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Estimates of the Neogene to Modern Regional Strain for Northern Walker Lane, Basin and Range Province, Usa

Estimates of the Neogene to Modern Regional Strain for Northern Walker Lane, Basin and Range Province, Usa

ESTIMATES OF THE NEOGENE TO MODERN REGIONAL STRAIN FOR NORTHERN , , USA

A Thesis Presented for the Master of Science Degree The University of Memphis

Norman Richard Mannikko August 1998 ABSTRACT

Northern Walker Lane is an intracontinental area of complex faulting. It is comprised of northwest-trending right-lateral strike-slip faults, northeast-trending left-lateral strike-slip faults, and north-trending normal faults. Regional strain causes the motion across active faults in the upper . The displacement of the rocks adjacent to these faults is the structural relief. The regional strain, therefore, can be estimated by examining the structural relief and topography assuming that they are a consequence of motion across active faults. The tool used to forward model the development of structural relief is a 3-dimensional boundary element program. An orthogonal far field strain, represented as a displacement gradient tensor, is imposed on a homogeneous elastic half-space with a series of dislocation elements. The relative displacement of these elements give the sense of slip along each . A horizontal inspection plane is placed at zero elevation to represent the earths surface. The boundary element algorithm explicitly accounts for the interaction of the faults and permits calculation of the vertical displacement of the inspection plane. This modeled structural relief can be used to discriminate between regional strain orientations. Volume strain and fault slip motion is also used to discriminate between models. The modeled e1 orientations with characteristics approximating northern Walker Lane are E-W through

N70˚W. The modeled e1 orientations of N70˚W through E-W show remarkable similarities to the structural relief and topographic features of the northern Walker Lane. The modeled volumetric strain show areas of positive volume strain (locations susceptible to volcanic activity) which correlate with the volcanic activity with few discrepancies. The modeled fault offsets are in agreement with their corresponding faults in northern Walker Lane. 1. INTRODUCTION

Northern Walker Lane is an intracontinental area of active deformation over 250 km east of the Pacific- margin (figure 1). The focus of this research is to estimate the Neogene to modern regional strain for an area of complex faulting within northern Walker Lane. Plate tectonic theory has provided a means to derive kinematics of plate margins, but analysis is limited when working on intracontinental deformation because, by definition, plates are rigid and do not deform. Nevertheless, knowledge of the relative poles of rotation between two plates allows us to derive components of the deformation field in a diffusely deforming zone between two plates (e.g., Jackson and Mackenzie, 1988). Other methods to derive the strain field include the use of high precision surveying (e.g., global positioning satellite system [GPS]) and various geologic markers (e.g., faults, dikes, etc.). The former is limited to time-scales that may be more representative of interseismic deformation and in response to the activity of perhaps a limited number of faults in any particular . In this case, these observations may not represent the long-term average (~105 - 106 years). The use of geological markers may be limited by the local setting (e.g., influenced by local anomalies in the regional stress field) or, in a practical sense, by the extensive amount of data needed to determine the regional stress field. In this thesis, I present a relatively new method of estimating the regional and long-term (~105 - 106 years) average strain field. If we make the assumption that the structural relief and topography is directly influenced by the motion across active faults, then the structural relief and topography reflects the regional strain. Therefore, we can estimate the regional strain by rigorously looking at the structural relief and topography of a faulted region such as northern Walker Lane. The method I use to make this estimate is with a three-dimensional boundary element model. The numerical model can help distinguish orientations of regional strain by comparing three of the modeled structural characteristics to the actual structural characteristics. One is by comparing the deformation of an originally horizontal surface displacement field to the local topography and structural relief; the second is by comparing modeled fault slip directions and rates to what is observed in the field; and thirdly, the volumetric strains can be compared to areas of volcanic activity. The results obtained here may be useful in two respects. First, they allow us to test the plate tectonic predictions and thereby evaluate the interactions among plates. Second, the boundary element model provides a means of determining the regional strain and provides quantitative estimates about fault slip-rates, which are useful in seismic hazard analysis.

Study area The study area is located near the northern extent of Walker Lane (figure 1). The Walker Lane Belt is described by Stewart (1980) as being a fundamental structural unit whose topography contrasts the typical north-northeast-trending ranges of the Basin and Range Province and the north-northwest-trending ranges of the Sierra . The belt is a diffuse zone of comparatively subtle topography and complex structural faults located in western Nevada and parts of . This northwest trending zone is about 700 km long and 100-300 km wide. The focus of this research is in the area of Reno, Nevada and vicinity and part of California extending 160 km x 120 km (figure 2). The study area runs from the Eastern extent of the block of Honey Valley south to Tahoe and extends east to the Walker River and Mason Valley then north to Lake Winnemucca.

Geology The geology of the study area is dominated (~ 90%) by Tertiary volcanic rocks and Quaternary deposits (Bonham, 1969). The major portion of Tertiary rocks are volcanic flows, breccias, and water-lain , the remainder are intrusive and non-marine sediments. The Quaternary sediments include glacial deposits, landslide debris, and fluvial and lacustrian deposits. The remaining approximately 10% of surface area is pre-Tertiary (Bonham, 1969). Most of the pre-Tertiary rocks are Mesozoic-age granitoid intrusions. The intrusions are of stock dimensions and intrude questionable Permian to Jurrasic-age metamorphic volcanic and sedimentary rocks. The Mesozoic intrusive rocks that crop out in the area consist of granitoid plutonic rocks. The metavolcanic rocks are locally interbedded with marine sedimentary rocks. Therefore, the volcanic rocks must have been, at least in part, laid down in a marine environment (Bonham, 1969).

Physiography Northern Walker Lane belt is characterized by ranges with varying topography and trends and strike-slip faulting breaking up the structural grain. The mountain ranges have moderate to high relief separated by Quaternary alluvial basins that frequently contain playas (Stewart, 1980). The relief, although typically moderate, varies throughout the study area. High relief is associated with the eastern extent of the Sierra Nevada, which is approximately 1150 m above the adjacent valley to the east. The average relief away from the Sierra Nevada is about 600 m +/- 100 m . 2. LINKING NORTHERN WALKER LANE TO PLATE TECTONICS AND DEVELOPMENT OF CENOZOIC STRUCTURES

We can use the relative poles of rotation between plates to derive components of the deformation field in a diffusely deforming zone. These velocity vector models can be tested based on regional strain determinations. The topography can be used to determine the best fit model of the regional strain. Therefore, it is prudent to investigate the tectonic history of northern Walker Lane to show that it may be part of a wide diffuse boundary between two plates and that the present topography seems to have developed since the Neogene, and therefore, reflects the motion across Cenozoic faults.

