This paper studies, under a small disturbance, the responses of seismic transient wave in the visco-elastic media and the analytic solution of the corresponding third-order partial differential equation. A plane wave ...This paper studies, under a small disturbance, the responses of seismic transient wave in the visco-elastic media and the analytic solution of the corresponding third-order partial differential equation. A plane wave solution of Kelvin-Voigt homogeneous visco-elastic third-order partial differ-ential equation with a pulse source is obtained. By the principle of pulse stacking of particle vibration, the result is extended to the solution of Kelvin-Voigt homogeneous visco-elastic third-order partial differential equation with any source. The velocities of seismic wave propagating and the attenuation of seismic wave in Kelvin-Voigt homogeneous visco-elastic media are discussed. The velocities of seismic wave propagating and the coefficient of attenuation of seismic wave in Kelvin-Voigt homogeneous visco-elastic media are derived, expressed as functions of density of the media, elastic modulus and visco-elastic coefficient. These results can be applied in inversing lithology parameters in geophysical prospecting.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.50490270)the National Basic Research Program of China(Grant Nos.2005CB221501 and 2002CB211707).
文摘This paper studies, under a small disturbance, the responses of seismic transient wave in the visco-elastic media and the analytic solution of the corresponding third-order partial differential equation. A plane wave solution of Kelvin-Voigt homogeneous visco-elastic third-order partial differ-ential equation with a pulse source is obtained. By the principle of pulse stacking of particle vibration, the result is extended to the solution of Kelvin-Voigt homogeneous visco-elastic third-order partial differential equation with any source. The velocities of seismic wave propagating and the attenuation of seismic wave in Kelvin-Voigt homogeneous visco-elastic media are discussed. The velocities of seismic wave propagating and the coefficient of attenuation of seismic wave in Kelvin-Voigt homogeneous visco-elastic media are derived, expressed as functions of density of the media, elastic modulus and visco-elastic coefficient. These results can be applied in inversing lithology parameters in geophysical prospecting.
