Estimating velocity and Q by fractional Laplacian constant-Q wave equation-based full-waveform inversion

2017 ◽  
Author(s):  
Hanming Chen ◽  
Hui Zhou
Keyword(s):  
Wave Equation ◽  
Fractional Laplacian ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Q Wave

Decoupled Fréchet kernels based on a fractional viscoacoustic wave equation

Geophysics ◽  
2021 ◽  
pp. 1-42
Author(s):  
Guangchi Xing ◽  
Tieyuan Zhu
Keyword(s):  
Wave Equation ◽  
Fractional Laplacian ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Physical Processes ◽  
Full Waveform ◽  
Adjoint State ◽  
The Finite Difference Method ◽  
Adjoint State Method ◽  
Laplacian Operators

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. We find that the lossless propagation kernel dominates the velocity kernel, while the dissipation kernel dominates the attenuation kernel over the dispersion kernel. After validating the Fréchet kernels using the finite-difference method, we conduct a numerical example to demonstrate the capability of the kernels to characterize both velocity and attenuation anomalies. The kernels of different misfit measurements are presented to investigate their different sensitivities. Our results suggest that rather than the traveltime, the amplitude and the waveform kernels are more suitable to capture attenuation anomalies. These kernels lay the foundation for the multiparameter inversion with the fractional formulation, and the decoupled nature of them promotes our understanding of the significance of different physical processes in the Q-FWI.

Q-compensated full-waveform inversion using constant-Q wave equation

2016 ◽  
Author(s):  
Zhiguang Xue ◽  
Tieyuan Zhu ◽  
Sergey Fomel ◽  
Junzhe Sun
Keyword(s):  
Wave Equation ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Q Wave

Laplace-domain wave-equation modeling and full waveform inversion in 3D isotropic elastic media

2014 ◽  
Vol 105 ◽  
pp. 120-132 ◽  
Author(s):  
Woohyun Son ◽  
Sukjoon Pyun ◽  
Changsoo Shin ◽  
Han-Joon Kim
Keyword(s):  
Wave Equation ◽  
Waveform Inversion ◽  
Equation Modeling ◽  
Full Waveform Inversion ◽  
Elastic Media ◽  
Laplace Domain ◽  
Full Waveform

scholarly journals Full-waveform inversion, Part 2: Adjoint modeling

2018 ◽  
Vol 37 (1) ◽  
pp. 69-72 ◽  
Author(s):  
Mathias Louboutin ◽  
Philipp Witte ◽  
Michael Lange ◽  
Navjot Kukreja ◽  
Fabio Luporini ◽  
...  
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Wave Equations ◽  
Waveform Inversion ◽  
Seismic Sources ◽  
Full Waveform Inversion ◽  
Optimization Framework ◽  
Full Waveform ◽  
Set Up ◽  
And Function

This is the second part of a three-part tutorial series on full-waveform inversion (FWI) in which we provide a step-by-step walk through of setting up forward and adjoint wave equation solvers and an optimization framework for inversion. In Part 1 ( Louboutin et al., 2017 ), we showed how to use Devito ( http://www.opesci.org/devito-public ) to set up and solve acoustic wave equations with (impulsive) seismic sources and sample wavefields at the receiver locations to forward model shot records. Here in Part 2, we will discuss how to set up and solve adjoint wave equations with Devito and, from that, how we can calculate gradients and function values of the FWI objective function.

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