## Zero-offset ray tracing in the smoothed Marmousi model

This is an example of the zero-offset ray tracing and of the calculation
of travel time derivatives with respect to the model parameters
(B-spline coefficients of P wave slowness field).

The calculation is performed in the smoothed Marmousi model
obtained by running the history file 'mar-inv.h', see the description
mar-inv.htm.

The initial surface (exploding reflector) corresponds to the velocity
discontinuity in the lower part of the original "hard" Marmousi model.
The points at the initial surface
have been found using the program
grdiso.for:

The initial surface is then interpolated by B-splines, see the data file
RPAR.

The receivers are located at the Earth's
surface, the distance between the receivers is 80 m. The two-point
ray tracing from the initial surface to the receivers is managed by
history file mar-crtz.h. The history file
generates also a plot of the calculated zero-offset two-point rays:

The end of the history file contains a simple example of calculation
of travel time derivatives with respect to the model parameters
(B-spline coefficients of P wave slowness field). The derivatives
along the zero-offset two-point rays are calculated by the program
invtt.for.