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This thesis presents new methods for the modeling of seismic waveforms based on ray theory and ray-Born integrals. The waveforms are used in forward modeling, imaging and full waveform inversion and are computed in 3D acoustic as well as viscoelastic media. These tasks are computationally expensive, especially in viscoelastic media. A main focus is therefore development of efficient methods, while retaining accuracy as much as possible. I first present a method for 3D acoustic ray-Born modeling in the time-domain using isochron surfaces. Here, integrals over isochrons are used to accurately compute seismograms for band-limited signals. This is a new development where the 3D ray-Born integral is reduced to a number of surface integrals. The surface integral formulation is optimal because the integration is only carried out for points that correspond to specific two-way traveltimes. I validate the new method by comparing ray-Born seismograms to seismograms computed with finite-differences. An alternative approach to the time-domain technique is to compute waveforms in the frequency domain. In this case, I focus on hardware oriented methods and use the graphics processing unit (GPU) for doing efficient computations. The frequency-domain GPU method is used to not only evaluate 3D viscoelastic ray-Born integrals for modeling, but also for the computation of viscoelastic imaging integrals. The GPU method is compared to a parallel implementation on CPU and the results show significant improvements in computational efficiency. The improved efficiency for evaluation of 3D ray-Born integrals on GPU is also of benefit for 3D full waveform inversion, a method that stands at the centre of current research in the industry to create models of the subsurface. The 3D inversion problem is analyzed by combining the GPU method with a memory efficient optimization scheme (L-BFGS). This approach allows for 3D waveform inversion on a workstation. As in the forward modeling case, I justify use of the ray-Born integrals for full waveform inversion by numerical examples and comparisons to finite-difference based inversion. Doktorgradsavhandling |
