`modelling`¶

`pyrocko.modelling.okada`¶

class AnalyticalSource(**kwargs)[source]¶

Undocumented.

♦ name¶: str, optional, default: ''

♦ time¶

builtins.float (pyrocko.guts.Timestamp), optional, default: 0.0

source origin time

♦ vr¶

float, optional, default: 0.0

Rupture velocity

clone(pool=None)¶

Clone guts object tree.

Traverses guts object tree and recursively clones all guts attributes, falling back to copy.deepcopy() for non-guts objects. Objects deriving from Object are instantiated using their respective init function. Multiply referenced objects in the source tree are multiply referenced also in the destination tree.

This function can be used to clone guts objects ignoring any contained run-time state, i.e. any of their attributes not defined as a guts property.

class AnalyticalRectangularSource(**kwargs)[source]¶

Rectangular analytical source model

♦ strike¶

float, default: 0.0

strike direction in [deg], measured clockwise from north

♦ dip¶

float, default: 90.0

dip angle in [deg], measured downward from horizontal

♦ rake¶

float, default: 0.0

rake angle in [deg], measured counter-clockwise from right-horizontal in on-plane view

♦ al1¶

float, default: 0.0

Distance “left” side to source point [m]

♦ al2¶

float, default: 0.0

Distance “right” side to source point [m]

♦ aw1¶

float, default: 0.0

Distance “lower” side to source point [m]

♦ aw2¶

float, default: 0.0

Distance “upper” side to source point [m]

♦ slip¶

float, optional, default: 0.0

Slip on the rectangular source area [m]

class OkadaSource(**kwargs)[source]¶

Rectangular Okada source model

♦ opening¶

float, optional, default: 0.0

Opening of the plane in [m]

♦ poisson¶

float, optional, default: 0.25

Poisson’s ratio, typically 0.25

♦ shearmod¶

float, optional, default: 32000000000.0

Shear modulus along the plane [Pa]

lamb¶

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 $\nu$ : $\nu = \frac{\lambda}{2(\lambda + \mu)}$ with the shear modulus $\mu$

seismic_moment¶

Scalar Seismic moment

Code copied from Kite Disregarding the opening (as for now) We assume a shear modulus of $\mu = 36 \mathrm{GPa}$ and $M_0 = mu A D$

Important

We assume a perfect elastic solid with $K=\frac{5}{3}\mu$

Through $\mu = \frac{3K(1-2\nu)}{2(1+\nu)}$ this leads to $\mu = \frac{8(1+\nu)}{1-2\nu}$

Returns:	Seismic moment release
Return type:	float

moment_magnitude¶

Moment magnitude from Seismic moment

We assume $M_\mathrm{w} = {\frac{2}{3}}\log_{10}(M_0) - 10.7$

Returns:	Moment magnitude
Return type:	float

source_patch()[source]¶

Build source information array for okada_ext.okada input

Returns:	array of the source data as input for okada_ext.okada
Return type:	`numpy.ndarray`, `(1, 9)`

source_disloc()[source]¶

Build source dislocation for okada_ext.okada input

Returns:	array of the source dislocation data as input for okada_ext.okada
Return type:	`numpy.ndarray`, `(1, 3)`

discretize(nlength, nwidth, *args, **kwargs)[source]¶

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.

Parameters:	nlength (int) – Number of discrete points in faults strike direction nwidth (int) – Number of discrete points in faults down-dip direction
Returns:	Discrete fault patches
Return type:	list of `pyrocko.modelling.okada.OkadaSource` objects

class DislocationInverter[source]¶

Toolbox for Boundary Element Method (BEM) and dislocation inversion based on okada_ext.okada

static get_coef_mat(source_patches_list, pure_shear=False, rotate_sdn=True, nthreads=1)[source]¶

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 $stress = coefmat \cdot displ$ . Here the coefficient matrix is build and filled based on the okada_ext.okada displacements and partial displacement differentiations.

Parameters:	source_patches_list (list of `pyrocko.modelling.okada.OkadaSource`) – list of all OkadaSources, which shall be used for BEM pure_shear (optional, bool) – Shall only shear forces be taken into account, or additionally include opening, default False. rotate_sdn (optional, bool) – Rotation towards strike, dip, normal, default True. nthreads (optional, int) – Number of threads, default 1
Returns:	coefficient matrix for all sources
Return type:	`numpy.ndarray`, `(len(source_patches_list) * 3, len(source_patches_list) * 3)`

static get_coef_mat_single(source_patches_list, pure_shear=False, rotate_sdn=True, nthreads=1)[source]¶

