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

• Main Authors: Bruce R. Julian, John R. Evans, Matthew J. Pritchard, G. R. Foulger
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Subjects: Iceland
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.536.8483; http://community.dur.ac.uk/g.r.foulger/Offprints/JulianEtAl_BSSA_v90_p1554.pdf

Abstract 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 pre-sented 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. The ACH Method The ACH method, developed by Aki, Christofferson, and Husebye (Aki et al., 1977) was the first application of tomography in seismology and has by now been used to study the three-dimensional structure of the crust and upper mantle beneath seismic arrays in dozens of places (Evans and Achauer, 1993). The method takes as input a collection of arrival-time residuals at the sensors of the array from a suite of distant earthquakes in various directions and gen-erates estimates of the wave speeds in a number of rectan-gular blocks under the array. We recently discovered, in a study of the structure be-neath Iceland (Foulger et al., 2000), that some computerized versions of the ACH method, including the program THRD (Evans and Achauer, 1993), contain an error in their treat-ment of azimuths, which increases with the size of the region under study and is particularly severe at high latitudes. This error leads to incorrect computed ray paths, which in turn distort the derived three-dimensional structure. This note ex-plains the origin and consequences of this error and presents ways of correcting it. The mathematical methods presented are likely to be useful in other geophysical problems that approximate a region of the Earth as being flat.