Strain accumulation at Yucca Mountain, Nevada,

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 104, NO. B8, PAGES 17,627-17,631, AUGUST 10, 1999 Strain accumulation at Yucca Mountain, Nevada, 1983-1998 J. C. Savage, J.L. Svarc, and W. H. Prescott U.S. Geological Survey, Menlo Park, California Abstract. A 14-station, 50-km aperture geodetic array centered on the proposed radioactive waste disposal site at Yucca Mountain, Nevada, was surveyed in 1983, 1984, 1993, and 1998 to determine the rate of strain accumulation there. The coseismic effects of the 1992 (Ms=5.4) Little Skull Mountain earthquake, which occurred within the array, were calculated from a dislocation model and removed from the data. The measured principal strain accumulation rates determined over the 1983-1998 interval are 1 = 2_+12 nanostrain/yr N87øW_+12 ø and 2 = -22_+12 nanostrain/yr N03øE_+l 2 ø (extension reckoned positive and quoted uncertainties are standard deviations). The N65øW extension rate is -2_+12 nanostrain/yr, significantly less than the 1991-1997 N65øW rate of 50_+9 nanostrain/yr reported by Wernicke et al. [1998]. The implied maximum right-lateral engineering-shear, strain accumulation rate is? =e -e2 = 23_+10 nanostrain/yr, a marginally significant rate. Almost half (el = 6 nanostrain/yr N90øW, e2 = -6 nanostrain/yr N00øE, and? = 12 nanostrain/yr ) of the measured strain rate can be attributed to strain accumulation on the Death Valley-Furnace Creek (50 km distant) and Hunter Mountain- Panamint Valley (90 km distant) faults. The residual strain rate after the removal of those fault contributions is not significant at the 95% confidence level. 1. Introduction On the basis of repeated surveys from 1991 through 1997 of the relative motion between geodetic monuments Claim, Black, Mile, 67TJS, and Wahomie (Figure 1), Wernicke et al. [1998] deduced a N65øW strain accumulation rate of 50 +_ 9 nanostrain/yr across the proposed high-level radioactive waste disposal repository at Yucca Mountain, Nevada. (In this paper extension is reckoned positive and all quoted uncertainties are standard deviations.) That strain rate is sufficient to suggest a higher than expected earthquake hazard at the repository. Savage [1998] argued that the strain rate reported by Wernicke et al. was contaminated by the coseismic and postseismic effects of the 1992 Little Skull Mountain earthquake (Ms=5.4), which occured at the edge of their array, and that the standard deviation assigned to their measurement was too small owing to the failure to include an allowance for monument instability. Savage et al. [1994] had earlier found the 1983-1993 N65øW strain rate to be 8 +_ 20 nanostrain/yr, a rate not significantly different from zero. Although the two (Wernicke et al. and Savage et al.) measurements of the N65øW strain rate are marginally consistent at the 95% confidence level (i.e., the 42+_22 nanostrain/yr difference is less than two standard deviations), the earthquake hazard implications are somewhat different. To resolve the discrepancy between the strain rates determined by Savage et al. [1994] and Wernicke et al. [1998], the strain array (Figure 1) employed by Savage et al. was resurveyed in late May 1998. The strain rate was inferred from This paper is not subjecto U.S. copyright.. Published in 1999 by the American Geophysical Union. Paper number 1999JB 900100. measurements of 29 distances between neighboring geodetic monuments (the distances used are shown by lines in Figure 1). The earlier measurements were made in 1983 and again in 1984 using a Geodolite, an electro-optical distance measuring instrument, with the refractivity correction determined from meteorological parameters measured from a small aircraft flying along the line of sight at the time of ranging. In 1993 the 14 lines terminating at either Mile or Shoshone (Figure 1) were again measured by Geodolite. In addition, all stations were surveyed in 1993 with Global Positioning System (GPS) receivers so that the relative position of each geodetic monument was determined with respect to all other monuments. The GPS survey was repeated in 1998. The standard deviation in the Geodolite measurement of a distance L is given by (a2+b2l2) 1/2, where a=3 mm and b=0.2 ppm [Savage and Prescott, 1973]. The standard deviation in the GPS location of one geodetic monument with respect to another is thought to be 4 mm in each horizontal coordinate (see the white noise model in Table 1 of Zhang et al. [1997]). We refer to these uncertainty estimates as the a priori standard deviations. 