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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Deciphering the Trace Element Characteristics in Kilbourne Hole Peridotite Xenoliths: Melt–Rock Interaction and Metasomatism beneath the Rio Grande Rift, SW USA
Jason Harvey,Jason Harvey,Masako Yoshikawa,Samantha J. Hammond,Kevin W. Burton,Kevin W. Burton,Kevin W. Burton +6 more
TL;DR: In this article, major and trace element and isotope data for variably metasomatized bulk-rock peridotites from spinel lherzolite and harzburgite xenoliths from the Kilbourne Hole volcanic maar was presented.
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SIPPI: A Matlab toolbox for sampling the solution to inverse problems with complex prior information
TL;DR: A generic toolbox for Matlab and Gnu Octave called SIPPI is presented that implements a number of methods for solving such probabilistically formulated inverse problems by sampling the a posteriori probability density function.
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A comparison of five different analyses in the interpretation of five borehole temperature data sets
A.E. Beck,Po Yu Shen,Hugo Beltrami,Jean-Claude Mareschal,Jan Šafanda,M.N. Sebagenzi,G. Vasseur,Kelin Wang +7 more
TL;DR: In this article, the effectiveness of various methods in inferring ground surface temperature history (GSTH) from perturbed borehole temperature data, five synthetic and real data sets were prepared and disseminated to interested groups for analysis.
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Uniqueness and Lipschitz stability of an inverse boundary value problem for time-harmonic elastic waves
TL;DR: In this article, the inverse problem of determining the Lame parameters and the density of a three-dimensional elastic body from the local time-harmonic Dirichlet-to-Neumann map is considered.
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Robust elastic frequency‐domain full‐waveform inversion using the L1 norm
TL;DR: In this article, the L1 norm has been used for frequency-domain full-waveform inversion of weakly redundant data in the presence of noisy multi-component seismic data and the L2 norm is shown to be highly sensitive to non-Gaussian errors in the data and gives rise to high amplitude artifacts in the reconstructed models.
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.