Research On Ray Tracing Algorithm Based On Fast Marching Method

In the theoretical research of seismic exploration,the numerical simulation of seismic wave field has been regarded as one of the important basic research fields.Seismic wave field numerical simulation through setting related parameters to simulation of seismic wave propagation in different lithology,physical property,structure distribution under complicated geological conditions,it is for the study of complex seismic data processing and interpretation of geological conditions has important theoretical guidance value.The numerical simulation based on wave function and ray tracing are two main methods to realize the forward modeling of seismic wave field.Ray tracing simulation is a fast and effective approximation method for wave field,that is,The location of known source points,the coordinates of receiving points and the velocity medium model,Seismic ray path and its time field for source location to receiving point.Although the theory is simple,mature technology but the technology itself has many application limitations of traditional ray tracing: such as the complex and physical changes in medium,the ray path is easy to produce "dovetail" phenomenon or difficult to penetrate the media;focal point and the receiving point will appear between the number of rays,easy to miss the minimum travel time path problem.Because the fast marching method has the advantages of unconditional stability,high computation accuracy and fast algorithm efficiency,and is proved to be effective in avoiding the limitations of traditional ray tracing methods,which is widely used in the field of ray tracing.The rapid advance of ray tracing simulation algorithm implementation process based on the first detailed discussion of the eikonal equation,which leads to the rapid advance of the algorithm is how to calculate the ray travel time formula and the difference operator and calculation formula,but due to the fast marching method can only solve the traveltime of ray did not directly determine the path algorithm,in this paper,Fermat the principle of solving this problem using reverse tracking method based on gradient.Aiming at the accuracy of the algorithm,we use three times B spline function to smooth the model interface,and use the encryption grid and local adaptive triangle mesh technology to improve the accuracy.In order to solve the problem of algorithm efficiency,this paper improves the routine heap sorting by using the empty space sinking method,and tests the difference of efficiency with the data.At last,the time field and ray path of seismic ray in two-dimensional inhomogeneous medium are calculated by the fast marching method and the ideal effect is obtained.