## Two-point ray tracing in 3-D

**Petr Bulant**
### Summary

Algorithms for solving the two-point ray tracing in a 3D medium
were developed. This study is devoted to the detailed
description of the method used in solving the two-point problem.
Using the algorithms designed, subroutines controlling the
shooting have been coded. The procedures determine the initial
conditions for computing the rays (i.e. ray parameters), and
they are independent of an initial-value ray tracer. The already
existing subroutine packages MODEL and CRT were used to
calculate the rays in inhomogeneous 3D block models. The
algorithms described were coded in Fortran 77.

Chapter 2 describes the fundamental ideas of the method
of solving the two-point problem. The algorithm
is described in detail, step by step, in Chapter 3.
Chapter 4 contains remarks concerning the
corresponding Fortran 77 code. For a numerical example
of using the two-point ray tracing program refer to
the preceding paper in this report.

### Revised version

This paper has been combined with

Bulant, P.:
Numerical examples of two-point ray tracing in 3-D.
In: Seismic Waves in Complex 3-D Structures, Report 3,
pp. 65-92, Dep. Geophys., Charles Univ., Prague, 1995.

The resulting revised paper is

Bulant, P.:
Two-point ray tracing in 3-D.
PAGEOPH, **148**(1996), 421-447.

In: Seismic Waves in Complex 3-D Structures, Report 3,
pp. 37-64, Dep. Geophys., Charles Univ., Prague, 1995.

SW3D
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