Research on model smoothing in ray type migration imaging

From the perspective of energy functional theory, based on velocity gradient, the smoothing formula for a velocity model based on partial differential equations is derived by the steepest descent method (Gradient method) , which can be used to solve the problem of the velocity model smoothed in ray type migration imaging. At the same time, considering the effect of the selection of threshold k in smoothness coefficient of partial differential equations on the velocity model, variations of spatial structure of the original velocity model are analyzed on a simple high-speed velocity model. By comparing the ray path and time field, it is proved that the smoothing of velocity model using partial differential equation is superior to convolution operator. Finally, the effectiveness of velocity model smoothing process using partial differential equation is verified by analyzing the migration imaging results on Marmousi and Sigsbee 2A original and smoothed velocity models.