Nonlinear Acoustic Wave Propagation in Stratified Media

Resumo

The acoustic waves propagation is a subject of great application in several areas of engineering, for
example in marine seismic for the detection of underwater objects, in hydrography and navigation for the detection
of the seabed, among others. In this work, a nonlinear model for the propagation of P-waves in a stratified
environment is developed. Starting from the nonlinear equations that governs the fluid motion of a compressible
fluid with mass source we obtain the nonlinear equations for the acoustic P-wave propagation. The set of equations
in the conservative form are solved numerically using the finite difference method applying the explicit strong
stability-preserving (SSP) multistep method. In order to achieve higher order accuracy in time, the fourth-order
SSP Runge–Kutta time discretization was implemented and the Courant-Friedrichs-Levy (CFL) criterion must be
satisfied for an adaptative time step along the simulation. The second order spatial derivatives are solved using the
minmod based MUSCL spatial discretization. A numerical code is written in Fortran language and simulations
with a Ricker-type pressure source were performed. Numerical results are in good agreement with those reported
in the literature.