2. Strain Measurement Because the earlier (1983 and 1984) surveys of the strain array in Figure 1 involved measurements of only the 29 distances shown in Figure 1, we have used in this analysis only the GPS measurements of those same distances in 1993 and 1998. The data then consist of 25 line lengths measured in the original 1983 survey (all lines in Figure 1 except for Bare-Mile and the three lines out of Rock), 27 line lengths measured in 1984 (all lines in Figure 1 except Mine-Pass and Specter-Well), 14 line lengths (all lines terminating at either Mile or Shoshone) measured by Geodolite in 1993, and all 29 line lengths measured by GPS in both 1993 and 1998. 17,627

17,628 SAVAGE ET AL.: YUCCA MOUNTAIN STRAIN RATE 37 ø 00' 36 ø 30' 117 ø 00' 116 ø 30' 116 ø 00' Figure 1. Map of the Yucca Mountain strain network (solid triangles). Also shown (open triangles) are three stations included in the 5 station array (Claim, Black, Mile, 67TJS, and Wahomie) used by Wernicke et al. [1998]. The lines connecting stations indicate distances used in calculating the strain rate. The proposed radioactive waste disposal site is near station Mile. The sinuous lines show active faults. The Death Valley- Furnace Creek (DVFC) fault s shown in the lower left corner. The star locates the epicenter of the Little Skull Mountain earthquake. The striped rectangle is the surface projection of the earthquake rupture and the dashed rectangle is the surface projection of its updip extension. Notice that monument Wahomie lies virtually on the surface trace of the fault plane. Because there is a systematic discrepancy of 0.28 _+ 0.10 ppm between distances measured by GPS and Geodolite [Savage et al., 1996], all distances measured by Geodolite have been decreased by 0.28 ppm. The monuments within the strain network were displaced by the 1992 Little Skull Mountain earthquake (Ms=5.4; epicenter shown in Figure 1). Because we wish to determine the rate of strain accumulation, we have used a dislocation model (Table 1) to estimate the effect of the earthquake on each line and removed the calculated offsets from the data. The fault plane for the dislocation model was taken from the focal plane solution of Meremonte et al. [1995]. Notice (Figure 1) that the fault trace for that solution passes very close to monument Wahomie, and one must expect some difficulties in fitting a simple dislocation model to data that involve that monument. The dimensions of the rupture (along-strike length and downdip width) were suggested by the aftershock distribution [Meremonte et al., 1995]. The slip on the fault was found from a fit to the observed changes in the 29 line lengths measured between 1983-1984 and 1993. That slip was largely determined by the changes in just three lines: Rock to Specter (observed 7.9_+5.2 mm, calculated 14.2 mm), Rock to Wahomie (observed-25.4_+4.8 mm, calculated-17.9 mm), and Rock to Well (observed-15.3_+4.9 mm, calculated-12.7 mm). The model fits all of the observed line-length changes within 2 standard deviations. Only dip slip on the fault was required to fit the data; the inclusion of strike slip did not significantly improve the fit. The seismic moment calculated for the model is (3.6_+0.5) x 1017 N m (compare (3.0_+1.3) x 1017 N m and Table 1. Parameters for the Dislocation Model the Little Skull Mountain Earthquake. Parameter Value Latitude Trace Midpoint 36 ø 46' 55" N Longitude Trace Midpoint 116 ø 20' 49"W Strike N55øE Dip 56 ø SE Depth of Top 6 km Downdip Width 5 km Length Along Strike 5 km Normal Slip 0.484 _+ 0.069 m Seismic Moment 3.6 x 1017 N m Moment Magnitude 5.6 of

