采用邻域近似算法估计环境参数不确定性

Estimating parameter uncertainties by a neighbourhood approximation algorithm

根据贝叶斯理论,逆问题的解可以用后验概率密度来表征,它包含了模型参数先验知识和观测数据信息,反映了反演参数的不确定性。一种快速吉布斯采样算法已经被用于后验概率密度的多维积分运算,但其需要调用大量的声场前向模型,在多个频率或水平变化的匹配场参数反演中,计算量仍然很大。基于邻域近似算法,提出一种比快速吉布斯采样算法更快的参数不确定性估计方法。对低维参数反演问题,邻域算法可以很好地逼近真实的后验概率密度;而对高维问题及其敏感参数,在模型参数样本量有限的条件下,邻域算法很难精确地估计后验概率密度。为了克服以上缺点,并完整地得到反演参数的不确定性信息,设计了一种多步估计方案。数值仿真和实测数据分析表明,多步邻域算法采用较少的计算代价,可获得与快速吉布斯方法相似的估计精度。

In Bayesian inference theory, the solution of an inverse problem is characterized by its Posterior Probability Density （PPD）, which combines prior information about the model with information from an observed data set. An efficient and Fast Gibbs Sampler （FGS） has been developed to estimate the multi-dimensional integrals of the PPD, which requires solving the forward model problems many times and leads to intensive computation for multi-frequency or range-dependent inversion cases. This paper presents an alternative approach in order to speed this estimation process based on a Neighbourhood Approximation Bayes （NAB） algorithm. For lower dimension geoacoustic inversion, the NAB can approximate the PPD very well. For higher dimensional problems and sensitive parameters, however, the NAB algorithm has difficulty to estimate the PPD accurately with limited model samples. According to the preliminary estimation of the PPD by NAB, this paper developed a multi-step inversion scheme, which adjusts the parameter search intervals flexibly, in order to improve the approximation accuracy of NAB and obtain more complete information about parameter uncertainties. The prominent feature of NAB is to approximate the PPD by incorporating all models for which the forward problem has been solved into the appraisal stage. Comparison of FGS and NAB for noisy synthetic benchmark test cases and Mediterranean real data indicates that NAB provides reasonable estimates of the PPD moments while requiring less computation time.