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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On the limits of linear moment tensor inversion of surface wave spectra
H. Dufumier,M. Cara +1 more
TL;DR: In this paper, some theoretical and practical limits to linear moment tensor inversion of surface waves are analyzed in detail, in particular when one or few stations are used for rapid determination of source parameters.
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Daily water stage estimated from satellite altimetric data for large river basin monitoring
Emmanuel Roux,Mathilde Cauhopé,Marie-Paule Bonnet,Stéphane Calmant,Philippe Vauchel,Frédérique Seyler +5 more
TL;DR: In this article, a methodology for obtaining time series with a one-day sampling period is proposed, based on a linear model exploiting data at a limited number of in situ limnimetric stations.
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Bayesian geological and geophysical data fusion for the construction and uncertainty quantification of 3D geological models
Hugo K.H. Olierook,Richard Scalzo,David Kohn,Rohitash Chandra,Rohitash Chandra,Ehsan Farahbakhsh,Chris D. Clark,Steven M. Reddy,R. Dietmar Müller +8 more
TL;DR: In this article, the Bayesian Obsidian software package is used to fuse lithostratigraphic field observations with aeromagnetic and gravity data to build a 3D model in a small region of the Gascoyne Province, Western Australia.
Journal ArticleDOI
Bayesian survey design to optimize resolution in waveform inversion
TL;DR: A Bayesian methodology for designing seismic experiments that optimally maximize model-parameter resolution for imaging purposes and a refinement of the algorithm minimizes the marginal uncertainties in a region of interest.
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Consequences of parametrization choices in surface wave inversion: insights from transdimensional Bayesian methods
Chao Gao,Vedran Lekic +1 more
TL;DR: In this article, a transdimensional Bayesian (TB) seismic inversion of surface wave data for crustal and upper-mantle structure is proposed to quantify model parameters uncertainties and trade-offs with fewer assumptions than traditional methods.
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.
Journal ArticleDOI
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.