Fault Kinematics and Surface Deformation Across a Releasing

Fault kinematics and surface deformation across a releasing

bend during the 2010 MW 7.1 Darﬁ eld, New Zealand, earthquake revealed by differential LiDAR and cadastral surveying

Brendan Duffy1,†, Mark Quigley1, David J.A. Barrell2; Russ Van Dissen2, Timothy Stahl1, Sébastien Leprince3, Craig McInnes4, and Eric Bilderback1 1Department of Geological Sciences, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand 2GNS Science, PO Box 30-368, Lower Hutt 5040, New Zealand 3Division of Geological and Planetary Sciences, California Institute of Technology, MC 170-25 1200 E. California Blvd., Pasadena, California 91125, USA 4Fox and Associates–Consulting Surveyors, 333 Harewood Road, Christchurch 8053, New Zealand

ABSTRACT INTRODUCTION LiDAR survey fl own 5 months before the earthquake was partly overlapped by LiDAR fl own a Dextral slip at the western end of the Over the past 10 years or so, documentation few days after the earthquake. Also, a cadastral east-west–striking Greendale fault during of earthquake fault surface rupture by well-es- survey was conducted 1 month before the earth- the 2010 MW 7.1 Darfi eld earthquake trans- tablished fi eld methods, including geological/ quake on a property through which the Green- ferred onto a northwest-trending segment, geomorphological mapping and geodetic sur- dale fault subsequently ruptured for ~2 km. across an apparent transtensional zone, here veying, has increasingly been supplemented by Rupture of the Greendale fault also temporarily named the Waterford releasing bend. We technologies such as interferometric synthetic diverted the course of the Hororata River. In this used detailed surface mapping, differential aperture radar (InSAR) (e.g., Reigber et al., study, we mapped the earthquake-induced fl ood, analysis of pre- and postearthquake light de- 1997; Price and Burgmann, 2002; Beavan et al., analyzed pre- and postearthquake LiDAR sur- tection and ranging (LiDAR), and property 2010a) and light detection and ranging (LiDAR ) veys, and undertook postearthquake cadastral boundary (cadastral) resurveying to produce (e.g., Hudnut et al., 2002; Quigley et al., 2012). resurveying of property boundaries, to further high-resolution (centimeter-scale) estimates In combination, these methods provide an op- aid understanding of the surface deformation of coseismic ground-surface displacements portunity to examine fault deformation and and displacement across the Greendale fault. across the Waterford releasing bend. Our kinematics in unrivaled detail and precision. These data sets span a zone where the fault strike results indicate that the change in orienta- Contemporary surface-rupture events, in favor- changed by ~40°, and they have allowed us to tion on the Greendale fault incorporates ele- able land-surface settings, provide primary characterize this fault bend in remarkable de- ments of a large-scale releasing bend (from evidence for the style and kinematics of fault tail. Documentation of this detail is the focus of the viewpoint of westward motion on the defor mation, and documentation of their char- this paper. south side of the fault) as well as a smaller- acter provides an invaluable interpretive ana- scale restraining stepover (from the view- logue for structural and kinematic studies of THE DARFIELD EARTHQUAKE point of southeastward motion on the north prehistoric fault deformation. side of the fault). These factors result in the The 2010 Darfi eld earthquake in Canterbury, New Zealand lies astride the boundary be- Waterford releasing bend exhibiting a de- New Zealand (Fig. 1), caused surface rupture of tween the Pacifi c and Australian plates, at a lo- crease in displacement to near zero at the the Greendale fault across a low-relief alluvial cation where they converge obliquely at rates of change in strike, and the presence within plain. The plain is an intensively farmed agricul- 30–50 mm/yr (DeMets et al., 2010) (Fig. 1A). the overall releasing bend of a nested, local- tural region and contains a multitude of straight Continental collision across the South Island ized restraining stepover with contractional lines in the form of roads, fences, and ditches drives uplift of the Southern Alps (Norris and bulging. The exceptional detail of surface that provided ideal piercing points for quantify- Cooper, 2001) and is expressed by varying deformation and kinematics obtained from ing fault rupture (Barrell et al., 2011; Quigley rates and styles of active deformation across this contemporary surface-rupture event il- et al., 2012; Villamor et al., 2012). Quigley et al. Canterbury (Pettinga et al., 2001; Campbell lustrates the value of multimethod investiga- (2012) took advantage of these piercing points et al., 2012). The rupture of a fault network tions. Our data provide insights into strike- to undertake detailed fi eld mapping and, in beneath the Canterbury Plains, eastern South slip fault bend kinematics, and into the combination with evaluation of LiDAR fl own Island, on 4 September 2010 generated the MW potentially subtle but important structures after the earthquake, were able to quantify 7.1 Darfi eld earthquake (Beavan et al., 2010b; that may be present at bends on historic and fault offsets to high precision. Serendipitously, Gledhill et al., 2010, 2011; Beavan et al., 2012), prehistoric rupture traces. two high-quality geodetic data sets had been which caused widespread ground shaking and acquired prior to the earthquake, in the vicin- damage (Cubrinovski et al., 2010; Gledhill †E-mail: [email protected] ity of the western end of the Greendale fault. A et al., 2010; Quigley et al., 2010a, 2010b, 2013;

GSA Bulletin; March/April 2013; v. 125; no. 3/4; p. 420–431; doi: 10.1130/B30753.1; 7 ﬁ gures; 3 tables.

165° E 170° E 175° E 180° 175° W fault trace, the strike change between the West Kermadec and Central segments is transtensional in na- 35° S 500 km Trench 35° S ture (Quigley et al., 2012), so the zone across which the strike change occurs is referred to 48F here as the Waterford releasing bend, taking Australian its name from a nearby farm. Dextral displace- plate ment of up to ~5.3 m on the Central segment

44F decreases to ~1.2 m on the West segment (Quig- 40° S ley et al., 2012). The West segment displayed Hikurangi 40° S

Trough a notably south-side-up vertical component of F offset (~1.5 m), which caused temporary partial 39 avulsion of the Hororata River (Quigley et al., Region affected 2010b; Barrell et al., 2011) (Fig. 2). Seismic Chch by earthquake Puysegur Alpine Fault Ash (Fig. 1B) source models indicate that the Greendale fault trench rupture proceeded bilaterally from the vicinity 45° S Canterbury Plains Pacific 45° S of the Waterford releasing bend, which itself lies A Southern Alps plate close to the intersection of the Greendale fault 165° E 170° E 175° E 180° 175° W with the northeast-southwest–striking Charing Cross reverse fault, on which the Darﬁ eld earthquake was initiated (Fig. 2) (Holden et al., 2011; Beavan et al., 2012).

