The A.D. 2014 M6.0 South Napa earthquake, despite its moderate magnitude, caused significant damage to the Napa Valley in northern California (USA). Surface rupture occurred along several mapped and unmapped faults. Field observations following the earthquake indicated that the magnitude of postseismic surface slip was likely to approach or exceed the maximum coseismic surface slip and as such presented ongoing hazard to infrastructure. Using a laser scanner, we monitored postseismic deformation in three dimensions through time along 0.5 km of the main surface rupture. A key component of this study is the demonstration of proper alignment of repeat surveys using point cloud–based methods that minimize error imposed by both local survey errors and global navigation satellite system georeferencing errors. Using solid modeling of natural and cultural features, we quantify dextral postseismic displacement at several hundred points near the main fault trace. We also quantify total dextral displacement of initially straight cultural features. Total dextral displacement from both coseismic displacement and the first 2.5 d of postseismic displacement ranges from 0.22 to 0.29 m. This range increased to 0.33–0.42 m at 59 d post-earthquake. Furthermore, we estimate up to 0.15 m of vertical deformation during the first 2.5 d post-earthquake, which then increased by ∼0.02 m at 59 d post-earthquake. This vertical deformation is not expressed as a distinct step or scarp at the fault trace but rather as a broad up-to-the-west zone of increasing elevation change spanning the fault trace over several tens of meters, challenging common notions about fault scarp development in strike-slip systems. Integrating these analyses provides three-dimensional mapping of surface deformation and identifies spatial variability in slip along the main fault trace that we attribute to distributed slip via subtle block rotation. These results indicate the benefits of laser scanner surveys along active faults and demonstrate that fine-scale variability in fault slip has been missed by traditional earthquake response methods.
On 24 August 2014 at 03:20 local time, the M6.0 South Napa earthquake ruptured over 12 km of mapped and unmapped fault traces in a complex pattern (Fig. 1). This earthquake caused one fatality and may have caused up to $1 billion in damage, primarily from shaking-related damage to infrastructure on alluvial soils (Bray et al., 2014). Initial scientific response indicated that surface rupture primarily occurred on left-stepping en echelon discontinuous fractures. In the zone of highest coseismic slip, most reports indicated initial dextral slip on the order of 0.10 m, with isolated observations of up to a few tens of centimeters of offset (Bray et al., 2014). However by the second morning, 25 August 2014, slip on the main surface rupture trace had increased by 0.10–0.15 m indicating that significant postseismic slip was occurring.
Postseismic slip (also called afterslip) is common after moderate earthquakes, and has been measured directly on cultural features such as paint stripes, curbs, and tire tracks (e.g., Hudnut et al., 1989; Sharp et al., 1989), and measured using more precise methods including multiple linear regression of offset formerly straight features (e.g., Lienkaemper et al., 1991) and repeat surveys on alignment arrays (Lienkaemper et al., 2006, 2014). These methods have proven effective at determining horizontal slip rates on a fault trace, but do not necessarily provide a three-dimensional (3-D) sense of surface deformation within the fault zone.
Postseismic slip is important to quantify because it presents an ongoing hazard in the days following a ground-rupturing earthquake (Hudnut et al., 2014) and provides insight into frictional and rheological properties of fault zones (e.g., Copley et al., 2012; Hsu et al., 2006; Wei et al., 2015). Furthermore, the occurrence of postseismic slip on a fault, if not recognized, could lead to an overestimation of past earthquake magnitude from geologic offsets. An example of this from the historical record is the disagreement between magnitudes based on offset features seen in triangulated data (Yu and Segall, 1996) and shaking and ground-motion modeling of the A.D. 1868 Hayward fault earthquake (California; Aagaard et al., 2012).
New technologies are changing how we measure the Earth’s surface. Here we describe the use of rapid, high-resolution mapping using 3-D laser scanning. We describe how these data can be used in geospatial analyses, including the use of solid modeling techniques common to engineering fields.
