Premium
ON THE CONSTRUCTION OF THE 3D BAND‐LIMITED EXTRAPOLATION OPERATOR IN THE SPACE‐FREQUENCY DOMAIN 1
Author(s) -
MAELAND EINAR
Publication year - 1993
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.1365-2478.1993.tb00875.x
Subject(s) - bessel function , extrapolation , mathematics , mathematical analysis , hankel transform , frequency domain , operator (biology) , chebyshev polynomials , fourier transform , space (punctuation) , computer science , biochemistry , chemistry , repressor , transcription factor , gene , operating system
A bstract Based on an expansion of the band‐limited 3D extrapolation operator in terms of orthogonal Chebyshev polynomials, a closed form expression of the space‐frequency response is presented. A key step is an evaluation of the (inverse) 2D Fourier transform of circularly symmetric functions, which is related to the (zero‐order) Hankel transform. Hankel transforms of individual members of the orthogonal set of polynomials are available from tables and summation of series; hence, the real and the imaginary parts of the space‐frequency response can be found in terms of cylindrical and spherical Bessel functions, respectively. The procedure permits an efficient and accurate evaluation of the space‐frequency response.