Research On Improving Logging Curve Resolution Based On Wavelet Theory

Finding out the correlations between the known low resolution and high resolution sound wave curves is the aim of this paper. Applying the correlations to the well with low resolution sound wave curves, then the high resolution and improved low resolution curves will be gained by the low resolution curves and the correlations.In fact, one can believe that the low resolution and high resolution sound wave curves are the signals or function which scope changes with the stratum depth and time. The analysis of the signal is depended on Fourier transform and filter etc. traditional signal analysis methods. Wavelet transform theory is a new branch of mathematics, which is a time-scale (time-frequency) analysis. That is, there are higher frequency resolution and lower time resolution at the low frequency, there are higher time resolution and low frequency, there are higher time resolution and low frequency resolution at high frequency.Assuming that the acoustic logging signal is a definite signal and changing the time domain into frequency domain with Fourier transform, one can believe that high resolution signal is the output respondence which is the result that the low resolution signal passing through discrete system. The discrete system is the correlations of the two signals at the frequency domain. Using linear system frequency analysis and the system's stability theory, and by testing and calculating, we know that system function is unstable. Assuming that well logging signal is a indefinite signal, it showed that the system function is also unstable with random signal modeling theory.The curves energy is different between high resolution and low resolution curves because of the different tools. Decomposing the wavelet domain with Wavelet transform and calculating the ratios of two signal energy, all frequency domain are magnified with the ratios and curve signals are reconstructed with each frequency domain segment. It is proved that this methodcan improve curve's resolution. Furthermore, applying the ratio to the other well, this method also can improve the resolution of low resolution curves.Analysising the characteristic of the high and low resolution acoustic well logging tool, well logging dynamic sequence, and the correlation of high and low resolution tools, then a difference equation will be gained. Put the high resolution curves signals into the difference equation, then low resolution curves will be gained, which is similar with the real low resolution curve in shaper. It shows that the difference equation is right. To calculate the high resolution curve with low resolution curves, it lacks init condition for the difference equation.Synthesizing several analysis method above, decomposing the known signal with wavelet transform at different frequency segment, energy compensation will be done at different frequency segment respectively, and reconstructing the low resolution curves is an effectively improving the resolution method. If the frequency domain can be divided more finely, the resolution will be improved very much.