Adaptive Shape Parameter RPIM for SP Log Analysis: Methods and Benchmarks

The attempt of a new general adaptive meshless method in simulating singular spontaneous potential (SP) logging problems is discussed in this article. This method was first proposed and designed by our team, and it is named adaptive overall shape parameter " c " radial base point interpolation method (OC-RPIM). A new model error evaluation method using twin matrices is proposed and used in the OC-RPIM local matrix construction. Based on this error evaluation index, the architecture of the adaptive ${c}$ algorithm is implemented. This method has excellent stability and accuracy without modifying the discrete point configuration and polynomial order. Furthermore, it is easier to deal with problems that have singularities. This study discusses the versatility and superiority of the architecture when the OC-RPIM algorithm is applied to SP simulation problems. The characteristic rules of c of the SP simulation curve under different formation conditions are analyzed. This method provides a new perspective on adaptive solving algorithms in computational geodetic electromagnetics (Geo-EM). The OC-RPIM code used for this study is already open source.