Table 1. Tensor Strain Rates (nanostrain per year) as measured by the USGS (2) referred to a coordinate system with the 1 axis directed east and the 2 axis north. Uncertainties are in standard deviations. Network e11 e12 e22 All lines 10 ± 20  2 ±  8  9 ± 21 Subnetwork 1 9 ± 22  5 ± 11  11 ± 23 Subnetwork 2 12 ± 23 3 ± 12  8 ± 24

First, I consider the effects of the Little Skull Mountain earthquake (rupture shown in Fig. 1). That earthquake and its aftershocks were well recorded by a dense network of seismic stations deployed in the area, and consequently the rupture area and mechanism are relatively well known (4). The seismic focal solution defines two planes, one dipping southeast and the other northwest; the former was identified as the fault plane on the basis of the distribution of aftershocks (4). The USGS (3) also found that its data indicated faulting on the southeast dipping focal plane. Because station RK59 was within a few kilometers of the earthquake epicenter (Fig. 1), the 1983-1993 changes in measured distance (3) between RK59 and nearby stations Wahomie, Well, and Spec constrain which of the two focal planes can be the fault plane. Whereas slip on the southeast dipping plane was consistent with the observed changes in line length, slip on the northwest dipping plane was not.

Station Wahomie lies close to the trace (Fig. 1) of the Little Skull Mountain rupture plane directly updip from the rupture (4). Although that location is close to a displacement node for the coseismic displacement, it is a location particularly subject to postseismic displacements if relaxation occurs on the coseismically stressed unruptured shallow segment of the fault plane. Substantial deformation near the fault trace has been observed after several earthquakes along the San Andreas fault in California that, like the Little Skull Mountain earthquake, did not produce surface rupture (5). Thus, anomalous motion at Wahomie after the Little Skull Mountain earthquake (mid-1992) might be explained by postseismic relaxation.

The major challenge to the strain rate reported by Wernicke et al. concerns whether they have underestimated the uncertainties in their measurements. I refer here not to their analysis of global position satellite (GPS) data, which I agree is state of the art, but rather that they did not account for the uncertainty introduced by monument instability. Their measurements are referred to monuments at the ground surface. Such monuments are not completely stable with respect to the rock at depth. Thus, two monuments located close together are expected to exhibit random motions with respect to one another. Wernicke et al. used as station marks ordinary survey monuments (6) designed for surveys orders of magnitude less precise than their GPS survey. Such monuments are thought to be subject to significant correlated random motions (7). Johnson and Agnew (8) suggest that monument wander can be modeled by a random walk with standard deviation bt, where b is a constant for a particular monument and t is the time interval involved. The overall measurement noise would then be the sum of the white GPS noise [SD as represented by the error bars in figures 2 and 4 in (1)] and the random walk of the monument. Because the random walk noise is correlated (where the mark is today depends on where it was yesterday), it introduces substantial uncertainty in rate estimates derived from fitting a straight line to a time sequence of observations. This degradation of rate estimates resulting from monument instability can be overcome by building more stable monuments or by extending measurements over a longer period of time. More frequent measurements within the same time interval (the strategy employed by Wernicke et al.) is generally not an effective way to suppress correlated noise (8). The concern of the geodetic community about monument stability is indicated by the fact that monuments costing about $15,000 (versus a few hundred dollars for an ordinary monument) are generally installed in continuous GPS arrays to minimize the instability, even though a clear demonstration of the stability of those improved monuments is not available (9).

I now apply these considerations to the data reported by Wernicke et al. Consider (Fig. 2A) the measurements of the distance between stations Mile and Wahomie as shown by Wernicke et al. (1) in their figure 4 (10). The data as plotted do not include a correction for the coseismic offset associated with the Little Skull Mountain earthquake, although Wernicke et al. did discuss that correction. Had rupture in that earthquake occurred on the northwest dipping focal plane, then the coseismic effect on the Mile-Wahomie line would have been <1 mm, and the data (Fig. 2A) would not have required correction. However, evidence cited above shows that the rupture occurred on the southeast dipping focal plane, and that would imply a coseismic lengthening of 7 mm on the Mile to Wahomie line. To represent strain accumulation, then, 7 mm should be subtracted from each of the postseismic measurements (Fig. 2B). The pre-earthquake (1983, 1984, and 1991) measurements in the corrected plot (Fig. 2B) are no longer predicted as well by an extrapolation of the trend defined by the postearthquake data (dashed line).

