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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Geochemistry and petrogenesis of the Lanzo peridotite body, western Alps
TL;DR: The plagioclase-lherzolite body of Lanzo (Italy Alps) is considered to be a residual piece of upper mantle, after MORB extraction as mentioned in this paper.
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Shear velocity structure and azimuthal anisotropy beneath eastern North America from Rayleigh wave inversion
TL;DR: In this article, the authors obtained shear velocity structure beneath the northeastern United States and southeastern Canada using Rayleigh wave phases and amplitudes and estimated the azimuthal dependence of phase velocity.
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Receiver function inversion by trans‐dimensional Monte Carlo sampling
TL;DR: In this article, a reversible jump Markov Chain Monte Carlo (MCMC) algorithm was proposed to solve the inverse problem of inferring 1-D subsurface elastic properties from teleseismic receiver function data.
Journal ArticleDOI
Complex lithospheric structure under the central Baltic Shield from surface wave tomography
Marianne Bruneton,Helle Pedersen,Véronique Farra,Nicholas Arndt,Pierre Vacher,U. Achauer,A. Alinaghi,J. Ansorge,Guenter Bock,W. Friederich,Marek Grad,A. Guterch,Pekka Heikkinen,S.E. Hjelt,Tellervo Hyvönen,J.-P. Ikonen,Eduard Kissling,K. Komminaho,Annakaisa Korja,Elena Kozlovskaya,M V Nevsky,Hanneke Paulssen,N. I. Pavlenkova,Jaroslava Plomerová,Tero Raita,O. Y. Riznichenko,Roland Roberts,S. Sandoval,I. Sanina,N. V. Sharov,Zaher Hossein Shomali,J. Tiikkainen,E. Wielandt,K. Wilegalla,J. Yliniemi,Y. G. Yurov +35 more
TL;DR: Complex lithospheric structure under the central Baltic Shield from surface wave tomography as discussed by the authors, which is the most similar to ours, was obtained by using wave-tomography.
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Stochastic model updating: Part 1—theory and simulated example
TL;DR: In this article, the theory of stochastic model updating using a Monte-Carlo inverse procedure with multiple sets of experimental results is explained and then applied to the case of a simulated three degree-of-freedom system, which is used to fix ideas and also to illustrate some of the practical limitations of the method.
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.
Journal ArticleDOI
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.