It is possible to interpret conventional airborne electromagnetic (EM) data acquired over ice-covered Arctic seas to obtain values of the sea ice thickness and, where needed, the actual sea ice keel geometry. To do so, we require high-frequency (inductive limit) data that allows us to assume that the ice is virtually transparent to the EM fields while the sea water forms a perfect conductor. Practically, a 100 kHz operating frequency is needed, but data acquired at a lower frequency can be scaled to obtain the required inductive limit anomaly. The data inversion is done by linking Occam's inversion method to a rapid numerical, two-dimensional, forward solution for the ice keel problem. A most useful feature of the adopted inversion scheme is the minimization of the roughness or the mean square slope of the keel boundary. In some cases, where the keel might be bounded by steeply dipping walls, this constraint may result in a less accurate solution than might be obtained with a conventional technique. In most cases the advantage in stability that it provides outweighs the possible loss of accuracy that it may occasion. Tests on synthetic data show a possible worst case ice thickness error of about 15 percent. The results of inversion tests for two sets of survey data acquired near Prudhoe Bay, Alaska, also indicate an accuracy of this order of magnitude. While some portion of the inversion error must be ascribed to the roughness constraint and is therefore inherent to the inversion technique used, the remainder must be ascribed to the instrumentation and is probably remediable.