Dosso Stan E, Nielsen Peter L
School of Earth and Ocean Sciences, University of Victoria, British Columbia, Canada.
J Acoust Soc Am. 2002 Jan;111(1 Pt 1):143-59. doi: 10.1121/1.1419087.
This paper applies the new method of fast Gibbs sampling (FGS) to estimate the uncertainties of seabed geoacoustic parameters in a broadband, shallow-water acoustic survey, with the goal of interpreting the survey results and validating the method for experimental data. FGS applies a Bayesian approach to geoacoustic inversion based on sampling the posterior probability density to estimate marginal probability distributions and parameter covariances. This requires knowledge of the statistical distribution of the data errors, including both measurement and theory errors, which is generally not available. Invoking the simplifying assumption of independent, identically distributed Gaussian errors allows a maximum-likelihood estimate of the data variance and leads to a practical inversion algorithm. However, it is necessary to validate these assumptions, i.e., to verify that the parameter uncertainties obtained represent meaningful estimates. To this end, FGS is applied to a geoacoustic experiment carried out at a site off the west coast of Italy where previous acoustic and geophysical studies have been performed. The parameter uncertainties estimated via FGS are validated by comparison with: (i) the variability in the results of inverting multiple independent data sets collected during the experiment; (ii) the results of FGS inversion of synthetic test cases designed to simulate the experiment and data errors; and (iii) the available geophysical ground truth. Comparisons are carried out for a number of different source bandwidths, ranges, and levels of prior information, and indicate that FGS provides reliable and stable uncertainty estimates for the geoacoustic inverse problem.
本文应用快速吉布斯采样（FGS）新方法来估计宽带浅海声学调查中海底地球声学参数的不确定性，目的是解释调查结果并验证该方法用于实验数据的有效性。FGS基于对后验概率密度进行采样来估计边际概率分布和参数协方差，将贝叶斯方法应用于地球声学反演。这需要了解数据误差的统计分布，包括测量误差和理论误差，而这些通常是未知的。引入独立同分布高斯误差的简化假设可以得到数据方差的最大似然估计，并导出一种实用的反演算法。然而，有必要验证这些假设，即验证所获得的参数不确定性是否代表有意义的估计值。为此，将FGS应用于在意大利西海岸外一个地点进行的地球声学实验，该地点之前已开展过声学和地球物理研究。通过与以下方面进行比较来验证通过FGS估计的参数不确定性：（i）对实验期间收集的多个独立数据集进行反演结果的变异性；（ii）为模拟实验和数据误差而设计的合成测试案例的FGS反演结果；以及（iii）现有的地球物理地面真值。针对多种不同的源带宽、距离和先验信息水平进行了比较，结果表明FGS为地球声学反演问题提供了可靠且稳定的不确定性估计。
