Migration/inversion for transversely isotropic elastic media
Migration/inversion for transversely isotropic elastic media
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DOI：
10.1111/j.1365-246x.1994.tb00148.x
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发表时间：
1994-11
影响因子：
2.8
通讯作者：
D. Eaton;R. Stewart
中科院分区：
文献类型：
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作者：
D. Eaton;R. Stewart
地震偏移和反演是获取地下图像的两个密切相关的过程。这两种技术都试图从地震数据中推断岩石物理和结构参数，并且都是由地球波传播的基本数学模型驱动的。从这个意义上说，迁移可以看作是一般线性化反演方案的第一步；本文采用这一观点，建立了各向异性弹性介质的联合偏移反演方法。我们的推导基于畸变波玻恩近似，其中背景介质的近似格林函数是用渐近射线理论确定的。我们还利用一个固定相位校正来解释二维地球模型中的面外散射。反演是一个离散的，广义的l2优化问题，我们使用先验模型方差正则化。利用准牛顿技术在一次或多次迭代中得到近似解。我们的实现是为具有横向各向同性（TI）对称性的弱各向异性弹性介质量身定制的，因此非常适合于以单组平行裂缝或周期性薄层为特征的地球模型的研究。对垂直入射窄孔径记录配置的几种TI模型参数化方案进行了评估。通过对反演中使用的近似Hessian算子进行奇异值分解，我们发现当介质的对称轴为垂直方向时，通过选择垂直阻抗参数、密度和Thomsen（1986）各向异性参数，条件数最小。当对称轴为水平或未知时，弹性刚度和密度可能是较好的参数化选择。在我们的窄孔径测试中，Hessian的有效等级（2-3）很小，这意味着表面反射数据的迁移反演（没有先验约束）可能不足以完全表征TI介质，这需要六个参数。然而，这一结果本身并不能证明使用更简单的各向同性反演方案是合理的，因为这里确定的主要特征向量代表了关于地球的“各向同性”和“各向异性”信息的混合。一组点衍射仪测试表明，反演中恢复的单个扰动幅度比原始模型中使用的小，但覆盖了更大的图像区域，与输入信号的带限性质一致。参数交叉耦合问题影响所有参数的反演结果，但在各向异性参数的反演图像中更为突出。在我们的测试中，线性化的反演结果在三次迭代后收敛到局部最小值，并且在一次迭代后反演图像中的散射分布基本固定。
SUMMARY Seismic migration and inversion are closely related processes for obtaining images of the subsurface. Both techniques attempt to infer petrophysical and structural parameters from seismic data, and both are driven by an underlying mathematical model for wave propagation in the earth. In this sense, migration can be regarded as the first step in’ a general linearized-inversion scheme; we adopt this viewpoint here in formulating a joint migration/inversion method for anisotropic elastic media. Our derivation is based on the distorted-wave Born approximation, where approximate Green’s functions for the background medium are determined using asymptotic ray theory. We also make use of a stationary-phase correction to account for out-of-plane scattering in a 2-D earth model. The inversion is cast as a discrete, generalized l2 optimization problem, which we regularize using a priori model variances. An approximate solution is obtained in one or more iterations using a quasi-Newton technique. Our implementation is tailored for weakly anisotropic elastic media possessing transversely isotropic (TI) symmetry, and so is well suited for investigations of earth models characterized by a singe set of parallel fractures or periodic thin layering. Several TI model parametrization schemes are evaluated for a vertical-incidence narrow-aperture recording configuration. By applying singular-value decomposition to the approximate Hessian operator used in the inversion, we find that when the symmetry axis of the medium is vertically oriented the condition number is minimized by choosing vertical impedance parameters, density and Thomsen’s (1986) anisotropy parameters. Elastic stiffnesses and density may be a better parametrization choice if the symmetry axis is either horizontal or unknown. The small effective rank (2-3) of the Hessian in our narrow-aperture tests implies that migration inversion (without a priori constraints) of surface-reflection data may be inadequate to fully characterize a TI medium, which would require six parameters. However, this result does not in itself justify the use of simpler isotropic inversion schemes, since the principal eigenvectors determined here represent a blend of ‘isotropic’ and ‘anisotropic’ information about the earth. A suite of point-diffractor tests shows that individual perturbation amplitudes recovered in the inversion are smaller, but cover a larger region of the image, than those used in the original model, consistent with the band-limited nature of the input signal. Parameter cross-coupling problems affect the inversion results for all parameters, but are more prominent in the inversion images for anisotropy parameters. In our tests, the linearized-inversion results converge to a local minimum after three iterations, and the scatterer distributions in the inversion images are essentially fixed after a single iteration.