Lemniscate representation for inversion of gravity and magnetic data through nonlocal optimization

A method of representing surfaces and volumes by a set of geometric points and a small set of auxiliary parameters, based on generalization of Bernoul li's notion of lemniscates is introduced. It provides for easy generation a nd modification of surfaces and volumes, which could be connected, disjoint or even with very irregular boundaries. This allows solving geophysical in version problems, without constraining the anomalous volumes to some ideal or simple forms. This is illustrated by the example of joint inversion of g ravity and magnetic data sets attributable to two-dimensional anomalous bod ies. A nonlocal optimization algorithm called segmented Hamming scan is use d for inversion. Comparison with nonlinear least-squares algorithm shows th e advantages of the chosen approach. The concepts of desideratal and proced ural detours are illustrated.