Earthquake source parameters for the January, 2010, Haiti mainshock and aftershock sequence

Transcription

1 Earthquake source parameters for the January, 2010, Haiti mainshock and aftershock sequence Meredith Nettles 1,2 and Vala Hjörleifsdóttir 1,3 1 Lamont-Doherty Earth Observatory of Columbia University 2 Department of Earth and Environmental Sciences, Columbia University 3 Now at Universidad Nacional Autónoma de México submitted to GJI May 27, 2010 Accepted - ; Received - ; in original form 2010 May 27 Abbreviated title: Haiti earthquake source parameters Corresponding author: Meredith Nettles tel: fax: nettles@ldeo.columbia.edu

2 1 Summary Previous analyses of geologic and geodetic data suggest that the obliquely compressive relative motion across the Caribbean North America plate boundary in Hispaniola is accommodated through strain partitioning between near-vertical transcurrent faults on land and low-angle thrust faults offshore. In the Dominican Republic, earthquake focal-mechanism geometries generally support this interpretation. Little information has been available about patterns of seismic strain release in Haiti, however, due to the small numbers of moderate-to-large earthquakes occurring in western Hispaniola during the modern instrumental era. Here, we analyze the damaging M W =7.0 earthquake that occurred near Port au Prince on January 12, 2010, and aftershocks occurring in the four months following this event, to obtain centroid moment-tensor (CMT) solutions for 50 earthquakes with magnitudes as small as M W =4.0. While the January 2010 mainshock exhibited primarily strike-slip motion on a steeply dipping nodal plane (strike=250, dip=71, rake=22 ), we find that nearly all of the aftershocks show reverse-faulting motion, typically on high-angle (30 45 ) nodal planes. Two small aftershocks (M W 4.2 and 4.6), located very close to the mainshock epicenter, show strike-slip faulting with geometries similar to the mainshock. One aftershock located off the south coast of Haiti shows low-angle thrust faulting. We also analyze earthquakes occurring in this region from and find evidence for both strike-slip and reverse faulting. The pattern of seismic strain release in southern Haiti thus indicates that partitioning of plate motion between transcurrent and reverse structures extends far west within Hispaniola. While we see limited evidence for low-angle underthrusting offshore, most reverse motion appears to occur on high-angle fault structures adjacent to the Enriquillo fault. Our results highlight the need to incorporate seismogenic slip on compressional structures into hazard assessments for southern Haiti. 24 Keywords: Earthquake source observations; Seismicity and tectonics; Caribbean tectonics 1

3 25 1 Introduction A large and destructive earthquake of M W 7.0 occurred on January 12, 2010, near the densely populated capital city of Haiti, Port au Prince. The earthquake occurred in a region of known, but poorly characterized, historical seismicity (e.g., Scherer, 1912), on the Enriquillo Plaintain Garden fault system. This system accommodates primarily transform motion between the Caribbean and North American plates (e.g., Mann et al., 1995). The overall relative plate motion is transpressional (e.g., Sykes et al., 1982; Deng & Sykes, 1995; Dixon et al., 1998; DeMets et al., 2000; Manaker et al., 2008), and many compressional geological features have been mapped in the region (Mann et al., 1995). However, the only mapped throughgoing fault structure near the source of the January 12 earthquake, the Enriquillo fault, exhibits primarily transcurrent motion, and is believed to dip nearly vertically (Mann et al., 1995, 2002). No earthquakes larger than M 5 have occurred in southern Haiti during the last 34 years, approximately the era of modern instrumental recording and the timespan ( ) covered by the Global Centroid Moment Tensor (GCMT) catalog (Ekström et al., 2005; Dziewonski et al., 1981). One earthquake in northern Haiti, on March 2, 1994, of M W 5.4, exhibits left-lateral strike-slip motion on a nodal plane striking east-southeast, consistent with the mapped geometry of the Septentrional fault associated with the northern part of the plate-boundary zone (Prentice et al., 1993; Mann et al., 1998). The most recent large earthquake on the island of Hispaniola, prior to the January 12, 2010, event, occurred on September 22, 2003, in the Dominican Republic, with moment magnitude M W 6.4. The focal mechanism for that event, as for all other earthquakes of M W 6.0 or larger occurring in the Dominican Republic and included in the GCMT catalog, shows thrust faulting. Paleoseismic investigations and historical reports make it clear that large earthquakes have occurred in Haiti previously (e.g., Scherer, 1912; Prentice et al., 1993). Recent studies using geological and geodetic data have also highlighted the potential for earthquakes of M on the Enriquillo and Septentrional faults (Calais et al., 2002; Manaker et al., 2008). Little is known, however, about the character of smaller, recent earthquakes in the Enriquillo fault region, or about 2

