Rate of E–W extension in the Volcanic Tableland, California (USA): A comparison of strain rates on two different timescales Open Access

Strain rates of fault zones are known to vary through time (e.g., Wallace, 1987; Sieh et al., 2008; Nicol et al., 2009; Cowie et al., 2012; Mechernich et al., 2018). To better understand the implications of short-term rates, it is therefore important to have knowledge of longer-term deformation rates as a reference point. Consequently, studies comparing deformation rates based on geodetic and geologic data across different timescales around the globe are numerous (e.g., Kreemer et al., 2004; Papanikolaou et al., 2005; Nicol and Wallace, 2007; Cowgill et al., 2009; Faure Walker et al., 2010; Mazzotti et al., 2011; Karakhanyan et al., 2013; Salomon et al., 2013; Hetzel et al., 2019; Iezzi et al., 2021). An important aspect is the timeframe used to interpret the respective rate. Rates determined by geodetic methods, e.g., the Global Positioning System (GPS), commonly reflect a period of <30 years and may therefore record any phase of a seismic cycle (e.g., Thatcher, 1983; Meade et al., 2013). Rates covering the Holocene or late Pleistocene may capture a period of earthquake clustering or quiescence (e.g., Nicol et al., 2009; Salditch et al., 2020; Martín-Banda et al., 2021). Intermediate-term (~300 k.y.–1 m.y.) rates are more likely to represent the true present tectonic (or interseismic) rate, while rates concerning >~1 m.y. may already be affected by changes in plate motion (e.g., Friedrich et al., 2003; Mouslopoulou et al., 2009).

A region whose deformation history has received considerable attention is the Eastern California shear zone/Walker Lane belt (see inset map of Fig. 1 for location) along the western boundary of the Basin and Range Province, USA (e.g., Reheis and Dixon, 1996; Berry, 1997; Lee et al., 2001, 2009; Unruh et al., 2003; Kirby et al., 2006, 2008; Guest et al., 2007; Le et al., 2007; Oskin et al., 2007, 2008; Ganev et al., 2010; Pérouse and Wernicke, 2017; DeLano et al., 2019; Lifton et al., 2021). Second to the San Andreas fault system, this zone accommodates ~25% of the strain related to dextral transtensional motion of the Pacific plate relative to the North American plate (e.g., Dokka and Travis, 1990; Dixon et al., 2000; Miller et al., 2001) and is subject to a high degree of seismicity (Hauksson, 2000). Of specific interest is the Owens Valley, one of the key areas in the Eastern California shear zone, which was hit by a M_w 7.4–7.9 earthquake in 1872 that was one of the largest historical earthquakes in the USA (Beanland and Clark, 1994; Hough and Hutton, 2008).

To improve our understanding of ongoing deformation in the Owens Valley and the Eastern California shear zone, this study compares GPS data with geologic data that record extensional strain since the mid-Pleistocene. A key element of the analysis is the ~765-k.y.-old Bishop tuff on the Volcanic Tableland (Sarna-Wojcicki et al., 2000; Andersen et al., 2017), which has experienced only ~1–2 m of erosion (Goethals et al., 2009; Fig. 1) and is dissected by a population of normal faults (Bateman et al., 1965; Sheridan, 1970; Dawers et al., 1993; Pinter, 1995; Fig. 2). Therefore, the Bishop tuff serves as a perfect time-marker for determining long-term permanent deformation. In addition, a number of GPS stations distributed in the area have recorded ground motions for ~15 years and provide an excellent database for assessing the present-day rate of elastic strain accumulation (Blewitt et al., 2018). This comparison provides a long-term reference to aid in the interpretation of late Pleistocene or younger fault slip rates in the Eastern California shear zone.

