强散射介质中的波动方程线性化及速度反演

迄今为止，强散射介质（异常体尺度大且波阻抗反差强）中的强非线性波动方程反演属于反问题研究的理论前沿与难点，尚未有公认的解决方案。通过分析波传播的物理规律并研究Born级数的振幅发散机制，本项研究发现前向散射波累积相位扰动的精确计算是弱化反问题非线性的关键，并通过：（1）采用不动点理论迭代计算散射波相位扰动的高阶近似；（2）在WKBJ意义下导出了前向散射波相位扰动与模型扰动的线性关系，将地震波的波形对模型的强非线性关系转化为散射波的相位扰动对模型扰动的拟线性关系，建立了强散射介质中的波动方程相位线性化理论。针对波形反演中残差测量的“周期跳跃”问题，本项目提出了一种能够凸显地震信号运动学特征差异性的测量方法，进而构造比波形残差目标函数凸性更好的反问题并给出其求解方法。本课题的研究为探索强散射介质中的波动方程反演提供了一种独特且可行的研究思路，有助于推动波动方程反演技术在实际应用中的发展和完善。

The local-optimization-based inversion theory is easy to get stuck into local minimum when dealing with wave-equation inverse problem due to the nonlinear relation between the waveform- and velocity perturbation. Up to now, the theoretical solution for strong nonlinear wave-equation inverse problem has not been fully developed for strong-scattering media (anomalies with large-scale and strong impedance contrast). By analyzing the amplitude-divergence nature of the Born series and following the physical law of wave propagation, we find that the accurate calculation of the accumulated phase-perturbation of the forward-scattered fields is the key issue to reduce the strong nonlinearity of the inverse problem and we propose two practical solutions: one is to calculate the higher-order approximation of the phase-perturbation using the fixed-point theory (the iterative solution); and the other is to solve the nonlinear Ricatti integral equation under the WKBJ approximation which creates a linear relation between the phase-perturbation and the model perturbation, reformulating the strong nonlinear relation between the waveform and model parameters into a quasi-linear relation between the phase-perturbations and model perturbations. To address the cycle-skipping problem of the classical waveform inversion method, we propose a robust method to estimate the kinematic difference of the reflection seismic data, which can an reformulate the classical waveform-fitting based inverse problem into a more convex inverse problem. Our research provides a particular prospective for wave-equation inversion in strong-scattering media, which is very helpful for practical applications of wave-equation inversion technique.