(3.8+1.9) x 1017 N m estimated from broadband and longperiod seismograms by Zhao and Helmberger [1994]), and the implied moment magnitude is 5.6, in reasonable agreement with the magnitudes (Ms=5.4 and Mœ=5.6) assigned to the quake. The coseismic effects of the earthquake were then removed from the data by adding the coseismic offset calculated from the dislocation model to each of the preearthquake (1983 and 1984) Geodolite length measurements. The observed line lengths corrected for the coseismic offsets and the Geodolite-GPS difference are shown as a function of time in Figure 2. The horizontal lines in that figure represent the expected locus of observations if there had been no deformation in the network. We have also calculated weighted (inverse square of the a priori standard deviations) least squares fits to the data for each line. The slopes in mm/yr E E 3OO 25O 200 150 100 50 0 80 85 90 95 300 x mile-yucca t --- }--... m ine-pass--- -.? z mine-shoshone... - - pass-shoshone.- -,,, rock-specter 200 --rock-wahomie-,-1 ] r'; rock-well ],... roses-wahomie - - --(,... 150 t & l roses-well... )-- --shoshone-timber. J -½ I i ', 100- ' z shoshone-wahomie, t... (i>'- -- ' hø' h øne'yucca'- q- I I specter-well ', & 0/... 80 85 90 Time, yr Figure 2. Corrected line-length L less a nominal constant length L o for each line plotted as a function of time. The coseismic distance change as calculated from a dislocation model has been added to the preearthquake (1983 and 1984) observations. The horizontal lines correspond to no change in length, and the error bars represent 2 standard deviations on either side of the plotted points. The vertical dashed line indicates the time of occurrence of the Little Skull Mountain earthquake. SAVAGE ET AL.: YUCCA MOUNTAIN S2RAIN RATE 17,629 Table 2. Yucca Mountain Strain Rates 1 in a Coordinate System with the 1 Axis East and the 2 axis North. Interval el 1 el2 e22 1983-1998 1.6_+12.0-1.3_+4.8-21.7_+12.4 1983-1993 3.7_+17.5-2.0_+ 7.0-27.9_+18.3 Geodolite only 6.0_+20.2-7.7_+10.5-16.5_+21.0 1993-1998 -8.4_+40.1-2.1_+15.3-8.3_+42.1 GPS only -9.2_+44.1-2.2_+16.5-8.7_+46.0 1 In nanostrain/yr for the ten steepest fits in descending order of absolute magnitude are Cane-Wahomie -1.07 + 0.41, Rock-Wahomie -0.90 + 0.44, Bare-Brick -0.73 + 0.41, Roses-Wahomie 0.71 + 0.44, Pass-Shoshone 0.62 + 0.41, Shoshone-Wahomie -0.59 + 0.43, Cane-Mile -0.54 + 0.41, Cane-Specter -0.54 + 0.41, Mile-Shoshone -0.47 +0.44, and Bare-Mile 0.47_+ 0.51. (The standard deviations of the slopes are based upon the a priori estimates of the standard deviations in the line-length measurements plus a nominal 1 mm/x/yr random walk allowance for monument instability [Langbein and Johnson, 1997].) The slopes of the first two of those fits are significant at the 95% confidence level, and both of those fits involve monument Wahomie. Indeed, four (Cane-Wahomie, Rock- Wahomie, Roses-Wahomie, and Shoshone-Wahomie) of the six lines out of Wahomie are in the list of the ten largest slopes. As will be discussed in section 3, we suspect that these changes may be related to the fact that Wahomie is located virtually on the surface trace of the Little Skull Mountain earthquake rupture (Figure 1). To detect the overall deformation of the network, we assume that the strain accumulation across the Yucca Mountain array is uniform in both space and time and find the uniform strain rate that best explains the corrected line-length changes. The procedure used was explained by Savage et al. [1986]. The best-fit, uniform strain rate for all of the 1983-1998 data is shown as the first entry in Table 2. The principal strain rates are œ1 = 1.6_+11.9 nanostrain/yr N87øW_+12 ø and œ2 = -21.8_+12.5 nanostrain/yr N03øE_+12 ø. The total engineering-shear accumulation rate is 7 = œ1-œ2-23.4_+9.9 nanostrain/yr and the areal dilatation rate is A = œ1+œ2 = -20.1_+22.3 nanostrain/yr. (The quoted standard deviations were calculated from the a priori standard deviations assigned to the line-length measurements. The standard deviations estimated from the fit of the observations to the uniform strain field would have been 4% smaller. Thus the a priori estimates of standard deviation are consistent with the actual fit to a uniform strain rate.) Only the engineering shear strain accumulation rate y is significant at the 95% confidence level. 3. Discussion The interseismic velocity field implied by the corrected (i.e., coseismic effects and Geodolite-GPS discrepancy removed) line-length changes can be calculated from the estimated rates of change in length of the 29 observed lines (i.e., slopes of the linear fits to the corrected lengths in Figure 2). As stated earlier, only two of those slopes are significant at the 95% confidence level. Because all of the measurements are internal to the network, the rigid-body motion of the network as a whole is undetermined. Here we choose the rigid-