The ~15-km-wide Volcanic Tableland is located in the northern section of the ~120-km-long, NNW-trending Owens Valley, which separates the Sierra Nevada block in the west from the White/Inyo Mountains block in the east (Fig. 1). The Owens Valley is part of the ~100-km-wide Eastern California shear zone, which accommodates long-lived extension and dextral strike-slip in response to initially westward and then northwestward motion of the Sierra Nevada block with respect to stable North America. The Eastern California shear zone formed in the middle Miocene and experienced ~E–W-directed extension until the early Pliocene, while dextral transtension has dominated since the late Pliocene (e.g., Stockli et al., 2003; Lee et al., 2009; Stevens et al., 2013, and references therein). Presently, this zone accommodates ~25% of the dextral strike-slip motion between the Pacific and North American plates (e.g., Dixon et al., 2000; Miller et al., 2001) and is subject to a transtensional rate of 10.6 ± 0.5 mm/yr toward N37°W (Lifton et al., 2013).

The northern Owens Valley is bounded to the east by the White Mountains fault (Fig. 1), whose age of initiation is considered to be either ca. 12 Ma (Stockli et al., 2003) or ca. 3 Ma (Lueddecke et al., 1998). In any case, significant extension and dextral strike-slip faulting occurred on this fault after ca. 3 Ma. To the west, at the latitude of the Volcanic Tableland, the northern Owens Valley is bounded by the Round Valley fault, whose age of initiation is unclear. This fault is generally described as a normal fault (dePolo et al., 1993), although a dextral component also exists (Phillips and Majkowski, 2011).

The Volcanic Tableland is formed by the Bishop tuff, which erupted from the Long Valley Caldera (Fig. 1) and is dated to 758.9 ± 1.8 ka (1σ; Sarna-Wojcicki et al., 2000) and 764.8 ± 0.3 ka (2σ; Andersen et al., 2017). The surface of the Bishop tuff is remarkably well preserved. High cosmogenic-nuclide concentrations in the tuff indicate that it has experienced no more than ~1–2 m of erosion since its deposition (Goethals et al., 2009). A population of ~N–S-trending normal faults has since formed and dissects the Bishop tuff as shown by well-developed fault scarps on the Volcanic Tableland (e.g., Bateman et al., 1965; Sheridan, 1970; Dawers et al., 1993; Pinter, 1995). Normal faulting on the Volcanic Tableland has been continuously active through the Pleistocene, as indicated by offset fluvial terraces at its southern margin (Ferrill et al., 2016), and it is still active today (Lienkaemper et al., 1987).

The ~N–S-trending normal faults cutting through the Bishop tuff indicate approximate E–W extension (Pinter, 1995; Ferrill et al., 1999; McGinnis et al., 2009). To determine the E–W-directed extension from these faults, the vertical offsets of each fault along four E–W profiles across the Volcanic Tableland were measured (Figs. 2–4). Faults crossed by the profiles were identified by analyzing data from a Lidar-based digital elevation model (DEM) collected by the National Center for Airborne Laser Mapping (2016: resolution of ~0.3 m in the horizontal plane), the Google Earth elevation model (<10 m resolution in the horizontal plane), Google Earth satellite imagery (0.2 m resolution), hillshade models, and published geological maps (Dawers et al., 1993; Pinter, 1995; Ferrill et al., 2016). Vertical offsets were determined using the Lidar-based DEM. For profile sections outside of the Lidar mapping area (Fig. 2), the Google Earth elevation model was used, which covers the Fish Slough fault zone along profiles A–C (Fig. 2). The vertical offset of a normal fault was measured as the vertical difference between the interpolated hanging and footwall surface at the midpoint of the fault scarp’s cross-profile (Figs. 3 and 4; cf. Bucknam and Anderson, 1979). Interpolating the flat surfaces of the hanging and footwall toward the fault allows the offset measurement to be unaffected by scarp erosion and near-scarp deposition that occurs on the Volcanic Tableland (Pinter, 1995) and is responsible for rounding the scarp profile.

