The mathematics for computing three-dimensional ray paths are developed for the case where medium consists of a series of constant-velocity layers separated by planes or spherical interfaces. These relations are used to investigate the cause of the LONGSHOT travel-time anomaly. The results of the investigation suggest that the anomaly could be caused by the presence of a thick slab of high-velocity material which dips steeply beneath the Aleutian arc and terminates at a depth of 300 km.

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