Abstract: At first, the paper indicates that in the thermoelastic medium, the basic forms of waves include the quasi-elastic longitudinal wave, transverse wave and the wave of temperature with a finite propagate velocity. The paper also indicates that the transverse wave does not attenuate in the process of propagation as in the purely elastic medium, but the quasi-elastic longitudinal wave and the temperature wave are concomitant and attenuate. Second, the paper points out two basic forms of the quasi-elastic longitudinal wave, which has two different propagate velocity. Finally, the seismic P-wave is regarded as the quasi-elastic longitudinal wave, which is excited from the initial displacements. Both fixed frequency and wavelength are supplied with calculating and approximating formulas for relevant Q_r. The approximate formula of Q_r the time-region provides a method for calculating Q_r value by using the seismic P-wave data from single seismic observation station.

Key words: Thermoelastic medium, Seismic wave, Attenuate property, Q_r value