Finite-Difference Simulation of Elastic Wave with Separation in Pure P- and S-Modes

Chen, Keyang

doi:10.1155/2014/108713

Cited by 6 publications

(5 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

“…vertical direction), and

ε

and

δ

are Thomsen's parameters. For an isotropic medium, we make

ε = 0

and

δ = 0

in equations () and () (Virieux, 1986; Han et al ., 2012; Chen, 2014).…”

Section: Theorymentioning

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%

See 2 more Smart Citations

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

Araujo

Pestana

2020

Geophysical Prospecting

View full text Add to dashboard Cite

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.

show abstract

Section: Elastic Wave Equation In Vti/tti Mediummentioning

confidence: 99%

“…vertical direction), and

ε

and

δ

are Thomsen's parameters. For an isotropic medium, we make

ε = 0

and

δ = 0

in equations () and () (Virieux, 1986; Han et al ., 2012; Chen, 2014).…”

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Araujo

Pestana

2020

Geophysical Prospecting

View full text Add to dashboard Cite

show abstract

“…The wavefields A and B are the divergence and second curl component of the vector (u, 0, w). Although not explicitly addressed by Chen (2014), the P-wave source fA and S-wave source fB are injected to wavefields A and B, respectively. Finally, α and β are the P-and S-wave velocities.…”

Section: Theorymentioning

confidence: 99%

“…In this report we use the adjoint state method and the pure P-and S-wave finite difference method of Chen (2014) to obtain elastic migration operators that generate P-and S-wave migrated images. The mentioned finite difference scheme also produces P-and S-wave vertical and horizontal displacements that are combined to generate PP and PS migrations.…”

Section: Introductionmentioning

confidence: 99%

Pure P- and S-wave elastic reverse time migration with adjoint state method imaging condition

Monsegny

Trad

2019

SEG Technical Program Expanded Abstracts 2019

View full text Add to dashboard Cite

We implemented an elastic reverse time migration based on a coupled system of pure P-and S-wave particle velocities. The system utilizes finite difference wavefields for P-and S-wave particle velocity in vertical and horizontal directions (vpx , vpz , vsx and vsz), and for 2-D displacement divergence and curl (A and B). In contrast with the usual elastic imaging conditions that cross-correlates vertical displacements to obtain the P-wave image and vertical and horizontal displacements to obtain the converted wave image, we devised P-and S-wave imaging conditions using the adjoint state method. The resulting imaging conditions cross-correlate spatial derivatives of A and B wavefields with P-and Swave displacements. The proposed migration shows a better reflector definition and more balanced amplitudes than the usual vertical and horizontal particle displacement cross-correlations.

show abstract

Up/down and P/S decompositions of elastic wavefields using complex seismic traces with applications to calculating Poynting vectors and angle-domain common-image gathers from reverse time migrations

et al. 2016

View full text Add to dashboard Cite

Separations of up- and down-going as well as of P- and S-waves are often a part of processing of multicomponent recorded data and propagating wavefields. Most previous methods for separating up/down propagating wavefields are expensive because of the requirement to save time steps to perform Fourier transforms over time. An alternate approach for separation of up-and down-going waves, based on extrapolation of complex data traces is extended from acoustic to elastic, and combined with P- and S-wave decomposition by decoupled propagation. This preserves all the information in the original data and eliminates the need for a Fourier transform over time, thereby significantly reducing the storage cost and improving computational efficiency. Wavefield decomposition is applied to synthetic elastic VSP data and propagating wavefield snapshots. Poynting vectors obtained from the particle velocity and stress fields after P/S and up/down decompositions are much more accurate than those without because interference between the corresponding wavefronts is significantly reduced. Elastic reverse time migration with the P/S and up/down decompositions indicated significant improvement compared with those without decompositions, when applied to elastic data from a portion of the Marmousi2 model.

show abstract

Finite-Difference Simulation of Elastic Wave with Separation in Pure P- and S-Modes

Cited by 6 publications

References 10 publications

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

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

Pure P- and S-wave elastic reverse time migration with adjoint state method imaging condition

Up/down and P/S decompositions of elastic wavefields using complex seismic traces with applications to calculating Poynting vectors and angle-domain common-image gathers from reverse time migrations

Contact Info

Product

Resources

About