Michael Schreiner - Böcker

This book presents, in a consistent and unified overview, results and developments in the field of today´s spherical sampling, particularly arising in mathematical geosciences. Although the book often refers to original contributions, the authors made them accessible to (graduate) students and scientists not only from mathematics but also from geosciences and geoengineering. Building a library of topics in spherical sampling theory it shows how advances in this theory lead to new discoveries in mathematical, geodetic, geophysical as well as other scientific branches like neuro-medicine. A must-to-read for everybody working in the area of spherical sampling.

New stimuli are given, and innovative ways of modeling geologic strata by mollifier magnetometric techniques are shown. Potential data sets primarily of terrestrial origin constitute the main data basis in the book.

This book presents, in a consistent and unified overview, results and developments in the field of today´s spherical sampling, particularly arising in mathematical geosciences.

Duringthelastdecades,geosciencesand-engineeringwerein?uencedbytwo essentialscenarios. First, thetechnologicalprogresshaschangedcompletely the observational and measurement techniques. Modern high speed c- puters and satellite-based techniques are entering more and more all (geo) disciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment, and about an expected shortage of natural resources. Obviously, both aspects, viz. (i) e?cient strategies of protection against threats of a changing Earth and (ii) the exceptional s- uation of getting terrestrial, airborne as well as spaceborne, data of better and better quality explain the strong need for new mathematical structures, tools, and methods. In consequence, mathematics concerned with geosci- ti?c problems, i.e., geomathematics, is becoming more and more important. Nowadays, geomathematics may be regarded as the key technology to build the bridge between real Earth processes and their scienti?c understanding. In fact, it is the intrinsic and indispensable means to handle geoscient- cally relevant data sets of high quality within high accuracy and to improve signi?cantly modeling capabilities in Earth system research.

Second, the canonical transition from spherical harmonics via zonal (kernel) functions to the Dirac kernel is given in close orientation to an uncertainty principle classifying the space/frequency (momentum) behavior of the functions for purposes of data analysis and (geo-)application.