P-SV波反射系数近似及其AVO属性特征

P-SV Wave Reflection Coefficient Approximations and Characteristics of AVO Attributes

为了使P-SV波反射系数随入射角的变化特征更为明确,便于利用多种属性进行AVO分析和参数反演,本文首先用斯奈尔定律将AKI&RICHARDS给出的P-SV波反射系数近似公式中与横波反射角有关的角度项余弦表示成入射角的正弦,然后对改写后的表达式按入射角的正弦进行二项式展开,对展开结果取前两项,并引入二倍角来保留与入射角有关的角度项余弦对反射系数的贡献,最后得到了一个形式简单、不涉及横波反射角和透射角的P-SV波反射系数近似公式。为了验证新公式的近似精度,我们选用了岩性界面条件下的不同实际含油气砂岩模型进行了定量计算,并与P-SV反射系数公式的解析解及AKI等近似公式进行了对比研究。对比结果表明:新的近似公式以内能够准确反映P-SV转换波的振幅随偏移距变化的规律,体现了很高的近似精度,甚至比AKI等原近似公式的效果还好。在此基础上,通过对新近似公式不同形式的表述,详细分析了不同AVO属性组合反映的背景趋势及在25个不同含油气地层模型上的AVO交绘图特征,同时还讨论了利用这些不同形式的AVO属性来提取密度差、速度差等基本地层参数的过程和构建多种地震属性剖面的方法。通过分析和讨论可以得出:本文给出的近似公式不仅具有较高的精度,而且还可以利用这些新的AVO属性及其组合构成多种属性的AVO交绘图特别是可以构建ΛΡ和ΜΡ型流体因子、剪切模量、及纵横波速比等非常规地震属性剖面。这些结论对于P-SV波AVO分析和多波AVO理论研究都具有重要意义。

To make variations of P-SV wave reflection coefficient characteristics with incidence angle clearer and more convenient for AVO analysis and parameter inversion with multi-attributes, the authors used Snell law to rewrite the angle of emergence related to shear-wave of P-SV wave reflection coefficient approximation given by Aki & Richards as sine function of incidence angle, employed binomial expansion to the latter, reserved the two headmost items and introduced the bi-angle of incidence to replace the terms related to cosine function of angle of incidence. On such a basis, a new approximation equation for P-SV wave was put forward which has a simple form and doesn′t involve the angles of incidence and emergence related to shear-wave. To analyze the accuracy of the new equation, the authors made computation and compared such reflection coefficient equations as Zoeppritz′s equation and Aki approximation with the new expression for different models under different lithologic interfaces. The results show that the new approximation can accurately describe characteristics of P-SV wave amplitude varying with offset when the angle of incidence is less than, with the precision even higher than that of Aki and Richards. Based on writing the new approximation in different forms, the authors also analyzed AVO background trends and characteristics of AVO crossplottings for 25 different gas sand models with different AVO attribute combinations, and dealt with the procedures of extracting fundamental lithologic parameters such as density contrast and velocity contrast and the methods for constructing variousseismic attribute sections from these new attributes. From the analysis and the corresponding discussion, it is concluded that the new expression has a high precision and can construct multi-attribute AVO crossplottings, and that one can easily construct such non-conventional seismic attribute sections as and fluid factors, shear modulus, and compression-to-shear-wave velocity. These conclusions are of significance in P-SV wave AVO analysis and elastic AVO theoretical investigation.