2-D ELECTRICAL MODELING OVER UNDULATED TOPOGRAPHY

The electrical response of a cylindrical inclusion in topographic reli ef has been treated analytically for a uniform electric field. The und ulated topography has been conveniently defined by a smoothly connecte d mathematical surface defining a hump or bump. A Born approximation o f Laplace's equation in a bipolar coordinate system has been derived b y solving for the mixed-boundary conditions, namely Neumann and Dirich let conditions, respectively. The topographic relief causes focusing a nd defocusing at the transition zones of flat and topographic relief a nd the central zone of the hump. Consequently, the electric field is w eakly linear within the Aat zone and entirely nonlinear within the hum p. The inclusion of a cylindrical target aggravates the field nonlinea rity, The electric field and induced polarization (IP) response over t he cylindrical target embedded in topographic relief are strongly depe ndent on the width and height of the hump and a steady function of inc rease in resistivity (rho(2)/rho(1)) as well as chargeability (m(2)-m( 1)) contrasts. The electrical field and IP response over the cylindric al target embedded in the topographic relief, after correcting for top ographic effect, resembles most closely the field measured on an equiv alent flat half-space of a particular elevation. The areas of the topo graphic surface above and below this unique datum bisecting the topogr aphic relief are exactly equal.