The West Napa fault zone was first mapped by Weaver (1949), and has been studied intermittently over the past several decades (Fox et al., 1973; Helley and Herd, 1977; Wagner and Bortugno, 1982; Fox, 1983; Hart and Bryant, 1999; Wesling and Hanson, 2008; Clahan et al., 2011). The West Napa fault zone initiated in the Neogene as a transpressive plate boundary element following the passage of the Mendocino triple junction, and much of the ongoing compressional tectonics leading to the current topographic configuration initiated in the latest Pliocene (Graymer et al., 2007). The fault zone is generally understood to be a secondary structure within the Pacific–North American plate boundary and is characterized by many anastomosing and en echelon faults that may connect with the Calaveras fault via the Contra Costa shear zone to the south (Brossy et al., 2010), and it may extend northward to the cities of St. Helena and Calistoga based on geomorphic evidence (Clahan et al., 2011) or may merge with the Maacama fault to the northwest based on geophysical evidence (Langenheim et al., 2010). The A.D. 2000 M5.2 Yountville earthquake was the most recent damaging earthquake on the West Napa fault zone prior to the 2014 earthquake, rupturing from north to south on the northern portion of the fault zone (Langenheim et al., 2006). The A.D. 1898 Mare Island earthquake may have occurred near the southern end of the fault zone (Hough, 2014).
Wesling and Hanson (2008) produced a detailed map of Quaternary traces of the West Napa fault zone and classified mapped fault strands in terms of apparent recency of activity. They also reviewed sparse paleoseismological studies that are limited to fault traces east of the main 2014 rupture trace. These studies demonstrate the potential for Holocene tectonic activity but do not provide reliable constraints on slip rates or earthquake chronology. The slip rate across the West Napa fault zone is poorly constrained. Modeling work in the recent UCERF3 effort (Field et al., 2014) suggests a slip rate of 1 mm/yr, but this is not constrained by direct evidence. The total slip across the fault zone is poorly constrained but may be 5–40 km based on possibly offset strata and correlated and offset magnetic bodies (Langenheim et al., 2010).
PREVIOUS WORK USING LASER SCANNING TO QUANTIFY COSEISMIC AND POSTSEISMIC DEFORMATION
The use of terrestrial laser scanning (TLS) to quantify tectonic deformation is not unprecedented. Kayen et al. (2006) reported on the visualization of postseismic deformation on a series of bridge pillars following the 2004 M6.0 Parkfield (California) earthquake and on surface and structural deformation from the 2004 M6.6 Niigita Ken Chuetsu (Japan) earthquake using terrestrial laser scan data. Gold et al. (2013) reported on the use of terrestrial scan data to quantify meter-scale slip magnitudes following the 2010 M7 El Mayor–Cucapah (Baja California, Mexico) earthquake. In a particularly detailed study, Wilkinson et al. (2010) used TLS to quantify millimeter-scale postseismic slip on a road affected by the 2009 M6.3 L’Aquila (Italy) earthquake. They minimized potential error by using only a single scan position (merging data from multiple scan positions can introduce error to surveys if not done properly), and, as such, covered a very limited area. Gold et al. (2012) proposed a workflow for use of TLS to determine 3-D deformation fields and applied it to the historic rupture at Dixie Valley in central Nevada (USA), but suggested the use of such data for event response as well.
The use of airborne laser swath mapping (ALSM), also referred to as airborne light detection and ranging (lidar), to quantify earthquake effects is becoming more common, though it remains technically challenging because refinement and alignment of multisource and multitemporal data is not trivial (Borsa and Minster, 2012; Nissen et al., 2012). Coseismic deformation patterns of several earthquakes have been constrained using pre- and post-event ALSM data: the 2010 M7 El Mayor–Cucapah earthquake (Oskin et al., 2012; Glennie et al., 2014), the 2008 M6.9 Iwate-Miyagi Nairiku (Japan) and 2011 M7.1 Fukushima Hamadori (Japan) earthquakes (Nissen et al., 2014), and the 2010 M7.1 Darfield (New Zealand) earthquake (Duffy, et al., 2012). Multitemporal ALSM has proven valuable for constraining coseismic slip patterns associated with slip magnitudes at decimeter to meter scale, but its application to finer-scale deformation patterns and postseismic slip is limited by data resolution. Mobile laser scanning (e.g., Brooks et al., 2013) has advantages over ALSM in speed of deployment and level of resolution, and over TLS in its ability to survey significantly larger areas much more quickly than static TLS methods, and is likely to be a key component of earthquake scientific response at Napa and other areas.