Regional METHODS shortening Christchurch Flood Mapping

Darfield We mapped the extent of avulsion-induced postearthquake ﬂ ooding (Figs. 2 and 3) by digi- Fig. 2 ^ tizing ﬂ ooded areas seen in a set of overlapping oblique aerial photographs taken ~12 h after the ^ Earthquake epicentre Darfield eq. surface rupture earthquake. We georeferenced the photographs Darfield eq. blind rupture using ArcGIS software with reference to digi- Post-Darfield eq blind ruptures tal topographic maps and pre-earthquake digital 20 km Other active faults and folds B orthophotos.

Figure 1. Regional setting. (A) New Zealand plate boundary and Cadastral Surveys relative motion vectors (mm/yr) between the Australian and Pacifi c plates (DeMets et al., 2010). Canterbury Plains form the low relief Cadastral surveys have been used to docu- east of the Southern Alps in the central South Island. Ash—Ash- ment surface displacements resulting from burton; Chch—Christchurch. (B) Location of the Greendale fault the Chi-Chi earthquake in Taiwan (Lee et al., west of Christchurch in mid-Canterbury. The extent of surface 2006, 2010, 2011). A cadastral property sur- rupture is from Quigley et al. (2012), and extents of blind ruptures vey done about 1 month before the earthquake are from Beavan et al. (2012). Known active (i.e., late Quaternary) in New Zealand spanned the northern half of faults and folds are based on GNS Science QMAP data sets (Cox and the West segment of the Greendale fault. Base- Barrell, 2007; Forsyth et al., 2008). Regional shortening direction is line surveying employed a Trimble R8 Global from Sibson et al. (2011). Navigation Satellite System (GNSS) real-time kinematic (RTK), and the survey was adjusted in “12d Model” software using simple loops and Van Dissen et al., 2011). Geodetic modeling Mesozoic graywacke rock, and propagated to the Bowditch adjustment method (Bowditch, has revealed that this single earthquake event the surface through a surfi cial 1–1.5-km-thick 1808). The survey was fi xed relative to local consisted of an interlinked succession of rup- cover of post–mid-Cretaceous sedimentary benchmarks by locating the RTK base station tures on several fault structures (Figs. 1B and 2) strata, including as much as 500 m of Qua- on a buried iron tube witness mark that was es- (Beavan et al., 2012). All remained blind, apart ternary fl uvial gravels (Browne et al., 2012; tablished relative to three local benchmarks in from the Greendale fault, which produced an Jongens et al., 2012). 2004. The fl at, unforested farmland provided a ~30-km-long surface rupture, predominantly The Greendale fault is composed of three favorable global positioning system (GPS) envi- strike slip with dextral sense (Quigley et al., geometric segments, each named for their rela- ronment, so the baseline survey over the survey 2010a, 2010b, 2012; Barrell et al., 2011). The tive locations (Quigley et al., 2012). The East extent of 2 km is likely to be internally accurate Greendale fault lies in a large sedimentary and Central segments strike east-west, whereas to within 2 cm, with exact accuracy depending basin . Fault rupture was initiated ~10 km deep, the West segment strikes northwest (Fig. 2). In on the detail of satellite geometry during the within indurated, slightly metamorphosed, the context of dextral rupture exhibited by the survey (Table 1).

Geological Society of America Bulletin, March/April 2013 421 Duffy et al.

172.03° E 172.05° E 172.07° E 172.08° E Surface rupture Selwyn River Blind rupture LiDAR structures NW Rivers B* OIT27 140 Flooding

1.0 Roads #

W 140 SW Dextral offset (m)# S 1.7

0.9 B* Horora # ta River PegB11 IT5 T11

O OIT1OIT11OI 43.58° S D #

0.75 Greendale Hawkins River

OIT9 1.1 130 village # CCF avulsion WSW

1.3 S node # OIT24 U D 0.7 WRBWRB CSCS CS2C 1.0 Post-quake LiDAR S 1.0 2 CS1C 1.2 1.15 S1 1.9 1.7 Vector scale Figure 5A U 120 43.59° S 1 km v h 1 m Pre-quake LiDAR

Figure 2. Fault map of the West segment (WS) and westernmost part of the Central segment (CS) of the Greendale fault. U and D denote relative upthrow and downthrow across the scarp. The immediate area of the change in strike between the segments is here named the Waterford releasing bend (WRB). CCF is the location of the subsurface tip of the blind Charing Cross fault (Beavan et al., 2012), teeth toward hanging wall. The extent of coseismic avulsion and resulting fl ooding is shown, as well as the location of pre- and postearthquake light detection and ranging (LiDAR). Arrows indicate displacement vectors for resurveyed cadastral witness marks (Table 2). Dotted red lines denote structures defi ned from LiDAR analysis in this study (Fig. 5). Dextral offset measurements are from Quigley et al. (2012). The Waterford releasing bend includes an ~1.5-km-wide zone where no surface deformation was able to be detected from fi eld mapping. Topographic contours (brown) are in meters above sea level. Contours, roads, and streams are from Land Information NZ digital data, Crown Copyright reserved (used with permission). OIT—old iron tube; NWB—NW boundary peg; SWB—SW boundary peg.

