Sequential and Simultaneous Joint Inversion of Resistivity and IP Sounding Data Using Particle Swarm Optimization

In order to interpret the vertical electrical sounding data more reliably and effectively in the case of lacking proper priori information, two inverse schemes are proposed to invert combined resistivity and induced polarization data by using particle swarm optimization technique. Based on the computational formula of induced polarization, the inversion for chargeability/polarizability data can be transformed into inverting equivalent resistivity data. Then, the inversion for combined data can be decomposed into two procedures: inverting resistivity data and inverting equivalent resistivity data. A sequential inversion scheme is presented to run the two procedures sequentially. Contrast to the sequential scheme, a simultaneous one is proposed to invert resistivity and induced polarization data simultaneously. Both the sequential and simultaneous schemes are performed via centered-progressive particle swarm optimization algorithm for more exploratory purpose. Numerical experiments show that both the designed inversion algorithms can invert resistivity and induced polarization data successfully with fast convergence and high accuracy, even performed in a large search space. The inverse results are comparable to the results from generalized linear method. As an approximate importance sampler, the particle swarm optimization based algorithm can provide posterior analysis conveniently. We employ the posterior probability distributions of inverted model parameters to evaluate the performance and uncertainty of inversion. The posterior analysis and further field data testing show that the proposed inversion algorithms perform good sampling of the equivalence region and make sure that the global optimum can locate in the high probability areas.