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
Citations
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The 2000 Tottori earthquake: A shallow earthquake with no surface rupture and slip properties controlled by depth
TL;DR: In this article, the authors adopt a two-plane fault geometry based on aftershock distributions and analysis of close station records, and show that surface slip occurs close to the surface, which contradicts the absence of clear surface slip reported by geologists.
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Areas prone to slow slip events impede earthquake rupture propagation and promote afterslip.
Frédérique Rolandone,Frédérique Rolandone,Jean-Mathieu Nocquet,Jean-Mathieu Nocquet,Patricia Mothes,Paul Jarrin,Martin Vallée,Nadaya Cubas,Stephen Hernandez,M. Plain,Sandro Vaca,Yvonne Font +11 more
TL;DR: In this article, the authors used continuous GPS (Global Positioning System) measurements following the 2016 Mw (moment magnitude) 7.8 Ecuador earthquake reveal that large and rapid afterslip developed at discrete areas of the megathrust that had previously hosted slow slip events.
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Inversion of electromagnetic data: an overview of new techniques
TL;DR: In this paper, the authors explore some of the newer techniques for acquiring and inverting electromagnetic data, including model parameterization, first order sensitivities, and methods for setting up a linearized inversion.
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Generalized least-squares solutions to quasi-linear inverse problems with a priori information.
TL;DR: In this article, a quasi-linear inverse problem with a priori information about model parameters is formulated in a stochastic framework by using a singular value decomposition technique for arbitrary rectangular matrices.
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bh_tomo-a Matlab borehole georadar 2D tomography package
TL;DR: bh_tomo as mentioned in this paper is an open source 2D tomography software package developed at the Ecole Polytechnique of Montreal (EPoM) in Quebec, Canada.
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.