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# https://pyrocko.org - GPLv3 # # The Pyrocko Developers, 21st Century # ---|P------/S----------~Lg----------
optional=True, default='')
default=0., help='source origin time', optional=True)
default=0., help='Rupture velocity', optional=True)
def northing(self):
def easting(self):
''' Rectangular analytical source model '''
default=0.0, help='strike direction in [deg], measured clockwise from north')
default=90.0, help='dip angle in [deg], measured downward from horizontal')
default=0.0, help='rake angle in [deg], ' 'measured counter-clockwise from right-horizontal ' 'in on-plane view')
default=0., help='Distance "left" side to source point [m]')
default=0., help='Distance "right" side to source point [m]')
default=0., help='Distance "lower" side to source point [m]')
default=0., help='Distance "upper" side to source point [m]')
default=0., help='Slip on the rectangular source area [m]', optional=True)
def length(self):
def width(self):
def area(self):
''' Rectangular Okada source model '''
default=0., help='Opening of the plane in [m]', optional=True)
default=0.25, help='Poisson\'s ratio, typically 0.25', optional=True)
default=32e9, help='Shear modulus along the plane [Pa]', optional=True)
def lamb(self): ''' Calculation of first Lame's parameter
According to Mueller (2007), the first Lame parameter lambda can be determined from the formulation for the poisson ration nu: nu = lambda / (2 * (lambda + mu)) with the shear modulus mu '''
def seismic_moment(self): ''' Scalar Seismic moment
Code copied from Kite Disregarding the opening (as for now) We assume a shear modulus of :math:`mu = 36 mathrm{GPa}` and :math:`M_0 = mu A D`
.. important ::
We assume a perfect elastic solid with :math:`K=\\frac{5}{3}\\mu`
Through :math:`\\mu = \\frac{3K(1-2\\nu)}{2(1+\\nu)}` this leads to :math:`\\mu = \\frac{8(1+\\nu)}{1-2\\nu}`
:return: Seismic moment release :rtype: float '''
elif self.poisson: self.shearmod = (8. * (1. + self.poisson)) / (1. - 2*self.poisson) mu = self.shearmod else: raise ValueError( 'Shear modulus or poisson ratio needed for moment calculation')
disl = (disl**2 + self.opening**2)**.5
def moment_magnitude(self): ''' Moment magnitude from Seismic moment
We assume :math:`M_\\mathrm{w} = {\\frac{2}{3}}\\log_{10}(M_0) - 10.7`
:returns: Moment magnitude :rtype: float ''' return mt.moment_to_magnitude(self.seismic_moment)
''' Build source information array for okada_ext.okada input
:return: array of the source data as input for okada_ext.okada :rtype: :py:class:`numpy.ndarray`, ``(1, 9)`` ''' self.northing, self.easting, self.depth, self.strike, self.dip, self.al1, self.al2, self.aw1, self.aw2])
''' Build source dislocation for okada_ext.okada input
:return: array of the source dislocation data as input for okada_ext.okada :rtype: :py:class:`numpy.ndarray`, ``(1, 3)`` ''' num.cos(self.rake * d2r) * self.slip, num.sin(self.rake * d2r) * self.slip, self.opening])
''' Discretize the given fault by ``nlength * nwidth`` fault patches
Discretizing the fault into several sub faults. ``nlength`` is number of points in strike direction, ``nwidth`` in down dip direction along the fault. Fault orientation, slip and elastic parameters are kept.
:param nlength: Number of discrete points in faults strike direction :type nlength: int :param nwidth: Number of discrete points in faults down-dip direction :type nwidth: int
:return: Discrete fault patches :rtype: list of :py:class:`pyrocko.modelling.OkadaSource` objects '''
mt.euler_to_matrix(self.dip*d2r, self.strike*d2r, 0.))
prop: getattr(self, prop) for prop in self.T.propnames if prop not in [ 'north_shift', 'east_shift', 'depth', 'al1', 'al2', 'aw1', 'aw2']}
[OkadaPatch( parent=self, length_pos=src_point[0], width_pos=src_point[1], north_shift=coord[0], east_shift=coord[1], depth=coord[2], al1=al1, al2=al2, aw1=aw1, aw2=aw2, **kwargs) for src_point, coord in zip(source_points, source_points_rot)], source_points)
''' Toolbox for Boundary Element Method (BEM) and dislocation inversion based on okada_ext.okada '''
rotate_sdn=True, nthreads=1): ''' Build coefficient matrix for given source_patches
The BEM for a fault and the determination of the slip distribution from the stress drop is based on the relation stress = coef_mat * displ. Here the coefficient matrix is build and filled based on the okada_ext.okada displacements and partial displacement differentiations.
