Journal ArticleDOI
Generalized Nonlinear Inverse Problems Solved Using the Least Squares Criterion
Albert Tarantola,Bernard Valette +1 more
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
Citations
More filters
Journal ArticleDOI
A comparative study of inverse methods for estimating climatic history from borehole temperature data
TL;DR: In this article, the authors compared three least squares methods: functional space inversion, spectrum inversion and singular value decomposition (SVD) based on the theory of 1-D heat conduction in a layered medium.
Journal ArticleDOI
A Bayesian criterion for simplicity in inverse problem parametrization
TL;DR: In this article, a Bayesian model selection criterion is proposed to rank different parametrizations from their posterior probability for a given set of geophysical measurements, which is computed using Bayes' rule.
Journal ArticleDOI
Elastic models for the magma intrusion associated with the 2000 eruption of Usu Volcano, Hokkaido, Japan
TL;DR: In this article, the authors review three different elastic models commonly used in volcano-geodesy (sphere, fault system, fissure zone) and invert the high-quality data using each of these models.
Journal ArticleDOI
Incipient hydration of mantle lithosphere at ridges: A reactive-percolation experiment
TL;DR: In this article, a reactive percolation experiment was conducted by injecting seawater into a permeable olivine aggregate at 190 °C and 19 MPa to explore the relationships between hydration reactions and hydrodynamic properties during the onset of serpentinization in the ultramafic lithosphere exposed at mid-ocean ridges.
Journal ArticleDOI
A Simulation Study of Smoothness Methods In Recovery of Regional Gravity Fields
Peiliang Xu,Reiner Rummel +1 more
TL;DR: In this paper, the authors investigate large-sample properties of some smoothness estimators in terms of mean-square error and bias problems, the best and worst performances, and the statistical properties of ridge parameters.
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
Linear Statistical Inference and Its Applications.
Journal ArticleDOI
Uniqueness in the Inversion of Inaccurate Gross Earth Data
George E. Backus,Freeman Gilbert +1 more
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.