Distinguishing changes in basal reflector depth and firn structure

Here we calculate the change, dT, in traveltime of the basal reflector as either the:

is perturbed. The point is to see whether the two types of perturbations can be distinguished. we use the vostok structure, underlain by rock at 2600 m depth.

Raypaths of the basal reflector through the ice for ranges of 0, 2000, 4000, ..., 10000 m, plotted as a common-midpoint gather. Note that for ranges greater than 5000 m, the rays spend a long time in the firn. (Postscript version).

Differential traveltime, dT, as the basal depth is increased by dh=0.1 m cm (bold curve), and as the firn velocity structure is perturbed by dv=1.0e-4*230*exp(-z/30.0) (mm/ns) (solid curve). Note that the two curves behave quite differently with range. In particular, the firn curve has a very large signal at ranges greater than 5000 m, due to the unusually large part of the ray path in the firn. (Postscript version).

We now perform a simple test designed to discover whether changes in firn structure can be descriminated from changes in basal reflector depth. We computed a synthetic dataset of differential traveltime vs. range for a model that has both a perturbation in firn structure (v0=250 mm/ns) and and perturmation in basal reflector depth (dh=0.1 m). We then compare these data to synthetic data computed on a grid of (dh, dv0) values, using the root-mean-squared deviation to quantift error. The critical question is whether the error surface has a single minima.

Error in differential traveltime contoured as a function of dh and v0, with respect to synthetic data with (dh=0.1, v0=250). Note that a single minimum at exactly the correct (dh, v0) occurs. This results suggests that, in the context of a vertically stratified structure, changes in firn velocity structure and basal reflector depth can be descriminated. (Postscript version).