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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Several location methods for underwater shots in the Gulf of Genoa (Western Mediterranean): Structural implications
TL;DR: In this paper, 50 underwater shots were detonated on a N-S section through the Gulf of Genoa running from the northern margin (44.12°N) towards Corsica (42.90°N), along the 9°E meridian.
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On a more rigorous approach to geothermic problems
A.E. Beck,P.Y. Shen +1 more
TL;DR: In this paper, the authors consider the correction of drilling disturbance in the estimation of bottom hole temperatures (BHTs), which are increasingly being used to estimate heat flow density (HFD), temperature, thermal conductivity and heat production.
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An inverse problem for the determination of the stress tensor from polyphased fault sets and earthquake focal mechanisms
TL;DR: In this article, a new method for determining the stress tensor from fault slip data is presented, which is obtained by minimizing the deviation between the stress ratio and a value corresponding to the maximum of a probability density function.
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A practical sequential lexicographic approach for derivative-free black-box constrained optimization
TL;DR: This study describes a cost-effective approach to performing engineering optimization problems involving models that might not exhibit the necessary smoothness to warrant efficient use of gradient algorithms, and demonstrates the performance advantage of the proposed method over traditional methods.
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Source estimation for wavefield-reconstruction inversion
TL;DR: A source-estimation technique specifically designed for WRI that considers the source functions as unknown variables and arrives at an objective function that depends on the medium parameters, wavefields, and source functions, and achieves accurate estimates of the unknown medium 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.
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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.