TIME-LAPSE INVERSION OF SELF-POTENTIAL DATA USING KALMAN FILTER

Abstract

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.