Traveltimes and rays - ttimerays

Various functions to calculate travel times and ray in a rectilinear grid.

pestoseis.ttimerays.buildtomomat(gridpar, rays, ttpick)

Build forward matrix from rays for traveltime tomography.

Parameters:

• gridpar (dict) – grid parameters dictionary (as defined by setupgrid())

• rays (ndarray of ndarrays) – seismic rays, as outputted by traceallrays()

• ttpick (ndarray) – traveltime picks at the receivers. [These are needed only to provide the vector of traveltime picks flattened for performing tomography in the same order than the tomography matrix]

Returns:

the ‘tomography’ matrix and the vector of traveltime picks

(flattened for performing tomography)

Return type:

(ndarray)

pestoseis.ttimerays.lininv(G, cov_m, cov_d, mprior, dobs)

Linear inversion under Gaussian assumptions.

Parameters:

• G – forward model matrix (d=Gm)

• cov_m,cov_d – covariances for model parameters and observed data, respectively

• mprior – prior model

• dobs – obsrved data

Returns:

the posterior mean model and the posterior covariance matrix

pestoseis.ttimerays.plotgrid(gridpar)

Plot staggered grid edges: traveltime at nodes and velocity in cells

Parameters:

gridpar – grid parameters dictionary (as defined by setupgrid())

pestoseis.ttimerays.plotrays(src, rec, rays)

Plot rays as polylines.

Parameters:

• src (ndarray) – coordinates of the sources

• rec (ndarray) – coordinates of the receivers

• rays (narray of arrays) – seismic rays, as outputted by traceallrays()

pestoseis.ttimerays.plotttimemod(gridpar, ttime, units='')

Plot traveltime array as an image.

Parameters:

• gridpar (dict) – grid parameters dictionary (as defined by setupgrid())

• ttime (ndarray) – traveltime array

• units (str) – optional string to specify the units of measurement for traveltime

pestoseis.ttimerays.plotvelmod(gridpar, velmod, vmin=None, vmax=None, units='', cmap=<matplotlib.colors.LinearSegmentedColormap object>)

Plot velocity model as an image.

Parameters:

• gridpar (dict) – grid parameters dictionary (as defined by setupgrid())

• velmod (ndarray) – velocity model

• vmin (float,float) – optional values to clip the colorbar min and max values

• vmax (float,float) – optional values to clip the colorbar min and max values

• units (str) – optional string to specify the units of measurement for velocity

• cmap (colormap) – optional parameter to specify a colormap. Defaults to “rainbow”.

pestoseis.ttimerays.rollmod(mod, nx, ny)

Reshape a flattened (a vector) model to 2D (an array).

Parameters:

• mod (ndarray) – input flattened model

• nx (float,float) – sizes of the input 2D model

• ny (float,float) – sizes of the input 2D model

Returns:

the reshaped model as a 2D array

Return type:

(ndarray)

pestoseis.ttimerays.setupgrid(nx, ny, dh, xinit, yinit)

Setup grid parameters.

Parameters:

• nx,ny – grid dimensions in x and y

• dx,dy – grid spacing (cell size) in x and y

• xinit,yinit – x and y axes origin

pestoseis.ttimerays.traceall_straight_rays(gridpar, srccoo, reccoo)

Trace multiple straight rays.

Parameters:

• gridpar (dict) – grid parameters dictionary (as defined by setupgrid())

• srccoo (ndarray) – position of the source, a 2D array with two columns, representing x and y

• reccoo (ndarray) – position of the receiver, a 2D array with two columns, representing x and y

Returns:

the coordinates of the ray paths

Return type:

(ndarray)

pestoseis.ttimerays.traceallrays(gridpar, srccoo, reccoo, grdsttime)

Trace multiple rays, for all sources and receivers.

Parameters:

• gridpar (dict) – grid parameters dictionary (as defined by setupgrid())

• srccoo (ndarray) – position of the source, a 2D array with two columns, representing x and y

• reccoo (ndarray) – position of the receiver, a 2D array with two columns, representing x and y

• grdsttime (list of ndarrays) – array of traveltime arrays [list of 2D arrays, one per source]

Returns:

the traced rays as (x,y) coordinates of the points defining the segments

Return type:

(ndarray of ndarrays)

pestoseis.ttimerays.tracerayhorlay(laydep, vel, xystart, takeoffangle, maxnumiterations=20000)

Trace rays in a horizontally layered model.

Parameters:

• laydep (ndarray) – input depth of layers

• vel (ndarray) – velocity for each layer

• xystart (ndarray) – origin coordinates of the ray

• takeoffangle (float) – take off angle

• maxnumiterations (int) – limit the number of ray segments to calculate, in case the ray never reaches the surface

Returns:

coordinates of the the ray path, traveltime

and distance covered

Return type:

(ndarray,float,float)

pestoseis.ttimerays.traveltime(velmod, gridpar, srcs, recs)

Calculate traveltime for all sources and receivers.

Parameters:

• velmod – input velocity model

• gridpar – grid parameters dictionary (as defined by setupgrid())

• srcs – coordinates of sources

• recs – coordinates of receivers

Returns:

traveltimes at the receivers and traveltime arrays

Return type:

ndarray,ndarray

pestoseis.ttimerays.unrollmod(mod)

Flatten a 2D model to a vector, using column-major Fortran order.

Parameters:

mod (ndarray) – input 2D model (probably velocity)

Returns:

the flattened model as a vector (1D)

Return type:

(ndarray)