The authors have investigated the possibility of using the background seismoacoustic noise generated Scholte-type surface waves on the ocean floor in order to study the structure of the geophysical medium using passive seismoacoustic tomography. The paper presents the results of reconstructing the deep structure of the Hawaiian Islands region by processing experimental data obtained by a network of broadband ocean bottom seismographs. The solution to the inverse problem consists of two stages. First, the dispersion relations of the phase and group velocities of surface waves are estimated by analyzing the cross-correlation function of the background noise between different pairs of bottom geophones. At the second stage, the problem of inverting the estimated dispersion curves into a vertically layered elastic model of the lithosphere is solved. Comparison of the inversion results with the known velocity models of the Hawaiian Islands region demonstrates the reliability of the estimates obtained with this approach. The results also indicate the possibility of reducing the time of data acquisition in a field experiment compared to methods that use earthquake signals, which involve sounding the studied area from different directions.