TTI介质弹性波相速度的一般性近似

弹性波速度是弹性波动力学研究的核心内容之一。倾斜横向各向同性(TTI)介质弹性波相速度的理论精确公式比较复杂。由于地球介质弱各向异性的普遍性,在理论研究和实际应用中常常采用弱各向异性假设进行简化,但是面对页岩等中强各向异性介质时,弱各向异性近似不能满足精度要求,甚至不再适用。基于前人的研究成果,从TTI介质弹性波相速度理论精确公式出发,利用近似的配方法将精确公式内的D项近似表示为两项的平方和,从而实现多项式的开方运算。在此基础上,推导了TTI介质qP波和qSV波相速度的一般性近似表达式。理论分析和数值计算结果表明:TTI介质弹性波相速度一般性近似表达式由于在推导过程中没有直接利用弱各向异性的假设,因此不仅适用于弱各向异性,也适用于中强各向异性的情况,即在较大范围内,一般性近似的精度高于弱各向异性近似的精度。并且对于同一种TTI介质,qP波的一般性近似式精度高于qSV波的精度。

Velocity research is one of the core contents of elastic wave dynamics.The exact expression of phase velocity for elastic waves in tilted transversely isotropic (TTI) media is complicated.The assumption of weak anisotropy,due to its universality within the Earth,is often used to simplify seismic media.However,the weak anisotropy approximation is not applicable for moderate to strong anisotropic media such as shale.Based on the exact expression of phase velocity for elastic waves in TTI media,this study approximated the D term in the exact expression of the quadratic sum of two terms,using an approximate method of completing the square,to realize the square-root operation of the polynomial.Thereafter,general approximate expressions of the phase velocity for qP waves and qSV waves in TTI media are derived.Theoretical analysis and numerical calculation show that the general approximate expression of phase velocity for elastic waves in TTI media is applicable to weak,moderate,and strong anisotropic media,because the weak anisotropy assumption is not directly used in the derivation.The accuracy with the general approximation is higher than that with the weak anisotropy approximation.Also,for the same TTI medium,the accuracy with the general approximation expression of the qP wave is higher than that of the qSV wave.

国家自然科学基金(41774137,41104053)共同资助。