The three‐dimensional DC sensitivity for surface and subsurface sources

Summary Four different methods of determining the DC sensitivity in three dimensions are presented: three numerical approaches for arbitrary conductivity structures and an analytical one for a homogeneous case using the sensitivity theorem. Since the sensitivity is a very important and indicative property in any interpretation process, its spatial distribution is shown as an overview for commonly used pole–pole, pole–dipole, and dipole–dipole arrangements at the surface and subsurface. Distinct regions of negative sensitivities appear for any configuration. For horizontal subsurface pole–pole configurations, they assume tube‐like, cylindrical shapes stretching from the electrode locations towards the surface and yielding a circular sign‐reversal pattern at the surface. These shapes and sign reversals occur as long as the electrodes are located at a finite depth. Similar forms occur for subsurface pole–dipole and dipole–dipole arrangements. A series of model studies are carried out to examine the validity of the homogeneous responses for more realistic inhomogeneous media. Generally, the spatial sensitivity patterns for homogeneous environments are good approximations for moderate conductivity contrasts not exceeding 1 : 10 if the source is located within conductive material. If the source is buried within a resistor, conductive structures perturb the homogeneous pattern more significantly. Finally, a crosshole model study reveals significant differences between 2‐D and 3‐D conductive bodies, suggesting a need to examine the target very carefully before approximating some structures in two dimensions.