For the sections covered by Lidar data, surface interpolation was performed by linear regression to fit a line through the data points. These surfaces consistently have a standard deviation of <0.3 m. Therefore, an uncertainty of ±0.6 m was added to each vertical offset measurement. A different approach was required for the Fish Slough fault zone located outside of the Lidar data, as only elevation profile graphs can be analyzed. Here, I visually fitted a range of admissible interpolation lines of different dips through the hanging wall and footwall surfaces. The vertical offset therefore varies with the dips of these lines. I used the mean between the smallest and largest offset obtained and the difference to the smallest/largest offset measured as the uncertainty.

Horizontal extension was calculated using this vertical offset and an assumed fault dip angle. From the southern margin of the Volcanic Tableland, McGinnis et al. (2009) reported dip values of 63 faults that range between 41° and 88°, with an average of 73°. For the calculation of the horizontal extension, I relied on these data, which are available from a stereographic projection plot (fig. 3B of McGinnis et al., 2009). The data were extracted from this plot using Stereonet software (Allmendinger et al., 2012; Cardozo and Allmendinger, 2013), and the resulting values are consistent with those reported by McGinnis et al. (2009), with a minimum of 41°, a maximum of 88°, an average of 72.2°, and a median of 73° (Fig. 5). As the data show a skewed distribution, I used the median for the horizontal extension calculation and the first and third quartiles (64° and 81°; Fig. 5) as a ± 9° uncertainty envelope (Table 1). A different fault dip was used for the Fish Slough fault, the largest fault on the Volcanic Tableland (Fig. 2), for which Phillips and Majkowski (2011) determined a dip angle of 58°. Here, I used a dip value of 58 ± 9° for this specific fault. Along each of the four E–W profiles, the total horizontal displacement is the sum of each fault’s horizontal offset crossed by the respective profile. The uncertainties of horizontal displacements were calculated with the Gaussian uncertainty propagation (Table A1).

The extension rate along each profile was calculated as the total horizontal displacement along the respective profile divided by the age of the Bishop tuff. Here, the 765 ka age of Andersen et al. (2017) was used; the small uncertainty of ± 0.3 ka (2σ) was neglected in the calculation. The strain rate was then calculated by dividing the extension rate by the original length of the profile. The original length of the profile is the present-day length minus the total horizontal displacement along the profile. For a better visualization, the strain rate is given as mm/yr per 10 km as well as in nanostrain/yr (Table 1).

With the Lidar-derived DEM, hillshade models, and visual inspection of Google Earth optical satellite imagery, fault scarps with >0.75 m of vertical offset were detected in this study (Table A1). The Google Earth DEM resolution that was used for profile sections not covered by the Lidar data is poorer. These sections concern the Fish Slough fault zone (Fig. 2). Nevertheless, judging from the assessment of the satellite imagery, the significant major faults were captured by the Google Earth DEM. Fault scarps with offsets of <0.75 m, which were not detected, resulted in a slight underestimation of the total vertical offset and, thus, the amount of extension. This is a common problem in stretching estimates based on fault populations (Fossen, 2020) and can be addressed by using a power-law distribution of offset fault populations (Walsh et al., 1991; Marrett and Allmendinger, 1992; Gauthier and Lake, 1993). If fault throw is plotted against the cumulative number of fault measurements in log-log space (Fig. 6), the power-law relation can be expressed as N = a S^–D, where N is the cumulative number of fault measurement, a is a constant, S is the vertical fault throw, and D is the slope of the regression line of the population (Marrett and Allmendinger, 1992; Walsh et al., 1991). Although this power-law relationship is rarely perfect, it appears to be valid for segments of the fault throw populations (Fossen and Rørnes, 1996). Here, the flat segment below throw values of <10 m was used to calculate slope D (Fig. 6). Using the equation above, it is possible to calculate the number of faults with offsets of between 0.75 m and 0.01 m that remained undetected and estimate their cumulative vertical throw. For profile A, this throw is 8.7 m; for profile B, 4.0 m; for profile C, 6.4 m; and for profile D, 5.7 m. These values were added to the vertical throw determined for each of the four profiles, A–D.