We collected data along a ∼0.5 km length of the main fault trace, along Cuttings Wharf Road from California State Highway 12 to where the fault trace crosses Withers Road, using a Riegl VZ400 laser scanner mounted on a tripod that was generally extended to 3–3.5 m height above ground (Fig. 2). This area was chosen because it was near the most obvious postseismic slip visible on Highway 12, because we had permission to access the fault trace on private land, and because it had obvious cultural features offset by the earthquake. We scanned the area three times: on 26 August (∼2.5 d post-earthquake), 15 September (22 d post-earthquake), and 22 October (59 d post-earthquake). The first and second scan epochs utilized nine scan positions, and complete 360° scans were performed with 0.03° steps, taking ∼5.5 min per scan. Each scan position’s resulting point cloud consists of multiple returns off of just over 40 million laser pulses. The third scan epoch consisted of 17 scan positions having the same duration and resolution as the first two epochs. The locations of scan positions can be found in the Supplemental File1. The first two scan epochs were collected and individual scan positions were aligned by using reflective targets set up over semi-permanent and temporary monuments (mostly survey nails in asphalt, but also existing features were used as temporary reflector locations). The semi-permanent monuments (survey nails in asphalt) were surveyed with a Leica Viva GS15 global navigation satellite system (GNSS) with ∼30 min static observations post-processed against a local base station, which was first post-processed using the NGS OPUS online service (www.ngs.noaa.gov/OPUS/). The third survey was performed using real-time positioning information fed from the Leica Viva GNSS system to the Riegl VZ400 scanner and several GNSS-measured targets (though targets were not used extensively for scan-to-scan alignment). This technique allows for initial centimeter-scale alignment of individual scan positions using real-time differential GNSS positions and the VZ400 internal electronic compass, and is significantly faster than target-based alignment. Regardless of field collection and initial coregistration techniques, each scan epoch was internally aligned to a single merged and aligned point cloud using a modified iterative closest point (ICP) algorithm (Besl and McKay, 1992) as implemented in the Riegl RiScan Pro Multi-Station Adjustment software tool. This tool relies on generation of simplified point clouds that represent only areas that can be locally modeled as centimeter-scale or larger planes with geometric normals. These reduced point clouds typically have tens of thousands of points with normal vectors. They are then used by the ICP algorithm to align each scan position point cloud to all others, eliminating any errors introduced by GNSS accuracy, errors from measurement of reflective target locations, or other possible systematic positional errors in the scan data. This is performed iteratively with decreasing tolerance to outliers and reduced point-to-point search radii in order to refine alignment to maximum accuracy using only objects scanned from multiple scan positions. The georeferenced point clouds were then filtered to remove error points (generally echoes off of the edge of objects) and intermediate and first laser returns, and were reduced using an octree filter to ∼30–50 million points per scan epoch.
Because we were interested in coseismic as well as postseismic deformation, we also integrated the 2003 Napa watershed ALSM data (NCALM, 2003) and the post-earthquake ALSM data collected on 9 September 2014 (16 d post-earthquake) (Hudnut et al., 2014; Towill, Inc., 2015) into our database. In order to quantify progressive deformation between the three TLS scans and the two ALSM data sets, a consistent local reference frame had to be established. Because laser measurements are inherently more accurate than GNSS measurements, multitemporal point cloud alignment relying on stable areas within laser point clouds provide the most accurate detection of relative change between scan epochs. For TLS data, this can easily be sub-centimeter accuracy or better, and for ALSM data, sub-decimeter accuracy can be expected. Therefore, we again relied on the modified ICP approach to align multitemporal data in a manner analogous to our internal alignment of multipositional TLS data. However in order to remove most effects of tectonic deformation on the multitemporal alignment, we removed all points within 2–3 m of the trace of the surface rupture because no obvious deformation was visible beyond that aperture, as well as all points west of the fault zone, from the points used in the alignment algorithm. We then applied the east-side alignment transformations to the full point clouds, creating an east-side-fixed reference frame. This method does have the potential to create misaligned data if there is significant off-fault deformation east of the fault trace, if it occurs between scan epochs. As such it may not be an appropriate method for large earthquakes with significant off-fault deformation (e.g., Rockwell et al., 2002).
After alignment of the multiple TLS and ALSM epochs using ICP methods, all points were classified as either ground, points within 2.0 m of ground, building, or unclassified (all other points). Points classified as ground were gridded for visualization and analysis of vertical ground-surface change.
We used a number of techniques to quantify ongoing deformation using the 3-D point clouds and derivatives thereof. In particular, we relied on natural and cultural objects within 2 m of the earth’s surface to make detailed measurements of lateral deformation, and used ground models to make measurements of vertical deformation. We used the solid modeling tools available in Leica Cyclone software to extract primitive shapes such as cylinders and planes from the TLS point cloud data. This type of solid modeling is commonplace in engineering applications for building information modeling, reverse engineering, and a range of 3-D design needs, but has, to date, had fewer applications in the earth sciences. These tools were used to assess ongoing lateral slip by simply measuring changes of location of features between each scan epoch.
