Nonlinear tube waves in permeable formations: Difference frequency generation

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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 = omega₁ - omega₂, due to an initial pulse consisting of carrier frequencies omega₁ and omega₂. 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.