The Application of the Wavelet Transform to the Prediction of Gas Zones

An accurately evaluate about the zone number and position of the gas zone is put forward in this paper. It provides the reliable basis for developing natural gas through synthetically analyzing the result of carrying on wavelet de-noising and wavelet package denoising disposal simultaneously to the density porosity curve and neutron porosity curve. If there is natural gas in the void of underground reservoir, it can increase the density well logging porosity D φ and decrease the compensation neutron porosity CNL φ . As long as overlapping these two kinds of porosity curves we can directly determine the zone meeting the condition of D CNL φ φ < is that one containing gas. While because of noise signals are contained in most of the well logging traces, small saw teeth will take place in the curves caused by some factors. Though this phenomenon is independent of the character of the zone, either of the explanation of the single curve or the two overlapping curves may run into obstacle, and makes the evaluation lack of accuracy. So it is obviously important to control the noise of the well logging traces. Despite a few ways existing for a long time in low frequency filter on the well logging traces, the rate of distinguish of the curves are reduces after dispose, so we can not explain gas zones effectively. Wavelet analysis, which has extensive application on the aspect of signal analysis and graph disposal, is a new developing branch of mathematics in recent years and achieves noticeable success. In this paper, in order to remove the signal noise of CNL φ and D φ , the one-dimension method of wavelet denoising and wavelet package denoising is used to achieve the purpose of prediction of parameters about gas zone. * This work was supported by the National Natural Science Foundation of China under the grand number 69903012 and 69682011. The Application of the Wavelet Transform to the Prediction of Gas Zones 431 1 The Principle of Wavelet Transform The one-dimension signal-de-noising disposal is the one of the important applications of the analyses of wavelet denoising and wavelet package denoising. The basic principle is as follow: A basic model of si containing noise signal: 1 , , 1 , 0 − = + = n i z f s i i i ! σ fi is the real signal, the part of noise is zi , which is often called Gauss vacant noise ) 1 , 0 ( N , σis the noise grade. The purpose of removing noise is to reduce the value of noise part and recover the real signal fi. The Steps of Wavelet De-noising: 1. The decomposition of the one-dimension wavelet signal Choose a wavelet of Sym8 and decide the number of layers of wavelet decomposition N=5, then decompose the one-dimension signal for the N zone. 2. To quantitatively determine the threshold of high frequency coefficient We adopt the principle of maximum and minimum to choose the threshold, as can achieve the minimum of the maximum mean square error. Quantitatively dispose high frequency coefficient of every zone according to the soft threshold from first to fifth layer. 3. To recompose the one-dimension wavelet According to the low frequency coefficient of the fifth zone and the high frequency coefficient after being modified from first to fifth zone we can calculate the recomposition of one-dimension wavelet. The idea of denoising by using wavelet package is as nearly same as that of wavelet denoising. The only difference between them, allowing wavelet package subdivide and quantitatively determine the threshold of parts of both low and high frequency simultaneously, lies in the more complicate and more flexible analysis way the wavelet package provides. The steps of wavelet package de-noising: The decomposition of one-dimension wavelet package. 1. To choose a wavelet of Sym8 and decide the zone of wavelet decomposition N=5, then decompose the one-dimension signal for the N zone wavelet package. 2. To compute the optimum tree (namely determine the optimum wavelet package base).The optimum tree is computed based on the minimum entropy criterion. 3. To quantitatively determine the threshold of wavelet package decomposition coefficient We adopt the principle of maximum and minimum to choose the threshold and quantitatively decide the threshold of each wavelet package decomposition coefficient, especially the low frequency decomposition coefficient. 4. To recompose the wavelet package. 432 Xiu Wen Yang et al. According to the fifth zone wavelet package decomposition coefficient and the quantitatively disposed coefficient, the signal wavelet package can be recomposed.