| Acoustic logging is one of the main methods in geophysical logging. Its basic idea is to calculate formations’ geological and petrophysical parameters based on acoustic wave propagation law, which will help to identify lithology and hydrocarbon reservoirs. Early acoustic logging can only measure arrival time or amplitude of Primary(Compressional) wave by only one source and one receiver. With technological advancements, in order to improve measurement accuracy, acoustic logging instrument with single transmitter and double receivers, acoustic logging instrument with double transmitters and double receivers, acoustic logging instrument with long space and array acoustic logging instrument have been launched one after another. Modern array acoustic logging instruments have monopole and dipole sources and several receivers. The two types of sources emit acoustic signals by different vibrations, while receivers acquire full waveform by various combinations. Compared with early instruments, they can obtain more abundant formations information at greater depths.However, array acoustic logging signals can directly provide geological information little, they must be processed and analyzed. At present, traditional processing method is to compute slowness(reciprocal of velocity) of each component wave, and to determining a variety of lithology using data from nearby boreholes and curves of slowness versus depth. The computations of slowness can be divided into two categories: time domain methods and frequency domain methods. The time domain methods are often initiated with waveform in time domain, and take advantage of repeated information; however, these methods ignore the effects of frequency dispersion, such as thresholding and slowness time coherence. On the other hand, the frequency domain methods, such as analysis of spectral and phase, Prony algorithm and Matrix Pencil algorithm, are often started with frequency spectrum, and frequency dispersion curves can be obtained. Slowness of frequency dispersion waves, like Stoneley wave and dipole shear wave, can be determined from the frequency dispersion curves.As is well known, an array acoustic logging signal is expressed by three physical quantities: time, frequency and energy(amplitude). Slowness is affected by the arrival time of each component wave in full waveform, so it can only reflect information in time domain. In other words, the traditional methods don’t pay enough attention to logging signals’ spectrums. Signals’ spectrum can be obtained by Fourier transform easily, but Fourier transform will make information of time domain lost. If we want to obtain information both in time and frequency domain, time-frequency analysis should be introduced. Time-frequency analysis can combine time, frequency and amplitude, which provides a distribution of amplitude in time-frequency coordinate system. Time-frequency analysis includes many methods, which are often divided into two categories: linear methods and non-linear methods. The linear methods mainly include short-time Fourier transform, wavelet transform, Hilbert-Huang transform and fractional Fourier transform, and the nonlinear methods mainly include Cohen class bilinear time-frequency distribution and Affine class bilinear time-frequency distribution. But if applying a single method to process array acoustic logging signals, the result is not as expected. There are two main problems. First, array acoustic logging signals are composed of several component waves, and their times and frequencies are often close to each other, which makes them difficult to identify. Second, amplitudes of component waves are quite different, and in time-frequency distribution, component waves with lower amplitudes are often invisible.Thus, this study combines fractional Fourier transform and Choi-Williams distribution, and filters Choi-Williams distributions of array acoustic logging signals in time-frequency domain by rotation of fractional Fourier transform. Then time-frequency distributions of P-waves and S-waves will be extracted. Through researching time-frequency characteristics of acquired P-waves and S-waves, and Stoneley waves which is easy to identify in origin Choi-Williams distributions, this study will explore a new method to process and interpret array acoustic logging data.The work performed in this study includes three parts: first, introduce the method of combining fractional Fourier transform and Choi-Williams distribution, and compile the related programs. Second, process array acoustic logging data, and obtain time-frequency characteristics of each component waves. Third, connect time-frequency characteristics with fractures of formations. The concrete study contents are as follow:1. This study introduces the method of combining fractional Fourier transform and Choi-Williams distribution, and discusses its physical and practical meaning. The programs in this study are divided into two parts: section processing and point processing. Section processing aims at computing the time-frequency distributions of all the array acoustic logging signals in some depth ranges, and then extracting the distributions of P-waves and S-waves. After, it need arrange these distributions corresponding to the full waveform by depth, which can help to obtain the change laws of the component waves’ time-frequency characteristics followed depth. For this part, this study applies the object-oriented programming by combining VB.NET and