Pre-Cenozoic Northern Walker Lane and western Nevada was a deep oceanic basin along the passive margin of during the early Paleozoic. This Atlantic-style margin changed to an Andean-style convergent margin in late Devonian time, and convergence continued through the . Two main thrust systems occurred in central Nevada as a result of this convergence. The Golconda and Roberts Mountain thrusts created a lower Triassic uplands in central Nevada that was a source of detritus to the east and west. Deposition from the highlands to the east had ceased by late Lower Jurassic. Northern Walker Lane was changing from a geosyncline to a subaerially exposed or near-shore marine environment. Moore (1960) pointed out in his discussion on the age of sequences of metabasalt and metarhyolite in Lyon, Douglas, and Ormsby Counties, that although the metavolcanic rocks are interbedded with marine sedimentary rocks and must be, at least in part, of submarine origin, the rarity of pillow lavas within the metavolcanics and the local association of the volcanic rocks with bedded gypsum indicates that a substantial part of the volcanics were formed in a subaerial or near-shore environment. This is also indicated by the occurrence of welded ash-flow tuffs within the volcanic section (Bonham, 1969). Subaerial exposure during the Mesozoic is also indicated by the decrease in abundance of marine sedimentary rocks and the scarcity of Cretaceous sedimentary rocks. Cenozoic The North American western margin makes a drastic change after its long duration of convergence to a new margin dominated by right-lateral strike-slip faulting during the Cenozoic. The convergent plate margin comes to a close along most of the California coast with the consumption of the and the East Pacific Rise. This tectonic change brought about structural changes throughout California. The magnetic anomaly patterns in the northeast Pacific combined with have been used to determine the tectonic setting and geometry of the western margin (Atwater, 1970; Severinghaus and Atwater, 1990). The Cenozoic is also a time of dramatic changes throughout Nevada. There is a decrease in marine deposition and an increase in volcanic debris or tuffaceous sedimentary units. Extensional Basin and Range structures of and are formed throughout Nevada and . Within the Walker Lane belt, many of the strike-slip faults that distort the structural grain of the Basin and Range features are initiated. The strike-slip faults that were initiated in the Mesozoic (Excelsior and Coaldale) are reactivated with a change in their sense of slip. The relatively young (Cenozoic) structures and topographic development of northern Walker Lane is inferred from the following: 1) the tectonic setting was of a barred basin east of the Sierra Nevada and west of the older fold-and-thrust structures in central Nevada; and 2) Paleocene to middle Eocene age rocks are sparse, which suggests that the area was stripped of these rocks, that they were never deposited, or that they are buried (unlikely because older rocks are exposed). The cessation of the Sierran magmatic belt and the far inland occurrence of magmatism and have been attributed to a shallowly dipping slab beneath the North American craton (e.g., Coney and Reynolds, 1977; Cross, 1986; Bird, 1984, 1988). To look at what would have contributed to the change in sediment accumulation, volcanic activity, and structural development during the Cenozoic, I refer back to the changes at the plate margin. The same tectonic conditions that were present at the end of the Mesozoic were still present early in the Cenozoic (the Farallon and Vancouver plate was still being subducted under the North American craton) (figure 3a). The East Pacific Rise was approaching the trench along the North American plate margin. Severinghaus and Atwater (1990) propose that young is thin and hot, so that after it will quickly equilibrate with the asthenosphere and thereby develop a slab gap (region of no slab, bordered on the north and south by coherent slabs). The stresses that developed the structural and volcanic features ascribed to the shallow slab would then change with the development of the slab gap. The westward migration of arc magmatism at some latitudes has been attributed to the plunging or disintegration of the proposed shallow slab (e.g., Coney and Reynolds, 1977; Cross and Pilger, 1978). In the late Cretaceous, the Sierran magmatic belt had ceased. The Cenozoic was a time of major igneous activity in Nevada, beginning about 43 My ago in the northernmost part of the state (Mckee et al., 1975) and spreading to the south between 43 and 34 Ma. Magmatic provinces were composed of moderate to highly potassic andesite, latite, quartz latite, and rhyolite (Blake et al., 1969; Mckee, 1971; Noble, 1972). As stated earlier, the tectonic history of Paleocene to middle Eocene in the Walker Lane, however, is obscure because the rocks of this age are sparse. Geologists have a better understanding about the more recent tectonics of the to the present. As the trailing edge of the Farallon plate and the East Pacific Rise move closer to the trench at the Farallon-North American plate margin, a narrow neck of the Farallon plate developed south of the Mendocino and Pioneer fracture zones. Plate segments north, and south of the neck (Vancouver [Menard, 1978] and Farallon plate respectively) moved independently of each other. The Vancouver plate was moving east relative to the and the Farallon plate was moving east-northeast. The geometry and thermal state of the subducting slab show that at 35 Ma the young crust nearest to the trench quickly reassimilated into the asthenosphere as it was being subducted (Severinghaus and Atwater, 1990). This is the subsequent site of a slab gap as the younger crust and East Pacific rise moves closer to the trench. Between the 25˚ and 30˚ north latitude the narrow neck broke free of the Farallon plate at about 30 Ma (figure 3b). Shortly after this, the Mendocino between the Vancouver, North America, and Pacific plate formed. At approximately 34 Ma, there was a significant change in the igneous activity within Nevada. There was voluminous eruptions of quartz latite and rhyolitic ash flow tuff until about 17 Ma (Blake et al., 1969; Mckee, 1971; Noble, 1972). Rhyolite and andesitic flows are interlayered with ash flow tuffs and occur in an irregular west-northwest-trending belt between 38˚ and 40˚ north latitude at Nevada’s western border and into California. By 20 Ma, the Mendocino triple junction had migrated north to approximately 33˚ north latitude and a slab gap had developed beneath the North American plate (figure 3c). The remaining two segments of the once large Farallon plate, separated by the strike-slip motion of the system, are now referred to as the Juan de Fuca plate to the north and the Cocos plate to the south. The Mendocino triple junction continued to migrate to the north along the trench between the Juan de Fuca plate and the North American plate and at about 10 Ma is positioned at approximately 35˚ north latitude (figure 3d). The slab gap east of the right-lateral San Andreas fault zone passed through the southern portion of Nevada by 10 Ma. Concurrent with this time step (20 Ma to 10 Ma), another change in igneous activity began about 17 Ma. Widespread eruption of mafic lavas and bimodal assemblages of rhyolite and occurred after 17 Ma (Mckee, 1971; Christiansen and Lipman, 1972). Western Nevada had extensive and voluminous andesitic volcanics. Also, andesite flow, in places capped by basaltic flow (Bonham, 1969; Moore, 1969), are extensive in western Nevada and through California. There is only a scatter of volcanic activity within the last 6 m.y., although, rhyolite domes do occur within the study area (Storey and southern Washoe Counties). Cenozoic Pacific-North American plate marginal tectonics changed from convergent to transform and concurrently changes in the deformational style of Nevada occurred. Extension began and produced the extensional block faulting that characterize the present day topography of the Basin and Range. Basalt or bimodal assemblages of basalt and rhyolite were erupted and continental sediments were entrapped in the fault related basins. Most, if not all, of the Walker Lane faults have been active in the Cenozoic. Most major faults cut Cenozoic rocks and have structural movement that is lateral, normal, or oblique-slip on high-angle faults. The Mendocino triple junction is presently located at approximately 40˚ north latitude (figure 4). If the Mendocino extends straight beneath the North American plate and the slab gap is directly south of it as proposed by Severinghaus and Atwater (1990) and Dickinson and Snyder (1979), then the northern Walker Lane is also in transition from being directly above a subducted slab between 10 Ma and the present. Atwater (1970) also proposed that we might consider western North America to be a very wide, soft boundary between two rigid, moving plates. It is clear that the change in the plate boundary type (subduction to transform) drastically changed the dynamics along the North American-Pacific plate margin but how much it directly affects the farther to the east is still unclear. The motion across many of the strike-slip faults of Walker Lane are well documented. The Hamblin Bay fault has 20 km based on the offset of the 11-13 m.y.-old Hamblin-Cleopatra volcano and its radial dike swarm (Anderson, R.E., 1973). Bohannon (1984) noted strike-slip movement on the Lake Mead fault zone 17 and perhaps 10 Ma that is reflected in the facies patterns of Miocene sedimentary rocks. The shear zone has 40-67 km of right-lateral offset. Much of the displacement may have occurred between 15 and 11 Ma (Fleck, 1970; Anderson, R.E. et al., 1972). Near Walker Lake there is overlap of landslide deposits, considered to be related to strike- slip movement, by 24 m.y.-old tuffs and deposition of a 22-24 m.y.-old tuff against a preexisting fault surface (Ekren and Byers, 1984). Offset of younger Tertiary rocks and of Quaternary alluvial deposits indicates that normal to strike-slip displacement has continued into the Holocene. The southern section of the study area is characterized by zones of northeast-trending faults of left-lateral displacement that interrupt the dominant northwest grain of the Walker Lane belt. Three fault zones are recognized, the Olinghouse fault zone to the north, the Carson Lineament in the middle, and the Wabuska Lineament to the south. Surface ruptures of the Olinghouse fault occurred during the magnitude 7 in 1869 (Sanders and Slemmons, 1979). The maximum vertical slip was 3 m and maximum left-slip displacement was 3.65 m. Four oblique- slip or dip-slip normal faults are also located within this section (figure 2). Two such faults bound the . The northern most section of the study area extends from the Honey Lake area of California to the Reno area, Nevada. This area is marked by three major northwest trending predominantly right-lateral strike-slip faults (Honey lake, Warm Spring Valley, and Pyramid Lake faults) and four north-trending dip-slip or oblique-slip normal faults bounding high, uplifted mountain ranges. The Pyramid Lake fault is associated with numerous en-echelon northwest and northeast-striking faults interpreted as Riedel and conjugate Riedel shears developed during right-lateral movement (Bell, E.J. and Slemmons, 1979). This area is characterized by sag ponds, elongate depressions and troughs, offset stream channels, transcurrent buckles, rhombohedral and wedge-shaped enclosed depressions, and recent scarps, all indicative of Holocene strike-slip (Anderson, L.W., and Hawkins, 1984; Bell, E.J., 1984; Bell, E.J., and Slemmons, 1979). Several of the minor faults also show Holocene offset (Bell, E.J. 1984; Bell, E.J., and Slemmons, 1979; Bell, J.W. 1984; Bohnam, 1969). In 1950, a magnitude 5.6 earthquake centered a short distance north of the Honey Lake fault near the California-Nevada state line (Slemmons, 1967) occurred and caused a small surface rupture along a north-trending normal fault (Fort Sage Mountain) (Giannella, 1957) .

