Journal ArticleDOI
Generalized Nonlinear Inverse Problems Solved Using the Least Squares Criterion
Albert Tarantola,Bernard Valette +1 more
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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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The use of multipulse zero lag data to improve incoherent scatter radar power profile accuracy
S Lehtinen Markku,Asko Huuskonen +1 more
TL;DR: This paper shows that multipulse zero lag information can be combined with the information from separate power profile channels leading to a significant improvement in the power profile estimate accuracy.
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Re-evaluation of Seismic Intensities and Relocation of 1969 Saint Vincent Cape Seismic Sequence: A Comparison with the 1755 Lisbon Earthquake
Elisa Buforn,Carolina López-Sánchez,Lucía Lozano,José Manuel Martínez-Solares,Simone Cesca,Carlos Augusto Fernandes de Oliveira,Agustín Udías +6 more
TL;DR: In this article, a 3D crustal velocity model for the Gulf of Cadiz region and a non-linear probabilistic location methodology were used to plot a new intensity map for the whole region affected by the 1969 Lisbon earthquake.
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Multifractal topography of several planetary bodies in the Solar System
TL;DR: In this paper, the authors use the multifractal approach to describe fields of topography, including height and slopes and other statistical moments of the field, taking into account the scale invariance.
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Inversion of ERT data with a priori information using variable weighting factors
TL;DR: In this article, a new way of introducing prior information regarding known resistivity distribution within the inversion procedure is proposed, where the prior information is introduced as an extra term into the objective function of the resistivity inverse problem which is minimized via the Lagrangian multiplier technique.
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Two‐dimensional inverse modeling of crustal thermal regime with application to East European geotraverses
P. Y. Shen,Kelin Wang,A.E. Beck +2 more
TL;DR: In this article, a Bayesian inverse formulation is employed for the estimation of heat flow density and temperature in the form of a joint Gaussian probability density function and a posteriori covariance matrix for the model parameters.
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.