Ambiguity Analysis and Joint Inversion of Potential Field and Other Data

Given a potential field on a plane, the set of source distributions that could generate the field is easily represented in the Fourier domain. The resulting solutions show a range of variability far larger than expected by many practitioners. This variability can be reduced or eliminated by seeking solutions that also minimize a regularizing functional expressing extra information regarding the solution. Unique, smooth solutions are obtained from Tikhonov stabilization using completely regularizing elliptic functionals. Our investigations indicate that novel partial regularization is effective in guiding the search towards non-smooth solutions resembling a given regional geological style. However, partial regularization using geostatistical and texture based criteria do not necessarily yield unique solutions. Additional partial regularization using limited underground sampling of the source distribution significantly reduces the remaining variability.