Surface cracks record long-term seismic segmentation of the Andean margin

Understanding the long-term patterns of great earthquake rupture along a subduction zone provides a framework for assessing modern seismic hazard. However, evidence that can be used to infer the size and location of past earthquakes is typically erased by erosion after a few thousand years. Meter-scale cracks that cut the surface of coastal areas in northern Chile and southern Peru preserve a record of earthquakes spanning several hundred thousand years owing to the hyperarid climate of the region. These cracks have been observed to form during and/or shortly after strong subduction earthquakes, are preserved for long time periods throughout the Atacama Desert, demonstrate evidence for multiple episodes of reactivation, and show changes in orientation over spatial scales similar to the size of earthquake segments. Our observations and models show that crack orientations are consistent with dynamic and static stress fi elds generated by recent earthquakes. While localized structural and topographic processes infl uence some cracks, the strong preferred orientation over large regions indicates that cracks are primarily formed by plate boundary–scale stresses, namely repeated earthquakes. We invert the crack-based strain data for slip along the well-known Iquique seismic gap segment of the margin and fi nd consistency with gravity anomaly–based inferences of long-term earthquake slip patterns, as well as the magnitude and location of the November 2007 Tocopilla earthquake. We suggest that the meter-scale cracks can be used to map characteristic earthquake rupture segments that persist over many seismic cycles, which encourages future study of cracks and other small-scale structures to better constrain the persistence of asperities in other arid, tectonically active regions.


INTRODUCTION
The characteristic earthquake model of seismic recurrence suggests that a given fault segment ruptures repeatedly in earthquakes of similar magnitude and areal extent (Schwartz and Coppersmith, 1984).While some historical (Comte and Pardo, 1991) and paleoseismic (Sieh, 1996) records support this model, it is unclear whether these seismic segments are truly long-lived, because geologic indicators of distinct earthquakes usually persist for only a few k.y.(up to ~10 events).To assess the longevity of the segmented nature of seismicity, we require data that reflect deformation caused by 100s to 1000s of repeated earthquakes.
Arrays of meter-scale surface cracks that penetrate coastal regions of the northern Chile and southern Peru forearc provide insight into the long-term nature of great earthquakes (magnitude 8 and larger) along the plate boundary.We use 2.5-m resolution satellite imagery available in Google Earth to map concentrations of cracks throughout the Andean forearc between 17.5º and 23.5ºS (Fig. 1); examination of regions outside these latitudinal bounds yields only sparse examples of cracking, likely due to slightly wetter climatic conditions (Ewing et al., 2006) and presence of unconsolidated sediment (Rech et al., 2003), both of which inhibit crack preservation.We complement the remote sensing with field observations at several localities (Loveless, 2008;Loveless et al., 2005) and, because cracks throughout the study area are morphologically similar, we generalize our field results to regions we have not visited.In general, crack clusters show preferred orientations that vary on spatial scales similar to great earthquake rupture areas.Between 19º and 23ºS, which mark the estimated latitudinal bounds of the great 1877 Iquique earthquake (Comte and Pardo, 1991), mean length-weighted crack strike rotates from NW to NNE.At several localities including east of the Mejillones Peninsula (23ºS), there are populations of cracks showing a bimodal distribution in strike, with one set striking NE and the other NW (Fig. 1).Cracks near Ilo, Peru strike at a high angle to the coastline and plate boundary, approximately parallel to the direction of plate convergence.
Hyperaridity in the region, which has persisted for at least the last 6 M.y.(Hartley and Chong, 2002), if not since before 16-18 Ma (Dunai et al., 2005;Rech et al., 2006), allows for long-term preservation of the cracks.The gypsum-indurated soil that covers much of the coastal region between elevations of 300 and 1200 m (Rech et al., 2003) provides a durable surface crust that further enhances crack preservation.Our field observations reveal crack apertures ranging from 10s of cm to more than 1 m; these cracks can be mapped using the imagery, but we cannot comprehensively define their apertures.Although many cracks are preserved in the gypsum-indurated crust (Fig. 1, inset), there are numerous fissures penetrating up to 12 m into bedrock.We interpret the numerous layers of gypsum plated vertically onto crack walls as indication of repeated episodes of sealing and reopening.The rate of gypsum accumulation is unknown, limiting the information that it can provide about the age of cracks.However, based on cosmogenic dating of the geomorphic surfaces into which the cracks cut and morphologically similar neotectonic structures (González et al., 2006), we propose that the cracks represent deformation as old as several hundred k.y., encompassing 1000s of ~100 yr interplate earthquake cycles (Loveless et al., 2005).
Local structural, topographic, and/or geomorphic effects and stresses related to earthquakes within the subducting slab (Marquardt et al., 2006) influence formation of some cracks.In particular, some cracks strike parallel to crustal faults (González et al., 2008) and drainages (Keefer and Moseley, 2004), indicating that pre-existing linear features can affect crack strike.However, the large scale patterns of strike change (Fig. 1) and the fact that cracks were generated by the 1995 M w 8.1 Antofagasta, Chile (González and Carrizo, 2003) and 2001 M w 8.5 Arequipa, Peru events (Keefer and Moseley, 2004) indicate that interplate earthquakes are the principal driver of formation.
Mode 1 cracks -which, based on the paucity of observed lateral offset, we infer most cracks to be (Loveless et al., 2005) -open in the direction of least compressional principal stress (σ 3 ) and therefore strike parallel to the most compressional direction (σ 1 ) (Pollard and Segall, 1987).By constructing a regional map of crack strikes, we effectively map the orientations of the principal stress axes responsible for their formation.The stress field produced by a subduction zone earthquake varies as a function of the slip distribution on the fault, with σ 1 axes varying from nearly parallel to the fault slip vector around the center of the rupture zone to oblique to the slip direction near the rupture terminations (Fig. 2).