17,630 SAVAG ET AL.: YUCCA MOUNTAIN STRAIN RATE body motion so as to minimize the sum of the squares of the velocities at a certain subset of the stations, the inner coordinate solution [Gu and Prescott, 1986]. The minimum velocity constraint was applied to include all monuments except the five (Cane, Rock, Specter, Wahomie, and Well) in the southeast corner of the array. Those five monuments are the closest to the epicenter of the Little Skull Mountain earthquake and most subject to possible postseismic offsets and to uncertainties in the coseismic correction calculated from the simple dislocation model. Figure 3 shows the minimum velocity field consistent with the observed linelength-change rates. In Figure 3 only the displacements at Wahomie and Specter are significant at the 95% confidence level. Those two monuments are close to the 1992 Little Skull Mountain rupture (Figure 1), and, as mentioned in section 2, are subject to postseismic readjustment and uncertainties in the coseismic correction. Wahomie is virtually on the trace of the Little Skull Mountain rupture plane (Figure 1), and the velocity there is probably a consequence of postseismic readjustment: Wernicke et al. [1998, Figure 4] show a postseismic 1.0 mm/yr S65øE component of motion at Wahomie relative to Mile that could reasonably be interpreted as a postseismic effect. No obvious overall pattern has been recognized in the velocity field shown in Figure 3. In particular, the subset of velocities (velocities at all monuments except the five in the southeast corner of the network) minimized in the inner coordinate constraint appear random. The regional 50 nanostrain/yr N65øW extension proposed by Wernicke et al. [1998] is not apparent. Strain rates for the intervals 1983-1993 and 1993-1998 are also shown in Table 2. Both strain rates were calculated by the same procedures as used for the calculation of the 1983-1998 strain rate, but only the data appropriate to the respective time intervals were included. (The entries labeled Geodolite only and GPS only use only 1983-1993 Geodolite and 1993-1998 GPS data, respectively.) The standard deviations in the strain rate estimates are inversely proportional to the time interval ' - 20 )Timber Mine B_. rick Yucca OQ - 1 O Shoshone Pass Cane -20 1 m/y e Specter -40-20 0 20 40 Distance East from Mile, km Figure 3. Map showing the minimum velocity field consistent with the observed 1983-1998 corrected (coseismic effects removed) line-length changes. The minimum velocity constraint requires that the sum of the squares of the velocities at all stations except the five in the southeast corner of the network be a minimum. The ellipses represent 95% confidence limits. I I involved. Thus, if the strain rate has in fact been constant over the 1983-1998 interval, the standard deviation in the strain rate estimate is inversely proportional to the time interval over which measurements were made. Savage et al. [1994] had previously estimated the strain accumulation for the 1983-1993 interval to be Sll= 10+20 nanostrain/yr, sl2 = -2_+8 nanostrain/yr, œ22 = -9_+21 nanostrain/yr, el = 10_+20 nanostrain/yr N87øW_+24 ø, 2 = -9_+21 nanostrain/yr N03øE_+21ø, y = 19_+16 nanostrain/yr, and A = 1_+37 nanostrain/yr. Savage et al. did not correct the observations for coseismic offsets associated with the Little Skull Mountain earthquake but rather eliminated data from the three lines terminating at Rock, the lines most affected by the earthquake. The resulting strain rates are in reasonable agreement with the rates reported in Table 2. The analysis reported here is subject to a bias associated with the uncertainty in the systematic difference between distances determined by Geodolite (the 1983, 1984, and part of the 1993 surveys) and GPS (part