Modeling acoustic wave propagation in heterogeneous attenuating media using decoupled fractional Laplacians

By T. Zhu, Jerry M. Harris. 2014

263 citations recorded by the source corpus.

We evaluated a time-domain wave equation for modeling acoustic wave propagation in attenuating media. The wave equation was derived from Kjartansson’s constant-Q constitutive stress-strain relation in combination with the mass and momentum conservation equations. Our wave equation, expressed by a second-order temporal derivative and two fractional Laplacian operators, described very nearly constant-Q attenuation and dispersion effects. The advantage of using our formulation of two fractional Laplacians over the traditional fractional time derivative approach was the avoidance of time history memory variables and thus it offered more economic computations. In numerical simulations, we formulated the first-order constitutive equations with the perfectly matched layer absorbing boundaries. The temporal derivative was calculated with a staggered-grid finite-difference approach. The fractional Laplacians are calculated in the spatial frequency domain using a Fourier pseudospectral implementation. We validated our numerical results through comparisons with theoretical constant-Q attenuation and dispersion solutions, field measurements from the Pierre Shale, and results from 2D viscoacoustic analytical modeling for the homogeneous Pierre Shale. We also evaluated different formulations to show separated amplitude loss and dispersion effects on wavefields. Furthermore, we generalized our rigorous formulation for homogeneous media to an approximate equation for viscoacoustic waves in heterogeneous media. We then investigated the accuracy of numerical modeling in attenuating media with different Q-values and its stability in largecontrast heterogeneous media. Finally, we tested the applicability of our time-domain formulation in a heterogeneous medium with high attenuation.

Subfields: Geophysics, Mechanics of Materials

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Citations in the corpus

fPINNs: Fractional Physics-Informed Neural Networks (2018, background): “Among these are solute transport in fractured and porous media [2, 3], acoustic wave propagation with frequency-dependent dissipation [4, 5, 6, 7], laminar and turbulent flows [8, 9, 10], viscoelastic constitutive laws [11], just to mention a few.”
Q-compensated reverse-time migration (2014, methodology): “The attenuation and dispersion values are calculated using signals recorded at the two receivers (Zhu and Harris, 2014).”
Local Elliptic Regularity for the Dirichlet Fractional Laplacian (2017, unknown): “Among others, we mention applications in elasticity [8], turbulence [2], anomalous transport and diffusion [5, 21], porousmedia flow [32], image processing [14], wave propagation in heterogeneous high contrastmedia [33].”
Q-compensated least-squares reverse time migration using low-rank one-step wave extrapolation (2016, methodology): “Using fractional Laplacians, Zhu and Harris (2014) proposed a constant-Q viscoacoustic wave equation with separate terms accounting for amplitude loss and velocity dispersion, which was further applied for Q-compensated RTM using both synthetic and field data (Zhu et al., 2014; Zhu and Harris,…”