Fast computation of eikonal and transport equations on graphics processing units computer architectures

Abstract

Eikonal models have been widely used for traveltime computations in the field of seismic imaging, but they are often criticized for having low accuracy and poor resolution of the output image. Including amplitude information can provide higher model resolution and accuracy of the images. We have developed a new approach for computing eikonal traveltimes and amplitudes, and we implemented it for multicore computer processing unit and graphics processing unit computer architectures. Traveltimes and amplitudes are computed simultaneously in iterations of the 3D velocity model. This is achieved by extending a fast sweeping method by computing amplitudes directly after the traveltimes with upwind numerical difference schemes. By performing the extra computations simultaneously with the traveltimes, the additional cost for the amplitude and raypaths is low. We tested our method on synthetic 3D data sets to compute traveltimes, amplitudes, and raypaths, from which the Helmholtz Green’s function was assembled. Using a grid of [Formula: see text] nodes, the computations were performed in less than 1 s. The proposed method could work as a feasible alternative to full waveform modeling in seismic applications, which suffers from demanding computations because it requires several order of magnitudes shorter computing times.