The TLS surveys covered a wide range of natural and built features and produced very detailed 3-D point clouds (See Animation 1). From the above-ground points (Fig. 3A), we extracted a wide range of natural and cultural features (Fig. 3B). The features that were modeled as cylinders include fenceposts (square and round), utility poles, tree trunks, sign posts, water tanks, cylindrical utility enclosures, and vineyard-row end posts. We extracted the center point of the lower extent of these cylinders in an effort to minimize potential effects of tilting between scan epochs, and used these in our two-dimensional analysis of surface deformation. We discarded a few modeled objects that indicated position change more than twice the magnitude of nearby objects on the same side of the fault. These were generally trees with irregular geometry that were likely quite sensitive to the look direction of the scanner, or objects that tilted between scan epochs.
Planar features were modeled as well; these were fence lines (not including large posts), building walls, and rows of young grapes. The offset and translation measurements derived from planar features were done in the 3-D model space and as such were non-unique. We generally measured plane-to-plane distance at the intersection of modeled planes with the ground surface in order to minimize any influence of tilting. In most cases, we picked points from a single plane near the fault zone, and distance was calculated as the shortest distance either to the same plane in a different epoch or to its corresponding offset plane projected across the fault zone. These methods are far simpler than full multiple linear regression, but still provide meaningful measurements. All measurements of separation across the fault were corrected for the angle between planes and the fault trend to provide proper quantification of fault slip.
Maps of the ground surface and of elevation change offer a detailed view of the pattern of landscape features and surface rupture through the study site (Figs. 4 and 5) and allow for mapping of vertical changes in the land surface. Because airborne lidar was collected in 2003 (NCALM, 2003), we were able to make measurements of total vertical deformation at locations having bare surfaces. We also were able to compare surface elevations among each of our scan epochs and with the 2014 airborne lidar data (Hudnut et al., 2014).
Cultural features that were built to be straight before the earthquake were used to estimate the magnitude of coseismic and postseismic deformation. The progressive motion of features after the earthquake provides rates and spatial patterns of postseismic slip. Traditionally, proper recovery of total slip magnitude from offset features assumed to be originally straight relies on precise surveying and multiple linear regression to extract the slip magnitude (e.g., Lienkaemper et al., 1991, 2012). We utilized this method, and additionally evaluated the simpler method of measuring the distance between modeled planar features (vineyard grape rows, building walls, and fence lines) as if they extended across the fault zone. We modeled the locations of fenceposts assumed to have been built straight along four fault-crossing fences, one at Withers Road and three very new steel-post fences along horse paddock edges at a private property on Cuttings Wharf Road, for formal multiple linear regression (MLR) analysis. The full MLR results for each scan epoch can be found in the Supplemental File.
To quantify vertical deformation, we gridded TLS classified ground points using triangulation with linear interpolation at a resolution of 0.025 m for a subset of the area and 0.05 m for the entire study area, and gridded ALSM ground points at a resolution of 0.10 m. We subtracted those grids from those of various epochs to map patterns of vertical deformation, and chose not to backslip the lateral offset across the fault because of the uncertainty in the amount of backslip required (slip variation is discussed later) and the very limited relief in the area that would cause significant apparent, rather than actual, vertical changes. A similar method was used to quantify millimeter-scale postseismic slip on a paved road surface following the 2009 M6.3 L’Aquila earthquake (Wilkinson et al., 2010).
The maps of vertical change that involve the 2003 airborne lidar data are quite noisy because of extensive land-use change, vegetation change, varying patterns of ground data distribution among the data sets, and, in particular, noise in the 2003 ALSM data. However, inspection of roads and bare-ground areas illustrate the dominant relative elevation increase west of the surface rupture (Fig. 6). The relative elevation increase between 2003 and 2014 in the study area may be as much as 0.20 m. This signal, though noisy, is detectable along the driveway through the horse paddocks and along Withers Road. The bump that formed where the fault trace takes a right step and crosses Cuttings Wharf Road (Fig. 6) appears to be caused by local subsidence east of the surface rupture rather than larger-scale uplift, and as such is not a reliable estimate of earthquake-related uplift magnitude. The kinematics of these areas will be discussed further below.
Comparison of ground elevations between the three post-earthquake terrestrial laser scan data sets provides the vertical component of postseismic slip (Fig. 7) and further illuminates the spatial pattern of vertical tectonic motions. Between 2.5 and 22 d post-earthquake, the land surface west of the fault trace increased its elevation relative to the east side of the fault by ∼0.02–0.03 m. However, this relative elevation change does not occur as slip along the fault plane, but rather as a broad uplift that decays from ∼0.03 m to 0 m over a distance of 50–100 m across the fault without a distinct step (Fig. 8). Furthermore, the vertical component of postseismic slip in the later scan epoch from 22 to 59 d post-earthquake is characterized by a very slight overall subsidence on the order of 0.002–0.003 m (below the minimum color scale value on Fig. 7D). This is indicated by the lower overall uplift magnitude that can be seen on Figure 7F when compared to Figure 7B.
