面向目标的图像域弹性最小二乘反向时间迁移

IF 2.2 3区 地球科学 Q2 GEOSCIENCES, MULTIDISCIPLINARY Journal of Applied Geophysics Pub Date : 2024-08-20 DOI:10.1016/j.jappgeo.2024.105496
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引用次数: 0

摘要

弹性最小二乘反向时间迁移(ELSRTM)作为一种成像方法,与传统的弹性反向时间迁移(ERTM)相比具有更高的分辨率、更好的振幅平衡、更低的串扰和更宽的带宽等优势。然而,传统的 ELSRTM 涉及数据域的迭代过程,导致计算成本较高。此外,由于数据域外推法的时间是连续的,因此无法完全聚焦于地下介质中的目标区域。相比之下,图像域 ELSRTM(IDELSRTM)具有较高的计算效率和对目标区域成像的能力。目前,图像域最小二乘反向时间迁移的研究主要集中在声波假设上,尽管弹性波更接近实际的地下介质,能提供更丰富的成像信息。在本研究中,我们在数据域 ELSRTM 的框架内,推导了 IDELSRTM 的目标函数,并在 L2 规范下引入了 L1 正则项,以增强反演稳定性。我们采用快速迭代收缩阈值算法(FISTA)设计了一种反演策略。此外,我们还借鉴光学中的点扩散函数理论,推导出了弹性多参数点扩散函数(PSF)与弹性多参数 Hessian 矩阵之间的映射关系,以及 Hessian 矩阵与 ERTM 图像之间的关系。我们提供了弹性多参数 Hessian 矩阵的计算方法,并将其用作 IDELSRTM 的线性化前向算子。通过数值实验,我们进一步阐明了 IDELSRTM 框架下 ERTM 图像与 Hessian 矩阵之间的关系,以及 ERTM 中串扰的来源。将我们提出的面向目标的 IDELSRTM 方法应用于分层模型和 Marmousi2 模型,我们证明了该方法在提高成像分辨率和质量方面的有效性,与传统 ERTM 相比,计算开销仅略有增加。
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Target-oriented image-domain elastic least-squares reverse time migration

Elastic least-squares reverse time migration (ELSRTM), as an imaging method, offers advantages over conventional elastic reverse time migration (ERTM), including higher resolution, better amplitude balancing, reduced crosstalk, and broader bandwidth. However, conventional ELSRTM involves iterative processes in the data domain, resulting in high computational costs. Moreover, since time is continuous during data domain extrapolation, it cannot solely focus on the target area within the subsurface medium. In contrast, image-domain ELSRTM (IDELSRTM) exhibits high computational efficiency and the ability to image target area. Currently, research on image-domain least-squares reverse time migration is predominantly focused on the acoustic wave assumption, despite elastic waves being closer to the actual subsurface medium and providing richer imaging information. In this study, within the framework of data domain ELSRTM, we derived the objective function for the IDELSRTM and introduced an L1 regularization term under the L2 norm to enhance inversion stability. We devised an inversion strategy employing the fast iterative shrinkage-thresholding algorithm (FISTA). Furthermore, drawing from the point spread functions theory in optics, we derived the mapping relationship between the elastic multi-parameter point spread functions (PSF) and the elastic multi-parameter Hessian matrix, and the relationship between the Hessian matrix and the ERTM images. We provided the computational method for the elastic multi-parameter Hessian matrix and utilized it as the linearized forward operator for IDELSRTM. Through numerical experiments, we further elucidated the relationship between the ERTM images and the Hessian matrix under the framework of IDELSRTM, along with the sources of crosstalk in ERTM. Applying our proposed target-oriented IDELSRTM method to layered models and the Marmousi2 model, we demonstrated its effectiveness in improving imaging resolution and quality with only a marginal increase in computational overhead compared to conventional ERTM.

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来源期刊
Journal of Applied Geophysics
Journal of Applied Geophysics 地学-地球科学综合
CiteScore
3.60
自引率
10.00%
发文量
274
审稿时长
4 months
期刊介绍: The Journal of Applied Geophysics with its key objective of responding to pertinent and timely needs, places particular emphasis on methodological developments and innovative applications of geophysical techniques for addressing environmental, engineering, and hydrological problems. Related topical research in exploration geophysics and in soil and rock physics is also covered by the Journal of Applied Geophysics.
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