:param source_patches_list: list of all OkadaSources, which shall be used for BEM :type source_patches_list: list of :py:class:`pyrocko.modelling.OkadaSource` :param pure_shear: Shall only shear forces be taken into account, or additionally include opening, default False. :type pure_shear: optional, bool :param rotate_sdn: Rotation towards strike, dip, normal, default True. :type rotate_sdn: optional, bool :param nthreads: Number of threads, default 1 :type nthreads: optional, int
:return: coefficient matrix for all sources :rtype: :py:class:`numpy.ndarray`, ``(len(source_patches_list) * 3, len(source_patches_list) * 3)`` '''
src.source_patch() for src in source_patches_list])
else:
'strikeslip': { 'slip': unit_disl, 'opening': 0., 'rake': 0.}, 'dipslip': { 'slip': unit_disl, 'opening': 0., 'rake': 90.}, 'tensileslip': { 'slip': 0., 'opening': unit_disl, 'rake': 0.} }
'strikeslip', 'dipslip', 'tensileslip'][:n_eq]): case['slip'] * num.cos(case['rake'] * d2r), case['slip'] * num.sin(case['rake'] * d2r), case['opening']])
source_patches, num.tile(source_disl, npoints).reshape(-1, 3), receiver_coords, lambda_mean, mu_mean, nthreads=nthreads, rotate_sdn=rotate_sdn, stack_sources=False)
results[:, :, (3, 6, 9, 4, 7, 10, 5, 8, 11)])
.reshape(-1, npoints*3).T
rotate_sdn=True, nthreads=1): ''' Build coefficient matrix for given source_patches
The BEM for a fault and the determination of the slip distribution from the stress drop is based on the relation stress = coef_mat * displ. Here the coefficient matrix is build and filled based on the okada_ext.okada displacements and partial displacement differentiations.
:param source_patches_list: list of all OkadaSources, which shall be used for BEM :type source_patches_list: list of :py:class:`pyrocko.modelling.OkadaSource` :param pure_shear: Flag, if also opening mode shall be taken into account (False) or the fault is described as pure shear (True). :type pure_shear: optional, bool :param rotate_sdn: Rotation towards strike, dip, normal, default True. :type rotate_sdn: optional, bool :param nthreads: Number of threads, default 1 :type nthreads: optional, int
:return: coefficient matrix for all sources :rtype: :py:class:`numpy.ndarray`, ``(len(source_patches_list) * 3, len(source_patches_list) * 3)`` '''
src.source_patch() for src in source_patches_list])
else: n_eq = 3
'strikeslip': { 'slip': unit_disl, 'opening': 0., 'rake': 0.}, 'dipslip': { 'slip': unit_disl, 'opening': 0., 'rake': 90.}, 'tensileslip': { 'slip': 0., 'opening': unit_disl, 'rake': 0.} }
'strikeslip', 'dipslip', 'tensileslip'][:n_eq]): case['slip'] * num.cos(case['rake'] * d2r), case['slip'] * num.sin(case['rake'] * d2r), case['opening']])
source[num.newaxis, :], source_disl[num.newaxis, :], receiver_coords, lambda_mean, mu_mean, nthreads=nthreads, rotate_sdn=rotate_sdn)
0.5 * ( results[:, 3:] + results[:, (3, 6, 9, 4, 7, 10, 5, 8, 11)])
rotate_sdn=True, nthreads=1): ''' Build coefficient matrix for given source_patches (Slow version)
The BEM for a fault and the determination of the slip distribution from the stress drop is based on the relation stress = coef_mat * displ. Here the coefficient matrix is build and filled based on the okada_ext.okada displacements and partial displacement differentiations.
