CAJ | 학술논문

本文用孔隙介质力学的方法来研究纵波在介观周期成层Patchy模型的传播问题.相对于White方法,该方法少了不同介质分界面处的流体压力不等的假设,推导过程更为严密;和Dutta的双相方程解耦方法比较,文中方法直接求解双相方程.形式上更为直观.当纵波通过周期成层孔隙模型时,在低频段用孔隙弹性力学得到纵波频散和衰减结果与用White公式得到的结果符合得很好;周期成层的Patchy孔隙模型由于其空间排列的周期性使其成为孔隙弹性声子晶体,在其频散和衰减曲线上的高频段会出现多个禁带和通带,这使得速度不会随频牢单调递增,衰减峰也不只一个.对于地震频段,随着渗透率降低模型的衰减峰向低频移动,这和实际观测结果一致,和传统Biot理论预测结果正相反;随着含气量上升纵波衰减峰值先上升后下降,其最大值出现在含气量0.1左右,这和相关实验结果一致.研究结果表明该模型可以定性解释观测到的地震衰减结果.
본문용공극개질역학적방법래연구종파재개관주기성층Patchy모형적전파문제.상대우White방법,해방법소료불동개질분계면처적류체압력불등적가설,추도과정경위엄밀;화Dutta적쌍상방정해우방법비교,문중방법직접구해쌍상방정.형식상경위직관.당종파통과주기성층공극모형시,재저빈단용공극탄성역학득도종파빈산화쇠감결과여용White공식득도적결과부합득흔호;주기성층적Patchy공극모형유우기공간배렬적주기성사기성위공극탄성성자정체,재기빈산화쇠감곡선상적고빈단회출현다개금대화통대,저사득속도불회수빈뢰단조체증,쇠감봉야불지일개.대우지진빈단,수착삼투솔강저모형적쇠감봉향저빈이동,저화실제관측결과일치,화전통Biot이론예측결과정상반;수착함기량상승종파쇠감봉치선상승후하강,기최대치출현재함기량0.1좌우,저화상관실험결과일치.연구결과표명해모형가이정성해석관측도적지진쇠감결과.
In this paper poroelasticity is used to study the P wave propagation in periodic layered-model with patchy saturation at mesoscopic scale. Compared with the White's method,the deduction by the proposed method is more rigorous from mathematical view,without the assumption that the fluid pressures are not equal at the boundaries of different mediums as White has done. The proposed method solves the poroelastic equations in more directly perceived way than Dutta's mathematic techniques to make the equations uncoupled for solutions. When a P wave passes through the periodic layered-model with patchy saturation,the results of dispersion and attenuation by the method in this paper are consistent with those by White. Because of its periodic structure the patchy model becomes a phononic crystal with several passbands and stopbands in high frequency band. So the velocity of the P wave won't increase monotonously while the frequency increases,and there are several peaks of attenuation. As for seismic band,the attenuation peak of the patchy model moves to the low frequency as the permeability decreases,in accordance with the factual observation,but contrary to the results by Biot's theory before. When the gas volume rises in the model,the value of the attenuation peak increases at first,then decreases,and the maximum of the attenuation appears when the fraction of gas is nearly 0.1.The numerical results are in line with those by the related experiments. Researches show that the periodic layered-model with patchy saturation can qualitatively account for the observed seismic attenuation.