This chapter discusses Monte Carol methods, the least-absolute values criterion and the minimax criterion, and their applications to functional inverse problems.Expand

Part 1. Discrete Inverse Problems. 1. The General Discrete Inverse Problem. 2. The Trial and Error Method. 3. Monte Carlo Methods. 4. The Least-Squares (l 2 -norm) Criterion. 5. The Least-Absolute… Expand

The nonlinear inverse problem for seismic reflection data is solved in the acoustic approximation. The method is based on the generalized least‐squares criterion, and it can handle errors in the data… Expand

We attempt to give a general definition of the nonlinear least squares inverse problem. First, we examine the discrete problem (finite number of data and unknowns), setting the problem in its fully… Expand

In inverse problems, obtaining a maximum likelihood model is usually not sucient, as the theory linking data with model parameters is nonlinear and the a posteriori probability in the model space may not be easy to describe.Expand

We examine the general non-linear inverse problem with a nite number of parameters. In order to permit the incorporation of any a priori information about parameters and any distribution of data (not… Expand

This is the first of a series of papers giving the solution of the inverse problem in seismic exploration. The acoustic approximation is used together with the assumption that the velocity field has… Expand

The problem of interpretation of seismic reflection data can be posed with sufficient generality using the concepts of inverse theory. In its roughest formulation, the inverse problem consists of… Expand