印兴耀, 邓炜, 宗兆云

中国石油大学(华东)地球科学与技术学院, 山东青岛　266580

基于逆算子估计的AVO反演方法研究

印兴耀, 邓炜, 宗兆云

中国石油大学(华东)地球科学与技术学院, 山东青岛266580

摘要传统反演算法以优化算法为主，而基于逆算子估计的AVO反演算法则利用了直接求逆的思路.算法的关键在于寻找存在逆函数的子域，进而可以在子域内直接求逆，这种解决反问题的思路不同于一般的优化类算法所采用的直接搜索解的方式，具有更高的效率.AVO反演利用了振幅随着偏移距的变化特征，反演的精度受到地震资料质量的影响，通过加入L1范数约束以及合理的初始模型有助于提高反演的稳定性以及准确度.模型测算和实际应用表明，基于逆算子估计的AVO反演方法具有较高的精确程度和可靠性.

关键词AVO反演； 逆算子估计； L1范数； 初始模型

Aki&Richards approximation is utilized to establish the inversion objective function. L1 norm constraint is considered on the basis of reasonable initial model in order to improve effciency and stability during AVO inversion process. Inverse operator estimation algorithm utilizes numerical approximation of objective function in empirically constrained subspaces. The existence of inverse mapping inside these subspaces is supposed, and thus the existence of its numerical approximation is also supposed. This numerical approximation is used for the prediction of the solution. It can be divided into the following four steps: (1) initialization, (2) selection, (3)prediction,(4) solution space correction. Since this method is approximate, the algorithm is arranged into iterative cycles and the solution is gained successively.

Model test in which noise immunity and stability based on L1 norm constraint are considered lays the foundation for the actual data inversion. In the model test, the inversion results based on synthetic seismogram with different SNR noise remain good consistency with the model value. L1 constraint is necessary, a relatively stable result can be obtained in multiple inversion processes and it helps reduce the number of singular values. The seismic data is from China′s land, inversion quality can be evaluated by well data and seismic data.Inversion results of actual seismic data maintain good consistency with logging curves.

Reliability of the solution, noise immunity and convergence speed can be improved by increasing the constraint requirements and considering reasonable initial models. Poor lateral continuity when dealing with actual data can be reduced by optimizing the objective function and the initial model. In general, AVO inversion based on inverse operator estimation is effective and potential.KeywordsAVO inversion； Inverse operator estimation; L1 norm; Initial model

1引言

叠前弹性参数反演是利用叠前地震信息、测井资料数据以及地质信息反演地下的相关参数、预测储层以及流体(杨培杰和印兴耀，2008;印兴耀等，2010,2014)的一种方法.相比于叠后反演方法，利用AVO反演方法可以更为精确地提取反映岩石含油气性以及岩性的属性参数(Goodway et al.,1997;Gray and Andersen,2001; Xingyao Yin and Shixin Zhang，2014；Zong et al.,2015;Yin et al.,2015)，从而提高流体识别和储层预测的精度.

基于逆算子估计的AVO反演方法是根据Zoeppritz方程近似式(Bortfeld，1961；Aki and Richards,1980; Shuey,1985;郑晓东,1991；Zong et al.,2012，2013a )直接求取三参数的方法，利用Aki&Richards近似方程建立反演方程，目标函数为正演数据与观测数据残差的L2范数，由于反演问题的不适定性，较小的噪声即……