Inverse problems of electromagnetic geophysical fields
In the introduction, the author briefly surveys the methods which may be used in electro prospecting. There are four chapters in the book. The first discusses the application of the so-called artificial magnetization method (MAM) to two-dimensional problems. In this the author points out that different approaches have to be taken according as to whether demagnetization exists or not. He then poses MAM problems in terms of complex variables and Cauchy-type integrals. A general theoretical inverse problem (TIP) is set up which can be solved exactly, whereas generally a least squares process is necessary. The concept of weak uniqueness is introduced and a discussion is also given of the SQ variation process. The second chapter deals with effective algorithms taking account of demagnetization. Amongst the topics covered are an integral equation approach, solution of an integral equation of the second kind where the parameter is near the first eigenvalue and the representation of Ore bodies by equivalent ellipsoids. In the third chapter, the author discusses some algorithms for the solution of three-dimensional inverse problems. The method of artificial magnetization is introduced, and an algorithm is given for fields within a stellar body, involving the minimization of a functional involving a parameter. Spread currents are discussed and examples of the use of two-stage methods are given. The fourth chapter is entitled explicit equations for inverse problems of electromagnetic field. This is mainly standard electromagnetic theory associated with the Stratton-Chu formula and its consequences, and an algorithm is given for solving the TIP equations for a class of stellar bodies. Each chapter is followed by a number of diagrams (it would be better these were in the relevant text) and the whole is followed by a list of references, nearly all in Russian. Considering the book as a whole, one is disappointed. There are misprints and the prose in several places reads oddly. In some equations a scalar is in Clarendon type and a vector is in italic type. The symbol æ is used for both to the Heaviside unit function and magnetic susceptibility. Some names are wrongly transliterated (Gilbert, Beeo, Savar) and there is no index at the end. The book appears to be one in a series of books by Russian authors, and the publishers have done this author a disservice by not arranging for a native English speaker to edit the book. The book contains some interesting work but it is expensive for its length, particularly in view of the above-mentioned faults.
scientific article; zbMATH DE number 1414338