Transferring the inhomogeneous wave equation into a homogeneous equation

TL;DR

This paper introduces a method to convert the inhomogeneous wave equation into a homogeneous form by adjusting initial conditions, potentially reducing computational costs in seismic inversion modeling.

Contribution

The novel approach replaces source terms with initial conditions, simplifying the wave equation for more efficient numerical modeling in seismic applications.

Findings

Reduced computational cost in wavefield simulations

Effective suppression of source terms in wave equations

Potential for improved seismic inversion techniques

Abstract

The inhomogeneous wave equation, triggered by point sources, forms the basis for the most modern computational techniques of seismic inversion. In this work, we propose to transfer the inhomogeneous wave equation into a homogeneous equation. We show that one can suppress the wavelet-based source term from the inhomogeneous equation in favour of setting the initial time derivative condition of the wavefield as a scaled wavelet of the same type. With the homogeneous wave equation, one can slightly reduce the computational cost of numerical modeling.