The final step in the analysis is to include monument noise following the procedure suggested by Johnson and Agnew (8). The noise in the GPS measurements has been taken as white with standard deviations as given by Wernicke et al. The b parameter in the random walk monument noise has been set at 1 mm/yr, which seems an underestimate: Langbein and Johnson (7) suggest as an average for an ordinary monument a value of b almost twice as large as used here (11). The linear fits to the data corrected for the coseismic offset and to the postseismic data only are shown in Fig. 2C. The standard deviations in the slopes are almost as large as the slopes themselves, and the proper interpretation of Fig. 2C is not obvious. Although the data might suggest postseismic relaxation at Wahomie following the Little Skull Mountain earthquake, they do not furnish convincing evidence for an anomalous long-term extension rate before the earthquake.

The significance of measurements of strain accumulation across the entire array is similarly obscured by uncertainties introduced by monument instability. The S65°E components of velocity at stations Claim, 67TJS, Mile, and Wahomie relative to Black as given in figure 3a in (1) are shown (Fig. 3) as a function of distance S65°E from Claim. The SD values (Fig. 3) were calculated from fits to the displacement measurements in figure 2 of (1). Those fits included an allowance in the weights for monument instability with b = 1 mm/yr. The N65°W extension rate calculated from the data in Fig. 3, with account taken of the covariance resulting from monument instability at the common station Black, is then 32 ± 18 nanostrains per year. That extension rate is determined largely by the velocities at Wahomie and Claim, both of which are somewhat suspect (12). Wernicke et al., not accounting for monument instability, found 50 ± 9 nanostrains per year for the same data. Although the estimates of the extension rate are similar, monument instability has more than doubled the uncertainty. Whereas the 50 ± 9 nanostrains per year strain rate reported by Wernicke et al. would properly be considered anomalous, the rate corrected for monument instability (32 ± 18 nanostrains per year) would not.

The important issue here is the stability of the monuments used to mark the GPS stations. The question of monument stability is still open, and the random walk representation may not be the last word on that instability (13). But my representation of monument wander (random walk with b = 1 mm/yr), which I regard as an underestimate, is more realistic than the assumption of complete stability.

Finally, the earlier USGS measurement (Table 1) of strain accumulation near Yucca Mountain is more reliable than the determination made by Wernicke et al. because of the broader area and longer time interval covered. The USGS measurements are also less contaminated by the coseismic and postseismic effects of the Little Skull Mountain earthquake. The strain rates for two separate parts of the USGS network (see entries Subnetwork 1 and Subnetwork 2 in Table 1) are similar. The N65°W extension rates found for those two subnetworks are 9 ± 22 and 6 ± 23 nanostrains per year.

J. C. Savage
U.S. Geological Survey, M/S 977,
345 Middlefield Road,
Menlo Park, CA 94025, USA
e-mail: jsavage{at}isdmnl.wr.usgs.gov

