A model expansion criterion for treating surface topography in ray path calculations using the eikonal equation

Abstract

Irregular surface topography has revolutionized how seismic traveltime is calculated and the data are processed. There are two main schemes for dealing with an irregular surface in the seismic first-arrival traveltime calculation: (1) expanding the model and (2) flattening the surface irregularities. In the first scheme, a notional infill medium is added above the surface to expand the physical space into a regular space, as required by the eikonal equation solver. Here, we evaluate the chosen propagation velocity in the infill medium through ray path tracking with the eikonal equation-solved traveltime field, and observe that the ray paths will be physically unrealistic for some values of this propagation velocity. The choice of a suitable propagation velocity in the infill medium is crucial for seismic processing of irregular topography. Our model expansion criterion for dealing with surface topography in the calculation of traveltime and ray paths using the eikonal equation highlights the importance of both the propagation velocity of the infill physical medium and the topography gradient.