Dependency Relationship Of Fracture Size,Anisotropy And Frequency In HTI Media Based On Developing Equivalent Media Model

With the continuous improvement of oil and gas field exploration and development level, we are facing increasingly complex problems. Meanwhile the anisotropy theory which takes into account underground fluid and anisotropy media is one of the leading edges and puzzles for application research of seismology and geophysics theory nowadays. It relates to knowledge of the hydrodynamic,elastodynamics,single-phase anisotropy theory, and other fields, which embodied the combination with macro-level development and micro-level in the seismic.It is successful for seismic anisotropy that the fracture orientation may be obtained from the fast shear wave polarization and fracture strength of the spatial distribution and be inferred from the time delay between the fast and slow shear waves. However, reservoir engineers are unwilling to accept seismic anisotropy which is described the routine techniques fractures. It couldn't provide information of fracture size and volume. In the paper, the model considered speed, frequency dispersion and attenuation caused by the two different scales jet mechanism grain scales (micro-cracks and equant porosity) and the fracture of formation scales.Currently, seismic anisotropy measurements in the ruptured rock is used to infer information about the direction of crack and the spatial distribution of rupture strength, which is successful for providing the aspect information. The model assumes usually unrelated to the frequency and can not distinguish between micro-fracture and macro-crack fracture, and the later controls many underground reservoir fluid flow. The size of the fracture for reservoir engineers is the basic information, and the suitable model sensitive to fracture scale becomes urgent. In the range of long-wavelength, many theories have been posed, for instance elastic response of broken rock is described through equivalent media theory, but these anisotropy models are assumed frequency-independent, we can not also distinguish between micro-crack and macro-fracture. In the Carbonate Karst Gap Reservoir how to distinguish different scale fractures is urgent to need to solve the problem. Chapman (2003) give the model focused on the effect of fracture scale and improved pore-elastic model, the model considers two different length scales: the grain scales with micro-cracks and equant porosity and the aligned fracture scales greater than it. He described the fracture scale, which is one of the key parameters, and frequency-dependent anisotropy (shear-wave splitting was meantime used). In the absence of fracture the model is back to grain scales squirt model of Chapman (2001). We start from this model to study independence relationship of fracture size, anisotropy and frequency in HTI media.Firstly, we trace the latest two-phase anisotropic media model theory, and test different elastic coefficient ci jkl formula of the new model in two articles published by Chapman (2003), and found that one of them is more reasonable and used to make numerical simulation.This paper studies developing equivalent media theories model, and proves that this model yet belongs to transverse isotropy. But its elastic coefficient is complex, therefore, there is strongly frequency dispersion and attenuation. Frequency is relative to anisotropy and fracture size and so on in this model. And then the paper makes the forward research for relationship among fractures, anisotropy and frequency based on the developing equivalent media model. The references mention that they use reflectance radio method to make new model of synthetic seismogram in frequency domain, but this paper adopts staggered grid high-order finite difference method (8-order approximation on space and 2-order in time) in the time domain. There is higher precision.Which is used to product - 7 -synthetic seismic record including the frequency-dependent anisotropic elastic coefficient, and get the data difficult to obtain in the field. At last, we make research for shear wave splitting to extract fractures density and fracture size. After the multi-component VSP data including fracture information which is obtained by the forward is processed by this method, we can extract the information on meso-scale fracture (the radius is between 100 and 101m) which conventional methods can not provide. The fracture density extracted by the methods has more stringent constraint than conventional methods.We achieved some new major achievements and knowledge by deep study. We derived phase velocity and the group velocity formulas of this new model for the first time. Compared with ordinary HTI media, the results show that P-wave velocity of is symmetrical by the incidence angle 450 and not 900, and that SV-wave velocity will be larger than SH-wave when the incidence angle grows over 300.Our calculation shows: With the increasing frequency, the shear wave splitting time delay and anisotropic factor decreases, the effect of frequency on the degree of anisotropy takes place change with the fracture size. Shear wave time delay or anisotropic factor decreases with the inceasing frequency, they are sensitive to fracture size and have the same sensitivity. In a certain sense, they are equivalent in our research. The shear wave anisotropy or time dely is more sensitive to larger scale fractures in the low-frequency band and the smaller scale fractures in the high-frequency band. The greater the frequency, the smaller time delay or shear wave anisotropy factor. The dependence relations between time delay or anisotropic and frequency is contrast with the relations between SV-wave and frequency. This shows that we can infer meso-scale fracture strike and determine the degree of anisotropy with the low frequency range. Shear wave anisotropy is more sensitive to small fracture (0.5-1.0m) with the high-frequency band, which can be used to determine the position of a small fracture. Therefore, the paper dares to stick its neck out to make a conjecture that there is possibility of interpretation for two kinds of anisotropic parameters if the aligned small fracture and the aligned meso-scale fracture are in different directions ( conjugate angle is a non-zero angle) ,respectively, in high frequency and low frequency. Accord these formulas, we also make according research and supply the best band which discriminate meso-scale different scales of fracture. Using Thomsen parameters formulas, the effect of frequency on anisotropy parameter is obtained. The results show Thomsen parameters for Thomsen, found with increasing frequency, based on a new model of media equivalent HTI medium, Thomsen parameters increase with the decreasing frequency and increasing fracture.Moreover, we make detailed analysis for data of the forward in the inversion course and describe its results. Of course, our analysis is mainly focused on the frequency-dependent anisotropy. Four-component shear-wave data first is filtered by a series of band-pass filters, and then rotated into natural observation coordinate system to effectively separate the fast and slow shear-waves. It is found that there is an inverse relation between frequency and anisotropic factor. We make use of linear regression for the anisotropy factor or time delay to condition them their respective change, and then we discover linear gradient anisotropy is Consistent with which shear-wave anisotropy factor or time delay increases with decreasing frequency changes. Finally, the anisotropy factor or time-frequency analysis method based on the wavelet transform is applied to data. It is noticeable that Shear-wave anisotropy factor or time delay change with the frequency in shear-wave anisotropy-frequency spectrum. According to the relationship among them and previous research, we can obtain fracture strike from the fast shear-wave, and discriminate fracture size from the shear-wave anisotropy factor or time delay. What need to be emphasized is to make use of time delay to inverse must chase the influence cancellation of thickness.Finally, we developed a set of software which extracts information on meso-scale fracture (fracture density and fracture size) from multi-component VSP data based on a developing equivalent media model, which will provide similar means and methods to process the actual VSP data of shear wave resources work.