REFERENCES AND NOTES

1. B. Wernicke et al., Science 279, 2096 (1998) [Abstract/Free Full Text] .
2. Uncertainties are in standard deviations.
3. J. C. Savage, M. Lisowski, W. K. Gross, N. E. King, J. L. Svarc, J. Geophys. Res. 99, 18103 (1994) [CrossRef].
4. M. Meremonte, J. Gomberg, E. Cranswick, Bull. Seismol. Soc. Am. 85, 1039 (1995) [Abstract/Free Full Text].
5. C. H. Scholz, M. Wyss, S. W. Smith, J. Geophys. Res. 74, 2049 (1969) [ISI]; J. C. Savage, M. Lisowski, J. L. Svarc, ibid. 99, 13757 (1994); J. C. Savage and M. Lisowski, Geophys. Res. Lett. 22, 759 (1995) [CrossRef]; J. C. Savage and J. L. Svarc, J. Geophys. Res. 102, 7565 (1997) .
6. The monuments at Claim, Black, and Mile are tablets set in drill holes in rock outcrops; at 67TJS the tablet is affixed to a rod driven into the ground to refusal, and at Wahomie the tablet is set in a drill hole in a 0.6-m-by-0.3-m boulder projecting 0.07 m above the ground surface.
7. J. Langbein, F. Wyatt, H. Johnson, D. Hamann, P. Zimmer, Geophys. Res. Lett. 22, 3533 (1995) [CrossRef]; J. Langbein and H. Johnson, J. Geophys. Res. 102, 591 (1997) ; F. Wyatt, ibid. 87, 979 (1982); ibid. 94, 1655 (1989).
8. H. O. Johnson and D. C. Agnew, Geophys. Res. Lett. 22, 2905 (1995) [CrossRef].
9. The principal authors of Wernicke et al. chose to use the improved monument design in a network installed in northern Nevada in 1996: R. A. Bennett, B. P. Wernicke, J. Davis, Geophys. Res. Lett. 25, 563 (1998) .
10. There are minor differences between figure 2A and figure 4 of the report by Wernicke et al. (1). The first data point (the 1983 observation) in figure 2A is 6 mm larger than the corresponding point in figure 4 of Wernicke et al. Because the measurement involved was made by the USGS, I am confident that the value shown in figure 2A is the correct one. The 1993 USGS observation shown in figure 2A was not shown by Wernicke et al. However, that data point was not included in the linear fits reported here. Finally, the suspect 1995 GPS observation shown in figure 4 of (1), but not used in their analysis [see their footnote 14 in (1)], is not shown in Fig. 2A.
11. The choice of b = 1mm/yr is intended to represent the random walk noise in the distance measured between two monuments. The component in one direction of the random motion of a single monument is then described by b = 0.7 mm/yr. The rms wander of a monument in a given direction over the 6-year interval 1991 to 1997 would be only 1.7 mm. Langbein and Johnson (7) suggest b = 1.3mm/yr as an average value for a single ordinary monument, almost twice the value used here.
12. As discussed earlier, it is likely that the motion of Wahomie, which is virtually on the trace of the Little Skull Mountain rupture plane, represents postseismic relaxation. Station Claim was the only monument not surveyed in 1997, and it can be seen in figure 2 of Wernicke et al. that the 1996 survey, the last survey at Claim, was notably short at all monuments (see particularly the east component). Thus, it is likely that, had Claim been surveyed in 1997, its velocity would have been higher (that is, more positive).
13. J. Zhang, et al., J. Geophys. Res. 102, 18035 (1997) [CrossRef].

Brian Wernicke et al. (1) used GPS measurements to document crustal strain rates across Yucca Mountain that greatly exceed those inferred from the geologic record. These geodetic results raise several important questions concerning how regional strain patterns influence rates of volcanism, seismicity, and faulting. The challenge posed by Wernicke et al. is to reconcile their geodetic observations, which record 10⁰ to 10¹ years of crustal motion with geological records that span and smooth 10⁵ to 10⁶ years of crustal deformation. This integration is important for hazard estimates at Yucca Mountain, the proposed site of the first permanent U.S. high-level radioactive waste repository, because of the 10³- to 10⁵-year period used to estimate the future performance of the repository.

To assess the GPS results (1) in terms of Yucca Mountain hazards, several salient details about the geological record of volcanism and faulting call for clarification. First, of the more than 100 radiometric age determinations of Lathrop Wells basalts, the most recent high-precision isotopic ⁴⁰Ar/³⁹Ar dates indicate that it has an age of 80 thousand years (ka) (2). Compilations of ⁴⁰Ar/³⁹Ar and K/Ar dates give an age of 131 to 141 ka (3). These data do not support the 10-ka age cited by Wernicke et al. Second, current estimates of recurrence rates of volcano or vent alignment formation in the Yucca Mountain region are 2 to 5 × 10⁶ events per year (4). If these rates have been underestimated by one order of magnitude (1), the regional recurrence rate during this episode of anomalous strain would be 2 to 5 × 10⁵ events per year. With the use of a value in this range (for example, 3 × 10⁵ events per year), we obtain a likelihood of volcano formation since 80 or 130 ka of 90% and 98%, respectively. The lack of a known Yucca Mountain region volcano younger than 80 to 130 ka diminishes the argument that volcanic recurrence rates have been underestimated by 1 order of magnitude since the eruption of Lathrop Wells. Third, available faulting data (Fig. 1) are inconsistent with the notion that the Lathrop Wells volcano is part of a current episode of anomalously high strain. Although of low resolution, these data provide a record of deformation that extends prior to the eruption of Lathrop Wells volcano; they do not delineate the onset of a continuing episode of anomalous high strain rate since 150 ka. Rather, they suggest a paucity of large fault displacements (>60 cm per event) since 50 ka.

