Nonlinear tube waves in permeable formations: Difference frequency generation

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.