Geophysical data interpretation by inverse modeling: Proceedings of the ninth International Seminar on Model Optimization in Exploration Geophysics, ... (Theory and practice of applied geophysics)

This volume contains a selection of papers presented at the Ninth International Seminar on Model Optimization in Exploration Geophysics held at the Free University of Berlin, February 18-23, 1991. It covers a wide spectrum of inverse modeling from basic mathematical theory to practical applications in different branches of geophysics - solving inverse problems, and discussing and evaluating the conditions, constraints and the area of its validity from the point of view of theoretical mathematics is of fundamental importance for the further development of geophysical research, in particular of exploration geophysics. Nowadays, there are essential new results in theoretical mathematics and in numerical mathematics that enable to treat the inverse problems of geophysics on better founded mathematical principles and functional relations. The particular requirements arising from practical aplications stimulate the development of new analytical and numerical methods, in particular the construction of approximate solutions and their stabilization which is necessary in the case of insufficient data sets. In general it is obvious that the type of the governing partial differential equation essentially determines how the inverse problem is to be treated. The first section of the book refers to the basic mathematical theory and to general approaches in dealing with inverse problems. The mathematical analysis of the special problem as given by the relevant partial differential or integral equation is presented. The role of the boundary conditions, variational inequalities, regularization methods, questions of stability in approximating parameters and spectral problems are discussed. There are also included discussions of fitting procedures and use of smoothness constraints in discrete models. The second section comprises several papers treating practical applications of inverse methods in gravity and magnetics. Here also the construction of the solution, as well as the region of stability in determining the parameters are discussed. The third section presents papers concerning seismics and geothermics, in mathematical respect problems being governed by the wave and heat flow equations, respectively.