We propose three alternatives to the suggestion by Wernicke et al. that the GPS-derived strain rates indicate the onset of a period of anomalous strain accumulation and thereby necessitate an order of magnitude increase in the estimates of volcanic and seismic hazards at Yucca Mountain.

1) The current strain rates observed by Wernicke et al., although high for the Basin and Range, are not anomalous, but represent an average rate for the Quaternary across the Yucca Mountain region. Total strain, however, is partitioned between geological processes that contribute to hazard estimates (that is, earthquakes and volcanoes) and those that do not (that is, small faults, fractures, and other aseismic deformation). In this interpretation, strain is assumed to be relatively constant, but the resulting deformation varies over time. Thus, the alignment of Quaternary cones in Crater Flat or the apparent clustered faulting at about 70 ka (Fig. 1) represent varied mechanisms of strain release.

2) The last 100 to 150 ka has been a period of anomalously high strain (as suggested by Wernicke et al.). As in the first alternative 1), however, this periodicity of strain has not resulted in a one order of magnitude increase in recurrence rate of volcanism or faulting. Unlike 1), clustered activity like the alignment of Quaternary cones in Crater Flat or the apparent clustered faulting at about 70 ka (Fig. 1) are representative of the periodicity of crustal strain accumulation and release.

3) Strain is episodic, with bursts of rapid strain accumulation and release covering 10³ to 10⁴ years between much longer periods of relatively low strain rates. In this case, average recurrence rates derived from the geologic record may not afford us a reasonable measure of hazard over the next 10³ to 10⁵ years.

In terms of the volcanic hazard, interpretations 1 and 2 are consistent with current estimates (4) that incorporate clustering and structural controls (6). We estimated the probability of volcanic eruptions through the proposed repository, given that a new volcano forms in the region, to be approximately 2 × 10² or less, using a range of parameters in Epanechnikov and Gaussian kernel models constrained by fault controls on volcano distribution (6). These values are up to two orders of magnitude greater than average rates of volcanism in the Western Great Basin (7), mainly because of recent and clustered basaltic volcanism around Yucca Mountain. This probability model predicts higher rates of volcanic activity between Lathrop Wells volcano and the proposed repository, and throughout southern Crater Flat, than elsewhere in the region, precisely because it accounts for tectonic controls on volcanism (Fig. 2). With the use of regional recurrence rates of volcanic events of 2 to 5 × 10⁶ events per year and probability density functions for alignment length, one can obtain probabilities of volcanic disruption of the proposed repository between 10⁸ per year and 10⁷ per year.

As with volcanism, interpretations 1 and 2 may not strongly affect current estimates of the seismic hazard (8). Given these interpretations, the dichotomy between the higher rates derived from GPS measurements and lower rates derived from the geologic record is not unique to Yucca Mountain (9) and not unexpected. Strain rates derived from each of these two techniques essentially represent end-member values. For example, trenching studies provide minimum estimates (10) because this technique captures only that portion of crustal strain evident from known earthquakes on large faults that rupture the ground surface. In contrast, strain rates derived from GPS data can be expected to include elastic strain energy stored in rock and an inelastic strain component partitioned among several processes such as fracture dilation and slow aseismic slip on preexisting faults and fractures. For example, a set of vertical fractures or joints spaced 2 m apart, each dilating 0.5 mm in the next 10 ky, could account for half of the extensional strain predicted by the GPS results.

Only interpretation 3 suggests that the GPS measurements should alter the current volcanic and seismic hazards at Yucca Mountain. Increasing recurrence rate by one order of magnitude gives an upper bound on volcanic eruptions at the site of 10⁶ events per year, or 10² in a 10⁴ events per year performance period. Similarly, assuming all the GPS strain is accommodated by large earthquakes distributed on faults between Yucca Mountain and Bare Mountain over the next 10⁴ years more than doubles the anticipated peak ground accelerations at Yucca Mountain (11).

