基于各向异性AVO的裂缝弹性参数叠前反演方法

基于各向异性理论,将具有水平对称轴的高角度裂缝介质等效为HTI介质。首先,通过分析HTI介质反射界面的纵波反射系数公式,研究裂缝介质振幅随偏移距和方位角的变化特征,探索了方位各向异性介质弹性参数和各向异性参数的叠前反演方法。其次,为更好地估测介质的弹性参数:纵波阻抗IP、横波阻抗IS以及各向异性梯度Γ,对反射系数近似式进行了简化,同时对简化公式的精度进行了对比分析。最后,选取2D逆掩断层模型,利用褶积公式制作不同方位的合成地震道集,并对合成地震道集添加随机噪声(信噪比为2∶1),将其应用于方位AVO叠前反演算法试算中。结果表明,当信噪比为2时,方位AVO叠前反演所得纵波阻抗、横波阻抗及各向异性梯度的估测值与模型真实值基本吻合,而且估测值能够较准确地反映原始模型的地层特征,验证了方位AVO叠前反演算法的准确适用性。     

Effects of pore fluid pressure on the seismic response of a fractured carbonate reservoir

An effective medium model for the stress-dependent seismic properties of fractured reservoirs is developed here on the basis of a combination of a general theory of viscoelastic waves in rock-like composites with recently published formulae for deformation of communicating and interacting cavities (interconnected pores/cracks and fractures at finite concentration) under drained loading. The inclusion-based model operates with spheroidal cavities at two different length scales; namely, the microscopic scale of the pores and (grain-boundary) cracks, and the mesoscopic scale of the fractures (controlling the flow of fluid). The different cavity types can in principle have any orientation and aspect ratio, but the microscopic pores/cracks and mesoscopic fractures were here assumed to be randomly and vertically oriented, respectively. By using three different aspect ratios for the relatively round pores (representing the stiff part of the pore space) and a distribution of aspect ratios for the relatively flat cracks (representing the compliant part of the pore space), we obtained a good fit between theoretical predictions and ultrasonic laboratory measurements on an unfractured rock sample under dry conditions. By using a single aspect ratio for the mesoscopic fractures, we arrived at a higher-order microstructural model of fractured porous media which represents a generalization of the first-order model developed by Chapman et al. (2002,2003). The effect of cavity size was here modelled under the assumption that the characteristic time for wave-induced (squirt) flow at the scale of a particular cavity (pore/crack vs. fracture) is proportional with the relevant scale-size. In the modelling, we investigate the effect of a decreasing pore pressure with constant confining pressure (fixed depth), and hence, increasing effective pressure. The analysis shows that the attenuation-peak due to the mesoscopic fractures in the reservoir will move downward in frequency as the effective pressure increases. In the range of seismic frequencies, our modelling indicates that the P-wave velocities may change by more than 20% perpendicular to the fractures and close to 10% parallel to the fractures. In comparison, the vertical S-wave velocities change by only about 5% for both polarization directions (perpendicular and parallel to the fractures) when the effective pressure increases from 0 to 15 MPa. This change is mainly due to the overall change in porosity with pressure. The weak pressure dependence is a consequence of the fact that the S waves will only sense if the fractures are open or not, and since all the fractures have the same aspect ratio, they will close at the same effective pressure (which is outside the analysed interval). Approximate reflection coefficients were computed for a model consisting of the fractured reservoir embedded as a layer in an isotropic shale and analysed with respect to variations in Amplitude Versus Offset and aZimuth (AVOZ) properties at seismic frequencies for increasing effective pressure. For the P-P reflections at the top of the reservoir, it is found that there is a significant dependence on effective pressure, but that the variations with azimuth and offset are small. The lack of azimuthal dependence may be explained from the approximate reflection coefficient formula as a result of cancellation of terms related to the S-wave velocity and the Thomson’s anisotropy parameter δ. For the P-S reflection, the azimuthal dependence is larger, but the pressure dependence is weaker (due to a single aspect ratio for the fractures). Finally, using the effective stiffness tensor for the fractured reservoir model with a visco-elastic finite-difference code, synthetic seismograms and hodograms were computed. From the seismograms, attenuation changes in the P wave reflected at the bottom of the reservoir can be observed as the effective pressure increases. S waves are not much affected by the fractures with respect to attenuation, but azimuthal dependence is stronger than for P waves, and S-wave splitting in the bottom reservoir P-S reflection is clearly seen both in the seismograms and hodograms. From the hodograms, some variation in the P-S reflection with effective pressure can also be observed.