Superstep wavefield propagation

TL;DR

This paper introduces a superstep method for wavefield propagation that precomputes propagator matrices to advance wavefields multiple time steps simultaneously, enhancing modularity and efficiency in finite-difference time domain schemes.

Contribution

It presents a novel superstep approach that precomputes propagator matrices for multiple time steps, enabling efficient wavefield propagation in various media.

Findings

Allows propagation of wavefields over multiple steps in a single operation

Applicable to isotropic, anisotropic, elastic, and acoustic media

Separates physics computation from implementation details

Abstract

This paper describes how to propagate wavefields for arbitrary numbers of traditional time steps in a single step, called a superstep. We show how to construct operators that accomplish this task for finite-difference time domain schemes, including temporal first-order schemes in isotropic, anisotropic and elastic media, as well as temporal second-order schemes for acoustic media. This task is achieved by implementing a computational tradeoff differing from traditional single step wavefield propagators by precomputing propagator matrices for each model location for k timesteps (a superstep) and using these propagator matrices to advance the wavefield k time steps at once. This tradeoff separates the physics of the propagator matrix computation from the computer science of wavefield propagation and allows each discipline to provide their optimal modular solutions.