Journal ArticleDOI
Generalized Nonlinear Inverse Problems Solved Using the Least Squares Criterion
Albert Tarantola,Bernard Valette +1 more
Reads0
Chats0
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
More filters
Journal ArticleDOI
The Shape and Internal Structure of the Moon from the Clementine Mission
TL;DR: Global topographic and gravitational field models derived from data collected by the Clementine spacecraft reveal a new picture of the shape and internal structure of the moon, indicating that the structure and thermal history of the Moon are more complex than was previously believed.
Journal ArticleDOI
A Fast and Reliable Method for Surface Wave Tomography
TL;DR: In this paper, the authors describe a method to invert regional or global scale surface-wave group or phase-velocity measurements to estimate 2-D models of the distribution and strength of isotropic and azimuthally anisotropic velocity variations.
Journal ArticleDOI
Whole-mantle radially anisotropic shear velocity structure from spectral-element waveform tomography
TL;DR: In this paper, a hybrid waveform-inversion approach was employed to combine the accuracy and generality of the spectral finite element method (SEM) for forward modeling of the global wavefield, with non-linear asymptotic coupling theory for efficient inverse modelling.
Journal ArticleDOI
Distance metrics and band selection in hyperspectral processing with applications to material identification and spectral libraries
TL;DR: This paper derives a technique called band add-on (BAO) that iteratively selects bands to increase the angular separation between two spectra and demonstrates that band selection can improve the discrimination of very similar targets, while using only a fraction of the available spectral bands.
Journal ArticleDOI
Optimization of endmembers for spectral mixture analysis
TL;DR: In this paper, the spectral endmembers are derived from the image data subject to a set of user-defined constraints, which are applied to the basic mixing equations, and then solved iteratively to derive a subset of spectral end members that can be used to solve the residual error.
References
More filters
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.