Turning-point filtering is a method to focus acoustic energy from a vertical line array receiver into an oceanographically meaningful image. The turning-point filter is a simple modification of the linear beamformer which compensates for the sound-speed variation in the water column. Focused peaks in the image (phase-speed, group- speed space) can be regarded as accurate samples of the underlying dispersion curve whenever the WKBJ approximation is valid. Applying this method to real data, still fails to produce a useful observable because of small-scale variations in the ocean. The ocean acoustic waveguide has limited space, time, and frequency coherences which limit the image sharpness. Accounting for this by incoherently combining the limited coherent subspaces generates easily measured observables as demonstrated.
Matthew A. Dzieciuch,
"Ocean acoustic tomography using turning-point filters", Proc. SPIE 4123, Image Reconstruction from Incomplete Data, (16 November 2000); doi: 10.1117/12.409259; https://doi.org/10.1117/12.409259