Homotopy scattering series for seismic forward modelling with variable density and velocity

Xiang, Kai; Eikrem, Kjersti Solberg; Jakobsen, Morten; Nævdal, Gunnar

doi:10.1111/1365-2478.13143

Cited by 3 publications

(2 citation statements)

References 48 publications

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“…Within the framework of seismic wavefield modelling, a limited number of works have been concluded using the volume integral method, and most of those focused on acoustic waves only (Alles and van Dongen, 2011;Malovichko et al, 2018;Jakobsen and Ursin, 2015;Xiang et al, 2021). An acoustic or elastic wave equation can be written as a corresponding integral equation of the Lippmann-Schwinger type, and different numerical techniques can be employed to solve this equation.…”

Section: Introductionmentioning

confidence: 99%

Integral equation method for microseismic wavefield modelling in anisotropic elastic media

Shekhar¹,

Jakobsen²,

Iversen³

et al. 2023

Preprint

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In this paper, we present a frequency-domain volume integral method to model the microseismic wavefield in heterogeneous anisotropic-elastic media. The elastic wave equation is written as an integral equation of the Lippmann-Schwinger type, and the seismic source is represented as a general moment tensor. The displacement field due to a moment tensor source can be computed using the spatial derivative of the elastodynamic Green's function. The existing matrix-based implementation of the integral equation is computationally inefficient to model the wavefield in a three-dimensional earth. An integral equation for the particle displacement is, hence, formulated in a matrix-free manner through the application of the Fourier transform. The biconjugate gradient stabilized method is used to iteratively obtain the solution of this equation. We apply the numerical scheme to three different models in order of increasing geological complexity and obtain the elastic displacement fields corresponding to the different types of moment tensor sources. The volume integral method has an advantage over the time domain methods in regard to adding multiple sources since it can work with discrete frequencies, one by one, and limit the computational cost. The generated synthetic data can be useful in inversion for the microseismic source and model parameters.

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Section: Introductionmentioning

confidence: 99%

Integral equation method for microseismic wavefield modelling in anisotropic elastic media

Shekhar¹,

Jakobsen²,

Iversen³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Within the framework of seismic wavefield modelling, a limited number of works have been concluded using the volume integral method, and most of those focused on acoustic waves only (Alles & van Dongen, 2011;Malovichko et al, 2017Malovichko et al, , 2018Jakobsen & Ursin, 2015;Xiang et al, 2021). An acoustic or elastic wave equation can be written as a corresponding integral equation of the Lippmann-Schwinger type, and different numerical techniques can be employed to solve this equation.…”

Section: Introductionmentioning

confidence: 99%

Microseismic wavefield modelling in anisotropic elastic media using integral equation method

Shekhar,

Jakobsen,

Iversen

et al. 2023

Geophysical Prospecting

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In this paper, we present a frequency‐domain volume integral method to model the microseismic wavefield in heterogeneous anisotropic‐elastic media. The elastic wave equation is written as an integral equation of the Lippmann‐Schwinger type, and the seismic source is represented as a general moment tensor. The actual medium is split into a background medium and a scattered medium. The background part of the displacement field is computed analytically, but the scattered part requires a numerical solution. The existing matrix‐based implementation of the integral equation is computationally inefficient to model the wavefield in a three‐dimensional earth. An integral equation for the particle displacement is, hence, formulated in a matrix‐free manner through the application of the Fourier transform. The biconjugate gradient stabilized method is used to iteratively obtain the solution of this equation. The integral equation method is naturally target oriented and it is not necessary to fully discretize the model. This is very helpful in the microseismic wavefield computation at receivers in the borehole in many cases; say for example, we want to focus only on the fluid injection zone in the reservoir‐overburden system and not on the whole subsurface region. Additionally, the integral equation system matrix has a low condition number. This provides us flexibility in the selection of the grid size, especially at low frequencies for given wave velocities. Considering all these factors, we apply the numerical scheme to three different models in order of increasing geological complexity. We obtain the elastic displacement fields corresponding to the different types of moment tensor sources, which proves the utility of this method in microseismic. The generated synthetic data is intended to be used in inversion for the microseismic source and model parameters.This article is protected by copyright. All rights reserved

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Seismic and medical ultrasound imaging of velocity and density variations by nonlinear vectorial inverse scattering

Jakobsen

Xiang

Dongen

2023

The Journal of the Acoustical Society of America

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We present an iterative nonlinear inverse scattering algorithm for high-resolution acoustic imaging of density and velocity variations. To solve the multi-parameter nonlinear direct scattering problem, the acoustic wave equation for inhomogeneous media in the frequency domain is transformed into a vectorial integral equation of the Lippmann–Schwinger type for the combined pressure and pressure-gradient field. To solve the multi-parameter nonlinear inverse scattering problem, we use the Newton–Kantorovich method in conjunction with matrix-free representations of the Fréchet derivative operators and their adjoints. The approximate Hessian information that is accounted for in our iterative solution of the (nonlinear) multi-parameter inverse scattering problem is essential for the mitigation of multi-parameter cross talk effects. Numerical examples related to seismic and medical ultrasound breast imaging illustrate the performance of the new algorithm for multi-parameter acoustic imaging.

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Homotopy scattering series for seismic forward modelling with variable density and velocity

Cited by 3 publications

References 48 publications

Integral equation method for microseismic wavefield modelling in anisotropic elastic media

Integral equation method for microseismic wavefield modelling in anisotropic elastic media

Microseismic wavefield modelling in anisotropic elastic media using integral equation method

Seismic and medical ultrasound imaging of velocity and density variations by nonlinear vectorial inverse scattering

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