基于波动方程解析解的块约束广义声阻抗反演

Generalized impedance blocky inversion based on analytic solution to wave equation

由于前期处理过程多数情况下基于声学介质假设,叠前地震道集更趋向于声学AVO特征。密度作为一种非常可靠的弹性参数在储层描述中起着关键作用,但反演过程不稳定。为此,提出基于声波方程解析解的块约束广义波阻抗反演方法。该方法通过部分叠加剖面反演随入射角变化的广义声阻抗,在此基础上提取稳定的速度和密度参数。针对常规阻抗反演方法忽略透射损失、层间多次波问题,基于推导的递归公式,对一维声波方程进行解析求解,获取不同入射角的全波场响应,并利用链式法则推导了对应的模型导数用于梯度类反演算法。为提高反演结果的分辨率,在贝叶斯理论框架下引入块约束,以获取稳定且边界清晰的反演结果。模型数据验证了所提出的正、反演方法的有效性;通过噪声测试验证了块约束反演方法的抗噪能力以及边界刻画能力;实际资料反演结果表明,新方法的反演结果分辨率高,边界刻画清晰,提取的速度、密度参数稳定且准确。

Since the pre-processing of pre-stack gathers is based on the assumption of acoustic medain in many cases,the the gathers tend to be with more acoustic AVO features.In addition,density inversion is unstable.This paper proposes a generalized impedance blocky inversion based on analytic solution to acoustic wave equation.The generalized acoustic impedance is inverted by apartially stacked profile,which varies with the angle of incidence;and on this basis,more accurate velocity and stable density are extracted.For the conventional impedance inversion method,transmission loss and interlayer multiples are neglected.Based on the recursive formula of derivation,the one-dimensional acoustic wave equation is solved analytically to obtain the full-wavefield responses at different incident angles,and the Fréchet derivatives are analytically derived for gradient-descent inversion algorithm.Most of the inversion methods are based on smoothing constraints,which fundamentally lead to unfocused boundaries for inversion results.In order to improve the resolution of the inversion results,blocky constraints can be introduced based on the Bayesian inference framework to obtain stable and high resolution inversion results.According to the above theory,we first uses model data to analyze the influence of the incompleteness of the forward method on seismic responses,further verify the validity of the inversion method,and extract the accurate velocity and density.Then the ability to characterize the boundary for blocky constraintis tested by adding noises.Both model and actual data prove that the inversion results from the new method have higher resolution,the boundary is clearer,and the extracted velocity and density profiles are stable and accurate.