An acoustic description of nonlinearity in seismic exploration

Kristopher A. Innanen

In 2008, the Priddis pump-probe experiment, in which the Earth was simultaneously subjected to a vibrating source and a transient source, was carried out by CREWES with the hope of detecting nonlinear behaviour in an exploration seismology setting. In this paper we present a theoretical description of such behaviour, assuming an acoustic medium. Through a simple extension of the order arguments by which fluid equations are typically manipulated to form a linear wave equation on the pressure p1 , we find a nonlinear equation for a corrective term, p2 , such that in total the field, p = p1 + p2 , is aware of the changes it itself makes in the medium through which it propagates.