Integral Transforms in Geophysics [Paperback]

Integral Transforms of Geophysical Fields serve as one ofthe major tools for processing and interpreting geophysicaldata. In this book the authors present a unified treatmentof this theory, ranging from the techniques of the transfor-mation of 2-D and 3-D potential fields to the theory of se-paration and migration of electromagnetic and seismicfields. Of interest primarily to scientists and post-gradu-ate students engaged in gravimetrics, but also useful togeophysicists and researchers in mathematical physics.Title of the original Russian edition: Analogi integrala tipa, Koshi v teorii geofizicheskikh, Polei ,Nauka, 1984Integral Transforms of Geophysical Fields serve as one ofthe major tools for processing and interpreting geophysicaldata. In this book the authors present a unified treatmentof this theory, ranging from the techniques of the transfor-mation of 2-D and 3-D potential fields to the theory of se-paration and migration of electromagnetic and seismicfields. Of interest primarily to scientists and post-gradu-ate students engaged in gravimetrics, but also useful togeophysicists and researchers in mathematical physics.I Cauchy-Type Integrals in the Theory of a Plane Geopotential Field.- 1 Cauchy-Type Integral.- 1.1 Definition.- 1.1.1 Cauchy Integral Formula.- 1.1.2 Concept of the Cauchy-Type Integral.- 1.1.3 Piecewise Analytical Functions.- 1.2 Main Properties.- 1.2.1 H?lder Condition.- 1.2.2 Calculation of Singular Integrals in Terms of the Cauchy Principal Value.- 1.2.3 Sokhotsky-Plemelj Formulas.- 1.2.4 Generalization of the Sokhotsky-Plemelj Formulas for Piecewise Smooth Curves.- 1.2.5 Cauchy-Tpye Integrals Along the Real Axis.- 1.3 Cauchy and Hubert Integral Transforms.- 1.3.1 Integral Boundary Conditions for Analytical Functions.- 1.3.2 Determination of a Piecewise Analytical Function from a Specified Discontinuity.- 1.3.3 Inversion Formulas for the Cauchy-Type Integral (Cauchy Integral Transforms).- 1lc)