ABSTRACT In multi‐parameter ray‐based anisotropic migration/inversion, it is essential that we have an understanding of the scattering mechanism corresponding to parameter perturbations. Because the complex nonlinearity in the anisotropic inversion problem is intractable, the construction of true‐amplitude linearized migration/inversion procedures is needed and important. By using the acoustic medium assumption for transversely isotropic media with a vertical axis of symmetry and representing the anisotropy with P‐wave normal moveout velocity, Thomsen parameter δ and anelliptic parameter η, we formalize the linearized inverse scattering problem for three‐dimensional pseudo‐acoustic equations. Deploying the single‐scattering approximation and an elliptically anisotropic background introduces a new linear integral operator that connects the discontinuous perturbation parameters with the multi‐shot/multi‐offset P‐wave scattered data. We further apply the high‐frequency asymptotic Green's function and its derivatives to the integral operator, and then the scattering pattern of each perturbation parameter can be explicitly presented. By naturally establishing a connection to generalized Radon transform, the pseudo‐inverse of the integral operator can be solved by the generalized Radon transform inversion. In consideration of the structure of this pseudo‐inverse operator, the computational implementation is done pointwise by shooting a fan of rays from the target imaging area towards the acquisition system. Results from two‐dimensional numerical tests show amplitude‐preserving images with high quality.

中文翻译：

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具有垂直对称轴的声学横向各向同性介质的散射模式分析和真幅度广义氡变换偏移

摘要 在基于多参数射线的各向异性偏移/反演中，我们必须了解与参数扰动相对应的散射机制。由于各向异性反演问题中的复杂非线性是难以解决的，因此构建真振幅线性偏移/反演程序是必要且重要的。通过使用具有垂直对称轴的横向各向同性介质的声介质假设，并用 P 波法向时差速度、汤姆森参数 δ 和非椭圆参数 η 表示各向异性，我们将三维伪声学的线性化逆散射问题形式化。方程。部署单散射近似和椭圆各向异性背景引入了一个新的线性积分算子，它将不连续的扰动参数与多发射/多偏移 P 波散射数据连接起来。我们进一步将高频渐近格林函数及其导数应用于积分算子，然后可以明确地呈现每个扰动参数的散射模式。通过自然地建立与广义Radon变换的联系，可以通过广义Radon变换反演求解积分算子的伪逆。考虑到这种伪逆算子的结构，计算实现是通过从目标成像区域向采集系统发射扇形光线来逐点完成的。