交叉偶极子声测井多频率反演地层三阶弹性常数和地应力研究  

Study of inversion for third order elastic constants and in situ stress by multifrequency dispersion of cross dipole sonic logging

作　　者：陈浩[1] 王秀明[1] 赵立新[2,3] 

机构地区：[1]中国科学院声学研究所声场声信息国家重点实验室,北京100190 [2]中国石油大学(北京),北京102249 [3]中海石油有限公司,北京100010

出　　处：《地球物理学报》2009年第6期1663-1674,共12页Chinese Journal of Geophysics

基　　金：国家自然科学重点基金项目(10534040);国家自然科学基金面上项目(10674148;40774099)资助

摘　　要：基于声弹性理论,本文详细论述了利用交叉偶极子多频率相速度反演地层三阶弹性常数和地应力的理论及信噪比对反演结果的影响.定性和定量分析表明在速度应力方程中,不含三阶弹性常数项与含三阶弹性常数项相比对速度的影响可以忽略,由此只利用一次测井资料同时反演地应力和三阶弹性常数是一个严重病态的问题或一个不确定性问题.针对不同的反演模型,详细考察了信噪比对各自简化模型和精确模型反演结果的影响.数值模拟结果表明,利用一次测井采用精确模型反演全部四个参数方法受信噪比影响严重.而利用不同流体压力下的测井资料进行反演时可以采用简化模型取代精确模型以便简化计算和提高反演速度,因为简化模型和精确模型有着几乎相同的精度;同时,分步反演的方法可以较好地反演出原位地应力及三阶弹性常数.Based on acoustoelastic theory, the method of inversion for third order elastic constants （TOECs） and in situ stress from the multi-frequency phase velocity of cross dipole sonic logging data and the effect of different signal to noise ratio （SNR） on the inversion result is studied. Qualitative and quantitative analysis shows that the contribution of the terms in acoustoelastic velocity-stress model not containing TOECs to the total velocity variation can be neglected, when compared to the contribution of the terms containing TOECs. This means that the inversion of TOECs and in situ stress is a severely ill-posed problem or an indeterminate one when only using the data at one time. The inversion stability is simulated for every accurate and approximate inversion model at different level SNR. Numerical result shows that the result inverted from the cross logging data at one borehole pressure using accurate model is affected heavily by noise. Both accurate model and approximate one in the inversion of data gotten at two different borehole pressures have the same accuracy. Thus, the latter can take place of the former to improve the computation speed and to simplify the model. The result also shows that the two- step method can give a better estimation of TOECs and in situ stress.

关 键 词：声弹性理论 三阶弹性常数 交叉偶极子 频散曲线 地应力 各向异性 

分 类 号：P631[天文地球—地质矿产勘探]