Abstract：Based on accurate theory of limited deformed mechanics,the paper created a nonlinear wave equation produced by explosive point source in infinite elastic medium and revealed evolutional phenomenon of amplitude and waveform of spherical wave. The studying results show that the classical elastic wave equation of spherical wave is only true for fixed amplitude phase and described only kinematic equation of phase velocity. From accurate analytic solution of wave equation given by Yrstlace double cyclic elliptic function with variable parameters,the paper demonstrated theoretically elastic dynamic nature of seismic wavelet(Ricker wavelet)evolution which has theoretic guided meaning to solve the problem of production in seismic exploration.
