基于卡尔曼滤波的自然电场数据时序反演

自然电场法常用于环境与工程等领域的监测作业,但各时刻观测数据往往单独反演解释.为了充分利用时序数据间的关联信息,提高监测数据的反演解释可靠性,提出基于卡尔曼滤波的自然电场监测数据时序反演方法.根据达西定律和阿尔奇公式建立污染物在孔隙介质中的运动扩散的动态地电模型,作为用于构建卡尔曼滤波的状态模型.而卡尔曼滤波的观测模型则通过常规的自然电场法正演获得.在建立状态模型和观测模型的基础上,构建起卡尔曼滤波递归,将地电模型演化信息与自然电场观测数据进行信息融合,实现自然电场监测数据的时序反演.加入噪声的自然电场模拟数据测试表明时序反演算法具有较好的鲁棒性,对噪声不敏感.沙槽物理实验监测数据的计算测试也同样证明时序反演能有效处理监测数据,实现对动态模型的准确重构.

Time-lapse inversion of self-potential data using Kalman filter

It is very common to use the self-potential methods in environmental and engineering applications, especially in some monitoring services. However, the monitored data of each time step are always inverted and interpreted independently. That means the valuable correlation information of time-lapse data is totally ignored. In order to take full advantage of the correlation information, a time-lapse inversion was proposed to promote the reliability of data interpretation. Based on the Darcy's law and Archie's formulas, a dynamic geoelectric model was built to simulate the transportation of contaminant plume in underground porous medium. Then this dynamic model can be used as a state model for the Kalman filtering. And the corresponding observation model can be obtained from conventional self-potential forward calculation. Thus, a Kalman filter recursion can be constructed by using the state model and observation model. During the recursion, the information of geoelectric model evolution and observed self-potential data are fused to achieve a time-lapse inversion of self-potential data. The time-lapse inversion algorithm was tested by both noise added synthetic self-potential data and laboratory observation data from self-potential monitoring over a sandbox. The numerical test shows the validity, robustness, and tolerance to noise of the time-lapse inversion. And the results of physical data test also demonstrate that the time-lapse inversion can invert real time-lapse self-potential data successfully and retrieve the dynamic geoelectric model exactly.