In conclusion, a one order of magnitude change in hazard rates does not necessarily follow from the GPS strain rates of Wernicke et al. Two suppositions must be evaluated before seismic and volcanic hazards can be reconsidered using GPS strain rates: (i) high strain rates (1, 9) persist on time scales (10³ to 10⁴ years) that affect hazard estimates compared to estimates derived from the geologic record (10⁵ to 10⁶ years), and (ii) episodic strain accumulation directly correlates with episodic volcanic eruptions or increased seismicity. If shown to be correct, these two suppositions would not only alter the general perception of relatively constant strain accumulation in crustal rocks, but allow us the possibility to evaluate seismic and volcanic hazards in a deterministic fashion by monitoring crustal strain.

C. B. Connor
J. A. Stamatakos
D. A. Ferrill
B. E. Hill
Center for Nuclear Waste
Regulatory Analyses,
Southwest Research Institute,
6220 Culebra Road,
San Antonio, Texas 78238, USA

REFERENCES AND NOTES

1. B. Wernicke et al., Science 279, 2096 (1998) .
2. M. T. Heizler, T. I. Wilch, J. Stroud, Eos 78, F771 (1997) .
3. B. D. Turrin, D. Champion, R. J. Fleck, Science 253, 654 (1991) [Abstract/Free Full Text] ; D. B. Turrin, D. E. Champion, R. J. Fleck, G. H. Curtis, R. E. Drake, K-Ar Ages and Paleomagnetic Directions from the Lathrop Wells Volcanic Center, Southwestern Nevada: An Evaluation of Polycyclic Volcanism, U.S. Geological Survey Open-File Rep. 98-44 (1998).
4. C. B. Connor and B. E. Hill, J. Geophys. Res. 100, 10107 (1995) [CrossRef]. Issue Resolution Status Report: Igneous Activity (U.S. Nuclear Regulatory Commission, Washington, DC, 1998); B. E. Hill, C. B. Connor, J. S. Trapp, NRC High-Level Radioactive Waste Program Annual Progress Report: Fiscal Year 1996, NUREG/CR-6513, (1997), pp. 2.1-2.32.
5. I. G. Wong and J. C. Stepp, Probabilistic Seismic Hazard Analyses for Fault Displacement and Vibratory Ground Motion at Yucca Mountain, Nevada, Final Report, Volume 2, Appendices, Milestone SP32IM3, WBS Number 1.2.3.2.8.2.6 (1998); J. W. Whitney, Ed., Seismotectonic Framework and Characterization of Faulting at Yucca Mountain, Nevada (U.S. Geological Survey, Washington, DC, 1996); L. Anderson, personal communication (1997).
6. Past volcanism near Yucca Mountain has clustered in time and space, and this clustering has a profound impact on estimates of probability of volcanic eruptions at Yucca Mountain (4). In addition, vent alignments are common features of volcanic activity near Yucca Mountain and there is ample evidence from this volcanic field and others that vent alignments, especially where correlated with faults, can reactivate after long periods of time. For example, the Quaternary Crater Flat alignment (Fig. 2) includes magnetic anomalies interpreted to be produced by basalts with normal and reversed remanent magnetizations buried by up to 150 m of alluvium. C. B. Connor et al., Eos 78, 77 (1997) ; E. I. Smith, T. R. Feuerbach, J. E. Faulds, Proceedings of the International Topical Meeting on High-Level Radioactive Waste Management, vol. 1 (American Nuclear Society/American Society of Civil Engineers, Las Vegas, NV, 1991), pp. 18-90; C. B. Connor et al., Eos 77, F20 (1996) [CrossRef]; F. M. Conway et al., J. Geophys. Res. 102, 815 (1997) .
7. At least 211 basaltic volcanoes <2 Ma occur in the Western Great Basin, a 82,000 km² region defined by Amboy volcano, the Big Pine volcanic field, and the Lunar Crater volcanic field, yielding an average recurrence rate of 2 × 10⁹ year¹ km²; R. G. Luedke and R. L. Smith, Map Showing Distribution, Composition, and Age of Late Cenozoic Volcanic Centers in California and Nevada, U.S. Geological Survey Miscellaneous Investigations Series Map I-1091-C (1981).
8. I. G. Wong, S. K. Pezzopane, C. M. Menges, R. K. Green, R. C. Quittmeyer, Proc. Am. Nuclear Soc. (1995), pp. 51-63.
9. L. J. Martinez, C. M. Meertens, R. B. Smith, Geophys. Res. Lett. 25, 567 (1998) [CrossRef] [ISI].
10. Several recent studies show that longer-term (that is, 10⁶ years), geologically derived slip rates also exceed those predicted from trenching results, supporting the theory that strain estimates from trenching studies represent only a fraction of the total strain budget. D. A. Ferrill et al., Faulting in the Yucca Mountain Region, U.S. Nuclear Regulatory Commission, NUREG/CR-6401; D. A. Ferrill et al., Geology 24, 559 (1996) [Abstract/Free Full Text]; J. A. Stamatakos, C. B. Connor, R. H. Martin, J. Geol. 105, 319 (1997) .
11. Calculated on the basis of seismic hazard curves comparing extension rates across the Yucca Mountain region of 0.2 to 2.0 mm/year, in which faulting takes place on a series of randomly placed normal faults with 60° dip, assuming maximum magnitude = 7.0. Fault slip is linked to recurrence. R. R. Youngs and K. J. Coppersmith, Bull. Seismol. Soc. Am. 75, 939 (1985) [Abstract/Free Full Text]. Response spectral attenuation relationship from N. A. Abrahamson and W. J. Silva, Seismol. Res. Lett. 68, 94 (1997) .