Figure 3. Deformation and fl ooding result- B ing from rupture of the West segment of the A Escape B flow Greendale fault. Solid line and dashed line * mark the crest and base of the surface trace, respectively, while U and D denote relative U Hororata River D upthrow and downthrow. Thin black arrows C show the direction of avulsion fl ow. (A) View to the northwest of the avulsion node (*) U D (Barrell et al., 2011). Here, ~1.5 m of oblique dextral southwest-side-up displacement im- D * peded the Hororata River channel (dashed white), leading to partial avulsion and widespread fl ooding. Block arrows show origi- nal fl ow direction. Large shed is 20 m long. (B) View to the southeast from the avulsion node showing scarp-parallel fl ooding and escape fl ow across the scarp via a pre- Selwyn River existing channel on the alluvial plain. Loca- CA tion/orientation of photo is indicated on A. D (C) Long view north showing the split of Escape the fl ooding due to southward escape from * flow U the scarp-directed fl ow. (D) View northeast across the scarp, showing relationship of fl ooding to dextral and vertical deformation of previously straight fence line (location indicated by white arrows). Location/orienta- C D tion of photo is indicated on photo in B.

422 Geological Society of America Bulletin, March/April 2013 Fault interactions at a releasing bend

After the Darfi eld earthquake, we re-occu- established by NZAM at Ashburton (Fig. 1A), river fl ow was high and relatively turbid, re- pied 13 of the cadastral survey marks lying and positional and vertical accuracy was verifi ed sulting from the expulsion of large volumes within 200–700 m of the West segment rupture by an independent commercial survey. Verti- of groundwater as a result of the earthquake. trace (Table 2). The ground-surface positions cal accuracy for ground returns in the Selwyn Within 2 km of the fault trace, the unconfi ned of two boundary pegs (NWB and SWB; Fig. 2) area was 0.07 m (1σ) across fi ve sites (Table 1). groundwater table rose by several tens of meters were established in the IGS05 reference frame NZAM checked the positional accuracy using (Cox et al., 2012), producing widespread un- by a 24-h-mode GPS survey on 14–15 April surveyed positions of vertical discontinuities controlled artesian fl ows from bores and from 2011, 7 months after the Darfi eld earthquake. such as bridges and walls and found it to be a earthquake-induced ground fi ssures. During Both marks lie northeast of the surface rupture, good fi t. The LiDAR data were supplied for this fi eld mapping, we observed numerous examples so a correction was applied to remove the ef- project as a 1 m pixel raster. of fi ssures, surrounded by localized deposits of fects of postseismic deformation, based on Postearthquake LiDAR was flown along sand and fi ne-gravel ejecta, which attest to the trends observed during repeat observations of the general line of the Greendale fault on force of the groundwater expulsion. nearby fi rst-order benchmarks a few kilome- 10 September 2010 at 600 m above ground, The newly formed scarp directed part of the ters north of the fault (Beavan et al., 2012). with a fi eld of view of 38°, but it did not en- Hororata River fl ow to the southeast (Fig. 2), The corrected observations were converted to compass the West segment because it had not, parallel to and generally within 100 m of the NZGD2000, then to the NZGD2000 Mount at that time, been delineated by mapping. This scarp (Fig. 3). Fortunately, the avulsion fl ooding Pleasant Circuit coordinate system, and then LiDAR survey was brought into terms of the was identifi ed from the air and recorded photo- fi nally to New Zealand Map Grid (NZMG), postearthquake geodetic reference system graphically within 12 h of the rupture, because replicating transformations applied to the pre- using a control site established by GNS Sci- the landowners moved rapidly to remediate the earthquake cadastral survey. Taking account ence. Vertical accuracy of ground returns was fl ooding by deepening the bed of the Hororata of the various error sources, the accuracy of determined using the GNS control site and River across the scarp. Documentation of the ground-surface displacements of these marks is adjusted to improve it from an average height onlap of avulsion fl oodwater along the scarp likely to be ±5 cm (John Beavan, 2011, GNS difference of ±0.03 m to 0.00 m (Table 1). was instrumental in defi ning the location of the Science, personal commun.; Table 1). Positional accuracy was checked by overlay- West segment, and guiding the fi eld mapping We resurveyed the cadastral marks using ing GNS Science survey data over LiDAR of displacements (Fig. 3D). Mapping of the a Trimble 5600 semirobotic total station and data, and a good fi t was observed. Postearth- distribution of fl oodwaters from georeferenced reduced the data using Trimble’s Terramodel quake LiDAR data were supplied for this proj- oblique aerial photographs revealed subtle fea- 10.41 survey software. We georeferenced the ect as a 0.5 m pixel raster. tures such as slight strike changes and the pres- total station survey by assigning the GPS survey Overlapping pre-earthquake LiDAR was ence of a small left stepover (Fig. 2). coordinates to pegs NWB and SWB. Pre- and subtracted from the postearthquake LiDAR, postearthquake surveys were combined in a and the difference was mapped at 1 m cell size, Kinematics of the West Segment of single AutoCAD drawing, and point displace- the resolution of the pre-earthquake LiDAR the Greendale Fault ments were measured in terms of azimuth and raster (Fig. 5). Subpixel correlation of the pre- horizontal (Table 2) and vertical components and postearthquake LiDAR rasters was carried Barrell et al. (2011) and Quigley et al. (2012) (Table 3; Figs. 2 and 4). out using COSI-Corr to determine horizontal reported that much of the dextral displacement, offsets (Leprince et al., 2007a, 2007b; Konca especially on the East segment, was accommo- LiDAR et al., 2010). dated by horizontal fl exure that was mappable only with reference to previously linear features. Aerial LiDAR surveys provide high-resolu- DEFORMATION AND KINEMATICS The West segment scarp was rounded rather tion topographic data using the two-way travel- OF SURFACE RUPTURE than sharp, and involved displacement of the time of laser pulses. Such data sets are used to order of 1 m, distributed over a zone typically image fault scarps in a variety of environments Coseismic Scarp Development and Avulsion ~20 m wide (Fig. 3D). No free faces were ob- (Hudnut et al., 2002; Muller and Harding, served on the West segment, which suggests that 2007). In this study, we documented the vertical As a result of the earthquake, the West seg- ground-surface deformation was an oblique- motions associated with uplift and subsidence in ment of the Greendale fault formed a coseismic dextral monoclinal fl exure of near-surface grav- the Waterford releasing bend area by differenc- scarp across a meander bend in the Hororata elly sediments above the fault plane (Fig. 4). ing pre- and postearthquake LiDAR data where River (Figs. 2 and 3A). The scarp impeded Cadastral survey marks show a distinct pat- they overlapped (see Fig. 2). This technique downstream fl ow and partly avulsed the Horo- tern of displacement relative to the West seg- has been widely applied in a diverse range of rata River onto an older, higher surface. The ment of the fault. On each side of the fault, the earth science disciplines, including volcanology (Marsella et al., 2009) and glaciology, and has recently been applied to fault surface rupture TABLE 1. ESTIMATED ACCURACY OF DATA USED IN DETERMINATION OF SURFACE DISPLACEMENTS Horizontal (m) Vertical (m) (Oskin et al., 2012). Lyttelton (1937) Two LiDAR data sets were collected in 2010 Survey IGS05 Relative in NZGeoid05 Relative using NZ Aerial Mapping’s (NZAM) Optech Pre-earthquake cadastral ±0.05 ±0.02 NA ±0.02 ALTM 3100EA LiDAR system with system PRF Postearthquake GPS ±0.05 0 Postearthquake cadastral * 0 < 0.16 NA ±0.15 set to 70 KHz. Pre-earthquake LiDAR was fl own Pre-earthquake light detection and ranging (LiDAR) <0.1† 0.07 in late March 2010 at 1300 m above ground with Postearthquake LiDAR <0.1† 0 a 40° fi eld of view. The pre-earthquake survey *Sum of postearthquake global positioning system (GPS) and error ellipse dimensions from Table 2. † was controlled using a geodetic reference mark Based on COSI-Corr results.

