Nonlinear tube waves in permeable formations: Difference frequency generation

TL;DR

This paper investigates how nonlinear tube waves in permeable formations generate a difference frequency, providing analytical and numerical insights that could help measure formation nonlinear properties using existing techniques.

Contribution

It extends previous work by analyzing the generation and propagation of difference frequencies in nonlinear tube waves within permeable formations.

Findings

Difference frequency generation is analytically and numerically demonstrated.

Generated difference frequency is measurable with current techniques.

Findings can help infer formation nonlinear properties.

Abstract

We extend earlier work on nonlinear tube wave propagation in permeable formations to study, analytically and numerically, the generation and propagation of a difference frequency, Delta omega = omega_1 - omega_2, due to an initial pulse consisting of carrier frequencies omega_1 and omega_2. Tube waves in permeable formations have very significant linear dispersion/attenuation, which is specifically addressed here. We find that the difference frequency is predicted to be rather easily measurable with existing techniques and could yield useful information about formation nonlinear properties.