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 differential 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. Keywords: Kelvin-Voigt visco-elastic velocity attenuation seismic wave.The earth media friction attenuates the energy of seismic wave. Obviously, that earth medium is treated as viscoelasticity is more appropriate than as elasticity. Seismic wave in visco-elastic media contains abundant lithology information of the medium. The investigations of the solutions of visco-elastic wave equations, velocities of seismic wave propagating and the attenuation of seismic wave in the visco-elastic media are very important for geophysical prospecting technology. Under a small perturbation, Ricker studied the solution of Stokes visco-elastic partial differential equation [1] . He obtained approximate power series and integral solutions by studying the behavior for attenuation of seismic wave in visco-elastic media. By introducing complex modulus in the visco-elastic equation [2] , complex velocity of seismic wave in visco-elastic media was obtained [2][3][4] . The method, using complex modulus to study phase velocity and attenuation of seismic wave in visco-elastic media, is widely applied [5,6] . This method is also used to investigate phase velocity and attenuation of seismic wave in anisotropic visco-elastic media [7] , attenuation and dispersion of the wave propagating in visco-elastic materials [8,9] . However, the visco-elastic media wave equation is the third-order partial differential equation [1] . The visco-elastic equation with complex modulus is actually a closed visco-elastic wave equation. This paper studies, under a small perturbation, the responses of seismic transient wave in the viscoelastic media with source and the analytic solution of

With the limitation of both shot and receiver numbers, seismic data are sometimes not sufficient for practical wide‐angle seismic experiments. In order to enhance the lateral continuity of seismic reflection events from the sparse wide‐angle seismic data, we present a new technique to reconstruct the resemblance section of the crust/mantle reflection structure based on the geometrical diffraction theory. The travel‐time conditions for reconstructing the semblance section are calculated using the reciprocity principle, and the travel‐time field from shots and receivers are computed using Eikonal solver, which have the advantage of high efficiency and accuracy. Compared with CDP mapping, the processing results of real wide‐angle seismic data in southeastern China demonstrates that this method can improve the lateral consistency of the imaging section.

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