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absorption approach Area Lima axial ray axis Bermuda Contours binormal bottom loss boundary break-points bridging curves calculations caustic Code computer program constant curvature data points decibels derivative differential equation discontinuities dZ/dC Enter evaluated Figure Frenet Formulas frequency function given grazing angle horizontal range initial angle input integral intensity interface iso-loss linear minimum obtain ocean bottom output Pennsylvania State University ping cycle plot potentiometers probability of detection problem pulse RANGE IN KYD ray equation ray path ray theory RAY TRACING ray-tracing rayplotter receiver depth reflection loss reverberation level security classification sediment segments shadow zone shown in Fig signal excess slope Snell's law solution sound field sound velocity source depth SPONSORING MILITARY surface layer tangent target depth threshold level tion torpedo torsion transmission loss U. S. Naval Ordnance Underwater Sound Laboratory vector velocity profile velocity-depth structure versus vertex vertical zero