Geological Society of America Bulletin, March/April 2013 423 Duffy et al.

marks showed only small amounts of vertical movement relative to one another (average of ~0.12 m), but the marks on one side of the fault shifted substantially and consistently relative to those on the other side (Table 3). On the northeast side of the fault, marks were downthrown by an

s average of 1.48 m (maximum 1.6 m) relative to t f i

h OIT11, the survey mark on the southwest side of S the fault closest to the fault trace (Fig. 2; Table 3). The northeast side of the fault moved horizontally an average of 1.45 m toward 137° (maximum 1.59 m toward 131.5°) (Fig. 2; Table 2); these vectors are approximately parallel to the strike of the fault. The southwest side of the fault 0.993 –1.060 0.076 1.454 0.120 136.999 0.074 11.770 0.108 0.015 0.076 3.035 –0.505 –0.272 0.584 242.095 moved horizontally an average of 0.58 m toward 242° (maximum 0.67 m toward 248.5°); these vectors are approximately perpendicular to and away from the fault trace, and thus perpendicular e k

a to displacement on the downthrown side. These u q h

t observations indicate that the West segment fault r a

e is extensional and may therefore be robustly in- t s

o ferred to dip toward the northeast. are grouped to show marks on the hanging wall (direction E) ordered from north P The ﬂ exural nature of the scarp means that ; OPEG—old peg; SWB—SW boundary peg. the West segment fault plane is not exposed, so we used the cadastral survey displacements to estimate the fault-plane attitude and the orientation and magnitude of the net slip on the fault (Fig. 4). The fault scarp through most of the e

k cadastral survey area strikes 138°. The horizon- a u

q tal displacements of the upthrown and down- h t r

a thrown sides were applied in their displacement e -

e directions and yielded an average horizontal r P component of net slip of 1.7 m toward 117.7° (maximum of 1.99 m toward 114°). Adding the 2432116.744 5735410.867 2432116.185 5735410.675 –0.560 –0.192 0.591 251.099 2432579.007 5736523.240 2432580.008 5736522.193 1.000 –1.047 1.448 136.307 2433753.819 5735597.614 2433755.013 5735596.558 1.194 –1.056 1.594 131.499 2432259.755 5736862.809 2432260.741 5736861.735 0.986 –1.074 1.458 137.433 2432779.314 5736217.303 2432780.285 5736216.250 0.971 –1.053 1.433 137.337 2432054.014 5735579.074 2432053.522 5735578.894 –0.493 –0.180 0.525 249.980 2433027.352 5734858.853 2433026.901 5734858.433 –0.451 –0.421 0.616 226.973 2432020.894 5735552.382 2432020.3702433036.960 5735552.204 5734832.804 –0.524 2433036.502 –0.178 5734832.378 0.554 –0.457 –0.426 251.225 0.625 227.037 2432097.694 5735401.008 2432097.075 5735400.764 –0.619 –0.245 0.665 248.416 2432121.319 5735543.383 2432120.900 5735543.212 –0.418 –0.171 0.452 247.822 vertical displacement between the southwest and northeast sides of the fault to the horizon- ″ ″ ″ ″ ″ ″ ″ ″ ″ ″ ″ tal slip returns an average net slip of 2.25 m 18 45 18 38 41 56 16 07 52 44 ′ ′ ′ ′ ′ ′ ′ ′ ′ 50 ′ ′ (maximum 2.55 m) (Fig. 4) on a fault dipping ~68° to the northeast (63° using maximum slip 64°42 alues are in meters, except azimuth, which is degrees. Data 308°57 308°57 310°49 319°58 316°33 320°49 values). For both average and maximum calcu- lations, the net slip rakes 45° from the south, which yields a transtensional dip-slip to strike- TABLE 2. WATERFORD FARM TRILATERATION NETWORK LOCATIONS AND SHIFTs NETWORK LOCATIONS TRILATERATION FARM 2. WATERFORD TABLE 9 0 4 0 1 6 6 5 6 5 1 3 3 2 2 1 4 1 2 2 slip ratio of 1:1. 0 0 0 0 0 0 0 0 0 0 ...... s 0 0 0 0 0 0 0 0 0 0 e s p i l l Kinematics of the Waterford e r o