Total Coseismic and Postseismic Deformation Magnitude
Multiple linear regression (MLR) analysis of fences provides the best estimates of total surface offset and formal error estimates. The fence at Withers Road has only a single post east of the visible fault rupture, so may be missing some distributed slip, but indicated a total strike slip of 0.258 ± 0.014 m ∼2.5 d after the earthquake. The error on the MLR offsets are formal errors from the statistical analyses of the fencepost positions. The fences along the Cuttings Wharf horse paddock indicated variability in total strike-slip magnitude approaching 0.1 m over a distance of <100 m. Figure 9 is a plot of the MLR results along with total displacement magnitude as measured from planes fit to the straight parts of fences and vineyard rows and projected across the fault. The variation in dextral displacement apparent from the modeled objects is more complex than the expected southward decrease in displacement as observed along the main trace of the fault over several kilometers (Hudnut et al., 2014; Bray et al., 2014), possibly indicating that a slip deficit caused by local phenomena is present. This is discussed in later sections.
Ongoing Postseismic Deformation
The ICP-aligned multitemporal point clouds provide a basis for change detection and provide hundreds of measurements of postseismic displacement from ∼2.5 d post-earthquake (at which time significant postseismic displacement had already occurred) onward (see the Supplemental File for a complete spreadsheet). The most accurate measurements come from simple, stable features that lend themselves well to reproducible solid modeling. In this case, round fenceposts (Fig. 10), water tanks, and flat planes such as fencing and building walls appear to be the most reliable features, though even the bare-earth digital elevation models that contain microtopography could be used to measure postseismic displacement (see Animation 1). The deformation field can be inferred from the numerous point measurements made across the study site. Figures 11A–11C display postseismic displacement magnitude and direction for the area near the horse paddock off of Cuttings Wharf Road. Figures 11D–11F display postseismic displacement adjacent to Withers Road. Vineyard rows and building walls also provide objects that can be used to measure postseismic displacement. One way to visualize this is to examine the increase in offset values on planes projected across the fault in the three scan epochs as shown in Figure 9. A more direct method that avoids error inherent in projecting modeled planes across the fault is to make direct measurements between locations of the same modeled planar objects between scan epochs. Table 1 indicates summary statistics of these measurements from both the east and west sides of the surface rupture. Values from the east side of the surface rupture indicate repeatability of stable features and have zero magnitude (within error). The values from the west side of the fault indicate dextral postseismic displacement. In general, aside from spatial variation in displacement discussed below, we observe approximately 0.08 m of postseismic displacement from 26 August to 15 September, and 0.02–0.04 m of postseismic displacement between 15 September and 22 October.
Sources and Magnitudes of Error
Although creating error budgets for analyses from multitemporal high-resolution 3-D data is challenging, we can discuss the factors that determine the reliability of our TLS comparison measurements. The principal sources of error are (1) inherent laser scanner error, (2) the effectiveness of the modified ICP algorithm that was used to refine internal alignment among scan positions within a scan epoch and to align the multitemporal point clouds between scan epochs, and (3) the repeatability of the solid modeling of any given object used for change detection.
All errors from the GNSS measurements are minimized by the use of the ICP algorithm. This includes errors in individual scan positions when the GNSS provided real-time locations to the scanner and in the GNSS measurement used to roughly align the various scan epochs. These only provided a first estimation of the location of data; the cloud-to-cloud alignment provided the final registrations.
The magnitude of laser error is very low, <0.002–0.003 m at the ranges at which we scanned the relevant landscape features. The error introduced by limitations of the modified ICP algorithm is not simple to quantify. However, the algorithm reports root mean square (RMS) deviation between point clouds for the selected alignment parameters (e.g., search distance, outlier tolerance). Within a scan epoch, these routinely were <0.01 m, and between scan epochs these were generally 0.01–0.03 m. Because these RMS deviations are simply a measure of how well colocated the points from the disparate scans are with each other, they do not necessarily indicate error that will affect change detection. There is no expectation that a point cloud of an object would have the same exact internal structure if an object was scanned at two times or from two locations, and the use of solid modeling removes any effect of point cloud heterogeneity within the point cloud of a modeled object. The error caused by repeatability of solid modeling is likely to be the most significant contribution to total error. Simple geometric shapes are likely to model in a highly repeatable fashion, whereas irregular objects such as deciduous tree trunks and tilted agricultural posts may not create unique X-Y locations. We inspected the fit quality of many of the modeled objects. Cylinders modeled from fenceposts had mean absolute errors of between 0.002 and 0.005 m and were generally modeled from between 400 and 800 individual points (after point cloud reduction by octree filtering). These exceedingly low errors are testament to the success of the ICP algorithm for internal scan registration and the clean nature of the processed point clouds.