Response: We would first like to thank Savage for pointing out an error in the value we used in our report for one of the trilateration measurements of the Mile-Wahomie line length (1). Correcting this error reduces the "no earthquake" rate by ~0.09 mm/year, or about 0.5. This minor change does not affect any of the rates reported for solutions performed without these earlier data or the conclusions of our report.

Savage argues that we did not give proper weight to the coseismic and postseismic effects of the Little Skull Mountain earthquake, and that we did not include effects of monument instability. We agree that these are important issues. We stated in our report (1, 2098),

The principal issues in evaluating the geophysical significance of these velocities is whether they represent steady-state strain accumulation, or whether all or part of the motion reflects other processes including (i) coseismic or rapid postseismic deformation (for example, afterslip or viscous relaxation) associated with the Little Skull Mountain [LSM] earthquake, (ii) monument instability or other sources of time-correlated error, (iii) error in correcting for the GPS-geodolite scale difference, or (iv) undetected GPS error.

The disagreement between Savage and ourselves seems to be primarily over the details regarding how these effects are dealt with. We point out that, "The last three effects are difficult to evaluate because we have no expectation of how they would contaminate the secular rates for these particular sites. It is unlikely that some or all of these factors would have conspired to yield significant rates, the strain pattern apparent in Fig. 3B [of our report], or the expected west-northwest elongation, but they remain important caveats in interpreting the data." In other words, one cannot, on the basis of the data, quantitatively assess the impact of these unknown errors. Furthermore, Savage did not comment on our observation that both the orientation (west-northwest) and the sense (extensional) of the observed deformation of figure 3B in our report are expected on the basis of other geologic and geophysical data.

Our treatment regarding the coseismic effects of the LSM earthquake seems more thorough than that of Savage. We performed four different solutions for the rate, using different methods to account for its effects. In these solutions, we (i) allowed for no coseismic offset; (ii) used the coseismic offset calculated using the model adopted by others [see note 10 in our report (1)], which includes a southeast-dipping fault plane; (iii) used the coseismic offset calculated using a model that includes a northwest-dipping fault plane; and (iv) allowed the coseismic offset to be estimated from the data themselves. We included this general treatment of the LSM earthquake because the seismic evidence is ambiguous [as outlined in note 10 in (1)]. Savage states in his comment that the previous geodetic data (2) admit only a southeast-dipping fault plane, whereas we find a reasonable solution for the geodetic data involving a northwest-dipping fault plane (3). Finally, as we point out (1), the geology of other faults in the area would point to a northwest-dipping fault plane. Given these unresolved issues, a conservative approach to the effects of the LSM earthquake was warranted, even though the southeast-dipping fault model has become the "accepted" solution. In any event, the choice of nodal plane is a second-order effect as regards the Mile-Wahomie velocity and does not affect the significant intersite motions observed west of Wahomie.