r Releasing Bend r E Differencing of the two 2010 LiDAR surveys reveals the displacement patterns across the 4 2 4 4 0 8 5 1 5 9 7 4 2 0 7 6 2 0 1 1 Waterford releasing bend between the West and 1 1 0 1 0 0 1 1 1 1 ...... 0 0 0 0 0 0 0 0 0 0 Central segments (Fig. 5A). The difference map has negative elevation values for subsidence and positive values for uplift. We note that vertical differences can arise from horizontal as well as vertical displacement of topographic features (e.g., Mukoyama, 2011; Oskin et al., 2012). Within Figure 5A, bright vertical anomalies 8 7 1 1 Coordinates are in New Zealand Map Grid coordinate system. All v Coordinates are in New Zealand Map Grid coordinate system. 4 4 4 denote horizontal displacement of the margins 1 7 4 8 1 B G G G 2 2 2 1 9 5 of streams and abandoned channels, as well as E E E G deviation footwall deviation hanging wall T T T T T T Note: I I P I I P P I I E σ σ SWB Fixed with GPS survey 0.000 0.000 2432664.006 5736120.018 2432664.882 5736118.971 0.875 –1.047 1.365 140.112 P to south, followed by marks on the footwall (direction SW), also ordered north south. OIT—old iron tube; NWB—NW boundary peg O Average footwall Average 1 Hanging wall O NWB Fixed with GPS survey 0.000 0.000 2432144.186 5736738.788 2432145.117 5736737.705 0.931 –1.083 1.428 139.308 O 310°07 O O 14°01 O 311°26 OLD POST 0.163 0.045 14°29 Average hanging wall Average 1 Point ID Major axis (m) axis (m) Minor Azimuth Easting Northing Easting Northing Easting Northing Magnitude Azimuth Footwall O O O braid channels of the Selwyn River that have

424 Geological Society of America Bulletin, March/April 2013 Fault interactions at a releasing bend

TABLE 3. RELATIVE ELEVATION CHANGE MATRIX FOR CADASTRAL MARKS Height adjustments OIT28 OIT27 OPEG 48 PEG B11 OPEG 47 OIT 5 OIT 11 OIT 9 OPEG 41 OIT 24 OIT28 Open 0 0.2156 0.1065 0.0819 –1.131 –0.9837 –1.3831 –1.2316 –1.0466 –1.1746 OIT27 0.173 0 –0.1091 –0.1337 –1.3466 –1.1993 –1.5987 –1.4472 –1.2622 –1.3902 OPEG 48 0 0 –0.0246 –1.2375 –1.0902 –1.4896 –1.3381 –1.1531 –1.2811 PEG B11 0.119 Hanging wall 0 –1.2129 –1.0656 –1.465 –1.3135 –1.1285 –1.2565 OPEG 47 0.071 0 0.1473 –0.2521 –0.1006 0.0844 –0.0436 OIT 5 0.113 0 –0.3994 –0.2479 –0.0629 –0.1909 OIT 11 0.102 0 0.1515 0.3365 0.2085 OIT 9 0.113 0 0.185 0.057 OPEG 41 0.113 0 –0.128 OIT 24 0.173 Footwall 0 Note: Negative values indicate that the mark listed in the row has subsided relative to the mark listed in the column. OIT—old iron tube; OPEG—old peg. migrated during the interval between the sur- segment, across a restraining bulge defi ned by Although fault-slip planes were not exposed veys. However, due to the subdued topography uplift contours, is the CS1 structure. The south- on the Central segment of the Greendale fault, within the study area, this latter effect is insig- eastern 300–400 m section of the CS1 structure the displacement of the northeast side of the nifi cant compared with tectonic displacements. strikes 120°, but westward, near the edge of the West segment toward the Central segment of the The differential elevation map (Fig. 5A) difference map area, it curves back to an east- Greendale fault (Fig. 2), coupled with consistent, shows that land to the south and west of the west strike. The vertical expression of the CS1 although slight, uplift to the south of the trace Water ford releasing bend was uplifted by structure constitutes a broad (~200 m wide) of the Central segment, implies that the Central amounts ranging from 0.4 m to 1.0 m. Land warp that is ~0.7 m high (profi le 2, Fig. 5B). segment has a southward dip and a minor com- north and east of the Waterford releasing bend Dextral displacement on CS1 was recorded by ponent of reverse slip. This is in keeping with subsided by between ~0.4 and 0.8 m. Both sub- Quigley et al. (2012), but vertical displacement geodetic modeling by Beavan et al. (Beavan sidence and uplift contributed to the physical on CS1, and its left-stepping relationship to the et al., 2010b, 2012). Similarly, the minor struc- expression of scarps on either side of the Water- Central segment, was only determined from the ture CS2 is compressional and uplifted to the ford releasing bend (Fig. 5B). Maximum sub- LiDAR data, because the broad, subtle, warping east, suggesting a component of eastward dip. sidence is recorded in a half graben developed was not visible in the fi eld. About 500 m farther Together CS1 and CS2 appear to defi ne a posi- on the downthrown side of the West segment, west, there is the north-northwest–striking CS2 tive fl ower structure. which subsided by at least 0.8 m. However, structure, which lies approximately subparallel Apart from the defi nition of CS2, pixel cor- profi le 1 (Fig. 5B), located 2 km east of the to the Selwyn River. CS2 was not detected in the relation in this study is generally noisy due to Waterford releasing bend, also records 0.4 m of fi eld. Although the vertical anomaly associated limited extent of the data and few suitable cor- net subsidence. The wide extent of subsidence with the CS2 structure is somewhat ambiguous relation points. Any north-south strike slip on northeast of the Waterford releasing bend is in (Fig. 5A), it is clearly revealed by horizontal CS2 is lost within this noise and is thus negli- keeping with east-west dilation on the West subpixel correlation of pre- and postearthquake gible compared with the east-west dip slip. The segment due to the dextral slip on the Central LiDAR rasters (Fig. 5C). Stacked horizontal dis- lack of COSI-Corr evidence for north-south dis- segment. Maximum uplift (~1 m) occurred on placement profi les across CS2 reveal east-west placements comparable with vertical displace- the south side of the Central segment, east of shortening of ~0.8 m (Fig. 5D), due to ~0.6 m ments at the releasing bend suggests that the the Waterford releasing bend (Fig. 5A), while of westward motion east of CS2 and ~0.2 m of dip of the Central segment is very steep. CS2 ~0.4 m of uplift occurred on the southwest side eastward motion between CS2 and the West seg- is almost perpendicular to the Central segment, of the West segment (profi le 3, Fig. 5B). ment. The 0.2 m of eastward motion occurred on which means that horizontal convergence across The vertical displacements revealed by the northeast side of the West segment. CS2 must have been fed by strike slip on the LiDAR difference mapping of the Waterford releasing bend clearly defi ne the strike of the fault and highlight subtle structures that are not other- Figure 4. Diagrammatic sketch Gentle strike slip Fenceline wise discernible. Most strikingly, LiDAR-deter- showing the results of cadastral flexure of fence piercing mined displacements highlight the overlapping resurveying and the derivation points of net slip across the West seg- U nature of the West and Central segments of the v SW side ment scarp from the survey surveyed Greendale fault across the Waterford releasing e d vector id h D ye s data. U and D denote relative e r bend. The Greendale fault does not simply curve rv to NE u c s e into a releasing bend, but rather transitions via at upthrow and downthrow across v the scarp. The surface “scarp” least two smaller-scale restraining left steps that SW Su are nested within the overall releasing bend. We is a monoclinal flexure of the 45°rake rvey 68° fa vertic ed ult d d al refer to this nested stepover region, which spans gravel above the fault plane ip ispla cem ~800 m, as the “restraining stepover” (Fig. 5A). and is typically at least 20 m Net slipm ents The left-stepping minor structures making wide (see Figs. 3 and 5B). The 2.25 up the restraining stepover are identifi ed here total width of the strike-slip NE as CS1 and CS2 (Fig. 5A). The western end defor mation zone may range Not to scale of the Central segment strikes 098° and has a up to several hundred meters well-defi ned surface scarp ~50 m wide (pro- (see, for example, Villamor et al., 2012). The cadastral survey provides a broader perspec- fi le 1, Fig. 5B). About 200 m beyond the west- tive on total displacement and does not depend on long straight linear features (e.g., fence ern limit of surface deformation on the Central lines) spanning the full width of the deformation zone.

