NATO Undersea Research Centre, Viale San Bartolomeo 400, 19126 La Spezia, Italy.
J Acoust Soc Am. 2010 Jul;128(1):28-38. doi: 10.1121/1.3397394.
Reverberation is commonly calculated by estimating the propagation loss to and from an elementary area, defined by transmitted pulse length and beam width, and treating the resulting backscatter from the area as a function of its range. In reality reverberation is strictly a function of time and contributions for a given time come from many ranges. Closed-form solutions are given for reverberation calculated both at fixed range and at fixed time isovelocity water and some variants of Lambert's law and linear reflection loss with an abrupt critical angle. These are derived by considering the shape of the two-way scattered multipath pulse envelope from a point scatterer. The ratio of these two solutions is shown to depend on the dominant propagation angle spread for the particular range or time. The ratio is largest at intermediate ranges (though typically less than 1 dB) and depends explicitly on the critical angle. At longer ranges mode-stripping reduces the propagation angle spread and the ratio reduces ultimately to unity. At short range the ratio is also close to unity although interpreting it requires care.
混响通常通过估计从一个基本区域（由发射脉冲长度和波束宽度定义）往返的传播损耗来计算，并将该区域的反向散射作为其距离的函数来处理。实际上，混响严格是时间的函数，给定时间的贡献来自许多范围。给出了在固定距离和固定时间等速水中以及 Lambert 定律和具有突然临界角的线性反射损耗的一些变体的混响的闭式解。这些是通过考虑来自点散射体的双向散射多路径脉冲包络的形状得出的。这两个解的比值被证明取决于特定距离或时间的主导传播角扩展。在中间范围（尽管通常小于 1dB）时比值最大，并且明确取决于临界角。在较长的距离上，模式剥离会降低传播角扩展，最终比值会降低到 1。在短距离上，该比值也接近 1，尽管解释它需要小心。
