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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Special Section — Marine Controlled-Source Electromagnetic Methods 1D inversion and resolution analysis of marine CSEM data
Niels B. Christensen,Kevin Dodds +1 more
TL;DR: In this article, a simple empirical noisemode descriptor is proposed for a resistive layer buried at a depth of 1500-1600 m below the seafloor, where the uncertainty depends on the depth of burial and the thickness of the layer.
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A candidate secular variation model for IGRF-12 based on Swarm data and inverse geodynamo modelling
TL;DR: In this article, an initial geomagnetic field model centered around 20143 is first constructed, based on Swarm magnetic measurements, for both the main field and its instantaneous secular variation This initial model is next fed to an inverse geodynamo modelling framework in order to specify, for epoch 20143, the initial condition for the integration of a three-dimensional numerical dynamo model.
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Crustal structure beneath the Galápagos Archipelago from ambient noise tomography and its implications for plume‐lithosphere interactions
TL;DR: In this paper, a tomographic study using high-frequency Rayleigh waves obtained from cross correlations of ambient noise was conducted to constrain the seismic velocity structure of the crust beneath the Galapagos Archipelago.
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Atmospheric muons as an imaging tool
TL;DR: In this paper, the authors provide an introduction to this vibrant research area, starting from the physical principles at the basis of the methods and reviewing several recent developments in the application of muography methods to specific use cases, without any pretence of exhaustiveness.
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Stochastic inversion for electromagnetic geophysics: Practical challenges and improving convergence efficiency
TL;DR: In this paper, two Markov Chain sampling algorithms (Metropolis-Hastings and Slice Sampler) were used to evaluate the uncertainty of magnetotelluric and controlled source electromagnetic data, and the statistics of the stochastic inversion allow for better reveal the measurement sensitivities of the two different electromagnetic techniques than traditional techniques.
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.