In the study area, a network of GPS stations exists, with recordings since 2005. The data are available from the Nevada Geodetic Lab (Blewitt et al., 2018; http://geodesy.unr.edu/). In addition, Kreemer and Young (2022) corrected the GPS velocities recorded by this network for postseismic viscoelastic relaxation, which is the response of the viscoelastic layers of the lithosphere to an earthquake and can impact the Earth’s surface motions for decades after an earthquake (e.g., Reilinger, 1986; Hetland and Hager, 2005; Hampel and Hetzel, 2015). A correction for this effect therefore provides a more reliable picture of the interseismic strain rate.

Across the Eastern California shear zone, nine GPS stations exist at the approximate latitude of the Volcanic Tableland, with data from both Blewitt et al. (2018) and Kreemer and Young (2022). These data are considered here (Fig. 1; Table 2). By plotting the east-directed velocities of these stations relative to stable North America onto an E–W profile, I determined the present-day E–W strain rate. The strain rate was calculated by least-square regression (Fig. 7; cf. Xu et al., 2021).

The analysis of fault scarps on the Volcanic Tableland across the four E–W profiles yields a large range of vertical offsets from 0.8 m to 57.2 m (excluding the Fish Slough fault), which converts to horizontal displacements of between 0.2 m and 17.5 m (with a fault dip of 73°; Table A1). For the Fish Slough fault (dip angle of 58°), the vertical offset ranges between 133.4 m and 171.9 m, which translates to a horizontal extension of 83.3–107.4 m (Fig. 4; Table A1). The total horizontal extension along profiles A–D ranges from 128 m to 237 m (Table 1). Keeping in mind the different lengths of the four profiles, formulating these values as per 10 km provides a better comparison. Accordingly, the range of horizontal extension is 149–228 m per 10 km (Table 1). Taking into account the age of the Bishop tuff (765 ka), the extensional strain rates are between 0.20 ± 0.11 mm/yr and 0.31 ± 0.10 mm/yr per 10 km (Table 1).

The E–W-directed extensional strain rate derived from the GPS velocities of Blewitt et al. (2018) is 0.38 ± 0.06 mm/yr per 10 km (Fig. 7A). Using the GPS velocities corrected for postseismic relaxation (Kreemer and Young, 2022) yields a slightly lower strain rate of 0.36 ± 0.05 mm/yr per 10 km (Fig. 7B). In the following sections, the latter rate is used, because it is considered to be a more realistic representation of the present-day interseismic E–W strain rate due to the correction for postseismic relaxation.

The E–W strain rates that were determined from the measurements of fault offsets along profiles A–C across the mid-Pleistocene Bishop tuff are very similar to one another, with average values of 0.31, 0.29, and 0.28 mm/yr per 10 km (Table 1). Despite an overlap of uncertainties of the strain rates, the lower strain rate of 0.20 mm/yr per 10 km of profile D diverges notably from those of the other three profiles. This profile is the only one that does not extend across the Fish Slough fault, because this fault is eroded at the latitude of the profile (Fig. 2). The effect of the Fish Slough fault on the strain rate can be explored by extending profile D to the east beyond the trace of the fault (to a total length of 11.2 km) and adding the horizontal displacement of the Fish Slough fault and adjacent eastward-facing faults of profile C (106.4 m). This approach leads to a strain rate of 0.28 mm/yr per 10 km for profile D—a value similar to those of profiles A–C. This highlights that the distribution of strain across the Volcanic Tableland is not uniform and that the Fish Slough fault contributes significantly to the accumulation of permanent strain. In summary, the E–W strain rates obtained for profiles A–C, with an average of 0.29 ± 0.10 mm/yr per 10 km, are interpreted as reliable.

