A modified version of the computer program HYPOINVERSE (Klein, 1978) was used to locate local earthquakes recorded by the UUSS network for the time period 1981-present. This program determines hypocenters by minimizing differences between observed and computed travel times using a generalized inverse (singular value decomposition) technique. Computed travel times are calculated by assuming a trial hypocenter and then finding the appropriate ray path through a horizontally layered velocity model to each station.
The velocity model used to locate earthquakes in the Yellowstone region has varied, but has been the following since 1992:
| Layer | Depth (km) | P-Velocity (km/sec) | S-Velocity (km/sec) | P/S Velocity Ratio (km/sec) |
| 1 | 0 to 1.9 | 3.90 | 2.30 | 1.70 |
| 2 | 1.9 to 8.0 | 5.67 | 3.37 | 1.68 |
| 3 | 8.0 to 21.0 | 6.02 | 3.59 | 1.68 |
| 4 | 21.0 to 40.0 | 6.70 | 3.94 | 1.70 |
| 5 | 40.0+ | 7.90 | 4.62 | 1.71 |
The top four layers of this model are based on a travel time inversion study for the Hebgen Lake, Montana, region by Nagy and Smith (1989). The underlying halfspace, representing the upper mantle, is based on selected seismic refraction profiles recorded during the summers of 1978 (Smith et al., 1982) and 1980 (Brokaw, 1985). Corrections for elevation are made to a datum of 2000 m above sea level using the angle of incidence and near-surface velocities of 3.4 km/sec for P waves and 1.95 km/sec for S waves.
Locations of earthquakes everywhere else within the UUSS network are done using a set of three velocity models. Two velocity models are used in order to approximate the transition in crustal structure across Utah from the Basin and Range province on the west to the Middle Rocky Mountains Colorado Plateau on the east. A third velocity model is used to model crustal structure for stations in the southeast/central Idaho western Wyoming area.
The first model, informally designated the “Wasatch Front model,” is applied to all stations south of 42º 45´ N latitude, with the exception of stations located within the Colorado Plateau province. It is also used for all temporary stations operated during 1994 in the Draney Peak region along the Idaho-Wyoming border (42º 30´ to 43º 10´ N), in order to have the same velocity model for all of these stations. The Wasatch Front model was determined by seismic refraction profiling (Keller et al., 1975) south of Salt Lake City along the Basin and Range Colorado Plateau transition zone using local quarry blasts. A 7.9 km/sec halfspace at 42 km depth has been added in order to fit observed travel time data from earthquakes at distances greater than about 250 km (Pechmann et al., 1984; Loeb, 1986). The model is specified by:
| Layer | Depth (km) | P-Velocity (km/sec) |
| 1 | 0 to 1.4 | 3.4 |
| 2 | 1.4 to 15.5 | 5.9 |
| 3 | 15.5 to 25.4 | 6.4 |
| 4 | 25.4 to 42.0 | 7.5 |
| 5 | 42.0+ | 7.9 |
The second model, informally designated the “Colorado Plateau model,” is applied to all stations located in the Colorado Plateau province of eastern Utah (as defined by Stokes, 1986), northern Arizona, and western Colorado, plus stations in the eastern Wasatch Plateau in central Utah. This model is modified from Roller (1965) and is specified by:
| Layer | Depth (km) | P-Velocity (km/sec) |
| 1 | 0 to 1.5 | 3.4 |
| 2 | 1.5 to 27.5 | 6.2 |
| 3 | 27.5 to 40.0 | 6.8 |
| 4 | 40.0 to 80.0 | 7.8 |
| 5 | 80.0+ | 7.9 |
The third model, informally designated the “southeast Idaho model,” is applied to all stations north of 42 45´ N latitude with the exceptions noted above. This model was determined for analysis of the 1983 Borah Peak, Idaho sequence using data from several seismic refraction profiles near Mackay, Idaho (Richins et al., 1987).
| Layer | Depth (km) | P-Velocity (km/sec) |
| 1 | 0 to 1.14 | 4.75 |
| 2 | 1.14 to 6.45 | 5.59 |
| 3 | 6.45 to 18.0 | 6.16 |
| 4 | 18.0 to 40.0 | 6.80 |
| 5 | 40.0+ | 8.00 |
The S wave velocities for the Wasatch Front, Colorado Plateau, and southeast Idaho models were calculated from the P wave velocity models using an empirically determined V=p/Vs ratio of 1.74, corresponding to a Poisson’s ratio of 0.25. Corrections for elevation were made to a datum level of 1500 m above mean sea level using the angle of incidence and near surface velocities of 3.4 km/sec for P waves and 1.95 km/sec for S waves. Some elevation corrections are as large as 0.3 sec for P waves.
Empirical station delays are not applied to the data due to the large geographical area involved and the practical difficulties of determining such delays for a constantly changing set of stations. Whenever possible, reliable S wave arrival times for stations less than ~80 km from the epicenter are used for the locations in addition to P wave arrival times. S wave arrivals prove particularly helpful in controlling locations near or slightly outside the boundaries of the network.
References
Brokaw, M.A. (1985). Upper crustal interpretation of Yellowstone determined from ray-trace modeling of seismic refraction data, M. S. Thesis, University of Utah, Salt Lake City, Utah, 179 pp.
Keller, G. R., R. B. Smith, and L. R. Braile (1975). Crustal structure along the Great Basin Colorado Plateau transition from seismic refraction studies, J. Geophys. Res. 80, 1093-1098, doi:10.1029/JB080i008p01093.
Klein, F. W. (1978). Hypocenter location program HYPOINVERSE, U. S. Geol. Surv., Open-File Rept. 78-694, 102 pp, doi:10.3133/ofr78694.
Loeb, D. T. (1986). The P-wave velocity structure of the crust-mantle boundary beneath Utah, M. S. Thesis, University of Utah, Salt Lake City, Utah, 126 pp.
Nagy, W. C., and R. B. Smith (1989). Simultaneous inversion and eigenanalysis for hypocenters and velocity structure using earthquake and refraction data, Yellowstone volcanic system, EOS, Trans. Am. Geophys. Union 70 (43), 1195, doi:10.1029/89EO00329.
Pechmann, J.C., W. D. Richins, and R. B. Smith (1984). Evidence for a “double moho” beneath the Wasatch front, Utah, EOS, Trans. Am. Geophys. Union 65, 988, doi:10.1029/EO065i045p00831.
Richins, W. D., J. C. Pechmann, R. B. Smith, C. J. Langer, S. K. Goter, J. E. Zollweg, and J. J. King (1987). The 1983 Borah Peak, Idaho, earthquake and its aftershocks, Bull. Seism. Soc. Am. 77, 694-723, doi:10.1785/BSSA0770030694.
Roller, J.C. (1965). Crustal structure in the eastern Colorado Plateau province from seismic-refraction measurements, Bull. Seism. Soc. Am. 55 (1), 107-119, doi:10.1785/BSSA0550010107.
Smith, R. B., L. W. Braile, M. M. Schilly, J. Ansorge, C. Prodehl, M. Baker, J. H. Healy, S. Mueller, and R. Greensfelder (1982). The Yellowstone-eastern Snake River Plain seismic profiling experiment: Crustal structure of Yellowstone, J. Geophys. Res. 84, 2583-2596, doi:10.1029/JB087iB04p02597.
Stokes, W. L. (1986). Geology of Utah, Utah Museum of Natural History and Utah Geological and Mineral Survey, Salt Lake City, Utah, 330 pp.