Fuzzy constrained Lp-norm inversion of direct current resistivity data

We evaluate the use of a fuzzy c-means clustering procedure to improve an inverted 2D resistivity model within the iterative error minimization procedure. The algorithm is coded in MATLAB language for the Lp-norm inversion of 2D direct current resistivity data and is referred to as fuzzy constrained inversion (FCI). Two additional input parameters are required to be provided by the interpreter: (1) the number of geologic units in the model (i.e., the number of clusters) and (2) the mean resistivity values of each geologic unit (i.e., cluster center values of the geologic units). The efficacy of our approach is evaluated by tests carried on the synthetic and field electrical resistivity tomography (ERT) data. Inversion results from the FCI algorithm are presented for conventional L1- and L2-norm minimization techniques. FCI indicates improvement over conventional inversion approaches in differentiating the geologic units if a proper number of the geologic units is provided to the algorithm. Inappropriate clustering information will affect the resulting resistivity models, particularly conductive geologic units existing in the model. We also determine that FCI is only effective when the observed ERT data can recognize the particular geologic units.