Inverse theories

The classical computer tomography (CT), including the medical one, has already been demonstrated its efficiency in many practical applications. At the same time, the request of the all-round survey of the object, which is usually unattainable, makes it important to find alternative approaches with less rigid restrictions to the number of projections and accessible views for observation. In the last time, it was understood that one effective way to withstand the extreme lack of data is to introduce a priori knowledge based upon classical inverse theory (including Maximum Entropy Method (MEM)) of the solution of ill-posed problems [1-6]. As shown in [6] for objects with binary structure, the necessary number of projections to get the quality of image restoration compared to that of CT using multistep reconstruction (MSR) method did not exceed seven and eould be reduced even further. 

William Menke. Geophysical Data Analysis Discrete Inverse Theory, Revised Edition. 1989 S. George Philander. El Nino, La Nina, and the Southern Oscillation. 1990 Robert A. Brown. Fluid Mechanics of the Atmosphere. 

V.P. Dimri - Deconvolution and Inverse Theory-Application to Geophysical Problems... 

M.S. Zhdanov - Geophysical Inverse Theory and Regularization Problems... 

A. Ben-Israel and T. N. Greville, Generalised Inverses Theory and Applications (Wiley-Interscience, 1974). 

In short, geochemical kineticists do not have the luxury of chemical kineticists and must deal with real-world and more complicated systems. Geochemists developed the theories and concepts to deal with inverse kinetic problems, reaction kinetics during cooling, and other geologically relevant questions. These new scopes, especially the inverse theories, reflect the special need of Earth sciences, and make geochemical kinetics much more than merely chemical kinetic theories applied to Earth sciences. 

Lasaga A.C. and Jiang J. X. (1995) Thermal history of rocks P-T-t paths from geospeedo-metry, petrologic data, and inverse theory techniques. Am. J. Sd. 295, 697-741. 

Hensel E (1991) Inverse theory and application for engineers. Prentice-Hall, Englewood Cliffs, New Jersey... 

Woodbury AD, Ulrych TJ (1996) Minimum relative entropy inversion theory and application to recovering the release history of groundwater contaminant. Water Resour Res 32 2671-2681... 

The last question of solution stability is a critical one in inversion theory as well. In fact, geophysical data are always contaminated by some noise (5d. The question is whether the difference in the responses for different models is larger than the noise level. For example, let two different models, mi and mg, and two different sources, Si and Sg, generate two different data sets, d] and dg, which can be expressed schematically as follows ... 

Another critical problem of inversion theory is instability. This problem reflects the practical fact that two observed data sets could differ only within the noise level, while the corresponding model parameter distributions could be completely different. 

Zhdanov, M. S., 1993, Tutorial regularization in inversion theory CWP-136, Colorado School of Mines, 47 pp. 

Menke, W., 1989, Geophysical data analysis Discrete inverse theory Academic Press, Inc., San Diego, 289 pp. 

In this Chapter I will introduce the basic equations governing the electromagnetic field in inhomogeneous conductive media, and review the basic physical laws important in developing electromagnetic inverse theory. 

By full analogy with the electromagnetic case, one can consider different ways of introducing the reflectivity coefficient A. In particular, two of these solutions play an important role in inversion theory. One is the so-called quasi-analytical (QA) solution, and the other is the localized quasi-linear (LQL) approximation. In this section I will introduce the QA approximation for the acoustic wavefield. 

We give below several additional definitions which play an important role in inversion theory. 

VP. DIMRI — DECONVOLUTION AND INVERSE THEORY - APPLICATION TO GEOPHYSICAL PROBLEMS... 

A.A. KAUFMAN AND P.A. EATON — THE THEORY OF INDUCTIVE PROSPECTING A.A. KAUFMAN AND P. HOEKSTRA — ELECTROMAGNETIC SOUNDINGS M.S. ZHDANOV AND P.E. WANNAMAKER —THREE-DIMENSIONAL ELECTROMAGNETICS M.S. ZHDANOV — GEOPHYSICAL INVERSE THEORY AND REGULARIZATION PROBLEMS... 

A more dramatic turning point for the Kirkwood-BufF theory occurred in 1978 after the publication of the inversion of the Kirkwood-BufF theory (Ben-Naim 1978). Symbolically, the inversion theory may be written as... 

These illustrative calculations have been carried out with a very simple inversion procedure based on Ecp (30). Rapid recent developments in the application inverse theory offer several possibilities Ibr improvement. First, the use of singular-value decomposition as a formal inversion framework (e. g.. Press et al, 1992)... 

M.S. ZHDANOV —GEOPHYSICAL INVERSE THEORY AND REGULARIZATION PROBLEMS... 

Phase inversion Theory viscosity ratio dependence Utracki, 1991... 

Menke W (1984) Geophysical Data Analysis Discrete Inverse Theory. San Diego, CA Academic Press. 

Vol. 1906 T. Schuster, The Method of Approximate Inverse Theory and Applications (2007)... 

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