Absolute earthquake locations with differential data

Notwithstanding the commonly held wisdom that "you can't determine the absolute location of earthquakes using the double-difference method," you can. We present a way of visualizing double-difference data, and use it to show how differential arrival-time data can, in principle, be used to determine the absolute locations of earthquakes. We then analyze the differential form of Geiger's Method, which is the basis of many double-difference earthquake-location algorithms, and show that it can be used to make estimates of the absolute location of earthquake sources. Finally, we examine absolute-location error in one earthquake-location scenario, using Monte Carlo simulations that include both measurement error and velocity model error, and show that the double-difference method produces absolute locations with errors that are comparable in magnitude, or even less, than traditional methods. The improvement in absolute locations arises from exactly the same, and often-cited, reasons that the double-difference method yields superior relative locations: observations of differential travel times determined via cross correlation have a much smaller error than observations of absolute travel times determined via phase picking; and predictions of differential travel times are less sensitive to unmodeled near-surface heterogeneity than are predictions of absolute travel times. Absolute earthquake locations that are already routinely produced by most implementations of the double-difference method have a better accuracy than has been credited.