## Computer program package TOMOS for a crosshole travel time tomography

** Jiri Jech **

### Summary

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.

SW3D
- main page of consortium ** Seismic Waves in Complex 3-D Structures **.