Inverting the head wave coefficient with the Werth equation

The head wave coefficient, the refraction analogue of the reflection coefficient, is a complex function of the densities and the P- and S-wave velocities in both the weathered and sub-weathered regions. In general, the head wave coefficient increases with increasing P- and S wave velocities in the weathered layer, but it decreases with increasing P- and S-wave seismic velocities in the sub-weathered layer. Unscaled S-wave velocities in the weathering and subweathering can be computed with a new approximation of the head wave coefficient and the detailed P-wave seismic velocities in each layer. In general, there is excellent agreement between the measured and computed values after ten iterations. However, a traveltime-based estimate of the S-wave velocities is required to calibrate the amplitude-based estimates.