Spatial and Temporal Characteristics of Paleoseismic Features in
Transcription
Spatial and Temporal Characteristics of Paleoseismic Features in
Spatial and Temporal Characteristics of Paleoseismic Features in the Southern Terminus of the New Madrid Seismic Zone in Eastern Arkansas Haydar J. AI-Shukri University of Arkansas at Little Rock Robert E. Lemmer Leighton and Associates, Inc. Hanan H. Mahdi and Jeffrey B. Connelly University of Arkansas at Little Rock ABSTRACT INTRODUCTION The focus of this study is to identify and characterize specific features related to historic or prehistoric earthquakes south of the southern terminus of the New Madrid seismic zone in eastern Arkansas. Aerial photography, field surveys, and trenching reveal the existence of several liquefaction features (sand blows) and linear structures as far as south of Marianna, Arkansas. This is more than 100 km from the currently active segments of the New Madrid seismic zone. Radiocarbon dating indicts that the event(s) that generated some of these features took place about 5500 years B.P. The discovered liquefaction features are significant because they are at a considerable distance from present-day earthquake activity. The implication of this is that they either represent a new earthquake source not previously recognized or that they are related to an earthquake(s) of very large magnitude in the source region of the New Madrid seismic zone. These liquefaction features have very large dimensions (-110 by 60 m), resembling features in the immediate vicinity of the New Madrid seismic zone, implying that regardless of where the source region was, the ground shaking had to be severe in order to generate them. Detailed investigation of these features may have important implications for earthquake risk mapping in the central United States, as they may provide important constraints on the southern terminus of the New Madrid seismic zone and the magnitude of the characteristic earthquake in the region. A basic assertion of paleoliquefaction studies is that largemagnitude earthquakes, of 6 or greater, may leave a record in the form of liquefaction-related features. Of primary significance among these features are sand blows, which form as a result of venting of sand-bearing water to the surface due to earthquake-induced liquefaction. The presence of sand blows in the geologic record provides opportunity to define the ages of prehistoric events. Employing modern dating techniques allows for evaluation of the recurrence times of large earthquakes and helps define the long-term behavior of seismogenic fault zones (Pavlides et al., 1999). The past 25 years of research and data collection concerning the seismicity of the central United States have resulted in a dramatic increase in our knowledge of this region. Our understanding of earth~ quake hazards in the New Madrid seismic zone (NMSZ), the Wabash Valley seismic zone, and other areas in the central and eastern United States has been profoundly changed by paleoseismic investigations. Hundreds of liquefaction features (Figure 1), believed to be the result of local earthquake ground motion, and evidence of recent faulting were systematically surveyed and studied by several investigators (e.g., Schweig et al., 1992; Tuttle et al., 1996; Li et al., 1998; Tuttle, 1999; Guccione et al., 2000; Broughton et al., 2001; Tuttle et al., 2002; Tuttle et al., 2005). Most efforts have concentrated on locating and dating these features within the current area of enhanced seismicity and the immediately adjacent areas. Limited research has been conducted to locate and study such features south of the currently known source region. 502 SeismologicalResearchLetters Volume76, Number4 July/August2005 9 4, f 6 4 6 4, o, t, 4 e4~ t < 4, ,,5" o o 4, r 4~ ,his 35~ C _ ~ ........ 5 0 K ~~ofAge B/ow Th/dmess ~1~ A.D. 1895 A A.D, 1811-1812 A A.D 1450+/- 150yr AAD 100yr A A,D. ~ +I- 200 yr A B.C. 1100 +/- 1500 yr A 0.1-0.49 m A 0.5-0.99 m 9 zl~ L~'kes(a//~s) 1811-1812 epiomlers Area ~ >1%d A 1.0-i.49 rn A 1.5-1.99 m A2.0-2.49 m _.