Strain models The Cenozoic initiation of most of the structures in Walker Lane, which have trends and direction of offset similar to the late Cenozoic San Andreas fault zone, have led many to look more closely at the correlation between these fault zones. Atwater (1970), suggested that late Cenozoic faults in the that parallel the San Andreas system may be part of a wide, soft boundary between two rigid moving crustal plates. Investigators have also noted that the slip rate along the San Andreas is too slow to accommodate all the motion between the Pacific-North American plates (e.g., Atwater, 1970; Argus and Gordon, 1991). At 36˚N, 120.6˚W, the San Andreas slip is 34 +/- 2 mm/yr (quoted uncertainties are plus or minus one standard error)(Sieh and Jahns, 1984; Minter and Jordon, 1984; Lisowski et al., 1991), whereas, the motion between the Pacific-North America plates is 48 +/- 1 mm/yr (DeMets et al., 1987, 1990). I use these observations to develop a model specifically for the study area based on the rotation of the North American plate with respect to the Pacific plate. This model uses the Nuvel 1A NA-Pa Euler pole (48.7˚N, 78.2˚W, 0.75˚/m.y.) to calculate the velocity vector for the study area relative to a fixed Sierra Nevada block. The velocity of North America relative to the Pacific at a point along the NA-Pa Euler pole great circle which passes through the study area and intersects the San Andreas Fault (N37.33˚,122.25˚W)(figure 5) is

