An efficient complex-frequency shifted-perfectly matched layer for second-order acoustic wave equation

2013 ◽  
Vol 97 (2) ◽  
pp. 130-148 ◽  
Author(s):  
Youneng Ma ◽  
Jinhua Yu ◽  
Yuanyuan Wang
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Perfectly Matched Layer ◽  
Second Order ◽  
Complex Frequency ◽  
Acoustic Wave Equation

Perfectly matched layer on curvilinear grid for the second-order seismic acoustic wave equation

2014 ◽  
Vol 45 (2) ◽  
pp. 94-104 ◽  
Author(s):  
Sanyi Yuan ◽  
Shangxu Wang ◽  
Wenju Sun ◽  
Lina Miao ◽  
Zhenhua Li
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Perfectly Matched Layer ◽  
Second Order ◽  
Acoustic Wave Equation ◽  
Curvilinear Grid

Two-way wave equation-based depth migration using one-way propagators on a bilayer sensor seismic acquisition system

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. S271-S278
Author(s):  
Jiachun You ◽  
Ru-Shan Wu ◽  
Xuewei Liu ◽  
Pan Zhang ◽  
Wengong Han ◽  
...  
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Seismic Data ◽  
Second Order ◽  
Acquisition System ◽  
Initial Condition ◽  
Acoustic Wave Equation ◽  
Data Set ◽  
Depth Migration ◽  
Migration Method

Conventional migration uses the seismic data set recorded at a given depth as one initial condition from which to implement wavefield extrapolation in the depth domain. In using only one initial condition to solve the second-order acoustic wave equation, some approximations are used, resulting in the limitation of imaging angles and inaccurate imaging amplitudes. We use an over/under bilayer sensor seismic data acquisition system that can provide the two initial conditions required to make the second-order acoustic wave equation solvable in the depth domain, and we develop a two-way wave equation depth migration algorithm by adopting concepts from one-way propagators, called bilayer sensor migration. In this new migration method, two-way wave depth extrapolation can be achieved with two one-way propagators by combining the wavefields at two different depths. It makes it possible to integrate the advantages of one-way migration methods into the bilayer sensor system. More detailed bilayer sensor migration methods are proposed to demonstrate the feasibility. In the impulse response tests, the propagating angle of the bilayer sensor migration method can reach up to 90°, which is superior to those of the corresponding one-way propagators. To test the performance, several migration methods are used to image the salt model, including the one-way generalized screen propagator, reverse time migration (RTM), and our bilayer sensor migration methods. Bilayer sensor migration methods are capable of imaging steeply dipping structures, unlike one-way propagators; meanwhile, bilayer sensor migration methods can greatly reduce the numbers of artifacts generated by salt multiples in RTM.

Second-Order Implicit Finite-Difference Schemes for Acoustic Wave Equation in Time-Space Domain

Geophysics ◽  
2021 ◽  
pp. 1-83
Author(s):  
Navid Amini ◽  
Changsoo Shin ◽  
Jaejoon Lee
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Second Order ◽  
Numerical Dispersion ◽  
Acoustic Wave Equation ◽  
Space Domain ◽  
Time Space ◽  
Implicit Finite Difference ◽  
2D And 3D

We propose compact implicit finite-difference (FD) schemes in time-space domain based on second-order FD approximation for accurate solution of the acoustic wave equation in 1D, 2D, and 3D. Our method is based on weighted linear combination of the second-order FD operators with different spatial orientations to mitigate numerical error anisotropy and weighted averaging of the mass acceleration term over the grid-points of the second-order FD stencil to reduce the overall numerical dispersion error. We present derivation of the schemes for 1D, 2D, and 3D cases and obtain their corresponding dispersion equations, then we find optimum weights by optimization of the time-space domain dispersion function and finally tabulate the optimized weights for each case. We analyze the numerical dispersion, stability and convergence rates of the proposed schemes and compare their numerical dispersion characteristics with the standard high-order ones. We also discuss efficient solution of the system of equations associated with the proposed implicit schemes using conjugate gradient method. The comparison of dispersion curves and the numerical solutions with the analytical and the pseudo-spectral solutions reveals that the proposed schemes have better performance than the standard spatial high-order schemes and remain stable for relatively large time-steps.

Nonsplit complex-frequency-shifted perfectly matched layer combined with symplectic methods for solving second-order seismic wave equations — Part 2: Wavefield simulations

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. T167-T179 ◽  
Author(s):  
Xiao Ma ◽  
Dinghui Yang ◽  
Xijun He ◽  
Xueyuan Huang ◽  
Jiaxing Song
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Free Surface ◽  
Seismic Wave ◽  
Wave Equations ◽  
Perfectly Matched Layer ◽  
Second Order ◽  
Surface Boundary ◽  
Complex Frequency ◽  
Symplectic Methods

The perfectly matched layer (PML) is an efficient artificial boundary condition that has been routinely implemented in seismic wave modeling. However, the effective combination of PML with symplectic numerical schemes for solving seismic wave equations has rarely been studied. In a companion paper, we have developed a complex-frequency-shifted convolutional PML (CPML) with a nonconstant compression grid parameter for solving the time-domain second-order seismic wave equation. Subsequently, we combine this CPML with two classes of symplectic methods to formulate symplectic partitioned Runge-Kutta (SPRK) + CPML and nearly analytic SPRK (NSPRK) + CPML, both of which are properly synchronized. To further investigate their validity, the two algorithms are then applied to acoustic and elastic wave simulations in typical geologic models, including a heterogeneous acoustic model, several isotropic and orthotropic elastic models, and an isotropic elastic model with a free-surface boundary. Relevant numerical results demonstrate the effectiveness of our CPML and combination algorithms. Specifically, the numerical accuracy and stability of the CPML that we develop are greatly improved compared with the classic split-field PML. Moreover, the final model with the free-surface boundary condition indicates that the nonconstant grid-compression parameter can eliminate the unstable modes at the free surface in the PML domain. The (N)SPRK + CPML that we propose is prospective for future application in other complex models and wave-equation-based migration and inversion.

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