Irregular Surface Seismic Wave Traveltime Calculation With Discontinuous Galerkin Method

In seismic exploration of irregular surface areas,seismic wave traveltime calculation can be applied to traveltime tomography to obtain near-surface velocity structures which have important applications.In this paper,we studied first arrival seismic wave traveltime calculation method based on Eikonal equation and got travel time fields result in various velocity structure models.As a nonlinear partial differential equation,the Eikonal function equation needs to satisfy the minimum travel time theorem and causality conditions to obtain the travel time solution.Under constraints of traveltime field features,the methods of obtaining traveltime solutions of Eikonal equations include the local discretion scheme to get traveltime and methods such as the fast sweep method and fast advance method to determine the global solver.Through the results of algorithm analysis and numerical examples,the numerical solutions of Eikonal equation with causality conditions can be given as the first arrival travel time field.Compared with the finite difference method,the discontinuous Galerkin method constructs the approximate solution of Eikonal equation with basis function space and calculates the numerical result as the traveltime field with the help of a suitable global sequence.Numerical experiments shows that methods can converge to actual traveltime results.In various velocity models,traveltime calculation results are consistent with the actual results and existing methods results,and high computational efficiency can be achieved through optimization.The calculation results of the method in the SEG/EAGE salt dome velocity model and the Marmousi velocity model show the effectiveness of the method.The discontinuous Galerkin method under irregular surface can establish a local solver under triangular mesh discretization and determine the global iteration sequence by reference points.In triangular meshes,the discontinuous Galerkin method of the Eikonal equations constructs the initial solution and the local solver of the traveltime from the weak form in the triangular elements.The algorithm uses the flux term to ensure that the numerical results conform to the propagation law of the traveltime field and converge to the traveltime solution of the Eikonal equation with discrete conditions.Compared with the traveltime calculation methods of Eikonal equation,the discontinuous Galerkin method can better adapt to the discrete model of triangular mesh under irregular surface.The solution of velocity models shows the accuracy of the travel time calculating algorithm in different velocity structures.