Efficient and accurate computation of seismic traveltimes and amplitudes

We describe two practicable approaches for an efficient computation of seismic traveltimes and amplitudes. The first approach is based on a combined finite-difference solution of the eikonal equation and the transport equation (the 'FD approach'). These equations are formulated as hyperbolic conservation laws; the eikonal equation is solved numerically by a third-order ENO-Godunov scheme for the traveltimes whereas the transport equation is solved by a first-order upwind scheme for the amplitudes. The schemes are implemented in 2D using polar coordinates. The results are first-arrival traveltimes and the corresponding amplitudes. The second approach uses ray tracing (the 'ray approach') and employs a wavefront construction (WFC) method to calculate the traveltimes. Geometrical spreading factors are then computed from these traveltimes via the ray propagator without the need for dynamic ray tracing or numerical differentiation. With this procedure it is also possible to obtain multivalued traveltimes and the corresponding geometrical spreading factors. Both methods are compared using the Marmousi model. The results show that the FD eikonal traveltimes are highly accurate and perfectly match the WFC traveltimes. The resulting FD amplitudes are smooth and consistent with the geometrical spreading factors obtained from the ray approach. Hence, both approaches can be used for fast and reliable computation of seismic first-arrival traveltimes and amplitudes in complex models. In addition, the capabilities of the ray approach for computing traveltimes and spreading factors of later arrivals are demonstrated with the help of the Shell benchmark model.