In regard to postseismic effects, the observations that Savage makes for the San Andreas fault are reasonable, although the strike-slip earthquakes he cites for evidence [see the references in note 4 of (2)] are substantially larger than the M_S = 5.4 LSM earthquake (Parkfield, M_L = 6.0; Morgan Hill, M_L = 6.2; Loma Prieta, M_S = 7.1; Landers, M_w = 7.3). There are two main mechanisms that govern postseismic deformation: (i) viscoelastic relaxation in an intracrustal asthenospheric layer (4) and (ii) afterslip in a velocity-strengthening region above the coseismic rupture zone (5). It is not clear whether an earthquake as small as the LSM earthquake is capable of exciting the first mechanism. Studies to date have dealt with large to great earthquakes which rupture the entire seismogenic zone (4). In any case, displacements associated with the first mechanism would be expected to be only a fraction of the coseismic displacements. Surface displacements associated with afterslip, on the other hand, could conceivably be as large as the coseismic slip. However, these surface displacements would be highly localized within the region surrounding the extrapolation of the fault plane into the near-surface material (5). Regardless of mechanism, geodetically observed postseismic decay times (5-8) are small. The relaxation time for Loma Prieta, for example, was inferred to be 1.4 years (7). The relaxation time observed using GPS for the Landers earthquake was ~30 days (8). In contrast, the Mile-Wahomie line change we found (1) showed no sign of decay. If the observed Mile-Wahomie line change is associated with postseismic deformation, then it would be a unique discovery and would appropriately be described as "anomalous." As in the case of the nodal plane issue, afterslip would not affect the four sites west of Wahomie that show significant motion.

We do not dispute Savage's mathematical calculations regarding the effects on the estimate of a strain-induced baseline rate if there is a contribution resulting from random-walk monument instability of the size that he assumes. There is no evidence, however, that this model characterizes the Mile-Wahomie line-length variations. None of the previous studies that have led to the characterization of monument wander as a random-walk process on the basis of power spectra use more than about 3 years of data (8-10), and none of them conclusively demonstrate that monument wander is the source of the correlated noise, even at the relatively high frequencies of the observed power spectra. Our GPS data cover a time span of 6 years, and the total time span including the trilateration data is ~14 years. Savage states that the 1 mm²/year random-walk variance (per unit time) is possibly an overestimate. Langbein and Johnson (10) indicate a range of random walk variances of 0.2 to 9 mm²/year (neglecting the monuments known to be unstable). Their data were obtained from monuments in just three localities in California, generally anchored in clay-rich soils with relatively high, strongly seasonal rainfall. Langbein and Johnson did not state (10) that these results generally apply to all geodetic monuments; their findings indicate that geology and monument type may play an important role. For example, in an earlier study by others, surface monuments placed in competent, weathered granite imparted apparent velocity variations of only 0.05 mm/year (8). Monuments used for our study (with the exception of 67TJS) are set in unweathered bedrock in an arid environment, and likely perform as well as or better than some others (8).

We prefer to assess these affects from the data themselves. With the use of the Mile-Wahomie baseline series, we used the maximum likelihood method (10) to solve simultaneously for the random-walk variance of the monument wander (assuming that this model applies at long periods) and for a baseline rate. When either no coseismic offset was allowed or the northwest-dipping fault model was used to calculate the coseismic offset, the estimated random-walk variance was zero. In other words, the time series [figure 1 in our report (1)] was "too linear" to admit any random-walk variations. When the southeast-dipping fault model was used to calculate the coseismic offset, the estimated random-walk variance is 0.17 mm²/year, yielding a rate estimate of 0.5 ± 0.2 mm/year. Thus, a 1 mm²/year random-walk variance appears to be a significant overestimate.

As to the "reliability" of the estimates, we do not argue that our GPS network covers as much area or generally represents as long a time span as some other data (2), although the full GPS-trilateration time series for Mile-Wahomie has a time span of 14 years. However, Savage seems to argue that the very small (3 nstr/year) disagreement in strain rates for the two parts of his network is a measure of this reliability. This is a statistically specious argument, because these strain rates have large uncertainties of ~20 nstr/year. Moreover, as Savage notes, the difference between the strain rates reported in our paper and in (2) is less than two standard deviations. The ±2 regions overlap greatly (32 to 48 nstr/year), and the upper bound that this overlap places on the strain rate still indicates a significant potential strain accumulation in the region. But it is not this apparently anomalous upper bound on strain rate to which Savage objects, but rather to the fact that the lower bound excludes zero. With the use of our data, Savage has obtained a solution which has an "acceptable" lower bound only by making three assumptions that we have shown cannot be supported: (i) the southeast-dipping fault model for the LSM earthquake is the unambiguously correct model, (ii) the random-walk model for monument motion applies at very long periods, and (iii) the value for the random walk variance is 1 mm² per year. Our analysis--based on the data themselves, rather than these assumptions--is, in this sense, more reliable.

