Journal ArticleDOI
Occam's inversion; a practical algorithm for generating smooth models from electromagnetic sounding data
TLDR
In this article, the authors proposed a smoothest model which fits the data to within an expected tolerance for the inversion of both magnetotelluric and Schlumberger sounding field data.Abstract:
The inversion of electromagnetic sounding data does not yield a unique solution, but inevitably a single model to interpret the observations is sought. We recommend that this model be as simple, or smooth, as possible, in order to reduce the temptation to overinterpret the data and to eliminate arbitrary discontinuities in simple layered models.To obtain smooth models, the nonlinear forward problem is linearized about a starting model in the usual way, but it is then solved explicitly for the desired model rather than for a model correction. By parameterizing the model in terms of its first or second derivative with depth, the minimum norm solution yields the smoothest possible model.Rather than fitting the experimental data as well as possible (which maximizes the roughness of the model), the smoothest model which fits the data to within an expected tolerance is sought. A practical scheme is developed which optimizes the step size at each iteration and retains the computational efficiency of layered models, resulting in a stable and rapidly convergent algorithm. The inversion of both magnetotelluric and Schlumberger sounding field data, and a joint magnetotelluric-resistivity inversion, demonstrate the method and show it to have practical application.read more
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Book
Parameter estimation and inverse problems
TL;DR: "Parameter Estimation and Inverse Problems, 2/e" introduces readers to both Classical and Bayesian approaches to linear and nonlinear problems with particular attention paid to computational, mathematical, and statistical issues related to their application to geophysical problems.
Journal ArticleDOI
Occam's inversion to generate smooth, two-dimensional models from magnetotelluric data
TL;DR: In this paper, the authors propose an extension of the existing 1-D algorithm, Occam's inversion, to smooth 2-D models using an extension to the existing Occam inversion.
Journal ArticleDOI
Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion
William Rodi,Randall L. Mackie +1 more
TL;DR: In this article, a nonlinear conjugate gradients (NLCG) algorithm was proposed to minimize an objective function that penalizes data residuals and second spatial derivatives of resistivity.
Journal ArticleDOI
Geophysical inversion with a neighbourhood algorithm—II. Appraising the ensemble
TL;DR: In this paper, a Monte Carlo direct search method is used to estimate the information in the available ensemble to guide a resampling of the parameters of the model space, which can be used to obtain measures of resolution and trade-off in the model parameters.
References
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A practical guide to splines
TL;DR: This book presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines as well as specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting.
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History of Western Philosophy
TL;DR: The History of Western Philosophy (HOWP) as mentioned in this paper is one of the most popular philosophy books of the 20th century and is the most important philosophical work of all time.
Journal ArticleDOI
Joint Inversion of Geophysical Data
K. Vozoff,David L.B. Jupp +1 more
TL;DR: In this paper, the combination of DC resistivity and magnetotelluric measurements on a layered medium is proposed to resolve the resistivity of the thin resistive second layer, even though neither of the two methods can do so alone.
Related Papers (5)
Occam's inversion to generate smooth, two-dimensional models from magnetotelluric data
Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion
William Rodi,Randall L. Mackie +1 more