# Source code for openquake.hmtk.seismicity.gcmt_utils

```#!/usr/bin/env python

'''
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.matrix([[0., 0., -1.],
[-1., 0., 0.],
[0., 1., 0.]])

[docs]def use_to_ned(tensor):
'''
Converts a tensor in USE coordinate sytem to NED
'''
return np.array(ROT_NED_USE.T * np.matrix(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 * np.matrix(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.

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().'''
if not isinstance(rotmat, np.matrixlib.defmatrix.matrix):
# As this calculation relies on np.matrix algebra - convert array to
# matrix
rotmat = np.matrix(rotmat)

def cvec(x, y, z):
return np.matrix([[x, y, z]]).T
ex = cvec(1., 0., 0.)
ez = cvec(0., 0., 1.)
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)

[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. * 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)
```