Computer program package TOMOS for a crosshole travel time tomography

Jiri Jech


The program package for the iterative inversion of arrival times of direct P or S waves in a crosshole profiling (CHP) and/or reverse seismic profiling (RVSP) or vertical seismic profiling (VSP) geometry is presented. It is based on the ray method and linearization approach. A velocity distribution in the considered region must be estimated at the beginning of the linearized inverse procedure. Rays, passing the model, are then calculated from sources to receiver and velocity perturbations with respect to the starting model are determined from differences of observed and calculated travel times in the least square sense. Consequently the starting velocity distribution is updated and the whole procedure can be repeated.

The velocity distribution in an investigated region is approximated smoothly using B-splines. Rays are calculated by numerical integration of the system of ray tracing differential equations. Two point ray tracing is solved with the help of paraxial ray approximation, which needs the calculation of dynamic ray tracing along the rays. The linear velocity perturbations are calculated using the damped least squares method.

The program package consists of two main programs TOMOS and INVERT. Data describing the starting velocity distribution, locations of sources and receivers and control data for a ray computation are read in the program TOMOS. Two point ray tracing is calculated then. The primary output of the program are theoretical travel times for a given model and a sources/receivers geometry and the matrix of the system of linear equations. The system of linear equations for unknown velocity perturbations is solved in the program INVERT. The method of conjugate gradients is used to solve the system in the damped least squares sense. The updated velocity distribution is on the output.

In: Seismic Waves in Complex 3-D Structures, Report 1, pp. 321-357, Dep. Geophys., Charles Univ., Prague 1994.
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