Open AccessOn the evaluation of explicit 2‐D extrapolation operators
Author(s) -
Maeland Einar
Publication year - 1994
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1994.tb02129.x
Subject(s) - extrapolation , fourier transform , wavenumber , frequency domain , offset (computer science) , mathematics , mathematical analysis , operator (biology) , window function , fourier analysis , inverse , fourier series , algorithm , computer science , physics , optics , geometry , spectral density , statistics , biochemistry , chemistry , repressor , transcription factor , gene , programming language
SUMMARY The 2‐D extrapolation operator in the wavenumber‐frequency domain is expanded in a series of Chebychev polynomials. Fourier‐type coefficients, depending on the extrapolation step, the frequency and the current velocity, are derived in terms of standard functions of mathematical physics. The inverse Fourier transform to the space‐frequency domain then gives an analytical solution of the explicit operator, which renders the calculation of filter coefficients a routine matter. Realizable operators are designed by application of suitable spatial window functions. Migration of synthetic zero‐offset data is used to illustrate the merits of the analysis.