Simulating propagation of decoupled elastic waves using low-rank approximate mixed-domain integral operators for anisotropic media

Cheng, Jiubing; Alkhalifah, Tariq; Wu, Zedong; Zou, Peng; Wang, Chenlong

doi:10.1190/geo2015-0184.1

Cited by 43 publications

(24 citation statements)

References 43 publications

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“…We can exploit this advantage to develop efficient spectral methods to simultaneously extrapolate and decompose the elastic wave modes, like in Cheng et al . (), Sun et al . (), but on the base of velocity–stress equations for anisotropic media.…”

Section: Discussionmentioning

confidence: 95%

Pseudo‐spectral method using rotated staggered grid for elastic wave propagation in 3D arbitrary anisotropic media

Zou

Cheng

2017

Geophysical Prospecting

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A B S T R A C TStaggering grid is a very effective way to reduce the Nyquist errors and to suppress the non-causal ringing artefacts in the pseudo-spectral solution of first-order elastic wave equations. However, the straightforward use of a staggered-grid pseudo-spectral method is problematic for simulating wave propagation when the anisotropy level is greater than orthorhombic or when the anisotropic symmetries are not aligned with the computational grids. Inspired by the idea of rotated staggered-grid finitedifference method, we propose a modified pseudo-spectral method for wave propagation in arbitrary anisotropic media. Compared with an existing remedy of staggeredgrid pseudo-spectral method based on stiffness matrix decomposition and a possible alternative using the Lebedev grids, the rotated staggered-grid-based pseudo-spectral method possesses the best balance between the mitigation of artefacts and efficiency. A 2D example on a transversely isotropic model with tilted symmetry axis verifies its effectiveness to suppress the ringing artefacts. Two 3D examples of increasing anisotropy levels demonstrate that the rotated staggered-grid-based pseudo-spectral method can successfully simulate complex wavefields in such anisotropic formations.Key words: Arbitrary anisotropy, Wave propagation, Pseudo-spectral method, Rotated staggered grid. I N T R O D U C T I O NThe numerical modelling of the seismic wave propagation in realistic media is a key element in earthquake and exploration seismology. Several approaches have been developed with different physical model approximations, different complexity levels of the numerical schemes, and different usage of computational resources; see, for example, Carcione et al. (2002) for an overview. The finite-difference method (FDM) remains the most popular numerical method for seismic modelling because it is robust and relatively simple to implement, and it offers a good balance between accuracy and efficiency (Moczo et al. 2007;Yang et al. 2010;Virieux et al. 2011;Liu 2013). Other methods such as the pseudo-spectral (Kosloff and Baysal 1982;Sun et al. 2016a), finite-element (Eriksson * E-mail: 923458778@qq.com and Johnson 1991), spectral elements (Komatitsech et al. 2000), discontinuous Galerkin (Chung and Engquist 2006;De Basabe et al. 2008), finite-volume (Benjemaa et al. 2007, and grid methods (Zhang and Liu 1999) are used to various extent in the geophysical community. Wave propagation simulation has attracted a renewed interest mainly because the so-called (acoustic or elastic) full-wave equation approaches have become a fundamental tool in seismic migration and waveform inversion, considering the new challenges in exploration, especially anisotropy (Operto et al. 2009;Lisitsa and Vishnevskiy 2010;Bartolo et al. 2015;Cheng et al. 2016).The pseudo-spectral method (PSM) (Kosloff and Baysal 1982) we used here is an attractive alternative to the FDM that exploits the fast Fourier transform (FFT) algorithm for computing the spatial derivatives. Its main advantage is that ...

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Section: Discussionmentioning

confidence: 95%

Pseudo‐spectral method using rotated staggered grid for elastic wave propagation in 3D arbitrary anisotropic media

Zou

Cheng

2017

Geophysical Prospecting

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“…Pseudospectral methods compute the spatial derivatives of the wavefield u ( x , t ) in the frequency‐wavenumber domain and the temporal derivatives of u ( x , t ) with finite differences using forward time‐stepping (Cheng et al . ).…”

Section: Waveform‐inversion Methodologymentioning

confidence: 97%

“…Pseudospectral methods (Cheng et al . ; Sun et al . ) provide a viable alternative to finite differences because they mitigate dispersion without the need to reduce the grid size.…”

Section: Introductionmentioning

confidence: 99%

“…Traditionally, most wavefield extrapolators for WI applications are based on finite-difference schemes, which suffer from numerical dispersion for events with high-frequency content. Pseudospectral methods (Cheng et al 2016;Sun et al 2016) provide a viable alternative to finite differences because they mitigate dispersion without the need to reduce the grid size.…”

Section: Introductionmentioning

confidence: 99%

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3D waveform inversion of downhole microseismic data for transversely isotropic media

Michel

Tsvankin

2019

Geophysical Prospecting

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3D anisotropic waveform inversion could provide high‐resolution velocity models and improved event locations for microseismic surveys. Here we extend our previously developed 2D inversion methodology for microseismic borehole data to 3D transversely isotropic media with a vertical symmetry axis. This extension allows us to invert multicomponent data recorded in multiple boreholes and properly account for vertical and lateral heterogeneity. Synthetic examples illustrate the performance of the algorithm for layer‐cake and ‘hydraulically fractured’ (i.e. containing anomalies that simulate hydraulic fractures) models. In both cases, waveform inversion is able to reconstruct the areas which are sufficiently illuminated for the employed source‐receiver geometry. In addition, we evaluate the sensitivity of the algorithm to errors in the source locations and to band‐limited noise in the input displacements. We also present initial inversion results for a microseismic data set acquired during hydraulic fracturing in a shale reservoir.

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“…That is the reason why the resulting wavefield still has S-wave artifacts in Figure 11b. Some advanced algorithms (Cheng & Fomel 2014;Cheng & Kang 2014;Cheng et al 2016) can be used to obtain clean P -wave from elastic wave result. However, they usually require extra cost.…”

Section: Numerical Examplesmentioning

confidence: 99%

Pure quasi-P-wave calculation in transversely isotropic media using a hybrid method

Liu

Alkhalifah

2018

Geophysical Journal International

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SUMMARYThe acoustic approximation for anisotropic media is widely used in current industry imaging and inversion algorithms mainly because P-waves constitute the majority of the energy recorded in seismic exploration. The resulting acoustic formulas tend to be simpler, resulting in more efficient implementations, and depend on fewer medium parameters. However, conventional solutions of the acoustic wave equation with higher-order derivatives suffer from shear wave artifacts. Thus, we derive a new acoustic wave equation for wave propagation in transversely isotropic (TI) media, which is based on a partially separable approximation of the dispersion relation for TI media and free of shear wave artifacts. Even though our resulting equation is not a partial differential equation, it is still a linear equation. Thus, we propose to implement this equation efficiently by combining the finite difference approximation with spectral evaluation of the space-independent parts. The resulting algorithm provides solutions without the constrain of ≥ δ. Numerical tests demonstrate the effectiveness of the approach.

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Simulating propagation of decoupled elastic waves using low-rank approximate mixed-domain integral operators for anisotropic media

Cited by 43 publications

References 43 publications

Pseudo‐spectral method using rotated staggered grid for elastic wave propagation in 3D arbitrary anisotropic media

Pseudo‐spectral method using rotated staggered grid for elastic wave propagation in 3D arbitrary anisotropic media

3D waveform inversion of downhole microseismic data for transversely isotropic media

Pure quasi-P-wave calculation in transversely isotropic media using a hybrid method

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