PaVNA(mm/yr)=w(˚/m.y.)111 sin d [1.1]

PaVNA=(.75)(111)sin 34˚

PaVNA=46.6 mm/yr Toward S34.9˚E where PaVNA= velocity vector of NA with respect to the Pacific, w= angular velocity, d= angular distance from the point of calculation to the Euler pole. ______

0 E

5 a = 5.1˚ 10 VSA CR = (PaVNA)sin 5.1˚ 15 Fault parallel = (PaVNA)(cos 5.1)-(VSA)

20 a CR = 4.14 mm/yr 25 Fault parallel = 12.42 mm/yr PaVNA 30 SAD

35

40 5 10 15 20 25 30 35 40 East velocity component mm/yr S Figure 5. Conceptual diagram showing the San Andreas discrepancy ______

Where SAD = The San Andreas discrepancy, VSA = The slip along the San Andreas discrepancy with respect to the Pacific, CR = The San Andreas Fault discrepancy perpendicular component, Fault parallel = The San Andreas Fault parallel component. The difference between the NA-Pa plate velocity and the slip observed along the San Andreas fault (34 +/- 2 mm/yr toward N40˚ +/- 1˚W) constitutes the San Andreas discrepancy vector (Minster and Jordon, 1984) (figure 2). The discrepancy minus the Coast Range contraction leaves only the parallel discrepancy, because the Coast Ranges (CR) are assumed to accommodate all of the San Andreas Fault perpendicular component of the discrepancy. A number of studies suggest that these ranges show the correct sense and magnitude of contraction (e.g., Namson and Davis, 1988; Oppenheimer et al., 1988; Mount and Suppe, 1987; Zoback, M.D. et al., 1987). The fault-parallel discrepancy is scaled to the angular distance from the point of calculation to the Euler pole and moved back along the NA-Pa Euler pole to the NE corner of the study area. In other words, if this discrepancy is assumed to be entirely accommodated in the Northern Walker Lane, this new velocity vector would represent the velocity of North America with respect to the Sierra Nevada. The resultant velocity vector for Northern Walker Lane (11 mm/yr toward S40˚E) is used to calculate the displacement gradient tensor, the strain tensor, rigid body rotation, and the orientation of maximum extension (e1) (figure 6a), 11 mm/yr = 1.1E-05 km/yr (1.1E-05 km/yr) x (1000 yrs) = 0.011 0.011 km/150 km = 7.33E-05 (1000 yrs. to compare to the 3-D boundary element model which uses 1000 yrs. and 150 km from the Sierra Nevada to the NW corner of the study area) D = [du/dx, du/dy, du/dz; dv/dx, dv/dy, dv/dz; dw/dx, dw/dy, dw/dz] D = [0, 7.3E-05, 0; 0, 0, 0; 0, 0, 0] E = [0, 3.7E-05, 0; 3.7E-05, 0, 0; 0, 0, 0] W = 3.7E-05 (radians) clockwise. where D = displacement gradient tensor, E = strain tensor, W = rigid body rotation. The displacement gradient tensor is essentially two dimensional (i.e., there is no vertical displacement or strain). Plate tectonic models are, by definition, two dimensional and do not have a vertical velocity component. The trend of the Sierra Nevada block and the trend of the displacement are parallel and indicate a right-lateral simple shear with a maximum extension direction oriented N85˚W. The displacement gradient tensor, strain tensor, and rotation are all for over a period of 1000 years to be comparable to the 3-D boundary element models, discussed in the methodology section. Argus and Gordon (1991) use geodetic measurements from very long baseline interferometry to point out that the Sierra Nevadan microplate, which is composed of the Sierra Nevada and the Great Valley, has a right-handed rotation of 0.61˚/m.y. about Latitude 32˚N, Longitude 128˚W. This predicts that the eastern edge of the Sierra Nevada relative to the stable North America has a velocity of 11+/- 1 mm/yr toward N36˚ +/- 3˚W (one standard deviation). Comparison of the direction of the motion of the Sierra Nevada with the ~N30W strike of the Sierra Nevada- boundary shows that motion nearly parallels the strike of the boundary. This geometry suggests that the westernmost Great Basin is undergoing near right- lateral simple shear with a maximum stretching direction oriented ~N75˚W (Argus and Gordon, 1991). This prediction agrees with results of geodetic surveys across (Savage et al., 1990). Based on these observations, I again apply them specifically for northern Walker Lane. A velocity vector at the NE corner of the study area can be calculated by holding the SN-NWL (Sierra Nevada-Northern Walker Lane) boundary fixed, Using eq [1.1] d = 12˚

