Because of their sensitivity to small variations in environmental parameters, ray travel time and modal phase are arguably two most important quantities in acoustic remote sensing of the ocean. Fluctuations in these quantities resulting from sound scattering on small-scale volumetric inhomogeneities and surface roughness are normally considered as noise in ocean acoustic tomography and thermometry. The travel times and phases are averaged over suitably chosen time periods to suppress the fluctuations. However, the statistical averages are biased, i.e., average travel time and modal phase are different from values of the respective acoustic quantities in the statistically-averaged medium. Although of the second order in amplitude of random scatterers, which is assumed small, the bias accumulates with range and may become significant at O(1 Mm) ranges of interest to the ocean acoustic tomography and thermometry. In this paper, we use a perturbation approach to study the bias within the ray and the "vertical modes - horizontal rays" theories. The perturbation approach allows one to express statistical moments of acoustic quantities as line integrals of respective statistical moments of environmental parameters along the trajectory of the sound wave in an unperturbed medium, leading to an efficient technique to evaluate the bias for various oceanographic processes. Propagation scenarios considered include continuous spectrum of internal gravity waves in deep ocean and mesoscale inhomogeneities. It is demonstrated that, unlike first-order scattering effects, a consistent account of horizontal refraction is crucial for the bias calculations.
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机译：由于它们对环境参数的小变化的敏感性，射线旅行时间和模态相可以说是海洋声学遥感中最重要的数量。由声音散射对小规模体积不均匀性和表面粗糙度产生的这些量的波动通常被认为是海洋声学断层摄影和温度测量的噪音。 The travel times and phases are averaged over suitably chosen time periods to suppress the fluctuations.然而，统计平均值是偏置的，即平均行程时间和模态相不同于统计平均介质中的各个声量的值。虽然在随机散射仪的幅度中的二阶阶数，但是偏压累积范围，并且可以在O（1mm）感兴趣的感兴趣范围内变得显着，并且可以在海洋声学层析成像和温度测量。在本文中，我们使用扰动方法来研究光线内的偏差和“垂直模式 - 水平射线”理论。扰动方法允许一个人表达声量的统计矩，作为沿着不受干扰的介质中声波的轨迹的环境参数的各个统计矩的线积分，从而实现了评估各种海洋过程的偏差的有效技术。所考虑的传播情景包括深海和Mesoscale不均匀的连续谱的内部重力波。据证明，与一阶散射效果不同，水平折射的一致解释对于偏置计算至关重要。
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