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    基于点扩散函数的成像域矢量弹性最小二乘逆时偏移方法

    Image-domain vector elastic least-squares reverse time migration based on the point spread function

    • 摘要: 与传统弹性逆时偏移相比,弹性最小二乘逆时偏移具有分辨率高、振幅平衡、串扰噪声少和频带宽等优势。然而,目前大多数弹性最小二乘逆时偏移方法在数据域实现,通常需要进行多次迭代计算,每次迭代计算成本较高,且获得的扰动反射系数模型与传统弹性逆时偏移的成像结果存在明显差异。为此,提出了一种基于点扩散函数的成像域矢量弹性最小二乘逆时偏移方法。首先利用光学领域的点扩散函数作为Hessian矩阵的局部近似构建成像域目标函数,在最小二乘反演框架下将空变反卷积与快速迭代收缩阈值算法相结合;然后对传统弹性逆时偏移成像结果进行优化处理,最终得到高精度的PP波与PS波成像结果。该方法的反演过程在成像域的模型空间中进行,与数据域方法相比具有较高的计算效率。地堑模型和SEG/EAGE盐丘模型的数值测试结果表明,该方法可在获得与传统弹性逆时偏移的地质构造保持高度一致的成像结果的同时,提高成像质量和分辨率。与弹性逆时偏移相比,所提方法得到的成像剖面旁瓣更少、波数覆盖范围更宽,成像分辨率得到显著提升。

       

      Abstract: Elastic least-squares reverse time migration (ELSRTM) offers higher resolution, better amplitude balancing, less crosstalk noise, and broader bandwidth compared to conventional elastic reverse time migration (ERTM). However, most ELSRTM methods are implemented in the data domain, typically requiring multiple iterations, each involving significant computational cost. Moreover, the reflectivity perturbation model obtained from ELSRTM differs remarkably from the imaging result of ERTM. To address this issue, we propose an image-domain vector elastic least-squares reverse time migration (ID-VELSRTM) method based on the point spread function (PSF). This method yields imaging results that are consistent with the geological structures obtained from conventional ERTM, while simultaneously improving imaging quality and resolution. The inversion is performed in the model space of the image domain, offering significant computational advantages over data-domain methods. Using the PSF from optics as a localized approximation of the Hessian matrix, we construct an image-domain objective function for ID-VELSRTM. Within the least-squares inversion framework, space-variant deconvolution is combined with the fast iterative shrinkage-thresholding algorithm (FISTA) to refine the ERTM imaging results and finally produce high-precision PP- and PS-wave images. Numerical experiments using a graben model and the SEG/EAGE salt model demonstrate the effectiveness of the ID-VELSRTM method. Compared to ERTM, ID-VELSRTM achieves better amplitude balancing, less crosstalk noise, broader wavenumber coverage, and significantly enhanced imaging resolution.

       

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