Geoelectric Modelling Based on Bessel Functions Integral and Damped Least-Square Inversion for Layered Earth Models

Abstract

Apparent resistivity formulations of a geoelectric method for layered Earth have been obtained analytically in the Bessel functions integral. This formulation is obtained through the application of two boundary conditions. First, the current density is zero at the Earth's surface. Second, current density and electric potential are continuous at the boundary between the layers. Geoelectric modelling can be done using several model parameters through this formulation. The modelling results show that apparent resistivity formulations based on Bessel function integrals can simulate apparent resistivity curves for layered earth models. The inversion process uses the apparent resistivity formulation based on Bessel function integrals. In this study, the inversion process uses a dumped Least-squared inversion method. The first step begins by testing the inversion program using synthetic data. After that, the inversion program is used in field data. The inversion results using field data from geoelectric data in Mount Pandan, East Java, show that the program was well done, with a minimal error value of 1.24%.