SNVNWL(mm/yr) = (0.583˚/m.y.)(111)sin 12˚

SNVNWL = 13.45 mm/yr toward S40˚E D = [0, 8.9E-050; 0, 0, 0; 0, 0, 0] E = [0, 4.5E-05, 0; 4.5E-05, 0, 0; 0, 0, 0] W = 4.5E-05 (radians) clockwise The results are similar to the NA-Pa Euler pole model and to Argus and Gordon’s (1991) observations with right-lateral simple shear parallel to the trend of the Sierra Nevada microplate and a maximum extension oriented N85˚W (figure 6b). The rotation has been revised from Argus and Gordon (1991) for consistency with recent revisions to the geomagnetic reversal time scale as was done in constructing the NUVEL 1A global plate motion model (Demets and Gordon, 1994). A model has been used to explain the development of structures from the San Andreas through the Basin and Range with a single orientation of regional strain. The model does not delineate the Walker Lane belt from the Basin and Range Province or the Sierra Nevada. The evidence of right-lateral displacement along the Northern - and ruptures that delineate the group of crudely aligned valleys of Walker Lane is used to develop a “mega-shear” model (Carey, 1958; Wise, 1963) in which the right-lateral faults of the Great Basin, together with the San Andreas fault zone, compose a major part of a large-scale right-lateral shear system. The normal faults, in the mega- shear model, are second-order features analogous to tension-gash fractures. The normal faults are also commonly cited as products of an oblique extension that combines components of westerly extension and right-lateral shear (Hamilton and Meyers, 1966). Objections to this model are that it lacks evidence of right-lateral displacement along the northeast margin of the shear system (Gilluly, 1970) and it inadequately accounts for the left-lateral faults (Davis and Burchfiel, 1973). Coeval strike-slip faulting and normal faulting have also been explained with the strike-slip faulting as conjugate shears produced in a nonrotational stress field (Allison, 1949; Donath, 1962; Shawe, 1965; Hill and Troxel, 1966). The shearing is formed from compression along a north to northeast-trending axis and the normal faults are release features striking parallel with the axis of compression. Gilluly (1963) states that the high angle strike-slip faults would be low angle thrust faults if this compression is taking place. Paleostress and present stress orientations have been investigated within Owens Valley and in the vicinity of Hoover Dam. The proximity of nearly parallel trending faults with contrasting sense of slip is interpreted that there has been two distinct stress fields with sub-horizontal s3 axes (Angelier et al., 1985; Zoback and Beanland, 1986). Angelier et al. (1985) looked at , 0.5 km3 of rock in the vicinity of the Hoover Dam, 40 km southwest of Las Vegas, Nevada. The sense of slip was determined on ~500 separate faults. the data was a mixture of primarily dip-slip and strike-slip motions. Their evaluation of the data illustrated two distinct stress fields with sub-horizontal s3 axes that trend N50˚E and N75˚W. The s1 and s2 axes permutate in two vertical planes that strike N40˚W and N15˚E. The s1 and s2 are close in value relative to s3 and relatively minor changes in the stress field will cause permutations in s1/ s2 and result in alternating and interfering patterns of strike-slip and dip-slip motion. Zoback and Beanland (1986), working in Owens valley along the Independence Fault, found two contrasting styles of offset on sub-parallel faults. They explain the contrast by large temporal fluctuations in the relative magnitude of the maximum horizontal stress (s1) oriented ~N- S, possibly accompanied by minor horizontal rotations of the principal stresses. Normal dip-slip mode occurs when the maximum horizontal stress is close in magnitude to the minimum horizontal stress and strike-slip when the maximum horizontal stress and vertical stresses are approximately equal. Investigation of the tectonic history of northern Walker Lane shows that this area was relatively flat subaerially exposed region prior to the Miocene. Volcanic and structural changes were taking place concurrent with the development of the slab gab along the North American- Pacific plate margin. The faults seem to have been activated in the Cenozoic and many are presently active. Tectonic velocity vector models (figure 6), along with geologic markers, place an orientation of e1 within the northwest quadrant (table 1). 3. METHODOLOGY

Estimates on the regional strain of northern Walker Lane are determined by two basic concepts. 1) The structural relief and topography is a direct consequence of relative displacement across crustal scale faults. 2) Faults slip in response to the regional strain. Using these assumptions, we can numerically model the response of an elastic medium to different orientations of regional strain. The detailed comparison of the modeled structural characteristics to the areal structural characteristics allow for the estimate of regional strain to be determined.

3-D boundary element model The boundary-element method (Crouch and Starfield, 1983) permits the determination of the exact stress or strain field within a deforming isotropic elastic continuum. The 3-D boundary element program I use for this study, which is a formulation of this method , is based on the the work by Gomberg and Ellis (1993,1994).

The schematics of the model are of rectangular, planar dislocations in a homogeneous elastic half-space and allows for the inclusion of a uniform background deformation field that can be specified as a stress, strain, or displacement gradient tensor (figure 7). The dislocations represent faults. The uniform background deformation field represents the regional strain which drives the motion across the faults and subsequent deformation of the medium. This dislocation model solves for the slip, or magnitude of the components of relative displacement, in order to minimize the strain energy in the medium while satisfying the displacement boundary conditions. The minimization of the strain energy is physically reasonable assuming that fault slip is the primary means of relaxing strains in the upper crust. The boundary element model also explicitly accounts for the interaction among faults (dislocations)(Gomberg and Ellis, 1994). The fault planes are divided into rectangular sub-elements and are continuous along the strike and dip of the fault. A set of boundary conditions are specified at the center of each sub- element as zero stress parallel to the strike, zero stress parallel to the dip, and zero displacement normal to the plane. This approximates the boundary conditions over the entire surface of the element. This gives stable results (results that do not change significantly upon further sub- division) While keeping the problem computationally tractable (Gomberg and Ellis, 1994). The relative displacement components of each sub-element is estimated such that the boundary conditions for each representative center point is satisfied and the strain energy is minimized. The displacement components of the hanging wall with respect to the footwall for each sub-element is represented as relative displacement vectors along the dip, strike, and normal to the plane. Once the relative displacements are derived, the deformation at any point (x,y,z) in the medium can be calculated by the superposition of the deformation due to slip on each set of planar dislocations and some uniform deformation field (Gomberg and Ellis, 1994).

