The Reverse Time Migration Using Weighted Runge-Kutta Discontinuous Galerkin Methods

With the development of oil and gas exploration,the exploration targets become in-creasingly complex,which makes it important to develop new seismic imaging methods of high precision and resolution.Concerning this issue,a new kind of reverse time migra-tion(RTM)tools,which the weighted Runge-Kutta discontinuous Galerkin(WRKDG)methods,are developed.The wave equations are solved by the WRKDG methods,which leads to flexibility in addressing both regular and irregular meshes,high precision and superiority in suppressing numerical dispersion.Firstly,the spatial and time discretizations of WRKDG methods are described and the weights in the time discretization are further optimized to achieve higher stability.Parallel computating strategies are presented for both rectangular and triangular meshes.The results of numerical convergence test show that⁶)WRKDG methods can achieve the optimal order of6)+1.The analysis of numerical stability shows that the maximal Courant numbers of WRKDG methods are higher than those of Strong Stability Preserving Runge-Kutta DG(SSPRKDG)methods.The numerical dispersion errors of²and³WRKDG methods are 1.76%and 0.37%respectively.Then the optimized WRKDG methods are applied to RTM for the first time.We provide several 2D synthetic datasets to investigate the applicability of WRKDG methods in RTM.The results for Marmousi model and Sigsbee2B dataset show that WRKDG methods can suppress the artifacts caused by numerical dispersion on coarse grids and provide seismic images of high quality.The results for Canadian Foothills dataset verify the superiority of WRKDG methods in RTM with rugged topography.On the other hand,we develop WRKDG methods for acoustic equations in VTI media and analyze its stability and dispersion errors.Then the WRKDG methods are applied to reverse time migration in VTI media.The numerical results show its ability to accurately simulate the acoustic wavefields in VTI media.The RTM results for Hess VTI dataset show that WRKDG methods can obtain high quality images of subsurfaces in VTI media.Finally,in order to address the problem of unbalanced image amplitude,we combine the WRKDG methods with the least-squares reverse time migration(LSRTM)and obtain a new kind of LSRTM methods which can handle topography and irregular meshes with flexibility.Dynamic source encoding and exponential decay moving average gradients are utilized to improve the convergence rate.The results for SEG/EAGE salt-dome model and Canadian Foothills model show the superiority of our methods in seismic imaging with rugged topography and complex structures.