An indication of repeatability of object modeling from TLS point clouds is the stability of object locations on the “stable” east side of the surface rupture between scan epochs. Of course in detail we know there is deformation within the block east of the fault, but the mean distance change (which is a combination of relocation error and actual object movement) between objects farther from the obvious deformation in the northern part of the study area is only ∼0.007, 0.008, and 0.009 m between scan epochs 1 and 2, 2 and 3, and 1 and 3, respectively, for over 50 objects in each scan epoch. The magnitudes of relocation error of planar features on the east side of the fault are reported in Table 1, and they are all <0.012 m for somewhat irregular vineyard rows, and approach 0.000 m for recently built fences.
Furthermore, we report sub-centimeter–level vertical change detection among TLS data sets. This would be impossible if relying solely on GNSS and target-based alignment procedures. The simplest way to assess error in these analyses is by analysis of stable, fiduciary surfaces such as paved road away from deformation. Along a ∼250-m length of Cuttings Wharf Road south and east of the horse paddock, the mean elevation distance between the first and second scans is 0.004 m (indicating a no more than millimeter-level vertical misalignment between scans or existence of very minor off-fault deformation that slightly skews the alignment results, or both) and a standard deviation of 0.002 m (indicating very high-precision change detection and low input to the error budget from laser accuracy or scan position alignment). These numbers provide confidence in our level of detection.
These observations indicate that while formal error estimates are challenging to perform, sub-centimeter position change detection can be considered routine using these methods. Iterative closest point algorithms in particular can remove any error from short-duration GNSS measurements inherent in airborne, mobile, or terrestrial laser scanning, and have the potential to correct any errors caused by moving or poorly modeled survey targets or monuments, all of which have the potential to affect landscape change detection significantly.
Rates and Patterns of Postseismic Slip
The high spatial and temporal resolution of the TLS data reveals the details of fault zone deformation in an unprecedented manner. Furthermore, these details provide context for other observations made in the study area. For example, an alignment array was installed along Withers Road to measure postseismic slip (Lienkaemper et al., 2014; Hudnut et al., 2014), and in order to properly forecast ongoing postseismic slip, a measure of total slip (coseismic plus postseismic slip to date) was required. We extracted this value, 0.258 ± 0.014 m, on 26 August 2014 from our MLR analysis of the fence adjacent to Withers Road.
When compared to displacement magnitude on vineyard rows and horse paddock fence #1 to the north (Figs. 4 and 9), this total displacement is ∼0.03–0.04 m lower, indicating either that some coseismic slip was not accommodated on the extent of the fence adjacent to Withers Road and may have been missed beyond the eastern extent of the fence (there is only one fencepost east of the visible surface rupture), or that even over these distances we detect the gradual southward reduction in slip magnitude toward the earthquake epicenter (Lienkaemper et al., 2014; Hudnut et al., 2014).
Also interesting is the variation in displacement and the spatial patterns of horizontal and vertical deformation along Cuttings Wharf Road adjacent to the horse paddock property (Figs. 7 and 11). If slip was measured on the horse paddock fence lines alone using traditional methods, the slip variability obvious in Figure 9 may have been observed, but the explanation for this deficit would be nearly impossible to determine. Furthermore, the vertical relief generated on Cuttings Wharf Road where the surface trace crosses the road could be attributed mistakenly to overall up-to-the-west movement on the fault plane itself instead of local subsidence due to a releasing geometry fault step as seen in elevation change mapping (Fig. 7).
