有效声速泰勒级数逼近的适用条件

Applicable conditions of Taylor series approximation formulae of effective sound velocity

在水下高精度声学定位和声纳水深测量中,需要高精度的有效声速参量。在实际中,精确计算有效声速需要声线跟踪算法,但计算成本较高。有效声速的泰勒级数逼近作为一种有效声速的近似逼近方法,可避免大量计算成本。讨论了有效声速泰勒级数逼近公式的不同阶数逼近情况,特别是给出了两类有效声速泰勒级数逼近公式的适用条件,以及他们随高度增大适用性和逼近精度的变化。研究表明,当声速剖面稀疏时,宜采用谐波平均声速下的泰勒级数改正公式;当高度角小于50°时,有效声速泰勒级数逼近精度出现明显的衰减。

In the underwater high-precision acoustic positioning and sonar bathymetry,effective sound velocities of high-precision are needed.In practice,the accurate calculation of effective sound velocity requires the ray tracking algorithm,but the calculation cost is relatively high.The taylor series approximation method of effective sound velocity can avoid a large number of computational costs in the ray tracing.In this paper,the Taylor series approximation formulae of effective sound velocity with different orders are discussed.In particular,the applicable conditions of two kinds of Taylor series approximation formulae are presented,and we find that their applicability and approximation accuracy change with the increase of height and the water column density of the sound speed profile.The results show that,when the sound velocity profile is sparse,the Taylor series correction formula under harmonic mean sound velocity is more accurate;When the elevation angle is less than 50 degrees,the Taylor series approximation accuracy of the effective sound velocity decreases obviously.