薄层反透射系数关于射线参数的低阶近似

Low-order approximation of thin-layer reflection and transmission coefficients with respect to ray parameters

随着我国油气田及煤田开发的不断深入,薄储层成为地震勘探面临的主要对象之一。然而,薄层精准反透射系数矩阵方程较为复杂,难以直接应用于薄层AVO分析及反演。为了得到较为简洁的薄层反透射系数公式,对薄层反透射系数与射线参数的关系展开了奇偶性讨论。研究认为:纵波入射时,薄层非转换波的反透射系数是射线参数的偶函数;而转换波的反透射系数是射线参数的奇函数。在此基础上,建立了两类典型薄储层模型(强阻抗差薄层和弱阻抗差薄层),并对其反射系数进行小角度范围内(≤30°)拟合,研究射线参数的高次项舍弃问题。模拟分析结果表明:保留射线参数奇、偶一次项即可高度拟合反射系数,该结论对薄层近似公式的提出具有指导性意义。同时,对比不同厚度下薄层反射系数与薄层顶、底界面反射系数可知:厚度较大时,薄层及上覆围岩弹性参数对薄层反射系数的影响较大;厚度较小时,薄层上、下围岩的弹性参数对薄层反射系数的影响较大。

With the development of oil and gas,and coal exploration,thin reservoirs have become one of the main targets of seismic exploration.However,the matrix equations to describe thin layers,which must include precise reflection and transmission coefficients,are complicated,and their direct application to thin-layer amplitude versus offset analysis and inversion is difficult.In order to obtain a relatively simple form of the thin-layer reflection and transmission coefficients,this paper discusses the relationship between the reflection and transmission coefficients of thin layers and the ray parameters.It is pointed out that the coefficients of the non-converted wave are even functions of the ray parameter when the incident P wave is approaching,while the coefficients of the converted wave are odd functions of the ray parameter.On this basis,two kinds of thin-layer models(strong impedance difference thin layer,and weak impedance difference thin layer)are established,the reflection coefficient is fitted in a small angle range(≤30 degrees),and the high-order discarding problem of the ray parameter is studied.Results of simulations showed that the reflection coefficient can be very well fitted after obtaining the parity first term,which has a guiding significance for the thin layer approximation formula.Simultaneously,Comparisons were also carried out between the different thickness of the top and bottom interfaces of the thin layer and that of a single interface composed of overlying surrounding rock and underlying surrounding rock.The results showed that,when the thickness of the thin layer is large,the parameters of the overlying rock have a great influence on the reflection coefficient of the thin layer.Conversely,when the thickness of the thin layer is small,the parameters of both the overlying and the underlying rock have a great influence on the reflection coefficient of the thin layer.