Affiliation:
1. National Geophysical Research Institute, Uppal Road, Hyderabad 500 007, India
Abstract
Ghosh’s method of designing filters (1970, 1971a, b) for computing apparent resistivity and electromagnetic (EM) sounding curves over a layered earth requires a set of known input and output functions satisfying the corresponding convolution integral. The spectrum of the filter in amplitude |H(f)| and in phase φ(f) is determined as [Formula: see text], [Formula: see text], respectively. Inverse Fourier transform of the spectrum results in the filter function, which is sampled to derive the filter coefficients. For different electrode or coil configurations, different sets of input‐output functions are chosen. The criteria for choosing them were given in Koefoed et al (1972) and Anderson (1975). An alternative method of designing a filter was given by Johansen and Sørensen (1979) who obtained an explicit series expansion for the filter function and handled the tail of the infinite summation analytically. Following Ghosh’s method, Anderson (1979) designed the filters for Hankel transforms of orders 0 and 1 where both filters have identical abscissas. This avoids repetitious kernel evaluations because the kernels of many of the integral transforms of orders 0 and 1 encountered in electrical prospecting are related to one another by simple algebraic relationships. Table 1 presents a 14‐point filter (six intervals per log decade; abscissa of the filter coefficient [Formula: see text] is +0.1343155) designed by the author for Schlumberger curve computation.
Publisher
Society of Exploration Geophysicists
Subject
Geochemistry and Petrology,Geophysics
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献