Locating Earthquakes: At What Distance Can the Earth No Longer Be Treated as Flat?

Abstract

Earthquake location programs for events recorded at regional to teleseismic distances have traditionally used travel-time tables such as the J-B tables (Jeffreys and Bullen, 1958), which were based on ray tracing in a laterally homogeneous spherical earth ( e.g., Boyd et al., 1984). Such travel-time tables may not give accurate locations for events located using stations at local to near-regional distances because of regional variations in the crustal and upper-mantle velocity structure—the regions of the Earth in which the first-arrival P and S waves spend most of their time for such events. Until recently, it was a nontrivial task to create travel-time tables for different spherical-earth velocity structures. Accordingly, for the past 30+ years, most locations for local and near-regionally-recorded events have used programs which used flat-earth ray tracing through constant-velocity layers. Examples of such programs are Hypo71 (Lee and Lahr, 1972), Hypoinverse (Klein, 1985), Fasthypo (Herrmann, 1979), and Hypoellipse (Lahr, 1999). With the advent of digital recording and advances in telemetry, there are an increasing number of data sets which include arrival times for small to medium-sized events at both local and regional distances. Most researchers are aware of the fact that the assumption of lateral homogeneity may be invalid for event-station paths at larger epicentral distances, but when shown results as given in Figure 1 below, seismologists often express surprise that the spherical-earth travel-time corrections became significant ( e.g., > 0.1 s) at what seemed relatively small epicentral distances. The purpose of this paper is to document the limitations of using a flat-earth velocity model to approximate travel times within the earth and to suggest strategies for minimizing errors in the analysis of events which are observed at distances for which the spherical-earth corrections become significant. A review of the math and physics involved in flat-earth and spherical-earth ray …