Geological Society of America Bulletin, March/April 2013 425 Duffy et al.

west segment 0.8 half graben A Selwyn River D D central segment –0.4 CS2 U

CS1 1 0 3 D 2 .4 WRB U e 0.2 e l e i l l i f i f o f r U o restrainingstepover o r P r

P P Increase to 0 500 1,000 m max 1.0 m uplift

) +1.1 +0.8 Δ elev (m) 3 +0.5 1 –0.9 0 2 Vertical Vertical and dextral –0.5 –0.8 East 0100 200 300 400 0100 200 300 400 Elevation change (m E-W motion B Distance along profile (m) West

C west segment central segment –0.4 CS2 0–0.2 m 0.4–0.6 m CS1 0.4 WRB 0.2

0 500 1,000 m fault D +0.4 0–0.2 m eastwards

0 0.4–0.6 m westward –0.4 0.6–0.8 m convergence –200 –100 0 100 200

Easting change(m) Position (east of discontinuity in m)

Figure 5. Results of light detection and ranging (LiDAR) differencing. U and D denote relative upthrow and downthrow across the scarp. (A) Post-minus-pre-earthquake LiDAR elevation difference map. White lines are simplifi ed uplift contours (negative values for subsidence). Heavy dashed black lines are faults. Note half-graben development west of the Selwyn River. Selwyn River passes through the surface rupture at a local uplift minimum on the Waterford releasing bend (WRB). (B) Same-scale topographic profi les of fault scarps of the Central segment (CS) (1, 2) and fault scarp of the West segment (3). Gray background indicates net subsidence. For location, see A. Central segment scarps (particularly profi le 2) are smaller and more diffuse than the clear scarp on the West segment (profi le 3). (C) COSI-Corr subpixel correlation of LiDAR difference model, showing the CS2 structure, along with uplift contours from panel A. The rectangle area was sampled to produce a stacked plot of east-west horizontal displacement (D) that demonstrates 0.6–0.8 m of convergence across the CS2 structure. The gray band denotes the CS2 structure, and the dotted lines represent the mean displacement trends.

Central segment, particularly on CS1. The east- displacement of CS1 at profi le 2, we calculate a than the strike of the fault in the cadastral survey west convergence of 0.8 m across CS2 therefore minimum net slip of 1.1–1.2 m on CS1. Again, area. The scarp of the West segment, which is provides a minimum measure of the strike slip this is compatible with RTK measurements but clearly defi ned in the northern part of the differ- on CS1, which is compatible with the minimum includes considerably less uncertainty regarding ence map (profi le 3, Fig. 5B), dies out toward 1.0 ± 0.25 m measured in the fi eld by Quigley the vertical component of displacement. the southeast, ~500 m south of the western end et al. (2012) using RTK. By adding a 0.8–1.0 m In the LiDAR overlap area, the West segment of the Central segment. The Waterford releasing horizontal displacement to the 0.7 m vertical strikes ~122°, which is slightly more westerly bend between the West and Central segments is