:param source_patches_list: list of all OkadaSources, which shall be used for BEM :type source_patches_list: list of :py:class:`pyrocko.modelling.OkadaSource` :param pure_shear: Flag, if also opening mode shall be taken into account (False) or the fault is described as pure shear (True). :type pure_shear: optional, bool :param rotate_sdn: Rotation towards strike, dip, normal, default True. :type rotate_sdn: optional, bool :param nthreads: Number of threads, default 1 :type nthreads: optional, int
:return: coefficient matrix for all sources :rtype: :py:class:`numpy.ndarray`, ``(source_patches_list.shape[0] * 3, source_patches_list.shape[0] * 3(2))`` '''
source_patches = num.array([ src.source_patch() for src in source_patches_list]) receiver_coords = source_patches[:, :3].copy()
npoints = len(source_patches_list)
if pure_shear: n_eq = 2 else: n_eq = 3
coefmat = num.zeros((npoints * 3, npoints * 3))
def ned2sdn_rotmat(strike, dip): rotmat = mt.euler_to_matrix( (dip + 180.) * d2r, strike * d2r, 0.).A return rotmat
lambda_mean = num.mean([src.lamb for src in source_patches_list]) shearmod_mean = num.mean([src.shearmod for src in source_patches_list])
unit_disl = 1. disl_cases = { 'strikeslip': { 'slip': unit_disl, 'opening': 0., 'rake': 0.}, 'dipslip': { 'slip': unit_disl, 'opening': 0., 'rake': 90.}, 'tensileslip': { 'slip': 0., 'opening': unit_disl, 'rake': 0.} } for idisl, case_type in enumerate([ 'strikeslip', 'dipslip', 'tensileslip'][:n_eq]): case = disl_cases[case_type] source_disl = num.array([ case['slip'] * num.cos(case['rake'] * d2r), case['slip'] * num.sin(case['rake'] * d2r), case['opening']])
for isource, source in enumerate(source_patches): results = okada_ext.okada( source[num.newaxis, :].copy(), source_disl[num.newaxis, :].copy(), receiver_coords, lambda_mean, shearmod_mean, nthreads=nthreads, rotate_sdn=rotate_sdn)
for irec in range(receiver_coords.shape[0]): eps = num.zeros((3, 3)) for m in range(3): for n in range(3): eps[m, n] = 0.5 * ( results[irec][m * 3 + n + 3] + results[irec][n * 3 + m + 3])
stress = num.zeros((3, 3)) dilatation = num.sum([eps[i, i] for i in range(3)])
for m, n in zip([0, 0, 0, 1, 1, 2], [0, 1, 2, 1, 2, 2]): if m == n: stress[m, n] = \ lambda_mean * \ dilatation + \ 2. * shearmod_mean * \ eps[m, n]
else: stress[m, n] = \ 2. * shearmod_mean * \ eps[m, n] stress[n, m] = stress[m, n]
normal = num.array([0., 0., -1.]) for isig in range(3): tension = num.sum(stress[isig, :] * normal) coefmat[irec * n_eq + isig, isource * n_eq + idisl] = \ tension / unit_disl
return coefmat
stress_field, coef_mat=None, source_list=None, pure_shear=False, epsilon=None, nthreads=1, **kwargs): ''' Least square inversion to get displacement from stress
Follows approach for Least-Square Inversion published in Menke (1989) to calculate displacements on a fault with several segments from a given stress field. If not done, the coefficient matrix is determined within the code.
:param stress_field: Array containing the stress change [Pa] for each source patch (order: [ src1 dstress_Strike, src1 dstress_Dip, src1 dstress_Tensile, src2 dstress_Strike, ...]) :type stress_field: :py:class:`numpy.ndarray`, ``(n_sources * 3, )`` :param coef_mat: Coefficient matrix to connect source patches displacement and the resulting stress field :type coef_mat: optional, :py:class:`numpy.ndarray`, ``(source_patches_list.shape[0] * 3, source_patches.shape[] * 3(2)`` :param source_list: list of all OkadaSources, which shall be used for BEM :type source_list: optional, list of :py:class:`pyrocko.modelling.OkadaSource` :param epsilon: regularize small values from the coefficient matrix, default None. :type epsilon: optional, float
:param nthreads: number of threads for the least squares inversion, default 1 :type nthreads: optional, int
:return: inverted displacements (u_strike, u_dip , u_tensile) for each source patch. order: [ [patch1 u_Strike, patch1 u_Dip, patch1 u_Tensile], [patch2 u_Strike, patch2 u_Dip, patch2 u_Tensile], ...] :rtype: :py:class:`numpy.ndarray`, ``(n_sources, 3)`` '''
source_list, pure_shear=pure_shear, nthreads=nthreads, **kwargs)
coef_mat[coef_mat < epsilon] = 0.
num.dot(coef_mat_in.T, coef_mat_in)), coef_mat_in.T, stress_field[idx]]) except num.linalg.LinAlgError as e: logger.warning('Linear inversion failed!') logger.warning( 'coef_mat: %s\nstress_field: %s', coef_mat_in, stress_field[idx]) raise e
'AnalyticalSource', 'AnalyticalRectangularSource', 'OkadaSource', 'DislocationInverter'] |