acoustic wave equation
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2021 ◽  
Rafael Aleixo ◽  
Francisco De Assis Silva Neto ◽  
Daniela Amazonas

2021 ◽  
Vol 9 ◽  
Xiaobo Zhang ◽  
Xiutian Wang ◽  
Baohua Liu ◽  
Peng Song ◽  
Jun Tan ◽  

Reverse time migration (RTM) is an ideal seismic imaging method for complex structures. However, in conventional RTM based on rectangular mesh discretization, the medium interfaces are usually distorted. Besides, reflected waves generated by the two-way wave equation can cause artifacts during imaging. To overcome these problems, a high-order finite-difference (FD) scheme and stability condition for the pseudo-space-domain first-order velocity-stress acoustic wave equation were derived, and based on the staggered-grid FD scheme, the RTM of the pseudo-space-domain acoustic wave equation was implemented. Model experiments showed that the proposed RTM of the pseudo-space-domain acoustic wave equation could systematically avoid the interface distortion problem when the velocity interfaces were considered to compute the pseudo-space-domain intervals. Moreover, this method could effectively suppress the false scattering of dipping interfaces and reflections during wavefield extrapolation, thereby reducing migration artifacts on the profile and significantly improving the quality of migration imaging.

Geophysics ◽  
2021 ◽  
pp. 1-39
Wenhao Xu ◽  
Bangyu Wu ◽  
Yang Zhong ◽  
Jinghuai Gao ◽  
Qing Huo Liu

The finite-difference frequency-domain (FDFD) method has important applications in the wave simulation of various wave equations. To promote the accuracy and efficiency for wave simulation with the FDFD method, we have developed a new 27-point FDFD stencil for 3D acoustic wave equation. In the developed stencil, the FDFD coefficients not only depend on the ratios of cell sizes in the x-, y-, and z-directions, but we also depend on the spatial sampling density (SD) in terms of the number of wavelengths per grid. The corresponding FDFD coefficients can be determined efficiently by making use of the plane-wave expression and the lookup table technique. We also develop a new way for designing an adaptive FDFD stencil by directly adding some correction terms to the conventional second-order FDFD stencil, which is simpler to use and easier to generalize. Corresponding dispersion analysis indicates that, compared to the optimal 27-point stencil derived from the average-derivative method (ADM), the developed adaptive 27-point stencil can reduce the required SD from approximately 4 to 2.2 points per wavelength (PPW) for a cubic mesh and to 2.7 PPW for a general cuboid mesh. Numerical examples of a 3D homogeneous model and SEG/EAGE salt-dome model indicate that the developed stencil is more accurate than the ADM 27-point stencil for cubic and general cuboid meshes, while requiring similar CPU time and computational memory as the ADM 27-point stencil for direct and iterative solvers.

Geophysics ◽  
2021 ◽  
pp. 1-83
Navid Amini ◽  
Changsoo Shin ◽  
Jaejoon Lee

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.

2021 ◽  
Vol 18 (2) ◽  
pp. 1-8
Yuzhu Liu ◽  
Weigang Liu ◽  
Jizhong Yang ◽  
Liangguo Dong

Abstract Angle domain common image gathers (ADCIGs), commonly regarded as important prestacked gathers, provide the information required for velocity model construction and the phase and amplitude information needed for subsurface structures in oil/gas exploration. Based on the constant-density acoustic-wave equation assumption, the ADCIGs generated from reverse time migration ignore the fact that the subsurface density varies with location. Consequently, the amplitude versus angle (AVA) analysis extracted from these ADCIGs is not accurate. To partially solve this problem and to improve the accuracy of the AVA analysis, we developed amplitude-preserving ADCIGs suitable for density variations with the assumption of acoustic approximation. The Poynting vector approach, which is efficient and computationally inexpensive, was used to calculate the high-resolution wavefield propagation. The ADCIGs generated from the velocity and density perturbations match the theoretical AVA relationship better than ADCIGs with constant density. The extraction of the AVA analysis of the various combinations of the subsurface medium indicates that the density is non-negligible, especially when the density contrast is sharp. Numerical examples based on a layered model verify our conclusions.

2021 ◽  
pp. 109963622199389
Muzamal Hussain ◽  
Muhammad N Naeem

Shell motion equations are framed with first order shell theory of Love. Vibration investigation of fluid-filled three layered cylindrical shells is studied here. It is also exhibited that the effect of frequencies is investigated by varying the different layers with constituent material. The coupled and uncoupled frequencies changes with these layers according to the material formation of fluid-filled FG-CSs. A cylindrical shell is immersed in a fluid which is a non-viscous one. These equations are partial differential equations which are usually solved by approximate technique. Robust and efficient techniques are favored to get precise results. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel’s functions of second kind designate the fluid influence. Mathematically the integral form of the Lagrange energy functional is converted into a set of three partial differential equations.

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