【摘要】 在球坐标系下用直接求解孔隙弹性方程的方法计算了介观尺度下空间周期排列的White球状Patchy模型中纵波传播问题.首先对纵波的衰减和频散进行了计算,并引入了物理学上声子晶体原理来解释高频时纵波在White球状模型中传播的异常现象.在含水饱和度和速度关系的研究中发现,在低频段用等效流体理论和Gassmann理论估计流体Patchy饱和岩石中的纵波速度完全能够满足当前地震勘探的要求.随后的具有相同含气饱和度但有不同周期的Patchy模型研究结果表明,随着空间周期变大,低频的纵波频散变得明显,纵波衰减峰频率向低频移动,但峰值几乎不变.最后,对单元外层含水中心含油的White球状Patchy模型和中心含气White球状Patchy模型进行研究、对比,发现孔隙流体流动对孔隙介质中的纵波频散、衰减影响显著.另外,在具体数值求解过程中用缩减方程组规模的方法解决了线性方程组严重病态得不到正确结果的问题.更多还原

【Abstract】 The P-wave’s characters of White’s sphere model, which is periodic in space and porous fluid patchy saturated in mesoscopic scale, is researched in this paper through directly solving poroelastic equations in sphere coordinates.First, the dispersion and attenuation of P-wave are computed and the principle of phononic crystal in physics is used to explain abnormal phenomenon at high-frequency.In the study of how water saturation affect the P-wave’s velocity, we find that at low-frequency, velocity estimated by the equivalent fluid theory and the Gassmann theory in fluid patchy saturated rocks meets the precision need in seismic exploration field.Then, results of models with different period magnitude in space show that increases the period magnitude, velocity disperses more at low-frequency and the attenuation peak moves to low-frequency with peak value nearly unchanged.Finally, a study is made on one White’s sphere model with patchy saturation with gas in central part and another White’s sphere model with oil in central part (both of which share water in the outer part).We compare the results and draw that fluid flow is a remarkable factor to affect the dispersion and attenuation of P-wave in porous media.In addition, during numerical solution process, based on a mathematic technique to reduce the size of equations the problem that a correct result can’t be got by original equations for ill condition is conquered.更多还原