基于贝叶斯理论的振幅随偏移距变化三参数同步反演

Simultaneous three-term AVO inversion based on Bayesian theorem

关键词:  贝叶斯理论  先验约束  Huber分布  参数协方差矩阵  地震资料处理

Key words:  Bayesian theorem  prior constraints  Huber distribution  parameter covariance matrix  seismic data process

摘要:

受多种因素的影响，常规叠后地震道波阻抗反演不能得到可靠的波阻抗及其他岩性信息，而叠前波阻抗反演 却可以得到比常规叠后波阻抗反演更丰富、更有效的岩性信息。为此建立了振幅随偏移距变化(AV0)波阻抗反演 公式的一阶差分模型及褶积模型，推导了基于贝叶斯理论的AV0波阻抗反演公式，给出了采用Huber分布作为模型 参数的先验分布及测井数据的参数协方差矩阵作为约束条件的实现方法，并利用共轭梯度法计算了纵、横波阻抗及 密度。结果表明，利用该方法可提高叠前反演问题的稳定性和反演结果的可靠性，反演得到的纵、横波阻抗及密度 可用来进一步计算流体及孔隙度等信息，为岩性及含油气性解释提供可靠依据。

Abstract:

Routine post-stack seismic trace inversion techniques affected by many factors can not get reliable impedance or other lithologic information. However, more abundant and more effective lithologic information can be obtained from pre-stack data inversion than that obtained from ordinary post-stack impedance inversion. The one order differential model and convolutional model of impedance formula of amplitude versus offset (AVO) inversion were established. Impedance inversion formula from AVO was derived based on Bayesian framework. Methods of using Huber function as prior model parameter distribution and covariance matrix from well log as constrains were developed. The P-wave impedance, S-wave impedance and density were calculated by the conjugate gradient algorithm. The numerical results show that the robustness of noise interference and the reliability of inverted result are improved by the method, and the inverted P-wave impedance, S-wave impedance and density are calculated to obtain more reliable information of fluids and porosity, which can provide reliable foundation for lithologic and oil-bearing interpretation.