Zoeppritz方程的近似及其应用

Approximation of Zoeppritz equation and its application,

本文提出以幂级数形式表示Zoeppritz方程近似公式。此式把纵波表示为射线参数p的偶次幂级数,把横波表示为射线参数p的奇次幂级数,它包含了目前广泛用于地震勘探的Aki和Richards公式,及Shuey公式。与前人的近似公式相比,本文提出的近似式具有形式简单、物理意义明确和岩性关系清晰等优点。此式有两个最显著的特征:第一个特征是易于识别和分离纵波和横波;第二个特征是幂级数项的系数A_n^R和A_n^P仅是介质的密度ρ、纵波速度α和横波速度β的函数,而幂级数的底则是入射角i的函数,幂级数的常数项A_O^R和A_O^T恰好是垂直入射时的反射系数和透射系数。所以利用曲线拟合方法很容易实现全部地震岩性参数的反演,并可提取零偏移距剖面。此外,利用此近似式可以得到一些以往已知的反射和透射规律,并能揭示一些新的反射和透射特征,还可以从常规的CDP道集记录中提取28种新的AVO特征剖面。

It is proposed that the approximate representation of Zoeppritz equation can be written in the form of power series.In the approximate representation, P-wave is expressed as the even power series of rayparameter p, and S-wave as the odd power series. In other words, the representation includes Aki, Richards and Shuey's formulas which are widely used in present seismic exploration.The representation has simpler form, more definite geophysical meaning and clearer lithology relation than the others. The representation has two very distinct properties. First, P-wave and S-wave are identified or separated off easily. Second, coefficients (A_n^R and A_n^T) of the rower series are the functions of medium density ρ, P-wave velocity α and S-wave velocity β; the base of power series is the function of incident angle i; and the constant terms (A_o^R and A_o^T) are just the reflectoin coefficient and transmission coefficient in the case of vertical incident wave.Consequently, with the use of curve fitting method, the inversion of all seismic lithologic parameters can be easy achieved, and zero-offset section can be obtained. Furthermore, using this approximate representation,we can know some new reflected and transmitted wave properties besides old ones, and extract 28 new AVO characteristic sections from conventional CDP gathers.