The deformation field is fully described by the displacement gradient tensor, [dux/dx, dux/dy, dux/dz; duy/dx, duy/dy, duy/dz; duz/dx, duz/dy, duz/dz], displacement vector in x,y,z coordinates for the point of investigation, and the material constants, Poisson's ratio and Young's modulus. The background deformation is specified in the 3-D program as the displacement gradient tensor. For Northern Walker Lane, this is determined from some basic assumptions. (1) Northern Walker Lane is deforming at a rate and gradient comparable to the Basin and Range Province. (2) A 1000 km length of the Basin and Range Province is extending at 1 cm/yr. This estimate is reasonable for the Cenozoic extension of the Basin and Range determined from geodetic measurements, strain rates assessed from brittle fracture associated with historic , and Quaternary paleostrain estimates (Minster and Jordon, 1984; Eddington et. al., 1987). (3) The area has experienced crustal thinning of 5 km since ~25 Ma. (4) The medium experiences no overall volume change. Using these a priori assumptions, the displacement gradient tensor is calculated for an increment of deformation over a period of 1000 years. The program is limited in number of fault planes and associated sub-elements it can computationally execute. Therefore, in order not to exceed this memory limit of the program, the faults within the area to be modeled (Northern Walker Lane) need to be simplified. Only the 15 major faults of Quaternary, or suspected Quaternary, motion are modeled. Some of these are fault zones or seismic lineaments which were estimated on a map as a single continuous fault. This excludes many minor faults which accommodate some of the strain for the region. Some of the major faults, particularly along the outer boundary of the region, are also excluded. The faults, or fault zones modeled were divided into segments and digitized from a 1:250,000 map. The fault segment characteristics are then entered into the program as the length along the strike, length along the dip, strike azimuth, and dip angle (table 2). The fault segments are divided into sub-elements. The numerical model provides a matrix of sub-element relative displacement components which describe the relative motion of the hanging wall relative to the footwall. For the 90 ˚ dipping faults, the hanging wall is determined from the orientation in which strike length is given. In other words, the hanging wall for faults 1-4 is the southwest side of the fault (figure 2). For faults 9, 11, 15, the hanging wall is the southeast side. The matrix of relative sub-element displacement components is plotted in Matlab™ as fault-slip vectors (figures A1-3 through J1-3). The mean slip-rate and the mean rake is also determined from these relative displacement components which can be directly compared to other estimated fault offset directions and slip rates for these faults.

Model Kinematics The tectonic models derived in the previous section (Northern Walker Lane) and estimates given by others (e.g., Minster and Jordon, 1984; Thompson and Burke, 1974; for the Basin and

Range Province) give an orientation of e1 within the northwest quadrant. Therefore, I start with a maximum extension orientation of E-W and rotate the orientation by increments of 10˚ clockwise for each model (figure 8). The final model has a maximum extension orientation of N-S. Each boundary element orientation model produces the numeric results of volume strain, sub-element relative displacement components, and the deformation of a specified surface inspection plane. 4. RESULTS

Modeled structural relief The vertical displacement of points of an inspection plane, specified to be originally horizontal and at zero elevation, is given in a matrix for each square kilometer of the study area. This matrix is plotted in Matlab™ and color coded to visually represent the structural relief produced by the deformation of the medium (figure 9a-c). The displacement is given in centimeters for an increment of 1000 years. Therefore, the uplift and subsidence rates can be calculated for a given regional strain. Independent calculations of uplift rates (e.g., via apatite fission track analysis) can help constrain my estimates of regional strain and this scaling of uplift can show that other structures not modeled help accommodate the strain. The visual and quantitative comparison of the modeled structural relief to the areal structural relief and topography is a powerful tool in discriminating the regional strain.

Volume strain The volume strain is also given in a matrix for a specified inspection plane. For volume strain, I used a horizontal inspection plane at a depth of 10 km below the surface. The image is color coded for positive and negative volume strains (figure 10). The negative volume strains are compressional strains and indicate areas of likely uplift. The positive volume strains are dilatational and infer likely areas of depression and susceptibility to volcanism (e.g., Ellis and King, 1991). Deep vs. shallow faults Three separate models were run with the same regional strain orientation. First, all the faults, or fault zones, were modeled with a down-dip depth of 15 km (table 2). This model explicitly accounts for the interaction of as many faults as the program memory can handle. It simulates short-term or coseismic deformation. Long-term deformation, in which the stress is relaxed below the brittle crust, is simulated by extending the shallow 15 km faults to an essentially infinite depth. This is done by adding fault plane elements to a depth of 100 km immediately below and coplanar to the shallow finite-dimensional faults (Gomberg and Ellis, 1994). The finite amount of program memory limits the number of fault plane elements and faults to be modeled. Therefore, the long-term models use only the strike-slip faults. The third model is run with only strike-slip faults to a depth of 15 km. The primary reason for running this model is to compare the changes in fault slip (direction and magnitude) and surface displacement field between the proceeding two models and to ascertain whether these changes are primarily due to normal fault interaction with the strike-slip faults or due to the relaxation below the seismogenic zone. It is evident that the normal faults influence the fault slip vectors of the strike-slip faults adjacent to, or in relative proximity to, the normal faults (figure 11a-e). Primarily the normal fault interaction changes the mean rake of the southeast segment of fault 3 and the southwest segment of fault 11. The long-term deformation model of deep strike-slip faults have slip vector magnitudes nearly double the shallow short-term models (figure 12a-b). The normal fault interaction also influences whether the surface inspection plane would be uplifted or depressed near faults 2, 3, 9 and 15 (figure 9a-c). They effect the magnitude of vertical displacement on the north side of fault 2, between 9 and 11, and the southeast segment of 11. The down dropped block adjacent to fault 14 limits the extent of western uplift from the tip of fault 15. The modeled deep strike-slip faults produce magnitude and directional differences in vertical surface displacements. The question is how to interpret these inconsistencies between models to effectively compare the modeled orientation characteristics to areal observations? I use the 100 km deep strike-slip faults to compare the characteristics associated with the motion across them because they best describe long-term stress. However, I keep in mind the adjacent normal fault effects on the magnitude and extent of vertical displacement, and the effects on the fault slip vector rake. The characteristics of the normal faults, although for a short-term deformation model, are used for the comparison of adjacent normal fault crustal deformation.

5. DISCUSSION Modeled orientations of regional strain provide fault-slip rates and directions, localized volumetric strain, and modeled structural relief of a surface inspection plane. These model characteristics can then be used to compare to geological markers (i.e., fault-slip orientations, dike swarms, etc.), seismic interpretations, and plate tectonic inferences and may discriminate which model regional strain best replicates the observations. The non-uniqueness inherent in this type of forward modeling suggests that a more practical approach is to eliminate candidate strain fields based on inconsistencies between the models and field observations.

