FAST HANKEL-TRANSFORMS

被引:158
作者
JOHANSEN, HK [1 ]
SORENSEN, K [1 ]
机构
[1] LAB GEOPHYS,DK-8200 AARHUS N,DENMARK
关键词
D O I
10.1111/j.1365-2478.1979.tb01005.x
中图分类号
P3 [地球物理学]; P59 [地球化学];
学科分类号
0708 ; 070902 ;
摘要
Inspired by the linear filter method introduced by D. P. Ghosh in 1970 we have developed a general theory for numerical evaluation of integrals of the Hankel type: (Formula Presented.) Replacing the usual sine interpolating function by sinsh (x) =a· sin (ρx)/sinh (aρx), where the smoothness parameter a is chosen to be “small”, we obtain explicit series expansions for the sinsh‐response or filter function H*. If the input function f(λ exp (iω)) is known to be analytic in the region o < λ < ∞, |ω|≤ω0 of the complex plane, we can show that the absolute error on the output function is less than (K(ω0)/r) · exp (−ρω0/Δ), Δ being the logarthmic sampling distance. Due to the explicit expansions of H* the tails of the infinite summation (Formula Presented.) ((m−n)Δ) can be handled analytically. Since the only restriction on the order is ν > − 1, the Fourier transform is a special case of the theory, ν=± 1/2 giving the sine‐ and cosine transform, respectively. In theoretical model calculations the present method is considerably more efficient than the Fast Fourier Transform (FFT). Copyright © 1979, Wiley Blackwell. All rights reserved
引用
收藏
页码:876 / 901
页数:26
相关论文
共 19 条
  • [1] ABRAMOWITZ A, 1965, HDB MATH FUNCTIONS
  • [2] Baranov W., 1976, Geophysical Prospecting, V24, P222, DOI 10.1111/j.1365-2478.1976.tb00920.x
  • [3] USE OF FILTERED BESSEL FUNCTIONS IN DIRECT INTERPRETATION OF GEOELECTRICAL SOUNDINGS
    BERNABINI, M
    CARDARELLI, E
    [J]. GEOPHYSICAL PROSPECTING, 1978, 26 (04) : 841 - 852
  • [4] Bichara M., 1976, Geophysical Prospecting, V24, P354, DOI 10.1111/j.1365-2478.1976.tb00932.x
  • [5] Bracewell R., 1965, FOURIER TRANSFORM IT, V3rd
  • [6] Das U. C., 1974, Geophysical Prospecting, V22, P476, DOI 10.1111/j.1365-2478.1974.tb00100.x
  • [7] Das U. C., 1974, Geophysical Prospecting, V22, P765, DOI 10.1111/j.1365-2478.1974.tb00117.x
  • [8] Ghosh D. P., 1970, THESIS
  • [9] Ghosh D. P., 1971, GEOPHYS PROSPECT, V19, P769, DOI DOI 10.1111/J.1365-2478.1971.TB00915.X
  • [10] Ghosh D.P., 1971, GEOPHYS PROSPECT, V19, P192, DOI DOI 10.1111/J.1365-2478.1971.TB00593.X