VSP migration based on high angle one-way wave equation in time-space domain and its applications

Migration is a key step in VSP data processing, VSP imaging commonly uses VSP-CDP conversion or Kirchhoff migration which has issues of poor amplitude conservation and low imaging precision, while wave equation prestack depth migration is an effective method to image complex structures. Arbitrarily wide-angle wave equation (AWWE) is a space domain one-way wave equation (OWWE) with a high accuracy and easy numerical implementation because of only including two-order partial derivative term. Compared with other OWWEs, AWWE is capable of imaging steeper dips, which enables it to be one of powerful migration tools. In this paper, we extended AWWE to VSP imaging and realized VSP migration based on high angle one-way wave equation in time-space domain. And the perfectly matched layer (PML) absorbing boundary condition was derived to provide a good approach to suppress artifacts arising at truncation boundaries at a price of limited additional computation cost. Meanwhile, we optimized reference velocities using nonlinear algorithm to enhance the approximation degree of square root operator and improved imaging precision of high-dip layers. Model tests proved the effectivity of the method and showed that it can obtain good imaging result in the case of steep-dip structures. The method was also applied to field VSP data, the comparison of VSP migration result and surface seismic section showed that VSP migration provides a higher resolution image.