Weber function computation in the interference reflected‐head wave amplitude

Abstract

In the critical region, the complex amplitude of the interfering system of a head wave and its associated reflected wave can be described by a single formula for all eight types of interference waves. The formula consists of transmission, reflection and head wave coefficients, geometrical parameters of the layers and an appropriate Weber function. The real and imaginary parts of the Weber function can be shown to be the solutions of a system of first order differential equations. The system may be solved numerically with the help of existing subroutines in the computer software libraries. Upon determining the Weber function, one may construct amplitude‐distance curves for the interference reflected‐head waves of any desired type. Some properties of the amplitude‐distance characteristics can be directly inferred from the Weber function. The very good matching between this method and asymptotic ray theory outside the critical region suggests that a combination of the two would provide an efficient technique for ray amplitude calculation.