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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Journal ArticleDOI
European emissions of halogenated greenhouse gases inferred from atmospheric measurements.
Christoph A. Keller,Matthias Hill,Martin K. Vollmer,Stephan Henne,Dominik Brunner,Stefan Reimann,Simon O'Doherty,Jgor Arduini,Michela Maione,Zita Ferenczi,László Haszpra,Alistair J. Manning,Thomas Peter +12 more
TL;DR: This study demonstrates the large benefits of adding a strategically well placed measurement site to the existing European observation network of halocarbons, as it extends the coverage of the inversion domain toward Eastern Europe and helps to better constrain the emissions over Central Europe.
Journal ArticleDOI
Review of the Generalized Least Squares Method
TL;DR: The generalized least squares (GLS) method as mentioned in this paper uses both data and prior information to solve for a best-fitting set of model parameters, and it has been shown that the covariance of the model depends on both the uncertainty in the data and the prior information.
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Anisotropy of the asthenosphere: The higher mode data of the Pacific revisited
M. Cara,J. J. Lévêque +1 more
TL;DR: In this article, the Love-wave phase-velocities were used to constrain upper mantle anisotropy in the Pacific Ocean and it was shown that the bottom of the anisotropic layer has been reached around 250 km.
Journal ArticleDOI
Deriving century‐long trends of surface temperature change from borehole temperatures
TL;DR: In this paper, a few-parameter estimation (FPE) technique was employed to derive information on past surface temperature variations from present-day borehole temperatures, which can separate reasonably well information on century-long trends of surface temperature change from borehole temperature within a wide range of noise levels.
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Efficient full decay inversion of MRS data with a stretched-exponential approximation of the T2* distribution
Ahmad A. Behroozmand,Esben Auken,Gianluca Fiandaca,Gianluca Fiandaca,Anders Vest Christiansen,Anders Vest Christiansen,Niels B. Christensen +6 more
TL;DR: In this article, a new inversion scheme is presented in which the entire data set is used, and the multi-exponential behaviour of the NMR signal is approximated by the simple stretched-Exponential approach.
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.