Advances in mathematical modelling to study complex sound propagation in an inhomogeneous moving ocean: Unlocking the Operational Advantage of the Oce

海洋是一个不断演变的巨大、复杂和动态的环境。模拟声音在海洋中的传播是一个多方面的、极具挑战性的问题。存在过多的影响声波在海洋环境中的传播的非平凡的时间相关现象，其来自环境因素（例如，温度、压力和盐度）、生物效应（与动物和植物种群的相互作用）、人类效应（航运、石油和天然气开采）。声音在海洋中的传播可以通过适当选择边界条件，用波动方程进行数学描述。有五个既定的解决方案的技术，其中每一个都有其局限性，如范围或频率依赖性，相关的数学近似应用，和计算负担。[1]、[2]和[3]的射线理论最适合高频应用，而[4]、[5]和[？]的正常模式（NM），和抛物线方程（PE）模型，[6]，[7]和[8]，更适合低频应用（在这些模型的描述中，1kHz被认为是分离低频和高频状态的典型频率，并且应用从低于几Hz扩展到几百kHz）。直接离散化方法，例如有限元（FE）或有限差分（FD），该项目的目的是开发新的自适应混合模型，能够根据环境和特定挑战的需求（包括操作或计算要求）在求解技术之间进行有效切换。上面列出的大多数数值解对于频率和距离相关性可能是有效的，但由于应用了各种假设和近似，这种速度上的优势在保真度上付出了代价。例如，低和中程频率散射和混响从海洋边界目前不包括在分层层模式，如NM和波数积分方法。同样，PE技术不能轻易地处理backscattering，是基于一个简化形式的波动方程。该项目试图通过研究动态和散射效应来解决这些问题，这与低频声纳建模以及国防和安全应用中所有频率下与距离和深度相关的声音传播密切相关。

The Ocean is a vast, complex and dynamic environment that is continuously evolving. Modellingthe propagation of sound through the ocean is a multi-faceted and extremely challengingproblem. There are a plethora of non-trivial time-dependent phenomena that affect the propagationof acoustic waves in an ocean environment, from environmental factors (e.g., temperature,pressure, and salinity), to biological effects (interactions with animal and plant populations),to anthropological effects (shipping, oil and gas extraction).The propagation of sound in the ocean may be described mathematically using the wave equationvia appropriate choice of boundary conditions. There are five established solution techniques,each of which has its limitations, such as range or frequency dependence, related to themathematical approximation applied, and computational burden. Ray theory, [1], [2] and [3],is best suited to high frequency applications, whereas normal mode (NM), [4], [5] and [?], andparabolic equation (PE) models,[6], [7] and [8], are better suited to low frequency applications(in the description of these models, 1 kHz is considered a typical frequency to separate low andhigh frequency regimes and applications extend from below a few Hz to several hundred kHz).Direct discretisation methods, such as finite element (FE) or finite difference (FD), are alsoused and are capable of solving the full wave equation but are computationally intensive.The aim of this project is to develop new adaptive hybrid models that are able to switchefficiently between solving techniques as the environment and specific challenges demand (includingoperational or computational requirements). The majority of the numerical solutionslisted above may be efficient for the frequency and range dependence for which they are valid,but this advantage in speed imposes a cost in fidelity through the various assumptions andapproximations applied. For example, low and medium-range frequency scattering and reverberationfrom the ocean boundaries are not presently included in stratified layer models suchas NM and wavenumber integration methods. Similarly, PE techniques cannot easily treatbackscattering, being based on a reduced form of the wave equation. This project seeks toaddress those issues by studying the dynamic and scattering effects, which are highly relevantfor low-frequency sonar modelling, as well as for range and depth-dependent sound propagationat all frequencies for defence and security applications.