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Keywords = decoupled fractional Laplacians

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14 pages, 8115 KB  
Article
A K-Space-Based Temporal Compensating Scheme for a First-Order Viscoacoustic Wave Equation with Fractional Laplace Operators
by Juan Chen, Fei Li, Ning Wang, Yinfeng Wang, Yang Mu and Ying Shi
Fractal Fract. 2024, 8(10), 574; https://doi.org/10.3390/fractalfract8100574 - 30 Sep 2024
Cited by 1 | Viewed by 1557
Abstract
Inherent constant Q attenuation can be described using fractional Laplacian operators. Typically, the fractional Laplacian viscoacoustic or viscoelastic wave equations are addressed utilizing the staggered-grid pseudo-spectral (SGPS) method. However, this approach results in time numerical dispersion errors due to the low-order finite difference [...] Read more.
Inherent constant Q attenuation can be described using fractional Laplacian operators. Typically, the fractional Laplacian viscoacoustic or viscoelastic wave equations are addressed utilizing the staggered-grid pseudo-spectral (SGPS) method. However, this approach results in time numerical dispersion errors due to the low-order finite difference approximation. In order to address these time-stepping errors, a k-space-based temporal compensating scheme is established to solve the first-order viscoacoustic wave equation. This scheme offers the advantage of being nearly free from grid dispersion for homogeneous media and enhances simulation stability. Numerical examples indicate that the proposed k-space scheme aligns well with analytical solutions for homogeneous media. Additionally, this method demonstrates excellent applicability for complex models and is more efficient due to its ability to adopt a larger time step compared with conventional staggered-grid pseudo-spectral methods. Full article
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13 pages, 6662 KB  
Article
Accurately Stable Q-Compensated Reverse-Time Migration Scheme for Heterogeneous Viscoelastic Media
by Ning Wang, Ying Shi and Hui Zhou
Remote Sens. 2022, 14(19), 4782; https://doi.org/10.3390/rs14194782 - 24 Sep 2022
Cited by 14 | Viewed by 3018
Abstract
The development of multi-component seismic acquisition technology creates new possibilities for the high-precision imaging of complex media. Compared to the scalar acoustic wave equation, the elastic wave equation takes the information of P-waves, S-waves, and converted waves into account simultaneously, enabling accurate description [...] Read more.
The development of multi-component seismic acquisition technology creates new possibilities for the high-precision imaging of complex media. Compared to the scalar acoustic wave equation, the elastic wave equation takes the information of P-waves, S-waves, and converted waves into account simultaneously, enabling accurate description of actual seismic propagation. However, inherent attenuation is one of the important factors that restricts multi-component high-precision migration imaging. Its influence is mainly reflected in the following three ways: first, the attenuation of the amplitude energy makes the deep structure display unclear; second, phase distortion introduces errors to the positioning of underground structures; and third, the loss of high frequency components reduces imaging resolution. Therefore, it is crucial to fully consider the absorption and attenuation characteristics of the real Earth during seismic modeling and imaging. This paper aims to develop an accurate attenuation compensation reverse-time migration scheme for complex heterogeneous viscoelastic media. We first utilize a novel viscoelastic wave equation with decoupled fractional Laplacians to depict the Earth’s attenuation behavior. Then, an adaptive stable attenuation compensation operator is developed to realize high-precision attenuation compensation imaging. Several synthetic and field data analyses verify the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Geophysical Data Processing in Remote Sensing Imagery)
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