杨氏模量和泊松比反射系数近似方程及叠前地震反演

Reflection coefficient equation and pre-stack seismic inversion with Young′s modulus and Poisson ratio

杨氏模量和泊松比等岩石弹性参数是表征页岩气储集体岩石脆性、评价储层含气特征的重要特征参数,而叠前地震反演是从地震资料中获取此类参数的有效途径.地震波反射系数方程是叠前反演的基础.首先,在平面波入射等假设条件下推导了基于杨氏模量(Y)、泊松比(σ)和密度(D)的纵波反射系数线性近似方程(YPD反射系数近似方程),该方程建立了地震纵波反射系数与杨氏模量反射系数、泊松比反射系数和密度反射系数的线性关系;其次,对该方程的精度和适用条件进行了分析,模型分析表明,在入射角为40°时,该方程具有较高的计算精度;最后,建立了一种稳定获取杨氏模量和泊松比的叠前地震直接反演方法.模型试算和实际资料试处理表明,基于新方程的反演方法能够稳定合理的直接从叠前地震资料中获取杨氏模量和泊松比参数,提供了一种高可靠性的页岩气"甜点"地震识别方法.

Young＇s modulus and Poisson ratio are two important rock parameters to indicate the ＂sweet spot＂ in gas shale. Pre-stack inversion based on reflection coefficient equation with different model parameterization is an efficient approach to obtain these parameters. Firstly, we derive the reflection coefficient approximate equation in terms of Young＇s modulus, Poisson ratio and density （YPD approximate equation） with the hypothesis of incident planar wave, which establishes the linear relationship between the reflection coefficient and Young＇ s modulus reflectivity, Poisson ratio reflection reflectivity and density reflectivity. Secondly, we analyze the precision and applicable condition of the novel reflection coefficient equation, and the model test shows that this equation is as accurate as the exact equation until the incident angle approaches to 40 degree. Finally, a robust AVA inversion procedure is introduced to test the possibility to invert for Young＇s modulus and Poisson ratio directly. Model and real data tests show that the introduced inversion method can obtain reasonable inversion results even with moderate Gaussian noise, which offers an efficient method to identify ＂sweet spot＂ with seismic data.