake.hmtk.seismicity.gcmt_utils

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4

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# Copyright (C) 2010-2022 GEM Foundation, G. Weatherill, M. Pagani,
# D. Monelli.
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'''
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. * np.copy(vect) vect_hor = sqrt(vect[1] ** 2. + vect[2] ** 2.) plunge = atan2(-vect[0], vect_hor) azimuth = atan2(vect[2], -vect[1]) if degrees: icr = 180. / pi return icr * azimuth % 360., icr * plunge else: return azimuth % (2. * pi), plunge
COORD_SYSTEM = {'USE': tensor_components_to_use, 'NED': tensor_components_to_ned} ROT_NED_USE = np.array([[0., 0., -1.], [-1., 0., 0.], [0., 1., 0.]])
[docs]def use_to_ned(tensor): ''' Converts a tensor in USE coordinate sytem to NED '''
[docs] return np.array(ROT_NED_USE.T @ tensor @ ROT_NED_USE)
def ned_to_use(tensor): ''' Converts a tensor in NED coordinate sytem to USE '''
[docs] return np.array(ROT_NED_USE @ tensor @ ROT_NED_USE.T)
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. 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.) ez = cvec(0., 0., 1.)
[docs] 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.: cos_alpha = 1. if cos_alpha < -1.: cos_alpha = -1. alpha = acos(cos_alpha) beta = np.mod(atan2(enodes[1, 0], enodes[0, 0]), pi * 2.) gamma = np.mod(-atan2(enodess[1, 0], enodess[0, 0]), pi * 2.) return unique_euler(alpha, beta, gamma)
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. * pi) < 1e-10: beta = 0. if fabs(beta) < 1e-10: beta = 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. <= beta < pi assert -pi <= gamma < pi if alpha < 1e-7: beta = np.mod(beta + gamma, 2.0 * pi) gamma = 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. / 3.) * (np.log10(moment) - 9.05) else: return (2. / 3.) * (log10(moment) - 9.05)