Detailed information about the sediment properties and microstructure can be provided through the analysis of digital ultrasonic P wave seismograms recorded automatically during full waveform core logging. The physical parameter which predominantly affects the elastic wave propagation in water-saturated sediments is the P wave attenuation coefficient. The related sedimentological parameter is the grain size distribution. A set of high-resolution ultrasonic transmission seismograms (~50-500 kHz), which indicate downcore variations in the grain size by their signal shape and frequency content, are presented. Layers of coarse-grained foraminiferal ooze can be identified by highly attenuated P waves, whereas almost unattenuated waves are recorded in fine-grained areas of nannofossil ooze Color-encoded pixel graphics of the seismograms and instantaneous frequencies present full waveform images of the lithology and attenuation. A modified spectral difference method is introduced to determine the attenuation coefficient and its power law alpha=kfn. Applied to synthetic seismograms derived using a ``constant Q'' model, even low attenuation coefficients can be quantified. A downcore analysis gives an attenuation log which ranges from ~700 dB/m at 400 kHz and a power of n~=1-2 in coarse-grained sands to few decibels per meter and n