scispace - formally typeset
Journal ArticleDOI

Generalized Nonlinear Inverse Problems Solved Using the Least Squares Criterion

Albert Tarantola, +1 more
- 01 May 1982 - 
- Vol. 20, Iss: 2, pp 219-232
Reads0
Chats0
TLDR
In this article, a general definition of the nonlinear least squares inverse problem is given, where the form of the theoretical relationship between data and unknowns may be general (in particular, nonlinear integrodierentia l equations).
Abstract
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 nonlinear form. Second, we examine the general case where some data and/or unknowns may be functions of a continuous variable and where the form of the theoretical relationship between data and unknowns may be general (in particular, nonlinear integrodierentia l equations). As particular cases of our nonlinear algorithm we find linear solutions well known in geophysics, like Jackson’s (1979) solution for discrete problems or Backus and Gilbert’s (1970) a solution for continuous problems.

read more

Content maybe subject to copyright    Report

Citations
More filters
Journal ArticleDOI

Integrating Geologic and Geodetic Estimates of Slip Rate on the San Andreas Fault System

TL;DR: Interseismic deformation measurements are generally interpreted in terms of steady slip on buried elastic dislocations. Although such models often yield slip rates that are in reasonable accord with the actual deformation as mentioned in this paper.
Journal ArticleDOI

High‐resolution, two‐dimensional vertical tomography of the central Pacific mantle using ScS reverberations and frequency‐dependent travel times

TL;DR: In this paper, a vertical tomogram is constructed for the mantle between Tonga and Hawaii using a complete Gaussian-Bayesian approach, using a data set comprising 304 ScS reverberation travel times with Frechet kernels computed by the paraxial ray approximation and 1122 frequency-dependent phase delays of turning and surface waves calculated by a normal-mode coupling algorithm.
Journal ArticleDOI

Genetic algorithms : an evolution from Monte Carlo methods for strongly non-linear geophysical optimization problems

TL;DR: It is shown that, in locating an optimal model, the new technique is far superior in performance to Monte Carlo techniques in all cases considered, and Monte Carlo integration is still regarded as an effective method for the subsequent model appraisal.
Journal ArticleDOI

Isotopic and chemical constraints on mantle-crust evolution

TL;DR: In this article, a growth curve for the continental crust is calculated on the basis of total inversion of the Sm-Nd isotopic data for all of Earth history and the curve suggests that by about 3.8 Ga ago, ~40% of the present continental volume was present.

Tomographic inversion in reflection seismology

TL;DR: In this paper, a least-squares optimization with a priori and step-length damping terms is proposed to deal with the unknown geometry of reflectors, which may be accomplished by a multiple-parameter class subspace method.
References
More filters
Book

Linear statistical inference and its applications

TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
Journal ArticleDOI

Uniqueness in the Inversion of Inaccurate Gross Earth Data

TL;DR: In this article, it was shown that a given set G of measured gross Earth data permits such a construction of localized averages, and if so, how to find the shortest length scale over which G gives a local average structure at a particular depth if the variance of the error in computing that local average from G is to be less than a specified amount.
Journal ArticleDOI

The general linear inverse problem - Implication of surface waves and free oscillations for earth structure.

TL;DR: In this paper, the discrete general linear inverse problem is reduced to a set of m equations in n unknowns and a linear combination of the eigenvectors of the coefficient matrix can be used to determine parameter resolution and information distribution among the observations.