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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Noise-based monitoring and imaging of aseismic transient deformation induced by the 2006 Basel reservoir stimulation
TL;DR: In this article, the authors analyzed the time-dependent properties of the ambient seismic wavefield between 0.1 and 8 Hz to detect, resolve, monitor, and image the deformation induced by the water injection associated with the stimulation of the 2006 Deep Heat Mining Project in the city of Basel, Switzerland.
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Anisotropic tomography of the Atlantic Ocean
TL;DR: In this paper, the authors presented the first regional 3D model of the Atlantic Ocean with anisotropy, derived from Rayleigh and Love wave phase velocity measurements, from the Moho down to 300 km depth with a lateral resolution of about 500 km.
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Elemental weathering fluxes and saprolite production rate in a Central African lateritic terrain (Nsimi, South Cameroon)
Jean-Jacques Braun,Jean-Jacques Braun,Jean-Christophe Maréchal,Jean Riotte,Jean Riotte,Jean-Loup Boeglin,Jean-Pierre Bedimo Bedimo,Jules Remy Ndam Ngoupayou,Brunot Nyeck,Henri Robain,Murapaka Chandra Sekhar,Stéphane Audry,Jérôme Viers +12 more
TL;DR: In this article, a comparison between contemporary and long-term weathering has been carried out in the Small Experimental Watershed (SEW) of Nsimi, South Cameroon in order to quantify the export fluxes of major and trace elements and the residence time of the lateritic weathering cover.
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Explicit expressions and numerical calculations for the Fréchet and second derivatives in 2.5D Helmholtz equation inversion
Zhou Bing,Greenhalgh +1 more
TL;DR: In this paper, the authors developed a method to compute the relevant derivatives for 2.5D resistivity and acoustic velocity inversion in order to perform resistivity imaging or sensitivity analysis of geophysical data.
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The ammonia–water system at high pressures: Implications for the methane of Titan
Olivier Grasset,J. Pargamin +1 more
TL;DR: In this paper, the behavior of methane within Titan is investigated using both data on methane clathrate stability and data on the ammonia-water system, which provides new constraints on the temperature and composition fields within the liquid layer of Titan.
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.