Matlab. Point processing is used to draw the figures that consist of four parts: acoustic full waveforms and time-frequency distributions of the original signals, the P-waves and the S-waves. It aims at acquiring the accurate time-frequency information of the component waves of the representative signals that is received in different formations by. For this part, this study uses Matlab to program, and makes the visual interface by the GUI tools.2. In the first place, the array acoustic logging signals should be pretreated, including removing the gain and equalizing each waveform. Then section processing should be used for the signals from several depth ranges, and the figures that show the changes of the time-frequency distributions of the original signals, the P-waves and the S-waves followed depth will be obtained. After that, representative signals can be chosen and, point processing should be adopted for them to obtain the time-frequency distributions of the original signals, the P-waves and the S-waves. By these figures, each component wave can be orientated and the amplitudes of them can be determined.3. Through the results of section processing, the change laws of the time-frequency characteristics of the component waves with some properties of the formations will be explored. Through the results of point processing, these laws can be cognized clearly and accurately. Then combined with other information of logging and geology, the laws should be explained by the principles of physics and geology, and connections between time-frequency characteristics and the different fractures of formations should be established.Through these studies, this study draws the following conclusions:1. In time-frequency distributions of array acoustic logging signals, only Stoneley waves are obvious, and P-waves and S-waves are difficult to identify. But by combining fractional Fourier transform and Choi-Williams distribution, the two waves can be extracted successfully.2. For a tight formation, the Choi-Williams distribution of the array acoustic logging signal is regular, and the amplitude of the Stoneley wave is much higher than the P-wave, the S-wave. Compared with the formation with an unfilled fracture of middle or low angle, the amplitude of each component wave shows slighter attenuation; each component wave is received earlier; the basic frequency of the P-wave and the S-wave is higher.3. For a formation with a fracture of high resistivity, the peak’s time and the basic frequency of each component wave will not change much, and the amplitude’s attenuation of each component wave is between the tight formation and the formation with an unfilled fracture of middle or low angle.4. For a formation with an unfilled fracture of middle or low angle, compared with the tight formation, the peak of the P-wave appears later, the basic frequency of the P-wave is lower and the amplitude of the P-wave shows more attenuation; similarly, the peak of the S-wave appears later, the basic frequency of the S-wave is lower and the amplitude of the S-wave shows more attenuation; the peak of the Stoneley wave appears later and the amplitude of the Stoneley wave shows more obvious attenuation.5. For a formation with an unfilled fracture of high angle, compared with the tight formation, the amplitude of the P-wave shows some attenuation, the amplitude of the S-wave has no significant changes and the amplitude of the Stoneley wave shows more attenuation; the peaks time and the basic frequency of each component wave change little.6. For a formation with an unfilled netted fracture, compared with the tight formation, the peak of the P-wave appears later, the basic frequency of the P-wave is lower and the amplitude of the P-wave shows more attenuation; the peak of the S-wave appears later, the basic frequency of the S-wave is lower and the amplitude of the S-wave shows more attenuation, as well; the peak of the Stoneley wave wave appears later and the amplitude of the Stoneley wave shows more obvious attenuation. Netted fractures have complicated influence on array acoustic logging signals, so that it’s difficult to find the accurate law. But by the method of this study, these formations can be easily distinguished from tight formations.7. By the method of this study, the formation with a fracture that conventional logging data are helpless can also be identified.8. Conversely, while the distributions of the original signals, the P-waves and the S-waves in are being obtained, if the peaks of component waves appear early, the amplitudes of component waves are high, and the basic frequencies of the P-waves and the S-waves are high, these formations can be considered to be tight, and be regared as references; if compared with tight formations, the amplitudes of the Stoneley waves are lower, there are fractures that are not entirely filled in formations; if compared with tight formations, the amplitudes of the P-waves and the Stoneley waves are lower, but the peaks’ times and the basic frequencies of component waves and the amplitudes of the S-waves change littile, there are unfilled fractures of high angle in formations; and if compared with tight formations, the amplitudes of component waves are lower, the peaks of component waves appear later, and the basic frquencies of component waves are lower, there are unfilled fractures of middle or low angle or unfilled netted fractures in formations. |
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