Journal ArticleDOI
Generalized Nonlinear Inverse Problems Solved Using the Least Squares Criterion
Albert Tarantola,Bernard Valette +1 more
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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
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A coherent crust-mantle model for the uranium-thorium-lead isotopic system
TL;DR: In this article, the mean age of the continents is found to be 1.9 ± 0.4 Ga, with a corresponding spread of 1.2± 0.6 Ga and a negative skewness.
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Inferences of mantle viscosity based on ice age data sets: Radial structure
H. C. P. Lau,Jerry X. Mitrovica,Jacqueline Austermann,Ophelia Crawford,David Al-Attar,Konstantin Latychev +5 more
TL;DR: In this paper, the authors perform joint nonlinear inversions of glacial isostatic adjustment (GIA) data, including the following: postglacial decay times in Canada and Scandinavia, the Fennoscandian relaxation spectrum (FRS), late-Holocene differential sea level (DSL) highstands, and the rate of change of the degree 2 zonal harmonic of the geopotential, J2.
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Satellite radar interferometric map of the coseismic deformation field of the M = 6.1 Eureka Valley, California Earthquake of May 17, 1993
Didier Massonnet,Kurt L. Feigl +1 more
TL;DR: In this article, a composite interferogram of pairs of synthetic aperture radar (SAR) images acquired by the ERS-1 satellite before and after the Eureka Valley, California earthquake of May 17, 1993 maps the coseismic deformation field.
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Upper mantle S-wave speed heterogeneity and anisotropy beneath the North Atlantic from regional surface wave tomography: the Iceland and Azores plumes
TL;DR: In this paper, the authors presented a high-resolution velocity and azimuthal anisotropy model for the upper mantle beneath the North Atlantic and surrounding region derived from the analysis of over 3000 fundamental and higher mode Rayleigh waveforms.
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On the Abyssal Circulation in the Glacial Atlantic
Olivier Marchal,William B Curry +1 more
TL;DR: In this paper, an inverse method is used to evaluate the information contained in sediment data for the Atlantic basin during the Last Glacial Maximum (defined here as the time interval 18-21 kyr before present).
References
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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.