Shanyuan Qin, Jidong Yang, Ning Qin, Jianping Huang, Kun Tian
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引用次数: 0
摘要
在地震建模和反向时间迁移(RTM)中,纳入各向异性对于精确的波场建模和高质量的图像至关重要。由于计算成本和模拟精度之间的权衡,纯准 P 波方程在描述倾斜横向各向同性(TTI)介质中的波传播时具有良好的精度。然而,它涉及一个依赖于各向异性参数的分数伪微分算子,因此不适合使用传统的分数算子求解器进行求解。为了解决这个问题,我们提出了一种在 TTI 介质中带有广义分数卷积算子的新型纯准 P 波方程。首先,我们将传统的纯准 P 波方程分解为椭圆各向异性方程和分数伪差分修正项。然后,我们使用广义分数卷积模板,通过求解逆问题来近似空间域伪差分项。所提出的近似方法是精确的,基于它的波场建模方法也能准确描述准 P 波在 TTI 介质中的传播。此外,与垂直横向各向同性(VTI)介质相比,它只增加了计算混合偏导数的计算成本。最后,建议的波场建模方法可用于 RTM,以校正地震成像中的各向异性效应。RTM 数值实验证明了所提方法的灵活性和可行性。
Quasi-P-Wave Reverse Time Migration in TTI Media with a Generalized Fractional Convolution Stencil
In seismic modeling and reverse time migration (RTM), incorporating anisotropy is crucial for accurate wavefield modeling and high-quality images. Due to the trade-off between computational cost and simulation accuracy, the pure quasi-P-wave equation has good accuracy to describe wave propagation in tilted transverse isotropic (TTI) media. However, it involves a fractional pseudo-differential operator that depends on the anisotropy parameters, making it unsuitable for resolution using conventional solvers for fractional operators. To address this issue, we propose a novel pure quasi-P-wave equation with a generalized fractional convolution operator in TTI media. First, we decompose the conventional pure quasi-P-wave equation into an elliptical anisotropy equation and a fractional pseudo-differential correction term. Then, we use a generalized fractional convolution stencil to approximate the spatial-domain pseudo-differential term through the solution of an inverse problem. The proposed approximation method is accurate, and the wavefield modeling method based on it also accurately describes quasi-P-wave propagation in TTI media. Moreover, it only increases the computational cost for calculating mixed partial derivatives compared to those in vertical transverse isotropic (VTI) media. Finally, the proposed wavefield modeling method is utilized in RTM to correct the anisotropic effects in seismic imaging. Numerical RTM experiments demonstrate the flexibility and viability of the proposed method.
期刊介绍:
ACS Applied Electronic Materials is an interdisciplinary journal publishing original research covering all aspects of electronic materials. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrate knowledge in the areas of materials science, engineering, optics, physics, and chemistry into important applications of electronic materials. Sample research topics that span the journal's scope are inorganic, organic, ionic and polymeric materials with properties that include conducting, semiconducting, superconducting, insulating, dielectric, magnetic, optoelectronic, piezoelectric, ferroelectric and thermoelectric.
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