Decoupled Fréchet kernels based on a fractional viscoacoustic wave equation

Xing, Guangchi; Zhu, Tieyuan

doi:10.1190/geo2021-0248.1

Title: Decoupled Fréchet kernels based on a fractional viscoacoustic wave equation

Journal Article · Wed Oct 06 00:00:00 EDT 2021 · Geophysics

DOI:https://doi.org/10.1190/geo2021-0248.1· OSTI ID:1829720

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Pennsylvania State Univ., University Park, PA (United States)

We formulate the Fréchet kernel computation using the adjoint-state method based on a fractional viscoacoustic wave equation. We first numerically prove that both the 1/2- and the 3/2-order fractional Laplacian operators are self-adjoint. Using this property, we show that the adjoint wave propagator preserves the dispersion and compensates the amplitude, while the time-reversed adjoint wave propagator behaves identically as the forward propagator with the same dispersion and dissipation characters. Without introducing rheological mechanisms, this formulation adopts an explicit Q parameterization, which avoids the implicit Q in the conventional viscoacoustic/viscoelastic full waveform inversion (Q-FWI). In addition, because of the decoupling of operators in the wave equation, the viscoacoustic Fréchet kernel is separated into three distinct contributions with clear physical meanings: lossless propagation, dispersion, and dissipation. Here, we find that the lossless propagation kernel dominates the velocity kernel, while the dissipation kernel dominates the attenuation kernel over the dispersion kernel.

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Research Organization:: Pennsylvania State Univ., University Park, PA (United States)

Sponsoring Organization:: USDOE; National Science Foundation (NSF)

Grant/Contract Number:: FE0031544; EAR-1919650

OSTI ID:: 1829720

Journal Information:: Geophysics, Vol. 87, Issue 1; ISSN 0016-8033

Publisher:: Society of Exploration GeophysicistsCopyright Statement

Country of Publication:: United States

Language:: English

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