4 background seismicity rates, because of the absence of a local seismic network in Haiti. Following the great 2004 Sumatra Andaman earthquake and the large tsunami it generated, the United States Geological Survey (USGS) invested in a significant improvement to broadband seismological observing capabilities in the Caribbean, installing nine broadband seismometers in the region (network code CU), each with near-realtime telemetry capabilities. The combined network coverage provided by the CU and global-network stations, along with improvements to moment-tensor determination techniques (Arvidsson & Ekström, 1998; Ekström et al., 1998) now make analysis of smaller earthquakes possible. Knowledge of seismic strain-release patterns prior to and following the January 2010 mainshock is important for understanding how strain is accommodated throughout the region, and for understanding possible effects of static stress changes related to the mainshock and larger aftershocks. The minimum magnitude threshold for global CMT analysis is normally set at M 5, which would lead to GCMT analyses of fewer than a dozen events for the current Haiti sequence. Here, we present centroid moment-tensor solutions for 50 earthquakes of the 2010 Haiti mainshock aftershock sequence, including events with magnitudes as small as M W =4.0. We also present analyses of four earthquakes of magnitude occurring prior to the mainshock, during the years Data and methods We apply the centroid moment-tensor approach (Dziewonski et al., 1981; Dziewonski & Woodhouse, 1983; Ekström et al., 2005) to obtain moment tensors, centroid locations and centroid times for the January 12, 2010, Haiti mainshock and aftershock sequence. We attempt to analyze all earthquakes in the map region shown in Figure 1 reported by the USGS National Earthquake Information Center (NEIC) as of May 20, 2010, with preliminary magnitudes of 4.0 and larger for the four months following the mainshock (2010/01/ /05/12). In addition, we attempt to analyze all events reported in the USGS monthly listing with magnitude 4.0 or larger during the 3

5 period For larger events (approximately M W 5.0), we follow the standard procedures used for global CMT analysis (Ekström et al., 2005). These analyses incorporate long-period body waves in the period range s; mantle waves in the period range s; and intermediate-period surface waves in the period range s. The determination of source parameters for smaller events relies primarily on the intermediate-period surface waves; the surface-wave analysis is implemented as described by Arvidsson & Ekström (1998) and Ekström et al. (1998). For some events, we adjust the filter towards shorter periods, which typically provide better signal-to-noise ratios for shallow earthquakes. Most such events are analyzed in the s band. For the smallest events, typically those of M W 4.5, the closest stations ( 15 ) are analyzed in the period range s. The filter is selected on a station-by-station basis in this case. We use data recorded at the stations of the GSN, Geoscope, Geofon, the Lamont-Doherty Cooperative Seismographic Network (LCSN), and the USGS Caribbean network (CU) for our analyses, as well as stations of the Abbreviated Seismic Research Observatory (ASRO) network for early events Analysis and Results We are able to obtain CMT solutions for 50 earthquakes of the January 12, 2010, sequence, and four events occurring prior to Focal mechanisms for these events are shown in Figure 1 and source parameters are presented in Supplementary Table 1. The source parameters can also be downloaded in electronic format from our website ( In the figures and table, we identify 14 of the events as having less-well constrained focal mechanisms. These are events with fewer usable data records, either due to small event size or the presence of large amplitude waveforms from earlier events. As can be seen in Figure 1, the results for these events are consistent with those for the best-constrained events. 4

