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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Lower mantle high-velocity zone beneath the kurils as inferred from p-wave travel time and amplitude data
TL;DR: In this article, travel time and amplitude data for teleseismic P-waves from intermediate and deep earthquakes in the Kurils were used to detect a high-velocity zone in the lower mantle beneath the Okhotsk Sea.
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Depth-to-the-bottom optimization for magnetic data inversion: Magnetic structure of the Latium volcanic region, Italy
TL;DR: In this paper, a Tikhonov regularization of the solution is introduced as a depthweighting function adapted from Li and Oldenburg (1996) to close the source toward the bottom.
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New constraints from seismology and geodesy on the Mw = 6.4 2008 Movri (Greece) earthquake: evidence for a growing strike-slip fault system
A. Serpetsidaki,Panagiotis Elias,Maya Ilieva,Maya Ilieva,Pascal Bernard,Pierre Briole,Anne Deschamps,S. Lambotte,S. Lambotte,Hélène Lyon-Caen,E. Sokos,G-Akis Tselentis +11 more
TL;DR: In this article, aftershocks from the 2008 Mw = 6.4 Movri earthquake were combined with GPS measurements of an already existing geodetic network in the area performed just after the earthquake, as well as with SAR interferograms, together with already published source studies, in order to refine already proposed models of this event.
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Formation temperatures determined from stochastic inversion of borehole observations
TL;DR: In this paper, a 1-D conductive finite element model and an inverse procedure for parameter estimation is proposed to estimate the equilibrium formation temperature in the North Sea Central Graben.
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Covariance-constrained difference inversion of time-lapse electrical resistivity tomography data
TL;DR: In this article, the covariance-constrained inversion (CCI) was applied to the time-lapse electrical resistivity tomography (ERT) inverse problem.
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.