The Green's function retrieval in media with horizontal boundaries usually only considers the extraction of direct and reflected waves but ignores the virtual head waves, which have been observed experimentally from ocean ambient noise and used to invert for geometric and environmental parameters. This paper derives the extraction of virtual head waves from ocean ambient noise using a vertically spaced sensor pair in a Pekeris waveguide. Ocean ambient noise in the water column is a superposition of direct, reflected, and head waves. The virtual head waves are produced by the cross-correlations between head waves and either reflected waves or other head waves. The locations of sources that contribute to the virtual head waves are derived based on the method of stationary phase. It is the integration over time of contributions from these sources that makes the virtual head waves observable. The estimation of seabed sound speed with virtual head waves using a vertical line array is also demonstrated. The slope of the virtual head waves is different from that of direct and reflected waves in the virtual source gather; it is therefore possible to constructively stack the virtual head waves. The predictions are verified with simulations.

中文翻译：

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海洋环境噪声中的虚拟头波：理论与模型

在具有水平边界的介质中进行格林函数检索通常仅考虑提取直接波和反射波，而忽略虚拟头波，这些头波已从海洋环境噪声中进行了实验观察，并用于反演几何和环境参数。本文使用Pekeris波导中的垂直间隔传感器对，从海洋环境噪声中提取虚拟头波。水柱中的海洋环境噪声是直接波，反射波和头波的叠加。虚拟头波是由头波与反射波或其他头波之间的互相关产生的。基于固定相位的方法，得出对虚拟头波有贡献的源的位置。随着时间的推移，这些来源的贡献得以整合，从而使虚拟头波可见。还演示了使用垂直线阵列估算虚拟头波引起的海底声速。虚拟头波的斜率与虚拟源集合中的直达波和反射波的斜率不同；因此，可以有建设性地堆叠虚拟头波。这些预测已通过仿真验证。