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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Seismicity, active faults and stress field of the North Muya Region, Baikal Rift: New insights on the rheology of extended continental lithosphere
Jacques Déverchère,Frédérique Houdry,Natalia V. Solonenko,Alexandre V. Solonenko,Vladimir San'kov +4 more
TL;DR: In this article, the authors presented the overall seismotectonic setting of the north Muya region, which is an along-strike transfer zone between two en echelon dip-slip fault systems, using both regional and local seismological networks, and the single-event focal mechanisms of 704 earthquakes recorded during 3 years, including the main period of activity of a very dense cluster, the Angarakan swarm.
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Retrieval of absolute thermospheric concentrations from the far UV dayglow: An application of discrete inverse theory
R. R. Meier,J. M. Picone +1 more
TL;DR: In this paper, a model based on the maximum likelihood method of nonlinear discrete inverse theory was proposed to extract information on the state of the thermosphere from limb scans of the dayglow.
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Stochastic inversion for scaling geology
TL;DR: In this paper, it was shown that the power spectra of these geophysical variables obey a scaling law, i.e., the power spectrum of a scaling variable is proportional to some power of the frequency, and that frequency-dependent noise models are more appropriate for modelling the spatial variation of geophysical parameters than the widely assumed white noise (frequency-independent) model.
Journal ArticleDOI
Amplitude and phase data inversions for phase velocity anomalies in the Pacific Ocean basin
Kiyoshi Yomogida,Keiiti Aki +1 more
TL;DR: In this article, phase data inversions are conducted assuming great circle paths so that the phase discrepancies are reduced to less than T. This procedure is essential for later inversions using amplitude data.
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Displacement field and fault model for the September 7, 1999 Athens Earthquake inferred from ERS2 Satellite radar interferometry
Charalampos Kontoes,Panagiotis Elias,Olga Sykioti,Pierre Briole,Dominique Remy,Maria Sachpazi,G. Veis,Ioannis Kotsis +7 more
TL;DR: In this article, a moderate (Mw=59) normal faulting earthquake occurred in the northwest of Athens (Hellas) causing heavy damages and casualties using interferometric combinations of ERS2 SAR images.
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.