A geometrical error in some computer programs based on the Aki-Christofferson-Husebye (ACH) method of teleseismic tomography

Some computer programs based on the Aki-Christofferson-Husebye (ACH) method of teleseismic tomography contain an error caused by identifying local gri d directions with azimuths on the spherical Earth. This error, which is mos t severe in high latitudes, introduces systematic errors into computed ray paths and distorts inferred Earth models. It is best dealt with by explicit ly correcting for the difference between true and grid directions. Methods for computing these directions are presented in this article and are likely to be useful in many other kinds of regional geophysical studies that use Cartesian coordinates and flat-earth approximations.