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A technique was developed to measure the speed of sound in marine sediments at discrete frequencies from 0.6 to 3 kHz by transmitting pulses from acoustic projectors within the water column and measuring the pressure and acceleration components of the acoustic field on vector sensors buried in the seabed. The burial depth and orientation of the vector sensors was determined by analyzing the amplitude and phase response of the acceleration signals to transmissions from three orthogonal directions, using two acoustic projectors also buried in the seabed and a third in the water column directly above the buried receivers. To determine the properties of the seabed, a sequence of transmitted pulses was repeated from ten different grazing angles, spanning from well above to near the nominal critical angle. Due to the interference of refracted and diffracted (mainly evanescent) components of the acoustic field that penetrate the seabed, the particle motion can be elliptical rather than rectilinear and is not necessarily aligned with the geometric ray path (i.e., according to Snell's law). A model was developed to quantify the effect of this interference. It revealed that the parameterization of the seabed as a sand half-space was incapable of explaining the frequency-dependent arrival angles measured by the vector sensors. Further modeling using a computer code for seismoacoustic propagation in horizontally stratified waveguides revealed that the measurement technique is very sensitive to the presence of thin layers with a high-impedance contrast. This modeling suggests that the presence of a thin muddy layer, 0.05-0.2 m thick within the top 1 m of the sediment, is dominating the complicated angular response of the vector sensors.