426 Geological Society of America Bulletin, March/April 2013 Fault interactions at a releasing bend

a transtensional right bend with respect to strike wall is calculated from pixel correlation at the the Waterford releasing bend, within our study slip on the Central segment (Fig. 6A[i]), but a restraining stepover to the Central segment area, the scarp on both segments is well defi ned contractional left bend with respect to strike slip (Fig. 5D). Strike-slip displacements increase (≤50 m wide; Fig. 5B, profi les 1 and 3). Closer on the West segment (Fig. 6A[ii]). The east-west east of Waterford releasing bend. A single es- to the Waterford releasing bend, the scarp be- shortening on segment CS2 effectively solves timate of 0.8 m of dextral displacement at the comes diffuse, and elevation change is distrib- the space problem created by transtension on location of profi le 2 (Fig. 5) is consistent with uted across 200–300 m (e.g., profi le 2, Figs. 5A the West segment extending south into the con- previously obtained at-fault displacement mea- and 5B). Between CS2 and the West segment, tractional fi eld of CS1 and the Central segment surements (Quigley et al., 2012). the uplift gradient declines to only around 0.2%, (Fig. 6B). The net vertical displacement also declines and no scarp is defi nable. The Selwyn River, in the area of the restraining stepover (Fig. 7B). either fortuitously or due to structural control Displacement Trends Relative vertical displacements in the cadastral (as inferred for the nearby Hawkins River by survey area range from 1.4 to 1.6 m. Within the Campbell et al., 2012), crosses the fault trace The combination of cadastral and LiDAR LiDAR map area, the vertical displacements on at this local minimum in vertical displacement mapping techniques clarifi es fault displace- the West segment immediately northwest of the (Figs. 5A and 7), and exhibits a reduction of its ment trends (Fig. 7). Strike-slip displacements restraining stepover totaled ~1.2 m, ~25% less bed gradient of only <0.1% over 600 m. The on the West segment increased slightly for than the 1.4–1.6 m vertical displacements across slight reduction in bed gradient, coupled with a 2.5 km southward from the northwestern end of the cadastral survey network. These data show 0.2% tilt toward the fault imposed by the half the surface scarp (Fig. 7A) and were generally a consistent reduction in vertical displacement graben, may increase the fl ood hazard in the consistent with, although as much as 25% larger south toward the Waterford releasing bend and vicin ity of the fault. than, the fi eld-survey displacement measure- its restraining stepover (Fig. 7B). This pattern of ments (Quigley et al., 2012). The discrepancy is decreasing displacement is associated with dy- DISCUSSION probably due in part to the lack of suitably long, ing out of a half graben that is highlighted by originally straight markers crossing this sector vertical displacement contours northwest of the The processes governing fault-rupture behav- of the fault zone, and in part to the survey marks Waterford releasing bend (Fig. 5A). ior at releasing bends are not well understood refl ecting the overall effects of larger displace- The 2.25 m of net slip calculated using our (Cunningham and Mann, 2007; Mann, 2007), ments at depth (e.g., Beavan et al., 2010b). cadastral-based vertical and strike-slip deter- in part because surface rupture at a fault bend Southeast of the cadastral survey area, strike- minations on the West segment is more than is commonly subtle and/or distributed (King slip displacements determined by LiDAR dif- double the 1 m of net slip estimated close to the and Nábělek, 1985; King, 1986; Devès et al., ferencing decline over a distance of 2.5 km, Waterford releasing bend at profi le 2 (Fig. 5A). 2011). Accurate, high-resolution documentation from 1.5 m to approximately zero at the The reduced displacement toward the Waterford of surface displacement provides an important Waterford releasing bend, where only 0.2 m releasing bend coincides with increasingly dif- piece of information on fault characteristics in of eastward horizontal motion of the hanging fuse and subtle scarp expression. Away from these zones. This study has illuminated the dis-

South side vector pulls away 1.2mto90° 1.13 from a mostly releasing right We XvY

bend mt st ZvX segment oward 1. Yv 7m Z to 1 297° 59° R F L CC C i Z CS1 L X Central segment ii Y North side vector converges on a WRB CS2 1.2 m dextral A restraining left step B restraining stepover (Quigley et al. 2012)

Figure 6. Structures contributing to the development of the Waterford releasing bend (WRB) area. (A) Sketch maps of the bend from the perspectives of surface displacement vectors on the south (i) and north sides of the fault (ii). L and R indicate left and right bends or steps. (B) The net result of combining the two sets of structures. CCF—location of subsurface tip of blind Charing Cross fault. The westward- directed south-side vector dilates the West segment. The minor left bend onto the overlapping southern tip of the West segment is accommodated by CS2. Convergence of the north-side vector with the Central segment is expressed by the nested restraining stepover onto CS1, and accommodated at a larger scale by underplating at the footwall of the CCF. (C) Vector calculation for relative horizontal displacement across the Charing Cross fault based on Equation 1, assuming a triple junction between the West and Central segments and the Charing Cross fault.

Geological Society of America Bulletin, March/April 2013 427 Duffy et al.

of strike-slip faults that cause local extension Quigley et al. (2012 - best) Quigley et al. (2012 - min) or contraction on continuously curved bound- Quigley et al. (2012 - max) This study (vert only) ing faults are typically referred to as releasing This study (dext & vert) and restraining bends, respectively. On the other hand, stepovers commonly transfer slip between

Cadastral y LiDAR d separate, subparallel, overlapping faults (e.g.,

2 t survey s survey s Christie-Blick and Biddle, 1985). The combi-

)

h t nation of investigation techniques shows that

( a the Waterford releasing bend, which appeared

D 1

n at ﬁ rst glance to be a simple curve in a single strike-slip fault (e.g., Sibson et al., 2011), marks a complicated transition from a steeply south- 0 dipping strike-slip fault (Central segment) to an 0 2500 5000 overlapping, northwest-dipping, dextral trans- A Distance SE along surface rupture (m) tensional fault (West segment) (Fig. 5). The transition incorporates elements of bend as well

y as stepover geometry.

d fault bend and

u t Compared with regional geodetic surveys 2 s Selwyn River

s i (Beavan et al., 2010b, 2012; Elliott et al., 2012),

)

