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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Volume budget of the eastern boundary layer off the Iberian Peninsula
J.P. Mazé,M. Arhan,H. Mercier +2 more
TL;DR: In this paper, a hydrographic array carried out in 1989 offshore of the Iberian Peninsula is used to determine the vertical distribution of zonal transports near the ocean eastern boundary (the so-called eastern boundary kinematic condition).
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Regolith mass balance inferred from combined mineralogical, geochemical and geophysical studies: Mule Hole gneissic watershed, South India
Jean-Jacques Braun,Marc Descloitres,Jean Riotte,Simon Fleury,Laurent Barbiero,Jean-Loup Boeglin,Aurélie Violette,Eva Lacarce,Laurent Ruiz,Muddu Sekhar,M. S. Mohan Kumar,S. Subramanian,Bernard Dupré +12 more
TL;DR: In this article, the authors proposed a method to assess the long-term chemical weathering mass balance for a regolith developed on a heterogeneous silicate substrate at the small experimental watershed scale by adopting a combined approach of geophysics, geochemistry and mineralogy.
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Permanent tremor of Masaya Volcano, Nicaragua: Wave field analysis and source location
TL;DR: In this article, the authors used both a cross-spectrum method and a correlation method to determine the wave delay time between the reference station and the other stations of an array and to quantify the wave field.
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Quantifying absolute water content of minerals using near-infrared reflectance spectroscopy
TL;DR: In this article, the relationship between absolute water content and water-related absorptions was quantified using common band parameters (e.g., band depth and mean optical path length).
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Finite-frequency Rayleigh wave tomography of the western Mediterranean: Mapping its lithospheric structure
Imma Palomeras,S. Thurner,Alan Levander,K. Liu,Antonio Villaseñor,Ramón Carbonell,Mimoun Harnafi +6 more
TL;DR: In this paper, a 3D shear wave velocity model for the crust and upper mantle of the western Mediterranean from Rayleigh wave tomography was presented, where the authors analyzed the fundamental mode in the 20-167 s period band (6.0-50.0 mHz) from earthquakes recorded by a number of temporary and permanent seismograph arrays.
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.
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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.