MODELING COSEISMIC STRESS FIELDS
In order to explore the relationships between the mode 1 surface cracks and plate boundary earthquakes, we calculate the coseismic principal deviatoric stress fields related to great earthquakes on four segments of the Andean margin: the 2001 Arequipa, 1868 M~8.5 southern Peru, 1877 M~8.5 Iquique, Chile, and 1995 Antofagasta events (rupture areas shown in Figure 1; Detailed discussion appears in data repository 1 ).We use published solutions for slip distributions of the 1995 (Pritchard et al., 2006) and 2001 (Pritchard et al., 2007) events and approximations of the historical earthquake slip patterns (Comte and Pardo, 1991).Figs.DR1-DR4 illustrate the relationships between the forward models of coseismic static stress fields and the permanent strain demonstrated by the surface cracks.
In general, there is good agreement between the observed mean strikes of cracks and the orientation of modeled σ 1 axes.In the case of the bimodal strike crack populations east of the Mejillones Peninsula, we find that the NW striking cracks are Publisher: GSA consistent with the NE-SW directed σ 3 axes induced by events on the Antofagasta segment (Fig. DR1), while the NE striking cracks are opened by the NW-SE trending σ 3 axes related to seismicity on the Iquique segment (Fig. DR2).Similarly, the bimodal crack clusters in northernmost Chile are affected by stress related to earthquakes on the Iquique and southern Peru segments of the margin (Figs.DR2, DR3).
The rotation of mean crack strike from NNE to NW from south to north along the length of the Iquique segment (Fig. 1) agrees with the stress field predicted by the forward models (Figs. 2, DR2).The cracks mapped near the city of Ilo, Peru lie near the center of the estimated rupture zone of the 1868 earthquake and strike nearly perpendicular to the σ 1 orientation predicted by the 1868 model, indicating that these cracks are minimally affected by the static stress caused by earthquakes on this segment, on which the great 1604 earthquake also occurred (Comte and Pardo, 1991).The mapped cracks are suggested to have formed either during or shortly after the 2001 Arequipa earthquake (Keefer and Moseley, 2004).En echelon map patterns of these cracks suggest accommodation of WSW-directed left-lateral shear in addition to opening, consistent with the kinematics reported for nearby faults (Audin et al., 2008).This indicates that the cracks near Ilo are mixed-mode (1 and 2) and thus we expect that σ 1 for the stress field that created them should be oblique to the crack strike as predicted by our model of the 2001 event (Fig. DR4).

INVERTING CRACK DATA FOR PALEOSEISMIC SLIP
Studies of historical seismicity have relied on qualitative written records of sustained damage (Comte and Pardo, 1991) to estimate event magnitude and location.
Given the agreement between predicted stress fields and observed crack strikes, we propose that cracks can provide quantitative constraints on the slip distribution of paleoearthquakes.Because the inferred rupture limit of the 1877 earthquake encompasses 16 of the 17 cracked regions, we use the cracks to invert for plausible slip distributions related to that event, or a sum of events occurring on the segment.In doing so, we make the assumption that cracks used to constrain the slip pattern open exclusively due to coseismic stress earthquakes on this segment, plus a contribution from regional stress (see text in data repository).
The mean residual magnitude between the observed crack strikes and those predicted by our preferred inversion is 8.2º (Fig. 3).While the solution for coseismic slip is non-unique (see text in data repository), several robust features are notable.The greatest resolved slip is concentrated ~35 km deep offshore Iquique (20.25ºS), consistent with the depth of maximum slip during the 1995 earthquake and ~1º north of the epicenter of the 1877 earthquake inferred from historical data (Comte and Pardo, 1991).
Smaller loci of moment release are located around 22.5ºS and 23.5ºS.The distance between slip patches suggests that they may represent separate earthquakes or widely spaced asperities that rupture during a single event.Because of the lack of temporal information contained in the data set, the crack-based strain field cannot distinguish a single earthquake with a heterogeneous slip distribution from several smaller events.
Based on aftershocks mapped by the United States Geological Survey, the November 2007 M w 7.7 Tocopilla earthquake ruptured the margin between ~22º and 23ºS (Fig. 3), indicating that it broke a portion of the plate boundary on which little Iquique event slip Publisher: GSA is predicted by the inversion.This suggests that much of the segment ruptures during truly great earthquakes such as that of 1877 but the portions remaining unbroken slip in smaller events.