6 The January 12, 2010, mainshock The source parameters obtained for the mainshock are similar to those for the quick CMT distributed within hours of the event. The refined solution has scalar moment M 0 = dynecm (M W =7.0). The presumed fault plane strikes 250 and dips 71 north-northwest. The slip angle of 22 indicates primarily left-lateral motion, with a moderate thrust component. The bestfitting moment tensor includes a non-double-couple component that is relatively large, with the intermediate eigenvalue 20% the size of the absolutely largest eigenvalue. The size of the nondouble-couple component is not well constrained, but is also consistent with a thrust contribution to the mainshock. The geometry of the focal mechanism obtained when the solution is required to represent a perfect double couple is very similar to the double-couple part of the unconstrained solution, with strike 252, dip 66, and rake 28. The mainshock focal mechanism, which corresponds to the best point-source representation of the earthquake geometry, is consistent with oblique slip on a single fault plane or, if the nondouble-couple component represents a source feature, nearly simultaneous slip on two separate fault planes experiencing left-lateral and reverse slip. To assess seismological constraints on the geometry of the mainshock fault or faults, we perform two analyses. First, we invert the waveforms used to determine the mainshock moment tensor for a CMT solution composed of two subsources to determine the geometry of the reverse mechanism that, paired with a near-vertical strike-slip fault, best explains the observed waveforms. One subsource is constrained to have a nodal plane oriented 250 with pure left-lateral slip and a dip of either 71 or 90, while the geometry of the second subsource is constrained to be a double couple, but otherwise left free. The retrieved geometry of the second subsource depends somewhat on the subsource time separation, but we find that a reverse-faulting subsource with a strike of , dip of 65, and scalar moment 30 40% that of the total moment, combined with a subsource of near-vertical dip and left-lateral slip, explains the data well. Second, we conduct an analysis of how well we are able to resolve the dip of the mainshock fault plane under the assumption that the fault slipped obliquely on a single planar fault. We 5

7 perform a series of inversions in a grid search over the source geometry. The strike is fixed to either 252 (for a north-dipping nodal plane) or 72 (for a south-dipping nodal plane), the rake is varied between 45 and +45 and the dip is varied between 55 and 90, in 5 increments, in an approach similar to that taken by Henry et al. (2000) for the Antarctic plate earthquake. The residual misfit between observed and synthetic waveforms is shown in Figure 2a. We find two minima in the misfit function, with the deeper minimum corresponding to the best-fit double-couple solution described earlier, with a north-dipping fault plane. The shallower minimum corresponds to a southdipping fault plane, with strike 72, dip 65 and rake 25. The residual variance is dominated by the contribution from the long-period mantle waves, and the difference in misfit for the northand south-dipping solutions is relatively small. However, the body waves for the south-dipping fault plane are fit poorly, especially at several stations in nodal directions. An example of the difference in waveform fits to the body waves for the north- and south-dipping fault planes is shown in Figure 2b. We conclude that the fault plane must indeed dip to the north, under the assumption that all of the slip occurred on a single planar fault The aftershock sequence The most surprising result of our CMT analysis is that nearly all of the aftershocks for which we are able to obtain solutions show reverse faulting (Fig. 1). Indeed, we find only two aftershocks, an M W 4.2 event on January 16 and an M W 4.6 event on February 23, both located very close to the mainshock hypocenter, that show dominantly strike-slip motion (Fig. 1). Most of the reverse-faulting events exhibit steeply dipping (30 45 ) nodal planes, though a few have one nodal plane of shallower dip. One event, which occurred off the south coast of Haiti (January 15, 2010; M W 4.6), shows underthrusting on a plane dipping 13 to the north. All of the events are found to be shallow ( 22 km), with most solutions returning depths of 12 km, the minimum depth allowed for standard CMT inversions in the absence of additional depth constraints. Aftershocks occurring immediately after the mainshock can be difficult to analyze because of interference from the large mainshock surface waves at all stations. We have paid particular 6