Fault slip directions Regional strain orientations that produced modeled slip directions opposing (direction nearly 180˚ opposite) published directions of fault offset could be eliminated on this criterion alone. Other characteristics, if not all, were also used to confirm the elimination of these orientations but they are not discussed unless more than fault slip directions where needed to conclusively eliminate them. The fault-slip vectors allow for the elimination of all modeled orientations from N40˚W clockwise through N-S (figures A1-5, B1-5, C1-5, D1-5, and E1-5). The strike-slip faults plot slip vectors in a direction opposing the sense of motion measured across these faults. The normal faults plot slip vectors with predominate strike-slip motion. The rotation of the maximum stretching direction clockwise through this range increases the component of lateral motion on the normal faults, and increases the magnitude of the of the strike-slip faults in the reverse direction of the known fault offset.

Models with an e1 orientations of N50˚W and N60˚W produce questionable fault-slip directions (figures F1-3 and G1-3). Although the amount of slip on the faults for a direction of

N50˚W is significantly reduced, relative to a more westerly orientation of e1, most strike-slip faults exhibit a direction reasonably compatible to the motion observed. Faults 3 and 9 however, have segments that produce opposing slip directions. The normal faults for this orientation produce oblique-slip motion with mean rakes ~27˚-40˚ with the exception of fault 14 which has a mean rake of ~55˚. Fault-slip vectors generated from an e1 of N60˚W yield borderline reasonable results and is enough to add to the list of criterion used for its eventual elimination. The northeast segment of fault 9 has very little slip and faults 5-8 and 10-13 produce right-lateral oblique-slip motion with rakes of ~45˚. The orientation ranges from E-W through N70˚W give reasonable slip magnitudes and directions and cannot be eliminated by this criteria (figures H1-3, I1-3, and J1-3). The fact that N70˚W produces normal faults with mean rakes from 45.9˚ to 78.4˚ is notable, however.

Volumetric strain and areas of volcanism The volumetric strain can be used as a first order comparison to areas of local volcanism and to local structural relief. Negative volume strains are regions undergoing compression, and therefore, possible uplift (Ellis and King, 1991). The 3-D boundary element program yields the volume strain on an inspection plain specified at 10 km below the surface. Positive volume strains are regions of dilatations and likely locations of intrusions, extrusions, and possible structural depressions (figure 10). The Pah Rah Range, positioned between faults 2, 8, and 9, has surface exposures of predominately Tertiary volcanic and sedimentary rocks. These rocks are Oligocene to late Pliocene in age and consist of basalt, basaltic andesite, and pyroxine andesite flows, pyroclasts and associated intrusive phases (Bonham, 1969). Models of e1 equal to E-W through N50˚W (i.e., those not eliminated by fault-slip results) yield positive volumetric strain values for this area. The Virginia Range, found between faults 9, 10, and 11, has a thick section of volcanic and sedimentary rocks overlying Mesozoic metamorphosed sedimentary and volcanic rocks. These rocks are of the Kate Peak formation (Miocene in age) and consist of flows, flow breccia, agglomerate, volcanic conglomerate and associated intrusives ranging in composition from pyroxene andesite to rhyodacite (Bonham, 1969). Orientation ranges from E-W through N50˚W give positive volume strains for this region. However, N50˚W’s positive volume strains do not cover the extent of the Virginia range as well as the other orientations. Tertiary volcanic rocks of flow breccia, lava flows, basaltic and rhyolitic rocks, and agglomerates with interbedded sediments are exposed between faults 11 and 15. E-W through N50˚W orientations result in positive volumetric strain within this area. The N50˚W orientation has a smaller magnitude and extent of positive volumes strains. Virginia Mountain to the north of fault 2 has Miocene volcanic and sedimentary rocks several thousand feet thick overlying Mesozoic plutonic rocks. These Miocene volcanic rocks are of the Pyramid sequence and consist of basalt, andesite, and dacite flows, flow breccia, mudflow breccia, agglomerates, tuffs and associated intrusives (Bonham, 1969). Volumetric strain values of N50˚W are very small positive values and do not cover the large area of these exposures. The volume strain increases in magnitude and extent as the maximum extension is rotated counterclockwise. None of the modeled orientations, however, give positive volume strains directly between faults 2 and 4. Northwest Dogskin Mountain, between faults 2 and 3, has a Mesozoic granodiorite basement which is unconformably overlain by welded ash-flow tuffs of the Hartford Hill Rhyolite (Bonham, 1969). N50˚W has zero to a very small positive volume strain in this area and as the maximum extension is rotated counterclockwise the volume strain increases. Seven Mountain is located on the southern side of the north west tip of fault 3 and Fort Sage Mountain is across the fault on the north. These have exposures of both the

Pyramid sequence and Hartford Hill Rhyolite. None of the e1 orientations (N50˚W through E-W) have positive volume strain in the location of Seven Lakes Mountain. N60˚W only has a small positive volume strain in the area of Fort Sage Mountain. This volume strain increases slightly with increasing counterclockwise model rotation. Honey Lake Valley is a structural depression located on the California Nevada border at the northern ends of faults 1 and 2. Across this valley to the north are exposures of basaltic flows and intrusions. N50˚W does not model this as a positive volume strain for this large area. Models of a more westerly orientation, however, do yield positive volume strains.

The simplified fault models (e1 equal to E-W through N60˚W) has produced volume strains which seem reasonable for the study area. The semblance of areal volcanism to modeled volumetric strain suggests to me that these modeled orientations of regional strain approximate the regional volume strain. Some anomalous volume strains, southwest of Pyramid Lake (between faults 2 and 4), along the Truckee Range (east of fault 4), and at Seven Lakes Mountain, do appear for all orientations still under investigation. These discrepancies may be due to the fact that (1) I modeled a single continuous fault (Seven Lakes Mountain and fault 3) where a zone of parallel strike-slip faults accommodate the strain, (2) I did not model all the faults (east side of fault 4 and west between faults 2 and 4) that accommodate strain, and (3) this area has had temporal changes in its regional strain.

An e1 orientation of N50˚W seems unlikely based on the fault-slip vectors and the volumetric strain comparisons.

Surface displacement field to topography and structural relief The surface displacement field represents the structural relief associated with the modeled orientation of regional strain. I use the surface displacement field representation to compare to the areal structural relief and topography. In order to make this comparison, I assume the topography is relatively young, or at least to the first order, it reflects the structural relief and the relative motion across the modeled faults. As with the fault-slip vectors, I use the shallow (15 km) fault model to compare displacement of structures adjacent to the normal faults and the deep (100 km) model to compare displacement of structures adjacent to the strike-slip faults. The orientations from N40˚W through N-S have been eliminated based on previous criteria. N50˚W is highly questionable and N60˚W has had some notable discrepancies.

