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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Anisotropy of Earth's inner core intrinsic attenuation from seismic normal mode models
TL;DR: In this article, the Earth's normal modes were used to study the attenuation anisotropy of both compressional and shear waves in the inner core, and they found that for compressional waves, the North-South direction is both fast and more strongly attenuating.
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Stochastic inversion of P-to-S converted waves for mantle composition and thermal structure: methodology and application
TL;DR: This work was supported by a grant from the Swiss National Science Foundation (SNF) project 200021_159907 as discussed by the authors, and B. T. was funded by a delegation from the CNRS and the Conge pour Recherches et Conversion (CRUC) from the Universite de Lyon to visit the Research School of the Australian National University (ANU).
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Variations in melt emplacement beneath the northern East African Rift from radial anisotropy
TL;DR: In this paper, the authors determined shear velocity and radial anisotropy in the magmatically rifting northern East African Rift to determine the locus and orientation of melt, both on and off-rift.
Posted Content
Seismic Inversion and the Data Normalization for Optimal Transport.
Björn Engquist,Yunan Yang +1 more
TL;DR: This paper has shown that the quadratic Wasserstein distance from optimal transport is to prefer as misfit functional over the standard $L^2$ norm, and resolved a puzzling contradiction in the results.
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Tomographic inversion for P wave velocity structure beneath the northeastern Japan arc using local and teleseismic data
TL;DR: In this paper, the authors determined three-dimensional P wave velocity structure up to a depth of 296 km beneath northern Tohoku, Honshu, Japan, by inverting arrival times of local and teleseismic events simultaneously.
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.