基于逆算子估计的AVO反演方法研究

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.

AVO inversion based on inverse operator estimation

Amplitude variation with amplitude or angle (AVO/AVA) inversion has been widely utilized in exploration geophysics to estimate the formation of elastic parameters underground. The traditional inversion algorithms are mainly optimization, while the AVO inversion based on inverse operator estimation is to inverse directly. The key is to find the subspaces which exist inverse mapping instead of searching for the solution directly as optimization algorithms do.#br# 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.#br# 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.#br# 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.