Zoeppritz equations form the theoretical basis of most existing amplitude variation with incident angle (AVA) inversion methods. Assuming that only primary reflections exist, that is, the multiples are fully suppressed and the transmission loss and geometric spreading are completely compensated for, Zoeppritz equations can be used to solve for the elastic parameters of strata effectively. However, for thin interbeds, conventional seismic data processing technologies cannot suppress the internal multiples effectively, nor can they compensate for the transmission loss accurately. Therefore, AVA inversion methods based on Zoeppritz equations or their approximations are not applicable to thin interbeds. In this study, we propose a prestack AVA inversion method based on a fast algorithm for reflectivity. The fast reflectivity method can compute the full-wave responses, including the reflection, transmission, mode conversion, and internal multiples, which is beneficial to the seismic inversion of thin interbeds. A further advantage of the fast reflectivity method is that the partial derivatives of the reflection coefficient with respect to the elastic parameters can be expressed as analytical solutions. Based on the Gauss–Newton method, we construct the objective function and model-updating formula considering sparse constraint, where the Jacobian matrix takes the form of an analytical solution, which can significantly accelerate the inversion convergence. We validate our inversion method using numerical examples and field seismic data. The inversion results demonstrate that the fast reflectivity-based inversion method is more effective for thin interbed models in which the wave-propagation effects, such as interval multiples, are difficult to eliminate.

中文翻译：

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基于快速反射率算法的薄互层AVA反演

Zoeppritz方程形成了大多数现有的随入射角（AVA）反演的幅度变化的理论基础。假设仅存在一次反射，即完全抑制了多次反射，并完全补偿了传输损耗和几何扩展，则可以使用Zoeppritz方程来有效求解地层的弹性参数。但是，对于薄夹层，常规地震数据处理技术不能有效地抑制内部倍数，也不能准确地补偿传输损耗。因此，基于Zoeppritz方程或其近似值的AVA反演方法不适用于薄夹层。在这项研究中，我们提出了一种基于反射率快速算法的叠前AVA反演方法。快速反射率法可以计算全波响应，包括反射，透射，模转换和内部倍数，有利于薄夹层地震反演。快速反射率方法的另一个优点是，反射系数相对于弹性参数的偏导数可以表示为解析解。基于高斯-牛顿法，考虑稀疏约束，构造目标函数和模型更新公式，其中雅可比矩阵采用解析解的形式，可以显着加速反演收敛。我们使用数值示例和现场地震数据验证了我们的反演方法。