I have used full waveform logs from the Nankai Trough exploratory well off central Japan to estimate both compressional and shear attenuation in sediments containing methane hydrate (MH). The attenuation estimates are based on a median frequency shift to the amplitude spectrum of the recorded waveforms. This paper is concerned with attenuation at sonic frequencies of 10--20 kHz for compressional waves and 500--1000 Hz for shear waves. I observed that the presence of MH increases the host sediments' seismic attenuation, and shear attenuation may be more helpful than compressional attenuation in detecting or characterizing MH-bearing sediments as compressional attenuation is affected by the presence of gas. Moreover, the ratio of compressional to shear attenuation is found to be a more sensitive indicator of the presence of low-saturation gas than the corresponding velocity ratio.