利用分数粘弹性波方程高精度模拟瑞利波

IF 3.6 2区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Fractal and Fractional Pub Date : 2023-12-12 DOI:10.3390/fractalfract7120880
Yinfeng Wang, Jilong Lu, Ying Shi, Ning Wang, Liguo Han
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引用次数: 0

摘要

瑞利波的传播通常伴随着频散,而频散随着固有衰减而变得更加复杂。准确模拟衰减介质中的瑞利波对于理解波机制、层厚度识别和参数反演至关重要。虽然真空形式主义或应力图像法(SIM)结合广义标准线性实体(GSLS)被广泛用于衰减介质中雷利波的数值模拟,但这类方法仍有其局限性。首先,GSLS 模型无法分割速度频散和振幅衰减项,因此限制了其在 Q 补偿反向时间迁移/全波形反演中的应用。此外,基于 GSLS 模型的波方程通常采用交错网格有限差分(SGFD)方法进行数值求解,这可能会因苛刻的稳定性条件而导致数值色散,并带来复杂性和计算负担。为了克服这些问题,我们提出了一种涉及分数粘弹性波方程和真空形式主义积分的高精度雷利波模拟方案。提出的方案不仅解耦了振幅衰减和速度色散,而且在相同网格尺寸下显著抑制了瑞利波的数值色散。我们首先使用均质弹性模型来证明与解析解相比的准确性,并通过比较相位速度和相移变换产生的色散图像来验证粘弹性半空间模型的正确性。然后,我们模拟了几个二维合成模型,分析了所提方法的有效性和适用性。结果表明,当精确度达到 95% 时,所提方法使用的空间步长是 GSLS 方法(通过 SGFD 方法求解)的两倍,所需时间是 GSLS 方法的 0.6 倍。
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High-Accuracy Simulation of Rayleigh Waves Using Fractional Viscoelastic Wave Equation
The propagation of Rayleigh waves is usually accompanied by dispersion, which becomes more complex with inherent attenuation. The accurate simulation of Rayleigh waves in attenuation media is crucial for understanding wave mechanisms, layer thickness identification, and parameter inversion. Although the vacuum formalism or stress image method (SIM) combined with the generalized standard linear solid (GSLS) is widely used to implement the numerical simulation of Rayleigh waves in attenuation media, this type of method still has its limitations. First, the GSLS model cannot split the velocity dispersion and amplitude attenuation term, thus limiting its application in the Q-compensated reverse time migration/full waveform inversion. In addition, GSLS-model-based wave equation is usually numerically solved using staggered-grid finite-difference (SGFD) method, which may result in the numerical dispersion due to the harsh stability condition and poses complexity and computational burden. To overcome these issues, we propose a high-accuracy Rayleigh-waves simulation scheme that involves the integration of the fractional viscoelastic wave equation and vacuum formalism. The proposed scheme not only decouples the amplitude attenuation and velocity dispersion but also significantly suppresses the numerical dispersion of Rayleigh waves under the same grid sizes. We first use a homogeneous elastic model to demonstrate the accuracy in comparison with the analytical solutions, and the correctness for a viscoelastic half-space model is verified by comparing the phase velocities with the dispersive images generated by the phase shift transformation. We then simulate several two-dimensional synthetic models to analyze the effectiveness and applicability of the proposed method. The results show that the proposed method uses twice as many spatial step sizes and takes 0.6 times that of the GSLS method (solved by the SGFD method) when achieved at 95% accuracy.
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来源期刊
Fractal and Fractional
Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
4.60
自引率
18.50%
发文量
632
审稿时长
11 weeks
期刊介绍: Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.
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