8 attention to these early aftershocks to assess whether they might exhibit transcurrent, rather than reverse, motion. In several cases, we have performed joint inversions for earthquakes occurring close in time to confirm that interference between wave packets does not bias our results. We find that even those events occurring within the first hours after the mainshock are dominated by reverse motion, including a M W 6.0 event seven minutes after the mainshock. The directions of maximum compression for the reverse-faulting events are oriented NE SW in all but three cases, with P-axis azimuths ranging from 0 50, and most falling in the range We find some suggestion for two preferred P-axis orientations, one near 10 and one near 30, but the clustering is not strong. We believe the variability in retrieved CMT parameters reflects true variability in the geometry of the earthquake sources: the relative orientations of the individual sources are well constrained by our analysis, which uses a nearly identical subset of stations for earthquakes of similar magnitude. The variation in source geometry is also clear in many of the waveforms, as shown in Figure Earthquakes prior to We are able to obtain CMT solutions for four earthquakes, of M W = , occurring prior to the January 2010 mainshock. The focal mechanisms we retrieve for the pre-mainshock events are consistent with those observed for the aftershock sequence: three of the four moment tensors show reverse faulting, with the fourth showing strike-slip faulting on an approximately E W trending nodal plane. The reverse-faulting events are located to the west of the January 2010 mainshock, and the geometry of the events occurring in the aftershock zone is similar to that observed for the 2010 sequence. The strike-slip event is located to the east of the 2010 mainshock, in a region of relatively weak aftershock activity. One event (December 31, 1990) for which we are unable to obtain a robust CMT solution nonetheless appears to have both a location and source geometry similar to the underthrusting event of January 15, 2010, off the south coast. As for the aftershocks, the P-axis orientations of these earlier events lie in the range

9 178 4 Discussion and Conclusions The dominance of reverse faulting in the aftershock sequence for this large strike-slip earthquake is unusual, and we are not aware of previous examples of aftershock sequences which are both so different from the mainshock geometry and so internally consistent. While the 1989 Loma Prieta earthquake generated an aftershock sequence in which many events differed in geometry from the mainshock, the aftershocks also exhibited great internal variability, with examples of left- and right-lateral strike-slip, normal, and reverse faulting (Beroza & Zoback, 1993). The locations of the Haiti aftershocks are distributed over a wide area, mostly to the west of the mainshock hypocenter. The centroid locations we determine are systematically shifted to the north with respect to the hypocenter locations reported by the NEIC, probably as a result of station coverage dominated by North American stations and because of the very slow raypaths through the Gulf of Mexico and northern Caribbean. However, the centroid locations remain as widely distributed as the reported hypocenter locations, and the combination of geographical distribution of the earthquake locations and the variation in focal geometry suggest that the aftershocks occur on multiple, distributed fault structures, rather than on a single reverse fault. Nearly all of the aftershocks occur on planes striking WNW ESE. If the reverse component of the mainshock occurred on a separate reverse fault, rather than as oblique slip on the Enriquillo fault, our analysis suggests that this reverse fault strikes ENE WSW to E W, like the Enriquillo fault itself, and that it must be large enough to accommodate an earthquake of approximately M W 6.8. However, further knowledge of the accommodation of reverse motion during the mainshock will require detailed analysis of higher-frequency body waves and satellite remote-sensing data. The reverse motion we observe in the Haiti aftershocks is consistent with the presence of multiple thrust structures mapped in the region (Mann et al., 1995) and with a measured component of compression across the island of Hispaniola (Manaker et al., 2008). However, previous studies of strain partitioning in the northern Caribbean have concluded that the overall east-northeastward motion is divided between the Enriquillo and Septentrional strike-slip faults on land and low-angle 8

10 underthrusting structures off the north and southeast coasts of Hispaniola (Mann et al., 2002; Manaker et al., 2008). Our results, from the aftershock sequence and earlier earthquakes, indicate that strain partitioning in southwest Hispaniola occurs through left-lateral slip on the Enriquillo fault and reverse slip on adjacent high-angle faults. We infer that many anticlinal structures observed on land (Mann et al., 1995) are fault cored. The prevalence of reverse faulting for the earthquakes analyzed, apart from the January 12, 2010, mainshock, emphasizes the need to incorporate seismogenic slip on compressional structures into hazard assessments for southern Haiti. While the reverse events appear to occur on multiple fault structures, rather than a single, large thrust fault, probably limiting the maximum size of such events, even earthquakes of M W 4 5 are large enough to cause damage at local distances. Further, we see some evidence for thrust faulting off the south coast of Haiti with geometry similar to that of larger underthrusting events that have occurred to the east in the Dominican Republic. The seismic deformation occurring on reverse faults should also be taken into account in stress-transfer models like those used to assess probable loading on the Enriquillo fault and its branches (e.g., Lin et al., 2010). 220 Acknowledgments We thank R. S. Stein, F. Waldhauser, T. Diehl, N. Seeber, and G. Ekström for suggestions and discussions. The GSN data were collected and distributed by IRIS and the USGS. We thank the operators of the GSN, LCSN, Geoscope, and Geofon for collecting and archiving the seismic data used here. This work was supported by NSF awards EAR and EAR

