The fine resolution of long geoseismic sections should permit the characterization of oceanic turbulence properties over several decades of horizontal scales. The range of horizontal scales actually probed by three different acoustic sources is found to be directly linked to their frequency content. The horizontal inertial range with a spectral slope of k(h)(-5/3) extend up to 3 km wavelength for the most intense acoustic reflectors which surround strong anticyclonic eddies. The in situ data analysis is confirmed by high resolution numerical simulations of oceanic anticyclonic vortices, in a rotating temperature-stratified fluid (no salt), which show the spontaneous emergence of a concentration of acoustic reflectors above and below the eddy. These show an anisotropy and a spectral slope consistent with the framework of stratified turbulence, which differs from that of Garret and Munk for internal waves. The implications are that a direct energy cascade to smaller spatial scales is occurring at the boundaries of energetic oceanic vortices and may provide a mechanism to drive mixing in the ocean interior.