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MATHEMATICAL ANALYSIS OF D.C. RESISTIVITY SOUNDING OVER A PARABOLOID *
Author(s) -
DASGUPTA S.P.
Publication year - 1987
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1987.tb00851.x
Subject(s) - paraboloid , curvilinear coordinates , computation , bessel function , geology , mathematical analysis , fourier transform , depth sounding , surface (topology) , geometry , geophysics , mathematics , algorithm , oceanography
ABSTRACT A complete mathematical analysis is proposed for direct current resistivity prospecting over the surface of a layered paraboloid. The analysis evaluates the Green's function in parabolic coordinates for a current source at the vertex. The general solution is obtained as a Fourier‐Bessel integral involving those curvilinear coordinates that have a kernel function which is similar to that of a half‐plane containing inhomogeneous layers. This similarity permits the computation of a class of sounding curves over such an oval surface providing a way to analyse field data over hilly terrain.