Unified equation for straightforward inversion scheme on vertical electrical sounding data

Abstract

A unified apparent resistivity equation is derived encompassing eight electrode configurations for Straightforward Inversion Scheme (SIS) on Vertical Electrical Sounding (VES) data. Suitable parameters are worked out to convert unified equation to a particular configuration viz. Wenner, Pole-Pole, Schlumberger, Pole-Dipole, Radial Dipole, Perpendicular Dipole, Parallel Dipole and Azimuthal Dipole. The derived equation is validated by forward computations of VES data for a 5-layer earth model that compares well with that of VES data obtained using existing individual equations for a particular configuration. SIS scheme is briefly described and a Schlumberger synthetic sounding data is generated using the unified equation over model riddled with equivalence /suppression and subsequently inverted using SIS to show the resolving power of the scheme via-a-vis low resistivity contrast between the layers. Two examples of field Schlumberger soundings from known lithology on a paleochannel in Mario Island in Northern Brazil are also included and the inverted continuous resistivity variation is presented to show the efficacy of the scheme.