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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Book ChapterDOI
Near-Surface Controlled-Source Electromagnetic Induction
Mark E. Everett,Max A. Meju +1 more
Abstract: The controlled-source electromagnetic (CSEM) induction method is emerging as a leading geophysical technique in hydrogeological studies. However, the technique is quite often misunderstood compared to other common techniques of applied geophysics: namely, seismic reflection and refraction, magnetics, gravity, and ground-penetrating radar (GPR). In this chapter we review the fundamental physical principles behind the CSEM prospecting technique, with emphasis on near-surface applications, and present some recent advances in this field that have been made by the authors. CSEM methods are defined here to be those in which the experimenter has knowledge of and control over the electromagnetic field transmitted into the ground and hence excludes magnetotellurics, related natural-source methods, and the various uncontrolled-source methods involving, for example, radio transmissions.
Journal ArticleDOI
The problem of heat flow density determination from inaccurate data
TL;DR: In this article, the authors present an inverse method for processing rough data from oil wells in order to evaluate the heat flow density and its standard deviation, assuming that the evaluations of temperatures and thermal resistivities present gaussian uncertainties.
Journal ArticleDOI
A comparison of cratonic roots through consistent analysis of seismic surface waves
TL;DR: In this paper, four cratonic regions are compared using existing dispersion curves and inverting these curves with an identical inversion method and parametrization, and the results show that the less physically-based models of constant shear velocity provide a better fit to the data for all of the areas; a low velocity zone in the deep lithosphere or below the lithosphere is resolved beneath the Kaapvaal while the three other areas have no such low velocity zones.
Journal ArticleDOI
Wavelength dependence of scattering properties in the VIS–NIR and links with grain-scale physical and compositional properties
Cedric Pilorget,Cedric Pilorget,J. Fernando,J. Fernando,Bethany L. Ehlmann,Bethany L. Ehlmann,Frédéric Schmidt,Frédéric Schmidt,Takahiro Hiroi +8 more
TL;DR: In this article, the phase function of a granular material is affected by both the absorptivity and the external and internal structure of the grains, from the millimeter scale down to the wavelength scale.
Journal ArticleDOI
Depth Extent and Kinematics of Faulting in the Southern Tanganyika Rift, Africa
Aude Lavayssière,C. Drooff,Cynthia Ebinger,R. J. Gallacher,R. J. Gallacher,Finnigan Illsley-Kemp,Finnigan Illsley-Kemp,S. J. C. Oliva,Derek Keir,Derek Keir +9 more
TL;DR: The TANG14 array was deployed in the southern Tanganyika rift, where earthquakes of magnitude up to 7.4 have occurred, to probe crust and upper mantle structure and evaluate fault kinematics as discussed by the authors.
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.