The full 3-D kinematics provided by the TLS surveys illuminate the spatial and temporal patterns that can explain the local apparent slip deficit along the fault trace and the scarp formation on Cuttings Wharf Road (Fig. 12). Along the fault trace in the northern portion of the horse paddock, the block east of the surface rupture rotated clockwise, and it subsided relative to the west side of the fault in a zone adjacent to a significant right step in the surface trace. This rotation allowed the eastern side of the fault to move along with the west side of the fault, causing the apparent 0.06–0.07 m (∼15%) slip deficit on paddock fences #2 and #3 (flanking the horse paddock property driveway) relative to paddock fence #1 (Fig. 4) and vineyard rows just a few tens of meters to the south. The rotation also led to subsidence at the right step in the fault zone, which caused local extension. This rotation and relative subsidence continued through the postseismic period—in fact, based on the lack of observed coseismic deformation where the surface rupture crossed Cuttings Wharf Road (Bray et al., 2014), this vertical deformation only happened in the postseismic period. This indicates that caution must be used when interpreting the importance of locally deformed features and in interpreting features in the paleoseismological or geomorphological record as faithful records of coseismic motion.
The apparent slip variability evident in Figure 9 is thus simply an artifact of incomplete measurement at the main fault rupture trace. Rockwell et al. (2002) observed that deformation away from the surface rupture mole track can lead to underestimation of overall earthquake slip. In the case of Napa, observed fence offsets underestimate total slip because some of the slip is accommodated as block rotation tens of meters from the fault zone. The apparent slip variability visible in Figure 9 is explained by the block rotation visible in Figure 12.
These observations highlight the complex spatial behavior of faults and that cultural features are often the best means of quantifying fault slip. In larger earthquakes such as the A.D. 1999 M7.6 Izmit (Turkey) earthquake, much of the slip can occur over a significantly wider aperture than initial near-fault observations would indicate, and this may only be revealed by careful surveying of cultural features that are more than 100 m from the surface rupture trace (Rockwell et al., 2002). Furthermore, study of major earthquakes such as the A.D. 1940 M6.9 Imperial Valley (California) and A.D. 2010 M7.1 Darfield (New Zealand) earthquakes utilized offset on natural and cultural features as measured from aerial photos and field surveys to document patterns of surface displacement (Rockwell and Klinger, 2013; Quigley et al., 2012). The quantification of spatial and temporal patterns of slip in moderate earthquakes is arguably more difficult than for these somewhat larger earthquakes, pointing to the use of terrestrial laser scanning as a beneficial development in earthquake response.
Vertical Deformation and Implications for Scarp Development along Strike-Slip Fault Zones
The coarse view of vertical changes in the study area as manifest in comparisons of post-event TLS and ALSM with pre-event airborne ALSM (Fig. 6) would suggest relative up-to-the-west motion along the 3-D rupture surface. However, the lack of scarp at many locations where the surface rupture crosses durable surfaces such as roads confounds that interpretation (e.g., Fig. 2). Furthermore, detailed inspection of the pattern of coseismic vertical change along Withers Road indicates that the ∼0.15–0.20 m of uplift is not accommodated on the fault trace but rather on a ∼100-m-long ramped uplift zone that spans the fault (Figs. 6, 8A) and on a ∼50-m-long ramp at the driveway to the horse paddock property (Figs. 7, 8B). Additionally, the vertical component of postseismic change, which provides remarkable detail regarding the patterns of vertical motion in the fault zone after the earthquake, broadly agrees with the pattern (though not the magnitude) of coseismic vertical change as visible in Figure 6. This 0.01–0.02 m of vertical postseismic change also spans the fault at the horse paddock property over a span of ∼50 m.
While it is likely that extensive areas west of the fault were uplifted a similar amount (up to ∼0.20 m beyond a few tens of meters from the surface rupture in this study area), the patterns of uplift are not as expected from uplift on the surface rupture fault plane. This suggests that the pre-existing fault scarp in the study area that was interpreted as relatively inactive based on its broad, gentle sloped morphology (Wesling and Hanson, 2008) may have a morphology that actually is representative of typical recent and/or repeated vertical movements associated with strike-slip earthquakes on the West Napa fault system. This suggests we may need to reevaluate how fault scarp morphology is interpreted in strike-slip fault systems. It is commonly thought that traditional scarp evolution methods could be used to a first order to estimate activity on strike-slip faults (e.g., Hilley et al., 2010). Conventional wisdom suggests that steep scarps exist along active faults, and broad, subdued scarps exist along faults with long recurrence intervals. Perhaps along some strike-slip faults, uplift occurs with less distinct surface expression and can lead to low, ramped fault scarps, even when fairly active, confounding the use of scarp morphology as evidence of level of seismic hazard. This may be a product of uplift occurring as longer-wavelength vertical bulging along fault strike accommodating lateral variations in slip, or due to vertical motions occurring at depth and not reaching the surface as slip on the fault plane. Slip at depth may be analogous to a fault-propagation fold and/or buried fault seen in classic thrust faulting scenarios (Suppe and Medwedeff, 1990), and may indicate a vertical manifestation of the observed shallow slip deficit phenomena (e.g., Dolan and Haravitch, 2014, and references therein).
