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.

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