Stratum Fracture Recognition Method Based On Fractional Fourier Transform

In geology, fracture is the surface space in which the Binding force is lost in the rock. It is widely concerned to determine fracture development areas and to describe the distribution of stratum fractures. Over the years, fracture detection theory and technology continues to be explored, which purpose is to be able to describe the distribution of underground fractures more effectively. In people’s continuous efforts to explore and research, recently, fracture prediction methods based on different theoretical bases have been proposed, some of which have achieved good results. However, due to the complex distribution of underground fractures, there are limitations of different prediction methods, the prediction of fractures is still an unsolved problem in the world.Acoustic logging is an important method for logging. Most of the current acoustic logging theories are based on the assumption of isotropic homogeneous medium or the assumption of horizontal layered isotropic medium, and it is axisymmetric. Previous full-wave acoustic research and application is mainly calculation and analysis of acoustic time difference and attenuation coefficient, effective use and study of time-frequency characteristics of various modes of vibration wave is very little. Research on the processing of array acoustic logging data is mainly concentrated in the aspects of wave separation of each component and the extraction of slowness. There are still many problems in the present research, which is the rich strata(lithology) information, fracture information and contact relationship. Therefore, it is an important way to study the data processing and analysis method of array acoustic logging, which is more scientific and effective.Based on the non-stationary signal characteristics of array acoustic logging, the paper takes the elastic wave propagation characteristics of fractured strata, and introduces a method of time frequency analysis. The fractional Fourier transform and the smooth pseudo Ville-Wigner distribution are combined. By changing the order of the fractional Fourier transform, the time-frequency distribution in some transitional domain of the logging signal is obtained by using the smoothed pseudo Wigner-Ville distribution. From such a new perspective to analyze the signal, we can research the time-frequency characteristics of acoustic logging signal in fractured stratum, obtain full-wave acoustic amplitude spectrum and time-frequency-amplitude(energy) spectral parameters, extract and analyze the structure time-frequency information contained in full-wave data for fractured strata, and study the intrinsic connection between the acoustic field parameters of wells and the anisotropic fracture structure of strata, which provides a more accurate and effective basis for fracture evaluation.Fractional Fourier transform is a linear operator. On the time-frequency plane, if the Fourier transform is viewed as rotating 90° from the time axis to the frequency axis, then the fractional Fourier transform is an operator of an arbitrary angle, thus the fractional Fourier transform is a generalized Fourier transform. For fractional Fourier transform: When the order is 0, the signal is not changed, and the time domain information of the signal is reflected; When the order is 1, it is equivalent to the traditional Fourier transform, which reflects the signal’s frequency domain information; And when the order is between 0 and 1, it reflects the information of some transition domain between time domain and frequency domain. In this paper, we can obtain the time-frequency distribution of signals in a transition domain, which is different from the traditional method.Wigner-Ville distribution can not only reflect the change of the time, but also can reflect the change of the signal with frequency. The time-frequency distribution of any multi-component signal has the cross terms. They come from the cross function of different signal components in the multi-component signal, and are the product of the interference, should be suppressed as far as possible.Combined with the above ideas, the fractional Fourier transform with smoothing pseudo Wigner-Ville distribution(FRFT-SPWD) of a single well logging data is realized by using MATLAB programming. Using the data of known faults, the data of segments of single lithology and the data of complex lithology sections, the fracture distribution is obtained. Distribution characteristics of non-fractured stratum of FRFT-SPWD: 1) P-wave arrival time is about 1 ms, frequency is about 15 kHz, and low amplitude; 2) superposition wave of shear wave and pseudo Rayleigh wave arrival time is about 2 ms, frequency is about 5 kHz, amplitude stability; 3) the Stoneley wave arrived at about 2.6 ms, frequency is about 5 k Hz, amplitude is about 1×107; 4) pseudo Rayleigh wave arrived at about 3.7 ms. Because of the complexity genesis of fracture, the distribution of FRFT-SPWD in the fracture stratum cannot be described quantitatively, but it generally has the characteristic of low amplitude. This is because that the structure of fractured stratum is broken, loose degree is strong, the friction increases when protons propagate, then the conversion of heat energy decreases, so the energy of the acoustic wave is reduced, and the amplitude is reduced.The interpretation of well logging is a combined interpretation for multiple curves with colse spatial position relation, so we need to design a data processing and mapping software to achieve the above ideas. The core task of the software is to complete the processing and mapping of transformation of each depth’s logging data, and then realize the comparison of these images. Using MATLAB and VB.NET 2010 mixed development approach to achieve software development, this is not only the use of MATLAB powerful data processing advantages and the mature program code of fractional Fourier transform with pseudo Wigner-Ville distribution, but also the use of VB.NET 2010 to solve the needs of batch image processing, contrast display of a large number of images, and size control of graphics and visual.A case study and analysis of the data from the main hole of the Chinese Continental Scientific Drilling is carried out to verify the validity of the method. First of all, the typical characteristics of the fracture were dissected. Four typical strata are chosen to analyze: non fractured stratum with single lithology, non-fractured stratum with complex lithology, fractured stratum with single lithology, fractured stratum with complex lithology. The study shows that the image features of the typical stratigraphic position of fractured and non-fractured stratum are consistent with the above mentioned FRFT-SPWD distribution, and the method is also verified by the method of acousto-electrical tomography.The data of 1 140-1 170 m of the main hole is processed analyze the acoustic characteristics of the underlying rock and structure. we can conclude that the 3D time-frequency distribution shows that the fractured stratum has different time-frequency distribution characteristics from that of non-fractured strata, and the depth fits well. Therefore, the time-frequency distribution method of fractional Fourier transform with smoothed pseudo Ville Wigner- distribution(FRFT-SPWD) is an effective method for the identification of fractured stratum.