Modeling nonlinear compressional waves in marine sediments
Abstract. A computational model is presented which will help guide and interpret an upcoming series of experiments on nonlinear compressional waves in marine sediments. The model includes propagation physics of nonlinear acoustics augmented with granular Hertzian stress of order 3/2 in the strain rate. The model is a variant of the time domain NPE (McDonald and Kuperman, 1987) supplemented with a causal algorithm for frequency-linear attenuation. When attenuation is absent, the model equations are used to construct analytic solutions for nonlinear plane waves. The results imply that Hertzian stress causes a unique nonlinear behavior near zero stress. A fluid, in contrast, exhibits nonlinear behavior under high stress. A numerical experiment with nominal values for attenuation coefficient implies that in a water saturated Hertzian chain, the nonlinearity near zero stress may be experimentally observable.