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 upper mantle degree 2: Constraints and inferences from global mantle wave attenuation measurements
TL;DR: In this article, an analysis of global lateral variations in anelasticity of the upper mantle, as measured from very long period Rayleigh waves observed on the GEOSCOPE network, is presented.
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Recent advances in optimized geophysical survey design
TL;DR: This review cites recent advances in statistical experimental design techniques applied in the earth sciences and reveals that a few optimally chosen frequencies offer as much subsurface information as the fullbandwidth.
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Hamiltonian Monte Carlo solution of tomographic inverse problems
TL;DR: The combination of HMC with adjoint techniques allows us to solve a fully nonlinear, probabilistic traveltime tomography with several thousand unknowns on a standard laptop computer, without any need for supercomputing resources.
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Seismic Modelling of the Earth's Large-Scale Three-Dimensional Structure
TL;DR: Several methods of seismic inversion and intercom pare the resulting models as mentioned in this paper, leading to a coherent picture of the Earth's internal heterogeneity, which can be used to explain some aspects of observed plate motion in terms of thermal convection in the mantle.
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On the use of an inverse shortest paths algorithm for recovering linearly correlated costs
D. Burton,Ph. L. Toint +1 more
TL;DR: This paper considers the inverse shortest paths problem where arc costs are subject to correlation constraints and a new method is proposed for solving this class of problems as a generalization of the algorithm presented in Burton and Toint (Mathematical Programming 53, 1992).
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.