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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Journal ArticleDOI
Determination of surface gravity anomalies using gradiometric observables
TL;DR: In this paper, the authors developed a new approach to obtain the best resolutions of mean gravity anomalies in terms of mean square errors, biases and error variances from the point of view of biased estimation.
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Local modification of the lithosphere beneath the central and western North China Craton : 3-D constraints from Rayleigh wave tomography
TL;DR: In this article, a 3D S-wave velocity model is constructed based on the phase velocity maps of 100 teleseismic events recorded by 208 broadband stations at 13 periods from 20 s to 143 s. The model is broadly consistent with the results of previous tomography studies, but shows more detailed variations within the lithosphere.
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A global shear velocity model of the upper mantle from fundamental and higher Rayleigh mode measurements
Eric Debayle,Yanick Ricard +1 more
TL;DR: In this article, the authors use an extension of the automated waveform inversion approach of Debayle (1999) which improves the mapping of the transition zone with extraction of fundamental and higher-mode information.
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Large-Sample Evaluation of Two Methods to Correct Range-Dependent Error for WSR-88D Rainfall Estimates
TL;DR: In this paper, the vertical profile of reflectivity (VPR) is estimated from volumetric radar data collected close to the radar and the second method takes into account the spatial variability of reflectivities and relies on solving an inverse problem in determination of the local profile.
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Inversion of massive surface wave data sets: Model construction and resolution assessment
Eric Debayle,Malcolm Sambridge +1 more
TL;DR: In this article, a Gaussian a priori covariance function controls the horizontal degree of smoothing in the inverted model, which minimizes some artifacts observed with spherical harmonic parameterizations.
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.