Global matrix formulation of wave phenomena in plane layered media

Abstract

A direct global matrix formulation for computing the multilayer Green's impulse response function in media with arbitrary depth-dependent elastic or fluid properties is reniewed, after recent work by Schmidt. The global Green's function matrix for solving the resulting linear system of elastodynamic equations is formally analogous to the global stiffness matrix in the direct Finite Element Method and proves both computationally efficient and numerically stable. This analogy and the matrix solution are discussed, as embodied in the general applications code, “SAFARI” ( ∗ SA clant FA st Field Program for R ange- I ndependent Environments ∗ ), developed by one of us (H.Schmidt). Cros s-disciplinary applications of this direct global matrix algorithm are considered for three pertinent areas of current research; namely underwater acoustic propagation, ultrasonic scattering, and crustal seismic modeling. Results obtained show that the SAFARI model correctly reproduces the complete wavefield response in plane-layered, welded, homogeneous media. Arbitrary source/receiver numbers, frequencies, locations, and geometries can also be considered over much larger-scale multilayered media models than previously feasible with extant propagator matrix-based codes. The physical simplicity, CPU savings, and flexible performance of the direct global matrix algorithm suggests that many more full wavefield phenomena can now be simulated without excessively complicated, specialized, or expensive modeling schemes.