ALBERT

Description / Table of Contents: PREFACE Through the last few decades inversion concepts have become an integral past of experimental data interpretation in several branches of science. In numerous cases similar inversion-like techniques were developed independently in separate disciplines, sometimes based on different lines of reasoning, and sometimes not to the same level of sophistication. This fact was realized early in inversion history. In the seventies and eighties "generalized inversion" and "total inversion" became buzz words in Earth Science, and some even saw inversion as the panacea that would eventually raise all experimental science into a common optimal frame. It is true that a broad awareness of the generality of inversion methods is established by now. On the other hand, the volume of experimental data varies greatly among disciplines, as does the degree of nonlinearity and numerical load of forward calculations, the amount and accuracy of a priori information, and the criticality of correct error propagation analysis. Thus, some clear differences in terminology, philosophy and numerical implementation remain, some of them for good reasons, but some of them simply due to tradition and lack of interdisciplinary communication. In a sense the development of inversion methods could be viewed as an evolution process where it is important that "species" can arise and adapt through isolation, but where it is equally important that they compete and mate afterwards through interdisciplinary exchange of ideas. This book was actually initiated as a proceedings volume of the "Interdisciplinary Inversion Conference 1995", held at the University of Aarhus, Denmark. The aim of this conference was to further the competition and mating part of above-mentioned evolution process, and we decided to extend the effect through this publication of 35 selected contributions. The point of departure is a story about geophysics and astronomy, in which the classical methods of Backus and Gilbert from around 1970 have been picked up by helioseismology. Professor Douglas Gough, who is a pioneer in this field, is the right person to tell this success story of interdisciplinary exchange of research experience and techniques [1-31] (numbers refer to pages in this book). Practitioners of helioseismology like to stress the fact that the seismological coverage on the Sun in a sense is much more complete and accurate than it is on Earth. Indeed we witness vigorous developments in the Backus & Gilbert methods (termed MOLA/SOLA in the helioseismology literature) [32-59] driven by this fortunate data situation. Time may have come for geophysicists to look into helioseismology for new ideas. Seismic methods play a key role in the study of the Earth's lithosphere. The contributions in [79 - 130,139 - 150] relate to reflection seismic oil exploration, while methods for exploration of the whole crust and the underlying mantle axe presented in [131 - 138, 151 - 166]. Two contributions [167 - 185] present the application of inversion for the understanding of the origin of petroleum and the prediction of its migration in sedimentary basins. Inversion is applied to hydrogeophysical and environmental problems [186 - 222], where again developments are driven by the advent of new, mainly electromagnetic, experimental techniques. The role of inversion in electromagnetic investigations of the lithosphere/astenosphere system as well as the ionosphere axe exemplified in [223 - 238]. Geodesy has a fine tradition of sophisticated linear inversion of large, accurate sets of potential field data. This leads naturally to the fundamental study of continuous versus discrete inverse formulations found in [262-275]. Applications of inversion to geodetic satellite data are found in [239 - 261]. General mathematical and computational aspects are mainly found in [262 - 336]. Nonlinearity in weakly nonlinear problems may be coped with by careful modification of lineaxized methods [295 - 302]. Strongly nonlinear problems call for Monte Carlo methods, where the cooling scedule in simulated annealing [303 - 311,139 - 150] is critical for convergence to a useful (local) minimum, and the set of consistent models is explored through importance sampling [89 - 90]. The use of prior information, directly or indirectly, is a key issue in most contributions, ranging from Bayesian formulations based a priori covariances e.g. [98 - 112,122 - 130, 254 - 261], over more general but also less tractable prior probability densities [79 - 97], to inclusion of specific prior knowledge of shape [284 - 294, 312 - 319]. Given the differences and similarities in approach, can we benefit from exchange of ideas and experience? In practice ideas and experience seldom jump across discipline boundaries by themselves. Normally one must go and get them the hard way, for instance by reading and understanding papers from disciplines far from the home ground. Look at the journey into the interdisciplinary cross-field of inversion techniques as a demanding safari into an enormous hunting ground. This book is meant to provide a convenient starting point.