2-D Electrical Modeling over Undulated Topography

The electrical response of a cylindrical inclusion in topographic relief has been treated analytically for a uniform electric field. The undulated topography has been conveniently defined by a smoothly connected mathematical surface defining a hump or bump. A Born approximation of Laplace's equation in a bipolar coordinate system has been derived by solving for the mixed-boundary conditions, namely Neumann and Dirichlet conditions, respectively. The topographic relief causes focusing and defocusing at the transition zones of flat and topographic relief and the central zone of the hump. Consequently, the electric field is weakly linear within the Aat zone and entirely nonlinear within the hump. The inclusion of a cylindrical target aggravates the field nonlinearity, The electric field and induced polarization (IP) response over the cylindrical target embedded in topographic relief are strongly dependent on the width and height of the hump and a steady function of increase in resistivity (rho(2)/rho(1)) as well as chargeability (m(2)-m(1)) contrasts. The electrical field and IP response over the cylindrical target embedded in the topographic relief, after correcting for topographic effect, resembles most closely the field measured on an equivalent flat half-space of a particular elevation. The areas of the topographic surface above and below this unique datum bisecting the topographic relief are exactly equal.