Modeling Wave Propagation In Media Research Articles

Nonlinear wave propagation in media with attenuation and dispersion modeled using a superposition of relaxation mechanisms

Michael Buckingham has long held interest in modeling wave propagation in media with nontraditional attenuation and dispersion, especially unconsolidated marine sediments exhibiting power-law attenuation [Buckingham, J. Acoust. Soc. Am. 138, 2871 (2015)]. The present authors have examined the implications of power-law attenuation and single relaxation mechanisms for modeling nonlinear propagation of compressional and shear waves [Cormack and Hamilton, Wave Motion 85, 13 (2019)]. Reported here are results for media that are modeled using multiple relaxation mechanisms. Below the lowest relaxation frequency, attenuation increases as frequency squared, and above the highest relaxation frequency, attenuation is constant. In between, the superposition may be tailored to approximate power-law attenuation that increases in proportion to frequency raised to an exponent between 0 and 2. Regardless of the source frequency and the number of relaxation mechanisms incorporated, there exists a critical source amplitude above which the mathematical model is incapable of offsetting nonlinear waveform distortion sufficiently to stabilize shock formation beyond the distance where an infinite gradient first appears in the waveform. Results are presented for birelaxing media corresponding to seawater and atmosphere, followed by models based on multiple relaxation mechanisms that approximate power-law attenuation over limited frequency ranges in sediment and tissue.

Wave propagation near a fluid‐solid interface: A spectral‐element approach

We introduce a spectral‐element method for modeling wave propagation in media with both fluid (acoustic) and solid (elastic) regions, as for instance in offshore seismic experiments. The problem is formulated in terms of displacement in elastic regions and a velocity potential in acoustic regions. Matching between domains is implemented based upon an interface integral in the framework of an explicit prediction‐multicorrection staggered time scheme. The formulation results in a mass matrix that is diagonal by construction. The scheme exhibits high accuracy for a 2-D test case with known analytical solution. The method is robust in the case of strong topography at the fluid‐solid interface and is a good alternative to classical techniques, such as finite differencing.