DISCUSSION
Recent studies (Llenos and McGuire, 2007;Song and Simons, 2003;Wells et al., 2003) have found a correlation between negative forearc trench-parallel gravity anomalies (TPGA) and zones of large-magnitude slip during strong subduction zone earthquakes.We construct a TPGA (Sandwell and Smith, 1997;Song and Simons, 2003) field for the Iquique segment to compare with the slip distribution resolved from our inversion of the crack-based strain data (Fig. 3).The region in which resolved slip is greatest coincides with an area of strongly negative TPGA.The lack of resolved slip at shallow depths south of 21ºS and occurrence of the smaller Tocopilla earthquake near 22ºS are consistent with the prevalence of positive TPGA, which predicts slip of lower magnitude during the characteristic Iquique event.The forearc gravity field is not a transient property, thus both the gravity field and our inversion of geological data place constraints on long-term patterns of great earthquake slip.
In addition to the static stresses, dynamic stresses associated with the passage of seismic waves can also cause cracking of the surface (Dalguer et al., 2003).We calculate the temporal evolution of stress induced at the surface by the 1995 and 2001 earthquakes and find that stress axes calculated from static dislocation models are reasonably similar in orientation to the dynamic principal stresses (Fig. DR7).This indicates that our regional-scale mapping of cracks places constraints on the extent and distribution of slip associated with plate boundary earthquakes, regardless of whether static or dynamic stress is the primary driver of crack evolution.The method used to calculate dynamic stress (Cotton and Coutant, 1997) does not take into account changes in material properties such as the presence of existing faults and lithologic heterogeneity that may localize deformation.We suggest that dynamic stressing is responsible for the formation of the cracks near Antofagasta, which formed in poorly consolidated sediments parallel to a nearby NE-striking fault scarp during the 1995 event (González and Carrizo, 2003) and may have been impacted by the soil characteristics and fault structure.
We suggest that great earthquakes along the northern Chile and southern Peru margin repeatedly rupture areas several hundred km in length in quasi-characteristic earthquakes.If the location of segment boundaries varied substantially on hundred k.y.timescales, we would expect cracks to show a range of strikes rather than one or two preferred orientations, or a greater frequency of lateral offset.Historic records show that not all segments completely re-rupture in single earthquakes but may sometimes break in several smaller events (Kanamori and McNally, 1982).However, our models of earthquake slip and crack formation indicate that on a regional scale, the stress field is more sensitive to the extent of slip than details of its distribution (Fig. DR6).This suggests that earthquakes on a given segment of the plate boundary may vary in their slip distribution, but the accumulated strain exhibited by surface cracks implies that the dimensions and boundaries of characteristic earthquake rupture remain relatively constant.
Publisher: GSA The existence of long-lived earthquake segments has several implications.Knowledge of segment dimensions and boundary locations is important for determining earthquake recurrence intervals and thus assess seismic hazard.Numerous explanations for the segmented nature of subduction zone earthquakes have been proposed, including topographic features on the slab, interaction with upper plate faults (Audin et al., 2008), and changes in upper plate structure, and our suggestion that segments are long-lived and can be mapped by surface features will provide important constraints on these hypotheses.Finally, surface cracks have been observed to form coseismically in numerous tectonic settings, including along strike-slip faults on the Tibetan Plateau (Bhat et al., 2007) and in the Middle East (Fielding et al., 2005), and our work motivates largescale mapping of these features using high-resolution global imagery, such as that available in Google Earth, to determine whether long-lived seismic segmentation exists in these and other areas.that strike in a perpendicular direction, parallel to the σ 1 direction (black axes).Near the rupture terminations, cracks strike oblique to the earthquake slip vector.(Maerten et al., 2005) the strain field represented by the populations of surface cracks for slip on the subduction interface.The mean crack strike at each mapped locality is shown by a red bar and the calculated σ 1 orientation at the same location is indicated by a blue bar; the mean residual angle between the observed and predicted crack strike is 8.2º.The contours are overlain on the trench-parallel gravity anomaly (TPGA) constructed for the Iquique segment.The region of greatest resolved slip for the Iquique event coincides with strongly negative TPGA, consistent with recent studies (Llenos and McGuire, 2007;Song and Simons, 2003;Wells et al., 2003).The approximate rupture area of the November 2002 M w 7.7 Tocopilla earthquake is shown as the dashed rectangle, based on information from the United States Geological Survey.

Figure 2 .
Figure 2. Schematic relationship between subduction zone earthquake rupture area

Figure 3 .
Figure 3. Preferred inverse model of the 1877 Iquique earthquake, shown as 1 m interval