The ABCS Program for the Analysis of Echo Sounder Returns for ...

DSTO-GD-0215Appendix 2: Geometric Errors when Converting to aReference Seafloor DepthConsider a ping of duration ∆t coming from an omnidirectional source. Thisenergy will radiate out from the source hitting the seafloor, and some of the energy willthen be backscattered back to the hydrophone. Since the energy emitted from thesource will be spherical in shape and only ∆t in duration, some of the beam will firstinsonify a circle on the seafloor. The circle will widen with time until the end of theping reaches the seafloor. Then an insonified annulus will form on the seafloor, whichwill move out radially from the centre.To show how the geometric errors occur, consider an insonified annulus on theseafloor with a reference seafloor depth of 50 m and an actual seafloor depth of 100 mwhich is transformed to the reference seafloor depth.Using a realistic case where the ping duration ∆t = 2 msec, θ = 30°, and the speed ofsound c = 1500 m/s (see Figure 21).For the 100 m case:dSince Cosθ = 2 (eq(36) appendix 4), therefore t=0.15396 sec at 100 m.ct2dAlso Cos( θ − ∆θ)=(eq(37) appendix 4)ct ( − ∆t)This gives ∆θ = 1.33° at 100 mdtoIf this was transformed to the reference seafloor depth of 50 m using t' = thedtime would become t’ = 0.07698 sec, but θ and ∆θ would still be 30° and 1.33°respectfully. This gives an insonified area of 236 m 3 at the reference seafloor depth.For the 50 m case:The time t would equal 0.07698 sec, but the ping duration ∆t would still be 2 msec.Doing the above calculation again gives ∆θ = 2.76° and an insonified area of 477 m 3 .This shows that the size of the insonified annulus on the seafloor is significantlydifferent when comparing the 100 m seafloor depth adjusted to the 50 m with thereference seafloor at 50 m depth.27