The Effect of Ignoring Earth Curvature on Near-Regional Traveltime Tomography and Earthquake Hypocentral Determination

Earthquake hypocenter determination and traveltime tomography with local earthquake data are normally conducted using a Cartesian coordinate system and assuming a flat Earth model, but for regional and teleseismic data Earth curvature is incorporated and a spherical coordinate system employed. However, when the study region is from the local to near-regional scale (1, it is unclear what coordinate system to use and what kind of incorrect anomalies or location errors might arise when using the Cartesian coordinate frame. In this paper we investigate in a quantitative sense through two near-regional crustal models and five different inversion methods, the hypocenter errors, reflector perturbation and incorrect velocity anomalies that can arise due to the selection of the wrong coordinate system and inversion method. The simulated inversion results show that the computed traveltime errors are larger than 0.1 s when the epicentral distance exceeds 150 km, and increases linearly with increasing epicentral distance. Such predicted traveltime errors will result in different patterns of incorrect velocity anomalous structures, a perturbed Moho interface for traveltime tomography and source position which deviate for earthquake locations. The maximum magnitude of a velocity image artifact is larger than 1.0% for an epicentral distance of less than 500 km and is up to 0.9% for epicentral distances of less than 300 km. The earthquake source location error is more than 2.0 km for epicentral distances less than 500 km and is up to 1.5 km for epicentral distances less than 300 km. The Moho depth can be in error by up 1.0 km for epicentral distances of less than 500 km but is less than 0.5 km at distances below 300 km. We suggest that spherical coordinate geometry (or time correction) be used whenever there are ray paths at epicentral distances in excess of 150 km.