P-SV波反射系数的一种近似算法及其在AVO资料反演中的意义

A Simple approximation to the P-SV wave reflection coefficients and its implication in the inversion of AVO data

清华大学工程力学系, 北京100084

Dept. of Eng. Mechanics, Tsinghua University, Beijing 100081

本文推导出作为射线参数函数的平面转换横波(P－SV)反射系数的一个近似公式。该近似式说明在非法线入射时,P－SV波反射系数主要取决于两个弹性参数：(1)△μ／ρ,反射界面两侧切变模量差与平均体密度之比；和(2)△ρ／ρ,反射界面两侧介质体密度之差与平均体密度之比。文中还给出了数值实例,以说明该式的计算精度,同时分析了其适用范围,并与Aki和Richards(1980)的近似式的数值结果作了比较。本文采用阻尼最小平方反演理论计算的反演参数结果表明,AVO资料线性反演中,估算△μ／ρ比估算泊松比差△σ精度高。

We derived an approximate formula for the plane P-SV wave reflection coefficient as a function of ray-parameter. The approximation formula shows that the behavior of the P-SV wave reflection coefficient at nonnormal angles of incidence is mainly controlled by two elastic parameters: (1)△ρ/ρ,the ratio of the contrast in bulk density to the average bulk density and (2 )△μ/ρ,the ratio of the contrast in shear moduli to the average bulk density. We also gave numercial examples to demonstate the accuracy of the formula, comparing with the approximate formula of Aki and Riehards (1980 ). Using a damped least-squares inversion of theoretical values for the reflection coefficients, we demonstrated that in a linear inversion of amplitude versus offset data.△μ/ρ could be better estimated than the estimation of the contrast of Poisson’s ratio △σ.