of the 1993 survey and all of the 1998 survey): Geodolite measurements were found to be 0.28_+0.10 ppm longer than GPS measurements of distance [Savage et al., 1996]. The correction for this discrepancy was determined from measurements made elsewhere (i.e., not the GPS and Geodolite measurements used in this paper), but the correction is subject to some uncertainty. The uncertainty in this correction of the Geodolite measurements would appear as an extraneous uniform dilatation rate in our strain rate estimates. We can avoid this contamination by comparing measurements in which only the same instruments were used. For example, the 14 lines terminating at Mile and Shoshone were measured with the Geodolite in 1993 and can be compared with the Geodolite measurements of those same 14 lines in 1983 and 1984. The resulting strain rate (Table 2, Geodolite only) agrees well with the 1983-1998 strain rate. Similarly the GPS measurements in 1993 and 1998 can be used to estimate the strain rate (Table 2, GPS only). However, the 5-year time interval for this latter determination is too short to determine the strain rate very accurately. Our determination of the strain rate may be criticized on the basis that it was estimated from some of the same data used to determine the slip on the fault dislocation model. Indeed, the slip in the dislocation model was estimated from the observed changes in line length between 1983-1984 and 1993 with the implicit assumption that the line length changes were unaffected by strain accumulation. Thus, in the estimate of the 1983-1993 strain accumulation, the dislocation model was used to explain as much of the deformation as possible, and the strain accumulation was determined from the residual deformation. The analysis is then biased to give zero strain accumulation because the dislocation model had already been chosen to explain as much of the deformation as possible. However, the dislocation model fit is largely determined by the changes in the three lines radiating from station Rock, and the coseismic effect on the other lines is minor. Moreover, the coseismic line length changes would not have been significantly different if the slip had been calculated from the moment deduced from the seismic record [Zhao and Helmberger, 1994] or even calculated from the observed magnitude (Ms=5.4 or M L=5.6) through the momentmagnitude relation log Mo=l.5 M +9.1, where M o is the moment in N m and M is the magnitude. Finally, as described above, the earlier estimate of the strain rate by Savage et al. [1994] did not correct for coseismic displacements and yet

SAVAGE ET AL.: YUCCA MOUNTAIN STRAIN RATE 17,631 found strain rates consistent with those found here. Thus we do not think that the coseismic correction has introduced any significant bias into the strain rates. Strain accumulation in the Yucca Mountain strain array may be associated with right lateral slip on the Death Valley- Furnace Creek (lower left corner of Figure 1) and Hunter Mountain-Panamint Valley fault systems, 50 and 90 km, respectively, southwest of monument Mile. The paleoseismological estimate of the secular slip rate on the Death Valley-Furnace Creek fault is 5 i 1 mm/yr and on the Hunter Mountain-Panamint Valley fault 2 i 1 mm/yr [Bennett et al., 1997, p. 3076]. Both faults strike roughly N4$øW. The rate of accumulation of engineering-shear strain at the surface due to a long strike-slip fault slipping at a rate b below the locking depth d is y=(bd/e)/(d2+x 2) [Savage and Burford, 1973] where x is the distance from the fault. The locking depth d is generally taken to be about 15 km but may be as large as 25 km or more for a fault that has not ruptured in over 100 years [Savage and Lisowski, 1998]. Thus the engineering-shear strain rate in the Yucca Mountain array due to strain accumulation on the Death Valley-Furnace Creek and Hunter Mountain-Panamint Valley faults is expected to be 10-14 nanostrain/yr. The principal strain rates in the Yucca Mountain array associated with that accumulation would then be el = 6 nanostrain/yr N90øW and e2- -6 nanostrain/yr N00øE. About half (10-14 nanostrain/yr) of the observed engineering-shear strain rate (23i10 nanostrain/yr) can be accounted for by strain accumulation on the Death Valley- Furnace Creek and Hunter Mountain-Panamint Valley faults. The remainder (9-13i10 nanostrain/yr) is not significantly different from zero. The 1993 and 1998 GPS surveys indicate that the average velocity of the monuments within the Yucca Mountain network is about 5 mm/yr N60øW with respect to the stable interior of North America (see web site http://quake.wr.usgs. gov:80/quakes/ geodetic/gps/yuccamtn/). The source of that relative motion has not been identified. 