~AHoloo~ne,age poorlyconstrained A Figure 1. Paleoseismologyin the New Madridseismiczone(afterTuttleet al., 2002). Historicand recentseismicityare alsoshown.For detailssee Tuttle et al. (2002). Seismological ResearchLetters July/August2005 Volume76,Number4 503 From the paleoseismic research conducted in the central United States, it is clear that this area has experienced repeated earthquakes in the last few thousand years. There is also mounting evidence supporting a moment magnitude of larger than 7 for some of these earthquakes. Due to the short duration of historic archiving of natural events in the central United States, paleoseismology is the primary source of information for seismic hazard mapping. Given the lack of knowledge about the spatial characteristics of prehistoric earthquakes in areas beyond the current microseismicity zones, and the uncertainty in recurrence periods and magnitudes, earthquake hazard will continue to be a debated issue and a fair subject of criticism. Until recently, the southernmost paleoseismic features identified were located about 20 km southwest of Marked Tree, Arkansas (Tuttle et al., 2002). More recently, however, Tuttle (personal communication) has identified features as far south as Madison, Arkansas (approximately 60 km southwest of Marked Tree). Van Arsdale et al. (2003) found evidence of widespread liquefaction features in the Memphis area east of the Mississippi River. We conducted reconnaissance, including aerial photography interpretation and land surveys, and trenching studies in eastern Arkansas. The surveys covered an area from immediately west of Helena to Marked Tree in eastern Arkansas (Figure 2). These surveys indicate that the spatial distribution of sand blows extends at least to Helena. These newly discovered features are more than 100 km southwest of the southern terminus of the current area of microseismicity, which ends at Marked Tree. Several features located west and south of Marianna, Arkansas (Figure 2) were found to be sand blows (AI-Shukri et al., 2000). Two possible hypotheses might explain their existence: (1) The liquefaction features may be the result of earthquakes generated by a source in the Marianna area. This source region currently shows little seismic activity, however, and the potential for reactivation is unknown. Gravity and magnetic analysis in this area (Hildenbrand, personal communication) indicate the existence of a major fault, the "Arkansas transform fault", bordering the study area to the south (Figure 2). (2) The liquefaction features might be related directly (major NMSZ events) or indirectly (aftershocks of NMSZ events) to the currently active source responsible for the NMSZ. This would place the southernmost features that we have identified approximately 100 km from the source region. If this is the case, then sand blows of this size and at this distance from the source region require a "major" earthquake. Given these observations, the questions that need to be addressed are: Where is the southern terminus of the NMSZ? What is the relationship between the recently discovered features, the historic earthquake series that took place in 1811-1812, and current microseismicity? If the issue of the relationship between these features and the current New Madrid earthquake activity can be resolved, how will these new findings change our understanding of the magnitude of the characteristic earthquake, the recurrence rate, and possi- ble migration of seismicity throughout the region? We feel that it is important to address these gaps in our knowledge about this enigmatic region through comprehensive geological, geophysical, and geochronological research in east-central and southeastern Arkansas. GEOLOGICALAND TECTONIC SETTING OF THE STUDY AREA The study area (Figure 2) is located in the Western Lowlands of the Mississippi embayment, immediately beyond the southern terminus of the NMSZ. The Mississippi embayment is a broad south-southwest plunging trough extending from westernmost Kentucky to the Gulf of Mexico. This trough is filled with Cretaceous to recent sediments (sand, silt, clay, and gravel) of shallow marine and fluvial origin. These embayment sediments unconformably overlie Cambrian clastic and Ordovician carbonate rocks deposited in the Reelfoot rift basin. The most prominent buried structure in the upper Mississippi embayment is the Reelfoot rift, which is a failed crustal rift of late Proterozoic to Early Cambrian age. The aulacogen was probably subjected to a second episode of rifting and subsequent failure during the late Mesozoic (Burke and Dewey, 1973; Ervin and McGinnis, 1975). The Reelfoot rift, which contains most of the earthquakes in the NMSZ, is about 70 kilometers wide and has 2-3 km of subsurface relief. It trends northeast-southwest for about 320 km from the Rough Creek graben in Kentucky south to the Arkansas transform fault (Hildenbrand and Hendricks, 1995; Langenheim and Hildenbrand, 