Decorrelative Mollifier Gravimetry

The lecture highlights arguments that, coming from multiscale mathematics, have fostered the advancement of gravimetry, as well as those that, generated by gravimetric problems, have contributed to the enhancement in constructive approximation and numerics. Inverse problems in gravimetry are delt with multiscale mollifier decorrelation strategies. Two examples are studied in more detail: (i) Vening Meinesz multiscale surface mollifier regularization to determine locally the Earth's disturbing potential from deflections of vertical, (ii) Newton multiscale volume mollifier regularization of the inverse gravimetry problem to derive locally the density contrast distribution from functionals of the Newton integral and to detect fine particulars of geological relevance. All in all, the Vening Meinesz medal  lecture is meant as an  \lq \lq appetizer'' served to enjoy the tasty meal "Mathematical Geoscience Today'' to be shared by geoscientists and mathematicians in the field of gravimetry. It provides innovative concepts and locally relevant applications presented in a monograph to be published by Birkhäuser in the book series “Geosystems Mathematics” (2021).