4. Conclusions The principal strain rates determined over the 1983-1998 interval are œ1 = 2_+12 nanostrain/yr N87øW_+12 ø and 2 = -22_+12 nanostrain/yr N03øE_+12 ø. The total engineeringshear accumulation rate is?= 1-2 = 23_+10 nanostrain/yr and the areal dilatation rate is A = el+e2 = -20_+22 nanostrain/yr. The N65øW extension rate is -2_+12 nanostrain/yr, significantly less than the 1991-1997 rate of 50-+9 nanostrain/yr reported by Wernicke et al. [1998]. Only the engineering-shear strain accumulation rate T is significant at the 95% confidence' level. However, almost half of the observed T can be attributed to strain accumulation on the nearby Death Valley-Furnace Creek and Hunter Mountain- Panamint Valley fault systems. Once that contribution is removed, the remaining engineering-shear strain rate is not significant. Acknowledgment. This research was supported by U.S. Department of Energy through the Yucca Mountain Project of the U.S. Geological Survey. References Bennett, R.A., B.P. Wernicke, J.L. Davis, P. Elosegui, J.K. Snow, M.J. Abolins, M.A. House, G.L. Stirewalt, and D.A. Ferrill, Global Positioning System constraints on fault slip rates in the Death Valley region, California and Nevada, Geophys. Res. Lett., 24, 3073-3076, 1997. Gu, G., and W.H. Prescott, Discussion on displacement analysis: Detection of crustal deformation, J. Geophys. Res., 91, 7439-7446, 1986. Langbein, J., and H. Johnson, Correlated errors in geodetic time series: Implications for time-dependent deformation, J. Geophys. Res., 102, 591-603, 1997. Meremonte, M., J. Gomberg, and E. Cranswick, Constraints on the 29 June 1992 Little Skull Mountain, Nevada, earthquake sequence provided by robust hypocenter estimates, Bull. Seismol. Soc. Am., 85, 1039-1049, 1995. Savage, J. C., Technical Comment: Anomalous strain accumulation in the Yucca Mountain area, Nevada, Science, 282, 1007, 1998. (available as www.sciencemag.org/cgi/content/full/282/5391/1007b/) Savage, J.C., and R.O. Burford, Geodetic determination of relative plate motion in central California, J. Geophys. Res. 78, 832-845, 1973. Savage, J.C., and M. Lisowski, Viscoelasti coupling model of the San Andreas Fault along the big bend, southern California, J. Geophys. Res., 103, 7281-7292, 1998. Savage, J.C., and W.H. Prescott, Precision of Geodolite distance measurements for determining fault movements, J. Geophys. Res., 78, 6001-6008, 1973. Savage, J.C., W.H. Prescott, and G. Gu, Strain rate accumulation in southern California, 1973-1984, J. Geophys. Res., 91, 7455-7473, 1986. Savage, J.C., M. Lisowski, W.K. Gross, N.E. King, and J.L. Svarc, Strain accumulation near Yucca Mountain, Nevada, 1983-1993, J. Geophys. Res., 99, 18,103-18,107, 1994. Savage, J.C., M. Lisowski, and W.H. Prescott, Observed discrepancy betweeen Geodolite and GPS distance measurements, J. Geophys. Res., 101, 25,547-25,552, 1996. Wernicke, B., J.L. Davis, R.A. Bennett, P. Elosegui, M.J. Abolins, R.J. Brady, M.A. House, N.A. Niemi, and J.K. Snow, Anomalou strain accumulation in the Yucca Mountain area, Nevada, Science, 279, 2096-2100, 1998. Zhang, J., Y. Bock, H. Johnson, P. Fang, J. Gertrich, S. Williams, S. Wdowinski, and J. Behr, Southern California permanent GPS geodetic array: Error analysis of daily position estimates and site velocities, J. Geophys. Res., 102, 18,035-18,055, 1997. Zhao, L.-S., and D.V. Helmberger, Source estimation from broadband regional seismograms, Bull. Seismol. Soc. Am., 84, 91-104, 1994. W.H. Prescott, J.C. Savage, and J.L. Svarc, U.S. Geological Survey, M/S 977, 345 Middlefield Rd, Menlo Park, CA 94025 (jsavage@ isdnml.wr.usgs.gov) (Received September 30, 1998; revised February 11, 1999; accepted March 4, 1999)