基于深反射地震资料的自适应波形反演重建地壳精细结构

Waveform inversion is a deep structutre imaging method to construct high-precision velocity model, which makes full use of the full waveform information. As the conventional waveform inversion methods usually have narrow convergence domain, it is easy to fall into local minima. As a result, the conventional waveform inversion methods are strongly dependent on the accurate initial velocity model or sufficient low-frequency information in the data. However, the real data usually does not meet the above two conditions. Thus, the conventional waveform inversion methods face severe challenges in real data. Adaptive waveform inversion uses matching filtering method, which constructs a specific objective function to drive this matching filter to approach the zero-lag delta function. It has a broad convergence domain that is easier to converge to the global minimum. Therefore, this project intends to carry out adaptive waveform inversion by computing the Wiener filter coefficients between the simulated and observed waveforms. Based on a adaptive bandwidth peanalty function, we construct a objective function to minimize the non-zero delay Wiener filter coefficients. We derive the gradient formula using the adjoint-state method and develop L-BFGS optimization method-based adaptive waveform inversion. Besides, we develop the OpenACC-based high-precision optimized cubature points-based triangular spectral element method to migitate the costlier computing demands in large-scale waveform inversion. Finally, we try to apply the developed method to the deep reflection seismic data in Jiaoliao area and reconstruct the fine velocity structures of the crust, which provides deep structural constraints for controlling the huge dolg mineralization in the North China Craton.

波形反演是利用全波形信息构建高精度速度模型的深部结构成像方法。由于传统波形反演方法具有较窄的收敛域，极易陷入局部极小解，使其强烈依赖于较精确的初始速度模型或数据中的充分低频信息。然而，对于不满足上述条件的实际问题，传统波形反演方法面临严峻挑战。自适应波形反演采用匹配滤波方法，驱动匹配滤波器向零延迟δ函数逼近，具有宽广的收敛域，较易收敛到全局最小解。为此，本研究拟开展自适应波形反演研究，计算模拟波形与观测波形的维纳滤波系数，基于自适应带宽罚函数构建目标函数，最小化非零延迟维纳滤波系数；利用伴随状态方法推导梯度公式，结合高效率的L-BFGS最优化方法发展自适应波形反演；发展基于OpenACC并行加速的高精度优化求积点三角网格谱元法，解决大尺度波形反演的高计算成本问题。本项目拟将发展的方法应用于胶辽地区的深反射地震资料，重建地壳精细速度结构，为华北克拉通破坏对巨量金成矿的控制提供深部结构约束。

本项目围绕深反射地震资料全波形反演开展了系统研究工作，取得了如下主要成果：.（1）采用期望最大化算法，通过估计地震资料中异常振幅和正常振幅服从的概率密度函数的特征参数，通过f-x域的滑动窗口自动识别异常振幅，并按照两者的特征参数比值对其衰减，实现异常高振幅自适应衰减。.（2）基于噪声增加Hankel矩阵秩的原理，通过降低其秩并并重建，实现信号增强；利用噪声分布在所有角度楔且振幅较小，而信号集中在特定角度楔且幅值较大的特征，通过软阈值滤波对深反射地震资料去噪。.（3）构建解析频散信号，通过匹配滤波提取地震资料中的面波成分，并作为曲波域稀疏促进贝叶斯反演的先验约束，通过迭代反演高精度分离地震资料的反射波和面波成分。.（4）考虑谱元法拉普拉斯算子的单元全局性，通过在正向传播震源波场过程中保存吸收层与计算区域边界节点加速度信息，在逆时传播过程中替换相应节点的边界信息，实现谱元法的高效震源波场重建，节省存储一个数量级。.（5）提出基于观测数据自相关函数包络自适应罚函数，发展了有效的自适应波形反演成像方法；基于二阶压力场声波方程，推导了直接拟合质点速度的伴随源公式，相比于拟合质点速度的传统一阶速度-应力声波方程，显著提高计算效率。.（6）开展了自适应波形反演成像方法在实际地壳尺度结果成像中的应用，在胶东地区的深反射地震资料中取得了良好的应用效果，获得了精细的地壳速度结构。