Brute force analysis of residuals arising from the near surface

Andrew Mills, Kristopher A. H. Innanen

Variations in the elastic properties of the near surface are known to cause issues with seismic imaging and inversion, with velocity, density, and thickness variations resulting in statics problems. In particular, in contemplating FWI on land, the sensitivity of amplitude and phase information to changes in the near surface is known to be complex, but we have little quantitative information to guide us here. In this paper, an initial model with a complex near surface and deeper reflectors is studied. Piece by piece, a single characteristic (velocity, density, or thickness) is altered for a single layer or unit. The resulting shot record is compared to the original, to gauge the effect that that rock property change or geometry change has on the recorded events, for both surface waves and reflections. By subtracting the original shot record from the result, we can quantify this effect in a residual, which is used to calculate the L2 norm. Velocity changes in shallower layers are found to have the greatest effect, with changes in thickness having a lesser effect. With increasing depth, property changes have a reduced effect on the L2 norm. It is shown that a minor change in the near surface has an effect on the L2 norm orders of magnitude greater than the same change made at greater depth, demonstrating the importance of understanding the properties of the near surface.