On the Mathematics of Using Difference Operators to Relocate Earthquakes

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Southern California Hypocenter Relocation with Waveform Cross-Correlation, Part 1: Results Using the Double-Difference Method (2005, unknown): “To investigate if poorly modeled velocity structure could affect our absolute hypocenters, as suggested by Wolfe (2002) and Michelini and Lomax (2004), we compared the Hauksson (2000) hypocenters with two sets of double-difference hypocenters determined for about 10,000 earthquakes in the southern…”
Absolute Earthquake Locations with Differential Data (2004, methodology): “Second, differential traveltimes can be predicted more accurately than absolute traveltimes, because errors in the velocity model tend to cancel out when traveltimes of neighboring events are subtracted [e.g. Slunga et al., 1995; Waldhauser and Ellsworth, 2000; Wolfe, 2002].”