Elastic modelling in tilted transversely isotropic media with convolutional perfectly matched layer boundary conditions

Han, Byeongho; Seol, Soon Jee; Byun, Joongmoo

doi:10.1071/eg12015

Cited by 20 publications

(10 citation statements)

References 26 publications

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“…The staggered formulation has been applied to anisotropic [121][122][123], viscoelastic [124][125][126], and poroelastic [127][128][129] models in velocity-stress form as in (67). Wave equations in second-order form may also be considered through an equivalent staggered-grid scheme [130].…”

Section: Finite-difference Methodsmentioning

confidence: 99%

Numerical modeling of mechanical wave propagation

Seriani

Oliveira

2020

Riv. Nuovo Cim.

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The numerical modeling of mechanical waves is currently a fundamental tool for the study and investigation of their propagation in media with heterogeneous physical properties and/or complex geometry, as, in these cases, analytical methods are usually not applicable. These techniques are used in geophysics (geophysical interpretation, subsoil imaging, development of new methods of exploration), seismology (study of earthquakes, regional and global seismology, accurate calculation of synthetic seismograms), in the development of new methods for ultrasonic diagnostics in materials science (non-destructive methods) and medicine (acoustic tomography). In this paper we present a review of numerical methods that have been developed and are currently used. In particular we review the key concepts and pioneering ideas behind finite-difference methods, pseudospectral methods, finite-volume methods, Galerkin continuous and discontinuous finite-element methods (classical or based on spectral interpolation), and still others such as physics-compatible, and multiscale methods. We focus on their formulations in time domain along with the main temporal discretization schemes. We present the theory and implementation for some of these methods. Moreover, their computational characteristics are evaluated in order to aid the choice of the method for each practical situation.

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Section: Finite-difference Methodsmentioning

confidence: 99%

Numerical modeling of mechanical wave propagation

Seriani

Oliveira

2020

Riv. Nuovo Cim.

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“…vertical direction), and and δ are Thomsen's parameters. For an isotropic medium, we make = 0 and δ = 0 in equations (5) and (6) (Virieux, 1986;Han et al, 2012;Chen, 2014). In a 2D TTI medium, the wave equation is also given by the following differential equation (Han et al, 2012):…”

Section: Elastic Wave Equation In Vti/tti Mediummentioning

confidence: 99%

“…According to Han et al (2012), in a 2D tilted transversely isotropic (TTI) medium, with a tilted axis of symmetry, the matrix of elastic constants has six independent components, so it can be rewritten as…”

Section: A P P E N D I X Derivation Of Elastic Constants -Tti Mediummentioning

confidence: 99%

“…The elastic wave equation has also often been formulated in the literature as a system of first‐order differential equations and have been expressed in terms of particle velocity and stress tensor (Virieux, 1986; Han et al ., 2012; Guo et al ., 2000; Chen, 2014). The first advantage of this formulation is that it does not need to differentiate the elastic constants.…”

Section: Introductionmentioning

confidence: 99%

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Time evolution of the first‐order linear acoustic/elastic wave equation using Lie product formula and Taylor expansion

Araujo

Pestana

2020

Geophysical Prospecting

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We propose a new numerical solution to the first-order linear acoustic/elastic wave equation. This numerical solution is based on the analytic solution of the linear acoustic/elastic wave equation and uses the Lie product formula, where the time evolution operator of the analytic solution is written as a product of exponential matrices where each exponential matrix term is then approximated by Taylor series expansion. Initially, we check the proposed approach numerically and then demonstrate that it is more accurate to apply a Taylor expansion for the exponential function identity rather than the exponential function itself. The numerical solution formulated employs a recursive procedure and also incorporates the split perfectly matched layer boundary condition. Thus, our scheme can be used to extrapolate wavefields in a stable manner with even larger time-steps than traditional finite-difference schemes. This new numerical solution is examined through the comparison of the solution of full acoustic wave equation using the Chebyshev expansion approach for the matrix exponential term. Moreover, to demonstrate the efficiency and applicability of our proposed solution, seismic modelling results of three geological models are presented and the processing time for each model is compared with the computing time taking by the Chebyshev expansion method. We also present the result of seismic modelling using the scheme based in Lie product formula and Taylor series expansion for the firstorder linear elastic wave equation in vertical transversely isotropic and tilted transversely isotropic media as well. Finally, a post-stack migration results are also shown using the proposed method.

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“…Each component of this matrix can be calculated from the matrix of VTI medium (eq. 2) by using the rotation tensor (Han et al, 2012).…”

Section: Elastic Constantsmentioning

confidence: 99%

Elastic anisotropic finite-difference full-wave modeling and imaging of the tilted transversely isotropic (TTI) media

Behera

2017

SEG Technical Program Expanded Abstracts 2017

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Imaging below the tilted transversely isotropic (TTI) media poses serious problems and distortions in the image, which is very common with imaging subsurface geological targets for hydrocarbon exploration in the fold-thrust belts or active tectonic areas. To model and image below the TTI media having symmetry axis orthogonal to the dipping anisotropic layers, a TTI thrust sheet is considered for elastic anisotropic finite-difference full-wave modeling to generate synthetic seismic data using staggered grid scheme of wave propagation. Free surface conditions at the top and absorbing boundary conditions for other three sides of the model have been imposed to reduce undesirable edge effects and suppress dispersions. The synthetic data generated are migrated using the Kirchhoff pre-stack depth migration (PSDM) technique followed by migration velocity analysis (MVA) algorithm with traveltime computations using anisotropic ray-tracing technique for the model to image below the TTI thrust sheet. The MVA algorithm adopted also estimates the final inversion parameters of the model showing flattening of the reflected events in the image gathers and is a powerful tool to handle tilts more than 60° without much distortions of the image gathers.

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Elastic modelling in tilted transversely isotropic media with convolutional perfectly matched layer boundary conditions

Cited by 20 publications

References 26 publications

Numerical modeling of mechanical wave propagation

Numerical modeling of mechanical wave propagation

Time evolution of the first‐order linear acoustic/elastic wave equation using Lie product formula and Taylor expansion

Elastic anisotropic finite-difference full-wave modeling and imaging of the tilted transversely isotropic (TTI) media

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