Models with an e1 orientation of N50˚W and N60˚W lack the magnitude of uplift for the Sierra Nevada block (uplifted blocks of faults 5 and 12) relative to the uplifted blocks of faults 8 and 10 (figures F4-5 and G4-5). Topographically, the Sierra Nevada blocks have a higher elevation than the ranges to the east, with the exception of the Carson Range (horst between fault 13 and 14). Also, the modeled basins lack the relative magnitude of the inferred depths for the study area. According to Thompson and White (1964), the faulted block which forms the Carson Range has a structural relief with respect to the bedrock of Carson Valley of more than 1525 m. Considering the depth of Lake Tahoe (~490 m) lying to the west, the structural relief of the Tahoe basin must be about as great. This suggests that the cross sections of the modeled surface displacement should produce basins of near equal depths (figure 13). The expected relative basin depths are well represented by the N80˚W through E-W orientations. Based on these cross sections and previous observations I eliminate the e1 direction of N50˚W from further investigation and, N60˚W is highly questionable. The Pyramid Lake depression also illustrates major vertical displacement within the study area. A well drilled at the north end of the lake places the Mesozoic basement rock at a depth of over 1220 m while at the south end of the depression these rocks are exposed at the surface. This could be due to strike-slip faulting, thrust faulting or rapid lateral facies change (Bonham, 1969). The north side of the left step over on fault 2 is modeled as being uplifted to unchanged or slightly depressed from orientations of E-W to N60˚W respectively, especially in the shallow fault models (figures G4-5, H4-5, I4-5, and J4-5). Located at this step over is the Black Canyon of the Virginia Mountains. This is the only area of Mesozoic plutonic rocks exposed amongst thousands of feet of Tertiary volcanic and sedimentary rocks. This suggests that this area is uplifted more, or not as structurally depressed as, the rest of the mountain range. Based on these structural and topographic observations and the discrepancies mentioned earlier, I eliminate the N60˚W e1 orientation. The N70˚W through E-W modeled surface displacement are consistent with the relative structural relief and topography of the study area.

Implications

I can use the e1 orientation estimates derived above (N70˚W through E-W) to test the velocity vector models (figure 6). The use of the relative poles of rotation for the North American plate with respect to both the Sierra Nevada and the Pacific plate result in a e1 orientation of N85˚W for northern Walker Lane. This orientation is within the range of my estimates based on the 3-D boundary element program. However, the Euler pole velocity vector models have right- lateral simple shear deformation that does not account for crustal thinning, which has been inferred for this region (Knuepfer et. al., 1987; Wernicke et. al., 1996). The 3-D boundary element model has right-lateral rotation and pure shear components of deformation, and therefore, does account for some crustal thinning associated with the orthogonal strain field. The orientation agreement between these models supports the e1 orientation of E-W through N70˚W. The lack of crustal thinning in the velocity vector models suggests that one of the following may have occurred. (1) There may have been a change in the Euler pole position over time as a result of a rate and/or directional change in the relative SN-NA plate motion. (2) Geodetic measurements in which the Euler pole location is based on (SN-NA) may not be representative of the long-term average motion. (3) The Sierra Nevada and northern Walker Lane is not a rigidly fixed boundary. This is suggested by the granitic intrusions, interpreted to be part of the , which have been stretched and exposed by the normal faults along this boundary. The methodology used here also allows us to provide estimates of rates and fault slip rates, useful in seismic hazard analysis. The fault-slip vectors give quantitative information on the mean slip-rates and directions. Knowledge of the regional strain along with the valuable information of fault-slip rates is invaluable in seismic hazard work. The modeled fault slip rates, when compared to fault slip rates provided by the University of Nevada-Reno Seismological Laboratory available on the Internet [www.seismo.unr.edu/htdocs/rnofaults.html], five out of the ten faults listed are within the ranges they provide and three are in close agreement (table 3). My numbers may be more reasonable than the University of Reno’s Seismological Laboratory fault slip rates when the latter are greater than my model results. However, because I use a simplified fault model which do not use all the faults that may be accommodating some of the regional strain, the faults with higher modeled slip rates may be less reasonable than the

Seismological Laboratory listings. 5. CONCLUSION

The limitation of tectonic models and geologic markers can be avoided by looking at a long-term (~105 - 106 year) average strain field over a large area. Assuming the structural relief and topography is directly influenced by the motion across active faults, and therefore, the structural relief and topography reflects the regional strain, then the 3-D boundary element program can accomplish this goal by modeling structural relief produced by strain for a large region over a long- term average. The 3-D boundary element program provides a good first order approximation to the topography and structural relief for northern Walker Lane, and intercontinental region of complex faulting. Model estimates of regional strain have been systematically eliminated by a rigorous investigation of the areal structural characteristics. The modeled e1 orientations with characteristics approximating northern Walker Lane are E-W through N70˚W. The e1 orientations of N70˚W through E-W show remarkable similarities between each other and the relative structural relief and topographic features of the area (figures H1-5, I1-5, and J1-5). The modeled volumetric strain show areas of positive volume strain that correlate with the volcanic activity with few discrepancies. The fault slip directions are well represented by these models, with some questionable mean rake angles for the normal faults of the N70˚W e1 orientation. The modeled fault slip vectors produce reasonable rates for many of the active faults in the region. The 3-D boundary element models have also been used to test the strain predictions of the tectonic velocity vector models for the NA-Pa Euler pole and SN-NA Euler pole. Tectonic models predict an e1 orientation of N85˚W. This is supported by the 3-D boundary element model e1 orientations of E-

W through N70˚W. Further constraints on the e1 orientations may be accomplished by several methods. More information on fault offset may allow for e1 elimination of N70˚W. An increase in the program memory may allow for a more detailed description of a greater number of faults. This should provide a more accurate surface displacement field. An independent source of uplift rates (i.e. apatite fission track analysis) could scale the models and provide another quantitative method of comparison.

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