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Inverse problem theory - and methods for model parameter estimation
This chapter discusses Monte Carol methods, the least-absolute values criterion and the minimax criterion, and their applications to functional inverse problems.
Inverse problem theory : methods for data fitting and model parameter estimation
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
Inversion of seismic reflection data in the acoustic approximation
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
Generalized Nonlinear Inverse Problems Solved Using the Least Squares Criterion (Paper 1R1855)
• Physics, Geology
• 1 May 1982
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
Monte Carlo sampling of solutions to inverse problems
• Computer Science
• 10 July 1995
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.
Inverse problems = Quest for information
• Mathematics
• 1982
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
LINEARIZED INVERSION OF SEISMIC REFLECTION DATA
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