Build coefficient matrix for given source_patches

Parameters:	source_patches_list (list of `pyrocko.modelling.okada.OkadaSource`) – list of all OkadaSources, which shall be used for BEM pure_shear (optional, bool) – Flag, if also opening mode shall be taken into account (False) or the fault is described as pure shear (True). rotate_sdn (optional, bool) – Rotation towards strike, dip, normal, default True. nthreads (optional, int) – Number of threads, default 1
Returns:	coefficient matrix for all sources
Return type:	`numpy.ndarray`, `(len(source_patches_list) * 3, len(source_patches_list) * 3)`

static get_coef_mat_slow(source_patches_list, pure_shear=False, rotate_sdn=True, nthreads=1)[source]¶

Build coefficient matrix for given source_patches (Slow version)

Parameters:	source_patches_list (list of `pyrocko.modelling.okada.OkadaSource`) – list of all OkadaSources, which shall be used for BEM pure_shear (optional, bool) – Flag, if also opening mode shall be taken into account (False) or the fault is described as pure shear (True). rotate_sdn (optional, bool) – Rotation towards strike, dip, normal, default True. nthreads (optional, int) – Number of threads, default 1
Returns:	coefficient matrix for all sources
Return type:	`numpy.ndarray`, `(source_patches_list.shape[0] * 3, source_patches_list.shape[0] * 3(2))`

static get_disloc_lsq(stress_field, coef_mat=None, source_list=None, pure_shear=False, epsilon=None, nthreads=1, **kwargs)[source]¶

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.

Parameters:	stress_field (`numpy.ndarray`, `(n_sources * 3, )`) – Array containing the stress change [Pa] for each source patch (order: [ src1 dstress_Strike, src1 dstress_Dip, src1 dstress_Tensile, src2 dstress_Strike, …]) coef_mat (optional, `numpy.ndarray`, `(source_patches_list.shape[0] * 3, source_patches.shape[] * 3(2)`) – Coefficient matrix to connect source patches displacement and the resulting stress field source_list (optional, list of `pyrocko.modelling.okada.OkadaSource`) – list of all OkadaSources, which shall be used for BEM epsilon (optional, float) – regularize small values from the coefficient matrix, default None. nthreads (optional, int) – number of threads for the least squares inversion, default 1
Returns:	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], …]
Return type:	`numpy.ndarray`, `(n_sources, 3)`

`pyrocko.modelling.cracksol`¶

class GriffithCrack(**kwargs)[source]¶

Analytical Griffith crack model

♦ width¶

float, default: 1.0

Width equals to 2*a

♦ poisson¶

float, default: 0.25

Poisson ratio

♦ shearmod¶

float, default: 1000000000.0

Shear modulus [Pa]

♦ stressdrop¶

numpy.ndarray (pyrocko.guts_array.Array), default: array([0., 0., 0.])

Stress drop array:[sigi3_r - sigi3_c, sigi2_r - sigi2_c, sigi1_r - sigi1_c][dstress_Strike, dstress_Dip, dstress_Tensile]

a¶: Half width of the crack

youngsmod¶: Shear (Youngs) modulus

disloc_infinite2d(x_obs)[source]¶

Calculation of dislocation at crack surface along x2 axis

Follows equations by Pollard and Segall (1987) to calculate dislocations for an infinite 2D crack extended in x3 direction, opening in x1 direction and the crack extending in x2 direction.

Parameters:	x_obs (`numpy.ndarray`, `(N,)`) – Observation point coordinates along x2-axis. If $x_{obs} < -a$ or $x_{obs} > a$ , output dislocations are zero
Returns:	dislocations at each observation point in strike, dip and tensile direction.
Return type:	`numpy.ndarray`, `(N, 3)`

disloc_circular(x_obs)[source]¶

Calculation of dislocation at crack surface along x2 axis

Follows equations by Pollard and Segall (1987) to calculate displacements for a circulat crack extended in x2 and x3 direction and opening in x1 direction.

Parameters:	x_obs (`numpy.ndarray`, `(N,)`) – Observation point coordinates along axis through crack centre. If $x_{obs} < -a$ or $x_{obs} > a$ , output dislocations are zero
Returns:	dislocations at each observation point in strike, dip and tensile direction.
Return type:	`numpy.ndarray`, `(N, 3)`

displ_infinite2d(x1_obs, x2_obs)[source]¶

Calculation of displacement at crack surface along different axis

Follows equations by Pollard and Segall (1987) to calculate displacements for an infinite 2D crack extended in x3 direction, opening in x1 direction and the crack tip in x2 direction.

Parameters:	x1_obs (`numpy.ndarray`, `(M,)`) – Observation point coordinates along x1-axis. If x1_obs = 0., displacment is calculated along x2-axis x2_obs (`numpy.ndarray`, `(N,)`) – Observation point coordinates along x2-axis. If x2_obs = 0., displacment is calculated along x1-axis
Returns:	displacements at each observation point in strike, dip and tensile direction.
Return type:	`numpy.ndarray`, `(M, 3)` or `(N, 3)`

Navigation

modelling¶

pyrocko.modelling.okada¶

pyrocko.modelling.cracksol¶

Navigation

`modelling`¶

`pyrocko.modelling.okada`¶

`pyrocko.modelling.cracksol`¶