A similar approach of determining extension across the Volcanic Tableland was conducted by Pinter (1995), who measured vertical fault offsets in the field along a single 14-km-long E–W profile with the pace-and-Brunton handheld compass approach and assumed an average fault dip of 60° to calculate the amount of extension. Pinter (1995) reported a total vertical displacement of 500 m. For a dip angle of 73 ± 9°, as used in the present study, this value yields a strain rate of 0.14 ± 0.08 mm/yr per 10 km, which is significantly lower than the rates obtained for profiles A–C. As the offsets obtained from the individual scarps were not provided by Pinter (1995), assessment of the data and the result is difficult. The discrepancy may be due to the fact that the profile of Pinter (1995) does not cover the Fish Slough fault, which has a significant impact on the strain rate in the Volcanic Tableland as discussed above.

GPS data indicate an E–W extensional strain rate of 0.36 ± 0.05 mm/yr per 10 km across the Eastern California shear zone over the past ~15 years, if the GPS velocities corrected for viscoelastic relaxation are used (Kreemer and Young, 2022). This rate reflects the accumulation of elastic strain that is currently induced to the Eastern California shear zone by the far-field tectonic stress. This regional extension rate can be compared with a local extension rate of the Volcanic Tableland. When using the two GPS stations P645 and P651 (Figs. 1 and 7), which lie at approximately the same latitude and directly east and west of the Volcanic Tableland, their W-directed velocity components yield an extensional strain rate of 0.30 ± 0.13 mm/yr per 10 km. The similarity between this local rate and the more regional rate shows that the Volcanic Tableland is currently accumulating elastic strain at the same rate as the Eastern California shear zone at the latitude of ~37.5°N.

Both the local and the regional present-day extension rates derived from GPS data are similar to the one obtained from the fault-scarp analysis of the Volcanic Tableland (i.e., ~0.29 mm/yr per 10 km). This finding indicates that the Volcanic Tableland is currently experiencing extension at a similar rate as the timed-average rate over the last 765 k.y. If the same applies to the entire Eastern California shear zone, this would imply that the E–W-directed strain rate induced by the far-field stress system has, on average, remained the same since the mid-Pleistocene. Of course, it cannot be ruled out that the rate has varied over time during this period, and a phase that is similar to that of the 765 k.y. average may now be underway. Assuming that the current strain rate across the Eastern California shear zone equals the long-term time-averaged rate allows calculation of the total amount of extension over the past 765 k.y., an extensional strain rate of 0.36 ± 0.05 mm/yr per 10 km and using 87 km as the extent of the Eastern California shear zone (i.e., the distance between GPS stations P723 – SYLV; Fig. 1) yields a total E–W extension of 2.4 ± 0.3 km.

The analysis of normal fault scarps in the mid-Pleistocene Bishop tuff reveals an E–W strain rate over the past 765 k.y. that is similar to the present-day strain rate derived from geodetic measurements in the Volcanic Tableland and across the entire Eastern California shear zone at this latitude. This finding suggests that the accumulation of permanent strain by normal faulting has remained constant since the eruption of the Bishop tuff and the formation of the Volcanic Tableland. If the Volcanic Tableland is representative of the greater region (as GPS data suggest), this would also indicate a constant extension rate across the Eastern California shear zone over this time period. These results underpin that extension rates assessed in the Eastern California shear zone at younger, shorter timescales should be interpreted in the context of a constant extensional strain accumulation since the mid-Pleistocene.

Ralf Hetzel and Silke Mechernich are thanked for helpful and constructive discussions on the subject. Constructive comments by two anonymous reviewers are gratefully acknowledged. David E. Fastovsky and Michael L. Williams are thanked for editorial handling. Salomon acknowledges financial support by Deutsche Forschungsgemeinschaft and Friedrich-Alexander-Universität Erlangen-Nürnberg within the funding program Open Access Publication Funding.