Pre-stack seismic inversion of the P- and S-wave velocities and bulk density is important in seismic exploration for evaluating lithological units and fluid properties. Generally, this inversion is based on ray-tracing modeling, which introduces errors and requires substantial pre-processing for stratified models due to its oversimplified single-interface assumption. To overcome those problems, we propose a pre-stack inversion method, using wave-equation-based modeling as a forward engine. Most wave-equation-based pre-stack inversions are based on the reflectivity method and adopt nonlinear optimization algorithms, although accurate, but computationally expensive. Hence, we use a fast propagator matrix (PM) method valid for layered media. To improve the stability and accuracy, the PP data inversion is extended to joint PP and PS PM-based inversion (JPMI). A linear inversion scheme is adopted to reduce the computational cost, and the Fréchet derivatives are computed accordingly. Moreover, to obtain an optimal model solution, the L-BFGS (Limited-memory Broyden–Fletcher–Goldfarb–Shanno) optimization algorithm and L-curve criterion, an adaptive regularization parameter acquisition method, are implemented. A posterior probability analysis shows that the method has a higher parameter sensitivity than the joint exact Zoeppritz-based inversion and gives better estimations than the single-data inversion. We discuss the effects of dataset weight, internal multi-reflections, time window setting, noise level and initial model by using model tests. Synthetic and real-data examples demonstrate that the algorithm is better than the single PP inversion in terms of stability and accuracy, especially for S-wave velocity and density estimations.

中文翻译：

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基于传播矩阵前向引擎的分层模型联合PP和PS叠前地震反演

P 波和 S 波速度和体积密度的叠前地震反演在地震勘探中对于评估岩性单元和流体性质很重要。通常，这种反演基于光线追踪建模，由于其过于简化的单接口假设，这会引入错误并且需要对分层模型进行大量预处理。为了克服这些问题，我们提出了一种叠前反演方法，使用基于波方程的建模作为正向引擎。大多数基于波浪方程的叠前反演基于反射率方法，采用非线性优化算法，虽然准确，但计算成本高。因此，我们使用对分层媒体有效的快速传播矩阵 (PM) 方法。为了提高稳定性和准确性，PP 数据反演扩展到联合 PP 和 PS 基于 PM 的反演 (JPMI)。采用线性反演方案来降低计算成本，并相应地计算 Fréchet 导数。此外，为了获得最佳模型解，实施了 L-BFGS（有限记忆 Broyden-Fletcher-Goldfarb-Shanno）优化算法和 L-曲线准则，一种自适应正则化参数获取方法。后验概率分析表明，该方法比基于联合精确 Zoeppritz 的反演具有更高的参数敏感性，并提供比单数据反演更好的估计。我们通过模型测试讨论了数据集权重、内部多重反射、时间窗口设置、噪声水平和初始模型的影响。