Three‐dimensional terrain corrections for mise‐à‐la‐masse and magnetometric resistivity surveys

Three‐dimensional modeling of topographic effects in mise‐à‐la‐masse and magnetometric resistivity surveys is accomplished using the surface integral equation method. The technique provides a means for (1) analyzing these effects on earth models of homogeneous conductivity; and (2) removing terrain effects from field data. A new method combining current source images with surface charge is developed to treat the electric field boundary conditions at the air‐earth interface. The method uses an image of each subsurface current source positioned above the surface, so as to induce a surface charge distribution which approximately cancels the charge distribution induced by the subsurface current source. The resulting residual surface charge distribution varies spatially more gradually than either of the original charge distributions, and hence may be represented accurately on a coarsely segmented model surface with simple basis functions. The topographic surface is modeled by a finite number of facets, each with constant slope and surface charge density. Charge values are obtained with an iterative solution technique. Surface electric fields are calculated from the surface charge distribution, current sources, and images. The magnetic field is found by evaluating a surface integral involving surface slopes and electric fields. The numerical solution is verified by comparisons with dipole‐dipole resistivity results from a two‐dimensional finite‐element model of a valley, and with analytic solutions for the magnetic fields over a dipping interface. Methods for terrain correcting mise‐à‐la‐masse and magnetometric resistivity data are demonstrated with examples using actual field measurements. The results of this study show that (1) rugged topography can significantly distort measurements in mise‐à‐la‐masse and magnetometric resistivity surveys; and (2) the described modeling technique provides an effective means of calculating terrain corrections for both the mise‐à‐la‐masse and magnetometric resistivity methods over complex three‐dimensional topography.