S wave envelope synthesis based on different scattering patterns

In order to reveal the scattering process of seismic waves in the small scale inhomogeneous medium of the crust and to describe the envelopment broadening phenomenon of seismic waves more accurately, a discrete wave-number method is used to solve the improved seismic wave energy density integral equation based on the multiple anisotropic scattering theory, and the scattering pattern represented by Gaussian autocorrelation function is selected to obtain the S wave energy density envelope. Firstly, we analyzed the contribution of single scattering and multiple scattering to the energy density envelope of S wave. Then, we discussed the effects of absorption coefficient and total scattering coefficient on the synthesis of S wave energy density envelope. Finally, we compared the differences of the energy density envelope of S wave synthesized in different scattering patterns. The results show that: ① The contribution of single scattering and multiple scattering to the seismic wave scattering process is consistent, and for the near earthquakes （hypocentral distance is less than 100 km）, the single scattering model can be used to match the S-wave energy density envelope. As the hypocentral distance increases, the multiple forward scattering pattern can approach the total energy density envelope more quickly. ② As the absorption coefficient increases, the amplitude of the direct S wave and the coda wave will decrease. And when the total scattering coefficient increases, the amplitude of the direct S wave will decrease, while the coda wave amplitude of the S wave will increase. ③ In the forward scattering pattern, with the increase of hypocentral distance, the energy density envelope of S-wave appears the peak delay, the envelope is widened, and the attenuation consistency of the coda wave is accelerated.