基于不等式约束的三维电阻率探测混合反演方法

三维电阻率探测的线性反演和非线性反演中均存在着多解性的固有难题.电阻率线性反演方法的效率较高,但反演结果对初始模型的依赖性较强,易陷入局部极小;而非线性反演方法不依赖初始模型,但搜索效率极低,尚未见到关于三维电阻率非线性反演的文献.针对上述问题,融合线性与非线性反演方法的互补优势,提出了最小二乘法(线性方法)与改进遗传算法(非线性方法)相结合的混合反演方法的概念和思想.首先,提出了将介质电阻率变化范围作为不等式约束引入反演方程的思路,以实现压制多解性、提高可靠性的目标.提出了宽松不等式约束和基于钻孔推断的局部严格不等式约束的获取及定义方法.在此基础上,分别提出了基于不等式约束的最小二乘线性反演方法和遗传算法非线性反演方法.其次,对于遗传算法在变异搜索方向控制、初始群体产生等方面进行了改进,优化了其搜索方向和初始群体多样性.然后,提出了混合反演方法及其实现方案,利用改进遗传算法进行第一阶段反演,发挥其对初始模型的依赖程度低的优势,搜索到最优解附近的空间,输出当前最优个体;利用最小二乘法进行第二阶段反演,将遗传算法得到的当前最优个体作为初始模型,在最优解附近空间执行高效率的局部线性搜索,最终实现地电结构的三维成像.最后,开展了合成数据与实际工程算例验证,与传统最小二乘方法进行了对比,发现混合反演方法在压制多解性、摆脱初始模型依赖和提高反演效果方面有较好效果.

Joint inversion method of 3D electrical resistivity detection based on inequality constraints

Non-uniqueness is one inherent problem in 3D electrical resistivity linear and non-linear inversion. The linear inversion method has a rapid calculation speed, but its result is strongly dependent on the initial model, which may result in falling into the local minimum. The nonlinear inversion method is independent on the initial model, but its search and inversion efficiency is extremely low. And there is no literature about 3D resistivity nonlinear inversion at present. To solve these problems, based on the complementary strengths between linear and nonlinear inversion method, this study proposed a joint inversion method combining the least square method (a linear inversion method) and improved genetic algorithm (GA) method (a nonlinear inversion method). At first, the resistivity varying range is considered as an inequality constraint, which is incorporated into inversion equation. Then the definition method of looser inequality constraint and stricter inequality constraint is given, which is deduced from drilling holes. And the least square linear inversion method and GA nonlinear inversion method based on inequality constraints are put forward separately. Secondly, the GA method is improved in aspects of mutation direction control, production of initial population, by which searching direction, evolutionary efficiency and population diversity are improved greatly. Then, the joint inversion method and its implementation scheme are presented. The improved GA is used in the first inversion-stage. The advantages of its low dependence on the initial model are utilized. When the space near the optimized solution can be searched, the optimal individual should be exported. Then the least square method is used in the second inversion-stage. The optimal individual obtained by GA is taken as the initial model and efficient local linear search is executed in the space near the optimized solution. In this way, 3D imaging of geo-electric structure can be achieved. At last, verification on synthetic data and real examples has been carried out. Comparing with the traditional inversion method of least square shows that this joint inversion method has significant advantages in suppressing non-uniqueness, getting rid of the initial model dependence and improving inversion effect.