A modal/WKB inversion method for determining sound-speed profiles in the ocean and ocean bottom

Two approaches to determining sound‐speed profiles in the ocean and ocean bottom using measured acoustic modal eigenvalues are examined. Both methods use measured eigenvalues and mode‐dependent assumed values of the WKB phase integral as input data and use the WKB phase integral as a starting point for relating the index of refraction to depth. Inversion method 1 is restricted to monotonic or symmetric sound‐speed profiles and requires a measurement of the sound speed at one depth to convert the index of refraction profile to a sound‐speed profile. Inversion method 2 assumes that the sound speed at the ocean surface and the minimum sound speed in the profile are known and is applicable to monotonic profiles and to general single duct sound‐speed profiles. For asymmetric profiles, inversion method 2 gives the depth difference between two points of equal sound speed in the portion of the profile having two turning points, and in the remainder of the profile it gives sound speed versus depth directly. A nume...