Comparison of Coseismic versus Postseismic Slip
Many observations made in the hours after the earthquake allow us to determine the relative significance of coseismic versus postseismic slip. These observations, however, provide sometimes-inconsistent magnitudes of fault slip. The morning of the earthquake, many scientists made observations about the amount of coseismic slip along the fault traces. In the area of this study, we know that right-lateral slip on Highway 12 was almost imperceptible just after the earthquake, increased to several centimeters later the day of the earthquake, to perhaps 0.20–0.25 m the day after the earthquake, and to >25 cm by several days after the earthquake (Bray et al., 2014; Hudnut et al., 2014; Lienkaemper et al., 2014). This pattern, documented by measurements made on painted highway lines, is consistent with our observations from TLS ∼200 m south of the highway.
At Withers Road, Morelan et al. (2015) measured 0.20 m of deformation ∼8 h after the earthquake. At Cuttings Wharf Road, observations the day of the earthquake indicated 0.0–0.02 m of surface displacement on the paved road, and 0.10 m of vertical relief by the next day (Bray et al., 2014; Morelan et al., 2015). Approximately 0.5 m of extension was observed in the vineyard adjacent to where the fault trace crossed Cuttings Wharf Road, and on the basis of the azimuth at which it crossed the road, it was properly noted as likely a releasing bend on the day of the earthquake (Morelan et al., 2015). Observations made at the horse paddock were apparently inconsistent among observers and may not have been intended to capture the overall offset across the fault trace. These include a measurement of 0.05 m of displacement on individual surface cracks on 5 September, and 0.04 m of right lateral offset on a small fence on 1 September (Bray et al., 2014). If these magnitudes were interpreted to be indicators of fault slip, they would greatly underrepresent the true value; TLS indicated that nearby features had been displaced at least 0.22 m by 26 August.
These diverse observations highlight the need to make standardized measurements of fault slip, present interpretations based on field measurements carefully, and use objective measurement methods such as TLS (this study), MLS (Brooks et al., 2013), or rapid, low-cost photogrammetric techniques (Johnson et al., 2014), and it is possible that inconsistencies could be mitigated by rapid scientific communication during event response (Morelan et al., 2015).
The 2014 M6.0 South Napa earthquake was accompanied by spatially and temporally complex deformation of the Earth’s surface. These effects were commonly subtle and, as such, traditional methods for measuring surface deformation provided somewhat inconsistent insight into the magnitude and patterns of deformation.
Surface slip resulting from the studied part of the South Napa earthquake rupture, as measured via several techniques that exploit airborne and terrestrial laser scan data, was dominated by postseismic slip. This took the form of lateral offset parallel to the fault strike, rotational movement adjacent to the fault, and complex patterns of uplift and subsidence within the fault zone. The patterns of uplift in particular indicate that vertical change associated with strike-slip faulting does not only occur along the fault plane at the surface trace, but also may occur as ramped uplift spanning the fault zone over tens of meters. If this behavior is indeed characteristic, it leads to a scarp morphology that appears old based on conventional thinking about scarp formation and degradation, but this rounded morphology may in fact result from recent fault activity in some locations.
Traditional methods of measuring coseismic and postseismic slip may measure “at-a-point” magnitudes that could be quite different from nearby values that better represent overall fault behavior and are only discernable through full 3-D analysis. In this study area, offset features provided evidence for ∼15% variation in slip that was accommodated on the surface rupture itself. A casually placed alignment array or slip measurement location could miss such distributed deformation. We suggest that ultrahigh-resolution 3-D survey methods such as terrestrial and mobile laser scanning and promising new photogrammetric methods are key components of a thorough scientific response to surface-rupturing earthquakes.
Furthermore, this study highlights the caution that must be taken when offset and deformed features observed in the paleoseismological, geomorphic, and even historical records are interpreted, because attributing apparent slip magnitudes to coseismic slip alone could lead to significant overestimation of coseismic moment.
We gratefully acknowledge David and Tammy Allendorf, who own the horse paddock property and graciously allowed us (and many other interested parties) repeated access to their property. We thank our many colleagues who helped us better understand the South Napa earthquake, especially K. Hudnut, T. Dawson, D. Schwartz, B. Brooks, D. Ponti, and C. Rosa. Thanks to S. Hecker and S. Corbett for helpful reviews of an earlier version of this manuscript. Thanks to P. Gold and an anonymous reviewer for careful reviews that improved the paper substantially.