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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The three‐dimensional shear velocity structure of the mantle from the inversion of body, surface and higher‐mode waveforms
TL;DR: In this article, a 3D model of shear heterogeneity in the whole mantle, derived from the inversion of hand-picked body, surface and higher-mode waveforms, is presented.
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Lithospheric layering in the North American craton
Huaiyu Yuan,Barbara Romanowicz +1 more
TL;DR: It is shown that changes in the direction of azimuthal anisotropy with depth reveal the presence of two distinct lithospheric layers throughout the stable part of the North American continent and suggests that the horizon detected in receiver function studies probably corresponds to the sharp mid-lithospheric boundary rather than to the more gradual lithosphere–asthenosphere boundary.
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Global mantle shear velocity model developed using nonlinear asymptotic coupling theory
Xiang-Dong Li,Barbara Romanowicz +1 more
TL;DR: In this article, a three-dimensional shear velocity model of the whole mantle was developed using S H waveform data, which is expressed horizontally in terms of spherical harmonics up to degree 12, and vertically in terms with Legendre polynomials up to degrees 5 and 7 in the upper and lower mantle, respectively.
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Linearized inversion of seismic reflection data
TL;DR: In this article, the authors give the solution of the inverse problem in seismic exploration using the Kirchhoff migration and the circle summation model, which can be obtained using an iterative algorithm.
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The anisotropic structure of the upper mantle in the Pacific
TL;DR: In this article, anisotropic inversions of surface wave data show that the variations in vertical shear velocity, pv, and anisotropy of the oceanic upper mantle in the Pacific are much smoother and more systematic functions of the age of the seafloor than has been reported in previous studies.
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.