Linear traveltime perturbation interpolation: a novel method to compute 3-D traveltimes

The linear traveltime interpolation has been a routine method to compute first arrivals of seismic waves and trace rays in complex media. The method assumes that traveltimes follow a linear distribution on each boundary of cells. The linearity assumption of traveltimes facilitates the numerical implementation but its violation may result in large computational errors. In this paper, we propose a new way to mitigate the potential shortcoming hidden in the linear traveltime interpolation. We use the vertex traveltimes in a calculated cell to introduce an equivalent homogeneous medium that is specific to the cell boundary from a source. Therefore, we can decompose the traveltime at a point on the cell boundary into two parts: (1) a reference traveltime propagating in the equivalent homogeneous medium and (2) a perturbation traveltime that is defined as the difference between the original and reference traveltimes. We now treat that the traveltime perturbation is linear along each boundary of cells instead of the traveltime. With the new assumption, we carry out the bilinear interpolation over traveltime perturbation to complete traveltime computation in a 3-D heterogeneous model. The numerical experiments show that the new method, the linear traveltime perturbation interpolation, is able to achieve much higher accuracy than that based on the linear traveltime interpolation.