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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Earth's multi-scale topographic response to global mantle flow
David Davies,Andrew P. Valentine,Stephan C. Kramer,Nicholas Rawlinson,Mark Hoggard,Caroline M. Eakin,Cian R. Wilson +6 more
TL;DR: In this paper, a hierarchical Bayesian approach to perform spherical harmonic analysis of the residual topography power spectrum of the oceans is proposed. But the results are not consistent with the geological record.
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Fault creep and kinematics of the eastern segment of the Pernicana Fault (Mt. Etna, Italy) derived from geodetic observations and their tectonic significance
TL;DR: In this paper, two local geodetic networks were installed along the eastern segment of the Pernicana Fault, one of the most active structures in the geodynamic framework of the volcano.
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Solutions, algorithms and inter-relations for local minimization search geophysical inversion
TL;DR: In this article, the Tikhonov regularization solutions, the smoothest model solutions, and the subspace solutions are revealed, from which the interrelationships between these solutions can be revealed.
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Seismicity at Somma-Vesuvius and its implications for the 3D tomography of the volcano
TL;DR: In this article, a 3D tomographic image of the volcanic structure was obtained by inversion of first P and S arrival times of local earthquakes, showing the existence of a sharp velocity contrast along a lineation oriented NW-SE, cutting the crater along the line separating the relict of the Somma caldera from the southwest part of the volcano.
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Interhemispheric exchanges of mass and heat in the Atlantic Ocean in January–March 1993
TL;DR: In this article, the authors combined hydrographic, geochemical, and direct velocity measurements along two zonal (7.5°N and 4.4°S) and two meridional (35°W and 4°W) lines occupied in January-March, 1993 in the Atlantic are combined in an inverse model to estimate the circulation.
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.
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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.
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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.