基于全局优化截断牛顿法的渗流场与电流场交叉梯度联合反演

Simulating seepage distribution and water channel connectivity is an important way to solve the groundwater seepage problem. The inversion method based on the prior constraint information is mostly limited to the ground information or limited borehole observation data, so that the inversion results of the groundwater seepage have multiple solutions. In order to improve the accuracy of seepage inversion and the distribution of groundwater seepage, a complete set of cross-gradient joint inversion theory is proposed, which combined with geological and geophysical methods, and studied the unified geological from multiple angles, to reducing the multiplicities of the problem. In order to improve the speed of free surface search, Element-free Galerkin method was performed for the whole field of seepage field. The seepage inversion method based on optimization variable scale method is studied. Based on the relationship between seepage field and electric current field, the geological joint modeling of seepage and resistivity structure is realized. In order to improve the efficiency of data collection, a new integrated observation system is created for observing permeability and resistivity of the underground structure synchronously. Global optimization truncated Newton inversion theory is built for isomorphism inversion to improve the inversion efficiency. Based on the theory of isomorphism inversion, the cross-gradient joint inversion study is carried out to realize multi-parameter joint inversion of seepage distribution. Predictably, the more accurately inversion results of the distribution and channel of seepage can be obtained by the multi-field joint inversion research, and can promote the development of multi parameter precise joint inversion technology for seepage distribution in complex geological body.

模拟渗流分布与水通道连通情况是解决地下水渗流问题的重要途径。基于先验约束信息的反演方法多局限于单一地表或有限的钻孔观测数据，使得地下渗流的反演结果存在多解。为提高渗流反演精度，全面认识地下渗流的多径向发展，申请人提出一套完整的交叉梯度联合反演理论，该理论联合地质、地球物理方法，从多角度研究统一地质体，减少问题多解性。针对渗流场饱和-非饱和全域采用无单元伽辽金法进行正演模拟，研究变尺度优化的渗流反演方法，拟构建全新的堤坝渗透系数-电阻率一体化观测系统，实现坝基渗流结构与电阻率结构的地质联合建模，并建立全局优化-截断牛顿反演理论，开展同构反演研究，基于同构反演理论，开展渗流场与电流场的交叉梯度联合反演研究，实现渗流分布的多参数联合反演。可以预见，通过对堤坝渗流的多场联合反演研究，能更精确地反演地下渗流场及渗流通道，促进复杂地质体中渗流分布的多参数精细联合反演技术的发展。

本项目针对饱和-非饱和土石坝渗流问题，主要开展了基于移动网格Galerkin有限元、固定网格光滑有限元(Smoothed Finite Element Method, S-FEM)的饱和渗流研究和基于无单元Galerkin、S-FEM的饱和-非饱和渗流研究；建立了基于无单元Galerkin的渗流场与电流场非耦合、耦合分析理论；实现了截断牛顿、监督下降的电阻率反演；并开展了电流场与渗流场非线性联合反演研究，为更精细的掌握地下渗流分布，实现复杂土石坝中渗流分析及多参数联合反演提供了理论基础和解决方案。.本报告的主要内容及结论是：.1. 针对饱和渗流，分别开展了基于移动网格的Galerkin有限元及固定网格的S-FEM无压渗流正演研究。移动网格方法无需处理自由面穿过的边界单元，每次迭代更新之后对新的计算区域采用非规则网格进行结构化剖分，并选取了新的步长参数和终止条件，兼顾计算精度和计算效率。固定网格方法，S-FEM利用光滑梯度技术实现积分降维，有利于总体刚度矩阵的合成。.2. 针对饱和-非饱和渗流，分别开展了基于无单元Galerkin及S-FEM无压渗流正演模拟。采用Van Genuchten方法修正非饱和区域介质的水力传导率，采用Signorini条件将流出边界转化为常规水头边界。通过正演计算获取整个研究区域的水文状态变量(如，含水量、饱和度等)，通过岩石物理关系可将水文状态变量转换为地球物理参数。.3. 以流场法理论为基础，采用特殊线源布设方式，建立与土石坝内渗流场拟合的电流场，开展基于无单元Galerkin的渗流场和电流场非耦合与耦合分析研究，通过水文状态变量及电场参数推断渗漏异常，为水文-地球物理反演提供理论基础，为采用水文地球物理方法进行渗流检测、获取水文参数提供新思路。.4. 实现了基于截断高斯牛顿与监督下降法的电阻率反演方法。在截断高斯牛顿反演中，为解决全变差正则化项的不可微问题，采用了变量分裂的交替方向乘子法，将优化问题从无约束问题转换成有约束问题，提高了反演的收敛效率。.5. 开展电流场与渗流场非线性联合反演方法，联合水文地质、地球物理，从多角度研究统一地质体，减少问题多解性，促进复杂土石坝多参数联合反演技术的进一步发展。