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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Spatial distribution of turn-of-the-century seismicity along the Alaska-Aleutian Arc
Thomas M. Boyd,Arthur Lerner-Lam +1 more
TL;DR: In this article, the authors used a modified least square criterion to estimate the location of earthquakes with surface-wave magnitudes above 6.8 in the Alaska-Aleutian Arc.
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Geochemistry of basic dikes in the Lanzo massif (Western Alps): Petrogenetic and geodynamic implications
TL;DR: The Alpine peridotite massif of Lanzo (Italy) contains three generations of basic dikes (gabbros and basalts) which were probably generated during a dynamic melting of a rising mantle diapir as mentioned in this paper.
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Multivariate statistical analysis and partitioning of sedimentary geochemical data sets: General principles and specific MATLAB scripts
TL;DR: In this article, the authors present an annotated MATLAB script for Q-mode factor analysis, a constrained least squares multiple linear regression technique, and a total inversion protocol based on the well-known approaches taken by Dymond (1981), Leinen and Pisias (1984), Kyte et al. (1993), and their predecessors.
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Underground structure defect detection and reconstruction using crosshole GPR and Bayesian waveform inversion
TL;DR: In this paper, the FDTD-DCT-DREAM (ZS) framework is used to detect and locate weakness zones in underground concrete structures using a finite-difference time-domain (FDTD) simulator and discrete cosine transform (DCT) method.
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Simultaneous determination of the three-dimensional crustal structure and hypocenters beneath the Kanto—Tokai District, Japan
TL;DR: In this article, the velocity structure is modelled by a hyperbolic function (tanh) and the configuration of each interface is expressed in a series of Chebyshev functions with coefficients which are unknown parameters.
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.