Wavelet Analysis Methods For Well Logging Data

Abstract: This paper aims to use wavelet analysis method in the analysis of logging data and extract the information characteristics of formation by using resolution analysis, weighting and reconfiguration, multiscale amalgamation, in order to analyze more accurate division of the stratigraphic sequence.First of all, use wavelet analysis theory, multi-resolution analyze on single logging curves, Several common wavelet basis for comparison, compare the dimension of the best wavelet bases , consumering square and maximal correlation factor, and select the best wavelet bases, analyze and compare high-frequency signals and low frequency signal obtained by decomposition of different scales, through the best wavelet bases decomposition of logging curves, and then get high frequency and low frequency coefficients after the wavelet transform, use the method of frequency division weighting reconfiguration, reconstructed information contained within logging curves, closer to the real situation of the formation, reflect more clearly the details of the formation can increase the resolution of logging curves.Because logging data contains a large number of geological information, the mutation or mutations in region of logging signal reflects the information of a change in formation sediment, analyze the logging signal by using the method of wavelet multiscale testing and wavelet filtering, to enhance the characteristics of the singular point of logging signal and eliminate the impact noise on logging signals, and ultimately the identification of sedimentary cycles and the division of sequence stratigraphy. First, use the wavelet the relationship between extreme value of wavelet transform modulus and Lipschitz index, multiscale edge detection on the log signal, exactly express the characteristics of the singular point of logging signal, in order to identify the formation cycle interface. Secondly, use wavelet transform to filter the logging signal, not only to remove the noise interference unrelated to the formation information, but also to retain the mutation position and the edge information of the signal. Therefore, optimize the six commonly used wavelet bases, and ultimately selected Sym8 wavelet basis as the optimal wavelet to filtering, it also has the smoothness, compact support and symmetry properties of the characteristics of the orthogonal wavelet. Through case analysis, wavelet filtering method can not only inhibit the signal noise, but also to retain the location information of the signal mutation. Finally, use multiscale edge detection, and mix together the data of several logging curves, make logging curves include more layering information, can not only provide the formation details, but also can significantly improve the accuracy of stratigraphic division.The different amplitude and frequency (scale) of logging curves directly response to the different characteristics between lithology and sedimentary features of sequence boundaries, and several sedimentary cycle superpose the logging curves, wavelet transform decompose logging curves obtained by representatives of different scales of sedimentary cycles of different periods, The change of sedimentary cycle form the sequence boundaries, so select specific wavelet basic function to do the wavelet transform the logging signal, is the key to divide sequence stratigraphy. This paper selects Morlet wavelet as the best wavelet function, because its scale factor have a good corresponding relationship with the formation of sedimentary cycles, through the Wavelet analysis can also clearly analyze the time - frequency characteristics of signal. Use oscillation amplitude and frequency characteristics of wavelet factor curves correspond with optimum Morlet wavelet scaled factor, to divide the interface of sequence stratigraphy unit and identify its internal cycle's type. use the Morlet wavelet basic function to do the multiscale analysis, The logging data from the one-dimensional extended to two-dimensional depth - scale domain space, achieve localization characteristics of the signal analysis of the time - frequency domain, effectively extract the signal of the time - frequency characteristics, based on the characteristics of wavelet coefficient curve of best scaled factor, divided into different levels of stratigraphic sequence interface unit, the application of this method supporting the division of sequence stratigraphy, improve the logging cycle sequence classification accuracy.