Abstract
This program package is for 2D and 3D first arrival traveltime tomography.
The models are parameterized on a uniform square grid (velocities
specified at equal node spacing in the x,y,z directions). The inverse
grid is cell-based with constant cell size in each direction, but
the sizes may be different in the x,y,z directions. The node spacing
used for the forward grid must divide equally into the x,y,z lengths
of the model, and the cell size of the inverse grid must also divide
equally into the x,y,z lengths of the model. The forward calculation
of traveltimes and raypaths uses the Vidale (1988, 1990) scheme modified
to handle large velocity contrasts according to the method of Hole
and Zelt (1995). Sources and receivers may be anywhere in the model,
although padding the model with at least a few nodes all around is
a good idea to avoid having rays hit the edge of the model (and terminate).
A point source is assumed. The tomographic method is regularized
inversion incorporating a user-specified combination of smallest,
flattest and smoothest perturbation constraints, the weights of each
being allowed to vary with depth. The regularization is a jumping
method in that the constraints are applied to the model perturbation
with respect to a background model (usually the starting model).
A starting model and iterative approach is employed in which new
ray paths are calculated for each iteration. The sparse linear system
of equations is solved using the LSQR variant of the conjugate gradient
method described by Nolet (1987). An interface may be specified above
which the model is held fixed, to allow either a layer stripping
procedure or the consideration of marine data in which the interface
is the bathymetric surface. The size of the velocity update at each
iteration may be bounded according to user-specified limits. The
forward modeling and most aspects of the inverse algorithm are described
in Zelt and Barton (1998). The package also includes x-window graphics
utilities for interactive plotting of ray paths, models, time files,
interfaces, etc. and generation of postscript files (the same graphics
package used by rayinvr). All codes are written in fortran except
for the lowest level x graphics libraries which are written in C.
The codes were developed on SPARC SUN workstations, but should be
adaptable to any platform with fortran and C compilers without too
much effort. It is not necessary to use the x graphics capabilities
to compile or run the codes or create the postscript files.
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