Recent shallow water experiments in sea channels have been performed using two vertical coplanar densely-sampled source and receive arrays. Applying a double beamforming algorithm on the two arrays both on synthetic numerical simulations and on experimental data sets, we extract efficiently source and receive angles as well as travel times for a large number of acoustic rays that propagate and bounce in the shallow water waveguide. We then investigate how well sound speed variations in the waveguide are reconstructed using a ray time delay tomography based on a Bayesian inversion formulation. We introduce both data and model covariance matrices and we discuss on the synthetic numerical example how to choose the a priori information on the sound speed covariance matrice. We attribute the partial sound speed reconstruction to the ray-based tomography and we suggest that finite frequency effects should be considered as vertical and horizontal size of the Fresnel zone significantly spreads in the waveguide. Finally, the contribution of different set of ray angles for tomography goal is also presented.