11 225 References Ali, S. T., Freed, A.M., Calais, E., Manaker, D. M. & McCann, W. R., Coulomb stress evolution in the Northeastern Caribbean over the past 250 years due to coseismic, postseismic and interseismic deformation, Geophys. J. Int., 174, Arvidsson, R. & Ekström, G Global CMT analysis of moderate earthquakes, M W 4.5, using intermediate-period surface waves, Bull. Seism. Soc. Am., 88, Beroza, G. C. & Zoback, M. D., Mechanism diversity of the Loma Prieta aftershocks and the mechanics of mainshock aftershock interaction, Science, 259, Calais, E., Mazabraud, Y., de Lapinay, B. M., Mann, P., Mattioli, G. & Jansma, P., Strain partitioning and fault slip rates in the north-eastern Caribbean from GPS measurements, Geophys. Res. Lett., 29, doi: /2002gl DeMets, C., Jansma, P., Mattioli, G., Dixon, T., Farina, F., Bilham, R., Calais, E. & Mann, P., GPS geodetic constraints on Caribbean North America plate motion, Geophys. Res. Lett., 27, Deng, J., & Sykes, L. R., Determination of Euler pole for contemporary relative motion of Caribbean and North American plates using slip vectors of interplate earthquakes, Tectonics, 14, Dixon, T.H., Farina, F., DeMets, C., Jansma, P., Mann, P. & Calais, E., Relative motion between the Caribbean and North American plates and related plate boundary deformation based on a decade of GPS observations, J. Geophys. Res., 103, 15,157 15,182. Dziewonski, A. M., Chou, T.-A. & Woodhouse, J. H., Determination of earthquake source parameters from waveform data for studies of global and regional seismicity, J. Geophys. Res., 86, Dziewonski, A. M. & Woodhouse, J. H., An experiment in systematic study of global seismicity: Centroid-moment tensor solutions for 201 moderate and large earthquakes of 1981, J. Geophys. Res., 88, Ekström, G., Dziewonski, A. M., Maternovskaya, N. N. & Nettles, M., Global seismicity of 10

12 : centroid-moment-tensor solutions for 1087 earthquakes, Phys. Earth Planet. Inter., 148, Ekström, G., Morelli, A., Boschi, E. & Dziewonski, A. M., Moment tensor analysis of the central Italy earthquake sequence of September October 1997, Geophys. Res. Lett., 25, Henry, C., Das, S. & Woodhouse, J. H., The great March 25, 1998, Antarctic Plate earthquake: Moment tensor and rupture history, J. Geophys. Res., 105, 16,097 16,118. Lin, J., Stein, R. S., Sevilgen, V. & Toda, S., USGS WHOI DPRI Coulomb stress-transfer model for the January 12, 2010, M W =7.0 Haiti earthquake, U. S. Geological Survey Open-File Report , 7 pp. Manaker, D. M., Calais, E., Freed, A. M., Ali, S. T., Przybylski, P., Mattioli, G., Jansma, P., Prépetit, C. & de Chabalier, J. B., Interseismic plate coupling and strain partitioning in the Northeastern Caribbean, Geophys. J. Int., 174, Mann, P., Taylor, F. W., Edwards, R. L. & Ku, T.-L Actively evolving microplate formation by oblique collision and sideways motion along strike-slip faults: An example from the northeastern Caribbean plate margin, Tectonophys., 246, Mann, P., Calais, E., Ruegg, J.-C., DeMets, C., Jansma, P. E. & Mattioli, G. S., Oblique collision in the northeastern Caribbean from GPS measurements and geological observations, Tectonics, 21, doi: /2001tc Prentice, C. S., Mann, P., Taylor, F. W., Burr, G. & Valastro, S., Paleoseismology of the North America-Caribbean plate boundary (Septentrional fault), Dominican Republic, Geology, 21, Scherer, J., Great earthquakes in the island of Haiti, Bull. Seism. Soc. Am., 2, Sykes, L. R., McCann, W. R. & Kafka, A. L., Motion of Caribbean Plate during last 7 million years and implications for earlier Cenozoic movements, J. Geophys. Res., 87, 10,656 10,

