Abstract：
Quantitative thickness estimation below tuning thickness is a great challenge in seismic exploration. Most studies focus on the thin-beds whose top and bottom reflection coefficients are of equal magnitude and opposite polarity. There is no systematic research on the other thin-bed types. In this article, all of the thin-beds are classified into four types: thin-beds with equal magnitude and opposite polarity, thin-beds with unequal magnitude and opposite polarity, thin-beds with equal magnitude and identical polarity, and thin-beds with unequal magnitude and identical polarity. By analytical study, an equation describing the general relationship between seismic peak frequency and thin-bed thickness was derived which shows there is a complex implicit non-linear relationship between them and which is difficult to use in practice. In order to solve this problem, we simplify the relationship by Taylor expansion and discuss the precision of the approximation formulae with different orders for the four types of thin-beds. Compared with the traditional amplitude method for thin-bed thickness calculation, the method we present has a higher precision and isn’t influenced by the absolute value of top or bottom reflection coefficient, so it is convenient for use in practice.
SUN Lu-Ping,ZHENG Xiao-Dong,LI Jin-Song et al. Thin-bed thickness calculation formula and its approximation using peak frequency[J]. APPLIED GEOPHYSICS, 2009, 6(3): 234-240.
[1]
Bai, G. J., Wu, H. N., Zhao, X. G., and Wang, J. H., 2006, Research on prediction of thin bed thickness using seismic data and its application: Progress in Geophysics, 21(2), 554 - 558.
[2]
Chung, H. M., and Lawton, D. C., 1995, Amplitude responses of thin beds: Sinusoidal approximation versus Ricker approximation: Geophysics, 60, 223 - 230.
[3]
Gridley, J. A., and Partyka, G. A., 1997, Processing and interpretational aspects of spectral decomposition: 67th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1055 - 1058.
[4]
Huang, Z. P., Wang, X. H., and Wang, Y. Z., 1997, Parameter analysis of seismic attributes and thickness prediction for thin bed: Geophysical Prospecting for Petroleum, 36(3), 28 - 38.
[5]
Okaya, D., 1995, Spectral properties of the earth’s contribution to seismic resolution: Geophysics, 60, 241 - 251.
[6]
Partyka, G. A., Gridley, J. A., and Lopez, J. A., 1999, Interpretational aspects of spectral decomposition in reservoir characterization: The Leading Edge, 18, 353 - 360.
[7]
Partyka, G. A., 2005, Spectral decomposition: SEG Distinguished Lecture:
[8]
Ricker, N., 1953, Wavelet contraction, wavelet expansion, and the control of seismic resolution: Geophysics, 18, 769 - 792.
[9]
Widess, M., 1973, How thin is a thin bed?: Geophysics, 38, 1176 - 1180.
2009, Vol. 6 
