Quijano Jorge E, Dosso Stan E, Dettmer Jan, Holland Charles W
School of Earth and Ocean Sciences, University of Victoria, 3800 Finnerty Road, Victoria, British Columbia, V8P 5C2, Canada.
Applied Research Laboratory, The Pennsylvania State University, State College, Pennsylvania 16804, USA.
J Acoust Soc Am. 2015 Oct;138(4):2106-17. doi: 10.1121/1.4930186.
This paper develops a fast numerical approach to computing spherical-wave reflection coefficients (SWRCs) for layered seabeds, which provides substantial savings in computation time when used as the forward model for geoacoustic inversion of broadband seabed reflectivity data. The approach exploits the Sommerfeld-integral representation of SWRCs as the Hankel transform of a function proportional to the plane-wave reflection coefficient (PWRC), and applies Levin integration to the rapidly oscillating integrand cast as the product of a (pre-computed) media-independent matrix and a vector involving PWRCs at a sparse sampling of integration angles. Compared to conventional Simpson's rule integration for computation of the SWRC, the Levin integration yields speed-up factors of an order of magnitude or more. Further, it results in reduced memory requirements for storage of pre-computed quantities, a desirable property when a graphics processing unit (GPU) is used for parallel computation of SWRCs. The paper applies trans-dimensional Bayesian inversion to investigate the impact of forward modeling in terms of PWRCs and SWRCs on the estimation of geoacoustic parameters and uncertainties. Model comparisons are quantified in simulated- and measured-data inversions by comparing the estimated geoacoustic parameters to the true parameters or core measurements, respectively, and by calculating the deviance information criterion for model selection.
本文提出了一种用于计算分层海床球面波反射系数（SWRCs）的快速数值方法，当该方法用作宽带海床反射率数据地声反演的正演模型时，可大幅节省计算时间。该方法利用SWRCs的索末菲积分表示形式，即将其表示为与平面波反射系数（PWRC）成比例的函数的汉克尔变换，并将莱文积分应用于快速振荡的被积函数，该被积函数被表示为一个（预先计算的）与介质无关的矩阵和一个涉及在稀疏积分角度采样处的PWRCs的向量的乘积。与用于计算SWRC的传统辛普森法则积分相比，莱文积分产生的加速因子达一个数量级或更高。此外，它减少了存储预先计算量所需的内存，这在使用图形处理单元（GPU）进行SWRC的并行计算时是一个理想的特性。本文应用跨维贝叶斯反演来研究基于PWRCs和SWRCs的正演建模对估计地声参数和不确定性的影响。通过分别将估计的地声参数与真实参数或岩心测量值进行比较，并计算用于模型选择的偏差信息准则，在模拟数据和实测数据反演中对模型比较进行量化。