13 277 Figure captions Figure 1. Top: Focal mechanisms for 50 earthquakes of the January 12, 2010, Haiti mainshock aftershock sequence. Bottom: Focal mechanisms for four earthquakes occurring in , prior to the 2010 mainshock. All events are plotted at the NEIC epicentral locations. The mechanisms shown in gray are less well constrained than those shown in red. Figure 2. (a) Residual misfit for pure double-couple solutions, with strike 252 (left side of image) and 72 (right side of image) and varying rake and dip; note non-linear color bar. There are two minima, one for the north-dipping fault plane (left) and one for the south-dipping fault plane (right). The residual misfit for the north-dipping plane is slightly smaller than that for the south-dipping plane. (b) An example of waveform fits to the body waves for the solutions corresponding to the two minima in (a). Shown is the vertical component of displacement (blue: data; red: model), band-pass filtered between 50 and 150 seconds, from station KDAK (Alaska), at a distance of 69 and azimuth of 326. Shaded regions lie outside the body-wave window and are excluded from the inversion. Figure 3. Observed (blue) and synthetic (red) surface-wave seismograms (vertical component of displacement) for events A (black arrows) and A (green arrows) at several stations located at epicentral distance and azimuth α. All records are band-pass filtered between 50 and 150 seconds. The relative amplitudes of the arrivals for the two events vary with azimuth, indicating different focal geometries for the two events, which have similar depths and source locations. The filter used in the analysis is acausal, leading to the apparent arrival of surfacewave energy prior to the event onset (0 seconds). 12

14 Figures Figure 1: Top: Focal mechanisms for 50 earthquakes of the January 12, 2010, Haiti mainshock aftershock sequence. Bottom: Focal mechanisms for four earthquakes occurring in , prior to the 2010 mainshock. All events are plotted at the NEIC epicentral locations. The mechanisms shown in gray are less well constrained than those shown in red. 13

15 (a) (b) North-dipping fault plane South-dipping fault plane Figure 2: (a) Residual misfit for pure double-couple solutions, with strike 252 (left side of image) and 72 (right side of image) and varying rake and dip; note non-linear color bar. There are two minima, one for the north-dipping fault plane (left) and one for the south-dipping fault plane (right). The residual misfit for the north-dipping plane is slightly smaller than that for the south-dipping plane. (b) An example of waveform fits to the body waves for the solutions corresponding to the two minima in (a). Shown is the vertical component of displacement (blue: data; red: model), band-pass filtered between 50 and 150 seconds, from station KDAK (Alaska), at a distance of 69 and azimuth of 326. Shaded regions lie outside the body-wave window and are excluded from the inversion. 14

16 = 1.7, α = 69 = 2.6, α = 307 = 14, α = 237 = 30, α = 188 Figure 3: Observed (blue) and synthetic (red) surface-wave seismograms (vertical component of displacement) for events A (black arrows) and A (green arrows) at several stations located at epicentral distance and azimuth α. All records are band-pass filtered between 50 and 150 seconds. The relative amplitudes of the arrivals for the two events vary with azimuth, indicating different focal geometries for the two events, which have similar depths and source locations. The filter used in the analysis is acausal, leading to the apparent arrival of surface-wave energy prior to the event onset (0 seconds). 15

17 Supplementary Table 1. Centroid moment-tensor solutions for 54 earthquakes occurring in southern Haiti, /2010. Headings are as in standard Global CMT reports (Ekström et al., 2005). Centroid Parameters Half Scale No. Date Time Latitude Longitude Depth Drtn Factor M0 Elements of Moment Tensor Y M D h m sec δt0 λ δλ0 φ δφ0 h δh0 10 ex Mrr Mθθ Mφφ Mrθ Mrφ Mθφ ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±0.22 indicates less-well constrained event (see text).