relation: https://episodesplatform.eu/eprints/1304/
title: Probabilistic Inverse Theory
creator: Debski, Wojciech
subject: Method and procesing
description: Geophysical investigations which commenced thousands of years ago in China from observations of  the Earth shaking caused by large earthquakes (Lee et al., 2003) have gone a long way in their  development from an initial, intuitive stage to a modern science employing the newest technological  and theoretical achievements. In spite of this enormous development, geophysical research still faces  the same basic limitation. The only available information about the Earth comes from measurement  at its surface or from space. Only very limited information can be acquired by direct measurements.  It is not surprising, therefore, that geophysicists have contributed significantly to the development of  the inverse theory — the theory of inference about sought parameters from indirect measurements.  For  a  long  time  this  inference  was  understood  as  the  task  of  estimating  parameters  used  to  describe the  Earth’s  structure  or  processes  within  it,  like  earthquake  ruptures.  The  problem was  traditionally solved by using optimization techniques following the least absolute value and least  squares criteria formulated by Laplace and Gauss.  Today  the  inverse theory  faces  a  new challenge  in  its  development.  In  many geophysical  and  related applications, obtaining the model  “best fitting”  a given set of data according to a selected  optimization criterion is not sufficient any more. We need to know how plausible the obtained model  is or, in other words, how large the uncertainties are in the final solutions. This task can hardly be  addressed in the framework of the classical optimization approach.  The probabilistic inverse theory incorporates a statistical point of view, according to which all  available information, including observational data, theoretical predictions and a priori knowledge,  can  be  represented  by  probability  distributions.  According  to  this  reasoning,  the  solution  of  the  inverse problem is not a single, optimum model, but rather the a posteriori probability distribution  over the model space which describes the probability of a given model being the true one. This path  of development of the inverse theory follows a pragmatic need for a reliable and efficient method of  interpreting observational data.  The aim of this chapter is to bring together two elements of the probabilistic inverse theory. The  first one is a presentation of the theoretical background of the theory enhanced by basic elements of  the  Monte  Carlo computational  technique.  The  second  part  provides  a  review of  the  solid  earth  applications of the probabilistic inverse theory.
publisher: Elsevier
contributor: Dmowska, Renata
date: 2010
type: Book Section
type: PeerReviewed
identifier:   Debski, Wojciech  (2010) Probabilistic Inverse Theory.   In:  Advances in Geophysics.   Elsevier, San Diego, USA, pp. 1-102.  ISBN 978-0-12-374910-9