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
Rupture history of September 30, 1999 intraplate earthquake of Oaxaca, Mexico (MW=7.5) from inversion of strong-motion data
B. Hernandez,Nikolai M. Shapiro,Shri Krishna Singh,Javier F. Pacheco,Fabrice Cotton,Michel Campillo,Arturo Iglesias,V. Cruz,Juan Martín Gómez,L. Alcántara +9 more
TL;DR: In this paper, two focal mechanisms (Harvard and NEIC CMT solutions) were tested for the source geometry of the 1999 Oaxaca, Mexico earthquake and the inversion results showed that the rupture mainly propagated from ESE to WNW and slightly downdip with an average rupture velocity of about 3 km/s.
Journal ArticleDOI
Multiscale inference of matter fields and baryon acoustic oscillations from the Lyα forest
TL;DR: In this paper, a multiscale, nonlinear, two-step approach is proposed for the reconstruction of the cosmological large-scale struc- ture based on multiple Lyforest spectra.
Journal ArticleDOI
The reconstruction of a band-limited function and its Fourier transform from a finite number of samples at arbitrary locations by singular value decomposition
TL;DR: The singular value decomposition (SVD) method is used to provide a series expansion that, in contrast to the method of sampling functions, permits simple identification of vectors in the minimum-norm space poorly represented in the sample values.
Journal ArticleDOI
Uncertainty estimates in geomagnetic field modeling
TL;DR: In this paper, an extension of the conventional uncertainty analysis which characterizes the sources of uncertainty in the coefficients of the geomagnetic field models is presented, which accounts for the systematic errors introduced by the omission of such sources as the presence of crustal fields, the external fields, and the field from the truncated terms.
Journal ArticleDOI
Crustal structure across the transition from rifting to spreading: the Woodlark rift system of Papua New Guinea
TL;DR: In this paper, the role of magmatism prior to the onset of seafloor spreading is investigated in the Woodlark rift system, where the authors observe three main structures.
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.