Study On Method Of Wavelet Transformation In Geophysical Well Log

Well log data contains a wealth of geological information, which chronicles the geological evolution history in some degree and reflects the conditions and factors of subterranean formation evoluation in different aspects. By far, well log is the geological data of the highest resolution and the best continuity, through studying the well log in the stratigraphic interpretation, which has important theoretical and practical value. Wavelet analysis has the function of signal filtering and detection of abnormal signal. In this paper, taking Chinese Continental Scientific Drill(CCSD) Main Hole for example based on the theory of wavelet analysis, which studies the logs wavelet filtering, identify the formation interface, detection the formation fracture zone, and solving potential partial differential equations. The study process and the obtained results are as following:(1) At the beginning, the paper talks about the limitation of the tranditional methods when deals with the well log data, and introduces the wavelet theory. After that, making a summary of research status and process of this paper about it contents, incuding well logs wavelet filtering, wavelet analysis in identifying formation interfaces, wavelet analysis in detecting formation fractured zone and solving partial differential equations.(2) By making a comparion the Fourier transform and wavelet analysis, this paper describes the advantages of wavelet analysis in signal processing. Also, it introduces the continuous wavelet transform(CWT), discrete wavelet transform(DWT) and dyadic wavelet transform. It discusses the orthogonality, the nature of regularity, compact support and symmetry of several common wavelet faction. It introduces the multi-resolution characteristic and two-scale equation and discusses it rapid decomposition and reconstruction algorithm based on wavelet analysis.(3) It filteres the noisy log signal of CCSD main hole, and study the characteristic of useful and noise signal, the useful signal is non-stationary signals, and noise signal is distributed in whole logs, the energy is distributed in the high frequency range. Make a filter of the ideal useful signal and noise signal, analyzing the performance in different scale by wavelet transform, as the scale increase, the modulus of useful signal wavelet maxima increased gradually, and the modulus of noise signal wavelet maxima decreased gradually. For the characteristic of useful and noisy signal, the paper disscuses modulus maxima reconstruction filtering method, which sets different thresholds related to scales in every scales, reconstructed the useful signal, and improved flitering effect. The spatial correlation filtering solves the noise threshold, wavelet coefficient offset and low sacle wavelet coefficient, which presents a new and modified spatial correlation filtering and improved the accuracy of filtering. Through the test of CCSD main hole well log data, it determined the optimal wavelet function. For the hard and soft threshold filtering method, which take a linear process. According to the wavelet coefficients changes by different sacles, it proposed non-linear threshold function, which can be better for CCSD main hole when filtering well log data.(4) For the ideal well log, which are deal with by wavelet transform, and the boundary data are extended to eliminate edge effects. This parts introduces the process of formation interface icentification by wavelet transform. The process is applied to CCSD main hole by continuous wavelet transform and discrete wavelet transform, obtained the wavelet coefficient sacleogram and high-frequency wavelet coefficient, which are used for formation interfaces identifaction. According to the stratigraphic column, it determined the optimal well log, wavelet function and sacle range.(5) For the lithology formation identification which demarcated by the performance of wavelet transform, a modified K-means clustering algorithm is proposed. Based on the traditional K-means clustering algorithm, Euclidean distance was replaced by Mahalanobis distance, and the initial cluster centers were acquired from the average of characteristic values, in addition, added weight value in each characteristic value of the objective function. The cluster center obtained by modified K-means clustering algorithm, as well as Haiming approach degree are performance to identify the formation lithology. For the same group samples(50 samples,5 kinds of lithology,10 samples in one kind), the modified K-means clustering algorithm is more accuracy than the tranditional K-means clustering algorithm, improves 10%.(6) By observing the CCSD main hole imaging logging data, the paper analysis the sensitive well logs to fracture zone, which are caliper, density, resistivity and acoustic travel time, and intergrates the four logs into one which can reflects the changed trends of fracture zones. After that, wavelet transform to the intergrated log, make a comprehensive use of high frequency energy wavelet coefficient and micropherical focused log to detect fracture zone. Make a relationship equation of high-frequency wavelet coefficients with fracture density, we can detect fracture zones and get the corresponding fracture density by the above equation.(7) Fourier transform makes the point source of three-dimensional structure of the potential and boundary problems into a two-dimensional problem with one parameter. Take a brief introduce of wavelet Galerkin method in solving partial differential equations potential. According to the one-dimensional CAS wavelet function, two-dimensional CAS wavelet function is established and two differential operator matrix are derived. The conversion potential V(x, y, z) is obtained by the method of wavlet-Galerkin based on the given parameter A, and make the conversion potential V(x, y, z) the inverse Fourier transform, get potential U(x, y, z). The value of wavelet analysis and measured have good agreement in numerical and curve shapes, and bigger of the parameters M and k, the more accuracy in identifying the thin layer. This method solves the problem of large calculation of conventional and slow convergence.