Conclusions and outlook

Gravity and magnetic field inversion for the determination of density distribution and material magnetization in the subsurface, respectively, require a special form of regularization, that can be specifically described by inverse mollifier problems of potential theory. SPE (FKZ 0324061) and SYSEXPL (FKZ 03EE4002A) have developed new linear as well as nonlinear mollifier resolution methods for the decorrelation of geologic structures and published them in the publications [34, 54, 55, 56] to the international scientific community. A special aspect is that an inverse problem such as gravimetry, magnetometry, etc. cannot obtain uniqueness of an interior geologic structure from only terrestrial data (see Figure 3.1). Any regularization method, i. e., also the mollifier multiscale methodology presented in this work, additionally requires some prior information from the interior of the area under investigation.