时移电阻率法归一化数据四维反演研究

In order to overcome the limitation that conventional resistivity inversion method can only obtain the space resistivity structure, and at the same time, reduce the influence of the data noise in the inversion result. Based on matured forward and inversion of resistivity method, this program will study on four-dimensional inversion algorithm of normalized data of time-lapse resistivity method. The time-lapse apparent resistivity data will be normalized by data differences and data ratio method to improve signal-to-noise ratio, and the two normalized data distribution characteristics are studied at the same time. Furthermore, a four-dimensional inversion algorithm of normalized data is implemented by establish a normalized data fitting term and a time model constraint term in the objective function, which can obtain the spatial and temporal distribution of resistivity structure. The normalized time-lapse data (synthetic data, physical stimulation data and field data) will be inverted by four-dimensional inversion to test the efficiency and stability of algorithm, and compare the advantages and disadvantages of the two normalized data inversion results. Then, the inversion algorithm will apply MPI parallel skills to accelerate the calculation process of solve equation and sensitivity matrix to improve the efficiency of inversion. The successful implementation of four-dimensional inversion algorithm of normalized data of time-lapse resistivity method is helpful for accurately monitoring subsurface resistivity structure variation. Thereby，it is more efficiently serve the monitoring tasks，like landslide stability and groundwater contamination spreading.

为了克服常规电阻率反演方法只能获得电阻率模型空间分布的局限性，同时降低数据噪声对反演结果的影响，本项目以成熟的电阻率法正反演为基础，研究时移电阻率法归一化数据四维反演算法。通过数据比和数据差归一化方法，使用初始时间观测数据归一化时移视电阻率数据，提高信噪比，同时研究两种归一化数据分布特征。通过在目标函数中建立归一化数据拟合项和时间模型约束项，实现归一化数据四维反演算法，以获得电阻率时空分布。对归一化时移数据（理论模型合成数据、物理模拟数据和实测数据）进行四维反演研究，以检验算法的稳定性和有效性，并对比两种归一化数据反演结果的优劣。引入MPI并行算法加速解方程和灵敏度矩阵相关计算，提高反演效率。成功实现时移电阻率法归一化数据四维反演算法，有利于精准监测地下电阻率结构变化情况，从而有效的服务于滑坡稳定性和地下水污染扩散等监测任务。

为了克服常规电阻率反演方法只能获得电阻率模型空间分布的局限性，同时降低数据噪声对反演结果的影响，本项目以成熟的电阻率法正反演为基础，研究了时移电阻率法归一化数据特征、时移电阻率法归一化数据四维反演算法及其应用，并通过MPI并行提高程序效率。相比视电阻率数据，归一化后的视电阻率曲线表现出较强的差异性，尤其在模型发生动态变化的区域，曲线差异性最大。数据差归一化处理各时刻的视电阻率结果表现出与数据比归一化结果同样的曲线形态和较强的差异性，数据比归一化的曲线两侧的尾支渐近线为选择的均匀半空间电阻率值，而数据差归一化的曲线两侧渐近线为0。项目研究了非线性共轭梯度（NLCG）和有限内存拟牛顿（LBFGS）时移电阻率法归一化数据四维反演，对比了棱柱体动态模型反演目标函数时间项的L1和L2范数反演结果，结果表明LBFGS的反演结果最优，其L1和L2范数时间项结果相似，无明显差别。时间项为L1范数的NLCG反演结果次之，时间项为L2范数的NLCG反演结果最差。根据合成数据算例，不同均匀半空间电阻率的数据比归一化反演效果不同，在数据比归一化反演中，选择合适的均匀半空间电阻率值也是数据比归一化反演的关键。通过合成数据和实测数据发现，归一化反演能够有效识别微小变化的电阻率结构，而常规电阻率反演结果很难发现电阻率结构的微小变化。另外，实现了时移反演的MPI并行程序。通过合成数据算例测试，当21个场源进行背景数据采集和1次时移观测，网格大小为45×33×31时，开辟16个进程执行程序，获得最大加速比4.56。项目成果能够有效的获取地下电阻率结构的时空特征，有利于精准监测动态变化的地下电阻率结构，更有效的服务于滑坡预警、垃圾填埋场液态物质泄露、地下水污染物扩散等浅地表监测任务。