Estimating P Wave Velocity and Attenuation Structures Using Full Waveform Inversion Based on a Time Domain Complex‐Valued Viscoacoustic Wave Equation: The Method

Abstract

To complement velocity distributions, seismic attenuation provides additional important information on fluid properties of hydrocarbon reservoirs in exploration seismology, as well as temperature distributions, partial melting, and water content within the crust and mantle in earthquake seismology. Full waveform inversion (FWI), as one of the state-of-the-art seismic imaging techniques, can produce high-resolution constraints for subsurface (an)elastic parameters by minimizing the difference between observed and predicted seismograms. Traditional waveform inversion for attenuation is commonly based on the standard-linear-solid (SLS) wave equation, in which case the quality factor (Q) has to be converted to stress and strain relaxation times. When using multiple attenuation mechanisms in the SLS method, it is difficult to directly estimate these relaxation time parameters. Based on a time domain complex-valued viscoacoustic wave equation, we present an FWI framework for simultaneously estimating subsurface P wave velocity and attenuation distributions. Because Q is explicitly incorporated into the viscoacoustic wave equation, we directly derive P wave velocity and Q sensitivity kernels using the adjoint-state method and simultaneously estimate their subsurface distributions. By analyzing the Gauss-Newton Hessian, we observe strong interparameter crosstalk, especially the leakage from velocity to Q. We approximate the Hessian inverse using a preconditioned L-BFGS method in viscoacoustic FWI, which enables us to successfully reduce interparameter crosstalk and produce accurate velocity and attenuation models. Numerical examples demonstrate the feasibility and robustness of the proposed method for simultaneously mapping complex velocity and Q distributions in the subsurface.

Reflection Full Waveform Inversion With Second‐Order Optimization Using the Adjoint‐State Method

“…Different parameter classes can be more or less coupled as a function of the aperture angle of the seismic observation (Tarantola, 1986). In the context of FWI, people have proven that the off‐diagonal blocks of the Hessian matrix play important role to mitigate the multi‐parameter trade‐offs (Operto et al., 2013; Pan et al., 2017; Yang et al., 2020). For the multi‐parameter RWI problems, the coupling would occur in a more complicated manner and hinder the updating of the background model and the estimation of the reflectivities.…”

Fractional laplacians viscoelastic wave equation low-rank temporal extrapolation

“…This kind of CQ wave equation also brings accuracy improvements in Q-compensated reverse-time migration (Q-RTM) methods, due to approximately decoupling the amplitude loss and phase distortion operators Sun et al, 2015;Li et al, 2016;Wang Y. et al, 2018;Chen et al, 2020a). Another benefit of the FLCQ wave equations is the explicit Q term in the equations, which facilitates developing full waveform inversion methods (Chen et al, 2017;2020b;Xing and Zhu, 2020;Yang et al, 2020;Xing and Zhu, 2022).…”

Modeling seismic wave propagation in the Loess Plateau using a viscoacoustic wave equation with explicitly expressed quality factor

“…Later, many hybrid-domain solvers, including local homogeneous approximation (Chen et al, 2016;Wang et al, 2017;Xing and Zhu, 2019;Wang et al, 2022), low-rank approximation (Sun et al, 2015), Hermite distributed approximation (Yao et al, 2017), are proposed to produce more accurate numerically solution. Recently, presented a complex-valued wave equation to simulate viscoacoustic wave propagation, which has an explicitly expressed Q and can be easily used in full-waveform inversion (Yang et al, 2020).…”