Abstract
In order to calculate the electric potential generated by a point current source that is placed at any position in a multilayered space, we have derived new theoretical formulas using the derivation process of recursive relations by Sato (2000). Individual coefficients of the formulas are described in the recursive equations based on upward and downward continuation processes. In the derivation of the recursive equations, we have considered the case where the point current source is placed at a layer boundary, which was not dealt with by Sato (2000).
Moreover, we have modified the derived formulas to stabilize the exponential terms for numerical computation using the linear filter method. We also show that the well-known resistivity transform (function) is derived by using the new formulas and derivation process. As Ando (2006) indicated for the seafloor measurement in multilayered seawater part and sub-bottom structure, we have demonstrated that the resistivity transfer function for the whole system is equal to the parallel connection of two resistivity transfer functions for the seawater part and sub-bottom structure using our formulas.