t our data provide improved constraints on the dis-

( d placements that occurred within an area where

n D 1 the InSAR decorrelated and where there were few high-order trigonometric points for GPS surveys. The horizontal displacements and the net 0 slip estimates from the cadastral survey detailed 0 2500 5000 here are consistent with those of Beavan et al. B Distance SE along surface rupture (m) (2010b) in azimuth and magnitude, and the GPS horizontal displacements measured by Beavan Figure 7. Displacement trends on the West and Central segments for the cadastral part of this study are incorpo- in the vicinity of the Waterford releasing bend. (A) Dextral and rated in the model of Beavan et al. (2012). Our (B) vertical displacement plots for the bend area comparing data determination of net slip of 2.25 m is greater than of Quigley et al. (2012; fi eld mapping) and this study. Note the dis- the near-surface value of 1.5 m calculated by placement minimum at the Waterford releasing bend at distance Elliott et al. (2012) from InSAR but consistent 5000 m. LiDAR—light detection and ranging. with their modeled slip at 1–2 km depth. Our calculated movement vectors show that the south and southwest side of the Greendale placement interrelationships that arose across leasing bend are greater than Beavan et al.’s fault shifted westward as a coherent block. a releasing bend between the West and Central (2010b) values, in terms of both maximum Therefore, seen from the south side of the fault, segments of the Greendale fault during a single, uplift (0.4 compared to 0.1 m) and maximum the Waterford releasing bend is indeed a trans- surface-rupturing, multifault earthquake. The subsidence (0.8 compared to 0.6 m). The total tensional right bend (Fig. 6A[i]). However, the deformation at the Waterford releasing bend is vertical displacements in the cadastral survey southeastern 500 m section of the West segment particularly subtle. We have shown that fi eld- area along the West segment of the Greendale is in a contractional quadrant for the Central seg- based fault mapping was only able to identify fault are even greater but cannot be stated in ment. In this context, the east-west contraction the main scarps of the West and Central seg- terms of absolute uplift and subsidence. The across the CS2 component of the restraining ments, but no deformation was detected in the greater uplift and subsidence at the West seg- step over (Fig. 5D) accommodates this conver- releasing bend area. Furthermore, this area lay ment, compared with the far-fi eld values, sug- gence (Figs. 6A[i] and 6B). in an ~1.5-m-wide low-coherence zone in the gest that the footwall of the West segment is Movement vectors on the north and northeast differential InSAR data (Beavan et al., 2010b; a southwest-tilted uplifted block and that the side of the Greendale fault are toward the east- Elliott et al., 2012), and therefore the InSAR hanging wall is downwarped into a half graben southeast, parallel to the West segment, and thus could not quantify the nature of deformation close to fault. This is consistent with elastic re- movement of the north side of the West segment across the Waterford releasing bend. Because bound on a normal fault (Koseluk and Bischke, converged toward a restraining left step onto the the postearthquake LiDAR was fl own prior 1981) or with a near-surface steepening of fault Central segment (Fig. 6A[ii]). The restraining to mapping of the West segment, and thus did dip (Bray et al., 1994). step is nested in the overall releasing bend (Fig. not cover that segment, the mapping of fault- Surface displacement on the Greendale fault 6B) and is at least 800 m wide, similar to the induced avulsion fl ooding provided a useful reaches a minimum at the Waterford releasing width of the restraining stepover that separates asset that was instrumental in helping defi ne the bend, and increases either side of the bend. This the Central and East Greendale fault segments location and geometry of the West segment and is consistent with predictions of slip distribu- (Quigley et al., 2012). Waterford releasing bend. tion at the intersection of two separate, differ- Restraint of strike slip on the West segment The vertical displacements shown by LiDAR ently oriented, same-sense fault zones (King is one way of kinematically reconciling the re- on the West segment near the Waterford re- and Nábělek, 1985). Changes in the orientation straining stepover nested within the Waterford

428 Geological Society of America Bulletin, March/April 2013 Fault interactions at a releasing bend

releasing bend. However, the blind Charing cluding the stepover between the San Andreas tion of net slip on the West segment, which, at Cross fault, on which the rupture sequence ini- and Imperial faults (Ben-Zion et al., 2012). 2.25 m, is substantially higher than previously tiated, forms a triple junction with the Central Ben Zion et al. postulated that such structures estimated from piercing point measurements. and West segments and therefore may have had are likely locations of rupture segmentation. This displacement decreases to near zero at the a role to play in the coseismic geometric rela- Similar subtle structures developed in bedrock restraining stepover. The clear documentation tionships expressed in and around the Waterford during the Duzce earthquake at the Lake Eften and characterization of deformation and struc- releasing bend. For a triple junction to remain releasing double bend (Duman et al., 2005, ture at this releasing bend provide insight into stable, the relative motion vectors at the triple their Fig. 3), which formed an overlap segment subtle, but potentially important, structures and junction should sum to zero, such that that ruptured during both the Izmit and Duzce issues that may be present at bends on strike-slip earthquakes (Hartleb et al., 2002; Akyüz et al., faults elsewhere.

XVY + YVZ + ZVX = 0, (1) 2002; Konca et al., 2010). Dextral slip on the Totschunda fault during the Denali earthquake ACKNOWLEDGMENTS where XVY is the motion of block Y relative to (Eberhart-Phillips et al., 2003) would almost This study was funded by the Department of Geo- block X (Fig. 6C). The Charing Cross fault is certainly have created similar structures at the logical Sciences, University of Canterbury, and by blind, so the exact location of its intersection intersection with the Denali fault. However, the New Zealand Earthquake Commission (EQC). with the Central and West segments is unclear. the types of structures that we detected at the B. Duffy was supported by a New Zealand Tertiary However, the best available estimate is provided Waterford releasing bend, which are subtle but Education Commission Top Achiever Scholarship. S. Leprince was partly supported by the Keck Institute by the surface projection shown by Beavan fundamental surface expressions of fault kine- for Space Studies and by the Gordon and Betty Moore et al. (2012), lying just outside the differential matics, are commonly indiscernible at single Foundation. We thank J. Beavan for global position- LiDAR (see Fig. 2). Based on that location, rupture displacement scales and particularly ing system survey data, landowners for fi eld access, block Y, which lies south of the Central segment in alluvial settings. At the Waterford releasing N. Carson, J. Campbell, S. Hornblow, and A. Mackenzie for fi eld assistance, and Environment Canterbury for and southwest of the West segment (Fig. 6), bend on the Greendale fault, the observations LiDAR data. We are grateful to Timothy Little, Paul moved 1.2 m west relative to the southeastern of subtle deformation and the location of the Mann, John Walsh, James Dolan, and Richard Norris side (hanging wall) of the Charing Cross fault nested restraining stepover in an active alluvial for thoughtful reviews that greatly improved the (block X on Fig. 6) (Quigley et al., 2012), and setting suggest that the preservation of these manuscript. ~1.7 m northwest relative to block Z, which is specific structures will be short-lived in the REFERENCES CITED the footwall of the Charing Cross fault (and also local geologic-geomorphic record. Neverthe- the hanging wall of the West segment). 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