Numerically Efficient Full Wavefield Approach to Synthetic Seismogram Computation

Abstract

A numerically efficient global matrix approach to the solution of the wave equation in horizontally stratified environments is presented. The field in each layer is expressed as a superposition of the field produced by the sources within the layer and an unknown field satisfying the homogeneous wave equations, both expressed as integral representations in the horizontal wavenumber. The boundary conditions to be satisfied at each interface then yield a linear system of equations in the unknown wavefield amplitudes, to be satisfied at each horizontal wavenumber. As an alternative to the traditional propagator matrix approaches, the present solution technique yields both improved efficiency and versatility. Its global nature makes it well suited to problems involving many receivers in range as well as depth and to calculations of both stresses and particle velocities. The number of arithmetic operations are reduced to a minimum and the resulting computer code (SAFARI) is almost an order of magnitude faster than available codes of the same type based on propagator matrices. These features are illustrated by a few numerical examples from crustal and exploration seismology.