Connor et al. comment on our suggestion that the observed strain rates in the Yucca Mountain area may reflect an epoch of strain accumulation that is ten times the geologic average, indicating a tenfold increase in the likelihood of magmatic or tectonic events in the region over the lifetime of the repository. They offer several alternatives to this proposed explanation, all of which are plausible, but also speculative.

Do the more recent measurements of the Lathrop Wells basalts age and recurrence rates for volcanism rule out the possibility that the rates are underestimated by a factor of, say, ten, as we speculated (1)? We were aware of the "most recent" age of 80 ka for the basalts cited by Connor et al. The data supporting this age are unpublished and we therefore conservatively chose to quote the entire range of published age estimates. However, let us assume, for the sake of argument, that the age range of 80 to 130 ka preferred by Connor et al. is correct, and that the recurrence rates under this assumption are 2 to 5 × 10⁵ per year. With the use of a nominal value for the recurrence rate of 3 × 10⁵ per year, Connor et al. calculated the likelihood of a volcanic event since the last event to be 90 to 98%. Given that such an event has not occurred, these high probabilities indicate that perhaps the recurrence rate is not so high. But if the complete range of recurrence rates is considered along with the range of ages, then a "complete" range of probabilities would be 80 to 99.9%. (The lower bound comes from coupling the lower bound in recurrence rate to the lower bound in age.) This lower bound in likelihood is still high, but not so high as to rule out the hypothesis of increased rates of volcanism.

James L. Davis
Harvard-Smithsonian
Center for Astrophysics,
Cambridge, MA 02138, USA
Brian P. Wernicke
Division of Geological and
Planetary Sciences,
California Institute of Technology,
Pasadena, CA 91125, USA
Richard A. Bennett
Harvard-Smithsonian
Center for Astrophysics

REFERENCES AND NOTES

1. B. Wernicke et al., Science 279, 2096 (1998) .
2. J. C. Savage, M. Lisowski, W. K. Gross, N. E. King, J. L. Svarc, J. Geophys. Res. 99, 18103 (1994) .
3. Observed significant baseline changes (2) resulting from the LSM earthquake were Rock-Well, 19 ± 5 mm; Rock-Wahomie, 17 ± 5 mm; and Rock-Specter, 12 ± 5 mm. (Site "Rock" is referred to as "RK59" in the comment of Savage.) These measurements have not been corrected for possible NNW extension between 1983 and 1993. We have reproduced the southeast dipping dislocation model results reported in (2) which gives: Rock-Well, 23 mm; Rock-Wahomie, 13 mm; and Rock-Specter, 12 mm. As reported in (2), these model displacements are consistent with the observed baseline length changes at the 1- level, with a ² residual per degree of freedom of 1.3. Starting with the northwest dipping fault plane implied by the focal mechanism and hypocenter as calculated by W. R. Walter [Geophys. Res. Lett. 20, 403 (1993)], we explored the fits of northwest dipping dislocation models to the published trilateration measurements (2). We found a northwest dipping dislocation model, consistent at the 1- level with the focal mechanism and hypocentral data of Walter, that fits the Savage et al. baseline length changes at the 1- level with ² residual per degree of freedom of 0.6. The displacements from this northwest dipping model are Rock-Well, 18 mm; Rock-Wahomie, 15 mm; and Rock-Specter, 15 mm.
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5. C. H. Scholz, Mechanics of Earthquakes and Faulting (Cambridge Univ. Press, New York, 1990); C. J. Marone, C. H. Scholz, R. Bilham, J. Geophys. Res. 96, 8441 (1991) [CrossRef].
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7. J. C. Savage, M. Lisowski, J. L. Svarc, J. Geophys. Res. 99, 13757 (1994) [CrossRef].
8. F. Wyatt, ibid. 87, 979 (1982).
9. ___, ibid. 94, 1655 (1989).
10. J. Langbein and H. Johnson, ibid. 102, 591 (1997).