Mathematical modeling of resistivity probing of ancient city at Prapathom Chadee, Nakhon Pathom, Thailand

Abstract

In this paper, the analytical solution of normalized apparent resistivity from DC source located on a two layered earth model is formulated. The conductivity of overburden is denoted by σ over (z) = σ 0 e −b(z−l) 2 /2 , 0 ≤ z ≤ d, where b and l are positive constants and l is used to locate the peak of the bulge, d is the thickness of overburden and σ 0 is a positive constant. The conductivity of host medium, z > d, is denoted by a constant and is given by σ host (z) = σ 0. The Hankel transforms and power series method are used to solve the partial differential equation to find the potential functions. The expression for the Wenner configuration is introduced to formulate the normalized apparent resistivity. In order to determine the normalized apparent resistivity, numerical solutions are computed to show the behavior of the curves by using Chave's algorithm while some parameters are given. The curves of computation results of normalized apparent resistivity are plotted against electrode spacing. The curves could be able to predict the depth of the underground water that could damage to the foundation of old building.