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A Geometrical Error in Some Computer Programs based on the Aki-Christofferson-Husebye (ACH) Method of Teleseismic Tomography

U.S. Geological Survey
345 Middlefield Rd., MS 977
Menlo Park, California, 94025
julian{at}usgs.gov
(B.R.J., J.R.E.)
Department of Geological Sciences
University of Durham
Durham, DH1 3LE, United Kingdom
(M.J.P., G.R.F.)

Some computer programs based on the Aki-Christofferson-Husebye (ACH) method of teleseismic tomography contain an error caused by identifying local grid directions with azimuths on the spherical Earth. This error, which is most severe in high latitudes, introduces systematic errors into computed ray paths and distorts inferred Earth models. It is best dealt with by explicitly 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.