Title: Normal mode parameters estimation by a VLA in single-shooting Show Chinese title

Title: 通过单次射击的VLA进行正常模态参数估计

Abstract: This paper proposes an orthogonality-constrained modal search (OCMS) method for estimating modal wavenumbers and modal depth functions using a vertical linear array (VLA). Under the assumption of a known sound speed profile, OCMS leverages the orthogonality of distinct modal depth functions to extract both the modal depth functions and their corresponding wavenumbers, even when the VLA and a monochromatic sound source remain stationary.The performance of OCMS is evaluated through numerical simulations under varying signal-to-noise ratios (SNRs), different VLA apertures, varying numbers of VLA elements, VLA tilt and sound speed profile (SSP) uncertainty. The results demonstrate that OCMS is robust against noise, VLA aperture variations, and changes in the number of VLA elements, meanwhile, the algorithm maintains reliable performance when SSP uncertainty < 1 m/s and VLA tilt angle <5{\deg}. Furthermore, the effectiveness of OCMS is validated using SwellEx96 experimental data. The relative error between the modal wavenumbers derived from experimental data and those computed via Kraken is on the order of $10^{-4}$. Show Chinese abstract

Abstract: 本文提出了一种正交约束模态搜索（OCMS）方法，用于使用垂直线性阵列（VLA）估计模态波数和模态深度函数。 在已知声速剖面的假设下，OCMS利用不同模态深度函数的正交性，即使VLA和单频声源保持静止，也能提取模态深度函数及其对应的波数。通过在不同信噪比（SNR）、不同VLA孔径、不同数量的VLA元件、VLA倾斜以及声速剖面（SSP）不确定性的数值模拟中评估OCMS的性能。 结果表明，OCMS对噪声、VLA孔径变化和VLA元件数量变化具有鲁棒性，同时当SSP不确定性小于1 m/s且VLA倾斜角小于5{\deg }时，该算法仍能保持可靠性能。此外，使用SwellEx96实验数据验证了OCMS的有效性。 从实验数据中得出的模态波数与通过Kraken计算得到的模态波数之间的相对误差在$10^{-4}$的量级。