1997). Several buried plutons border the rift to the northwest and southeast (e.g., Jonesboro pluton, Paragould pluton, and Covington pluton). The Blytheville arch, a zone of arched and faulted strata, is located in the center of the rift system (Hamilton and McKeown, 1988). The arch is approximately 15 km wide and 110 km long and has been mapped to within 20 km of the study area. In the last several thousands of years, the NMSZ has been the source of several seismic events or sequences of events that were large enough and had sufficient ground motion to cause widespread and severe liquefaction similar to that in 1811-1812 (Tuttle, 1999; Tuttle et al., 2002; Tuttle et al., 2005). Some of these liquefaction features have been associated with the New Madrid seismic events of 1811-1812. In the last few years, however, numerous other features have been correlated with older events. Dating, measuring, and interpretation of many large liquefaction features over a broad region have led to the development of a New Madrid event chronology (Tuttle, 1999; Tuttle et al., 2002). Kelson et al. (1992, 1996), Tuttle and Schweig (1995), Li et al. (1998), and Tuttle et al. (2002) have documented liquefaction features from at least two seismic events occurring prior to the 1811-1812 earthquakes. These two events occurred A.D. 900 _+ 100 years and A.D. 1450 _+ 150 years and were likely similar in strength to those of 1811 and 1812 (Tuttle et al., 2002). Two prior events in A.D. 300 _+200 years and 2350 504 SeismologicalResearchLetters Volume76, Number4 July/August2005 37.0 ~ 32.5 ~ .94.0 ~ -89.5 ~ A Figure 2. Location of study sites (Nancy 1, Nancy 2, and Parkin 1). The map also shows the locations of Cox et al. (2004) study sites. Red crosses represent earthquake locations. Thick solid line (ATF) represents the approximate location of the Arkansas transform fault (Hildenbrand, personal communication). B.C. _+200 years have also been interpreted from liquefaction data (Tuttle et al., 2005) The boundary of the study area extends from approximately 45 km southwest of Marked Tree, Arkansas to south of Helena, Arkansas (Figure 2). The area is underlain by Cretaceous to Tertiary sediments that range in thickness from 775 m in the north to 930 m in the south (Cushing et al., 1964; Boswell et al., 1965; Hosman et al., 1968). These sediments are mantled by fluvial and eolian deposits, including multiple Pleistocene braided stream surfaces of the Mississippi River that are crosscut and/or reoccupied by Holocene meander belts of smaller streams (Boswell et al., 1968; Blum et al., 2000). ANALYSISAND RESULTS An aerial survey in eastern Arkansas reveals numerous features throughout the research area that appear to have seis- Seismological Research Letters July/August2005 Volume 76, Number4 505 ._= A: . .......... ,A, Figure 3. Aerial photograph of a linear feature near Parkin, Arkansas (indicated by the arrows). Dark solid line indicates the location of the trench (see Figure 2 for location). mogenic origins (Figures 3 and 4). These features are light sandy patches surrounded by dark silty soil and are easily distinguishable from the air (and on the ground) (Figure 4). Most of the features south of Interstate 40 are semicircular to elliptical and are relatively large. The region north of Interstate 40 yielded fewer and more widely spaced features than the Marianna area. This region, however, has experienced more flooding than the areas to the south, and this may have obscured additional features. Ground reconnaissance surveys were also performed. The intent was to evaluate features identified from the air to determine which features warranted further investigation and evaluation. Evaluations included measuring feature size and orientation and determining nearsurface stratigraphy with a hand auger and digging test pits. Trenching Results Four trenches at three sites (Figure 2) were excavated. The dimensions of these trenches range between 35-95 m long; they were 1.2 m wide and 3 m average depth. Two of the sites were near Marianna, Arkansas (Nancy 1 and Nancy 2), and one was near Parkin, Arkansas (Parkin 1). One trench was excavated at Nancy 1 and two trenches were excavated at Nancy 2. Parkin 1 was trenched to investigate a 1.5-km-long linear feature (Figure 3). The lineament trends N56~ and has a ground surface that is 2.75 km higher on the southeast side. No fault was observed in the trench, but sand and clay layers tilted to the northwest were observed on the down side of the lineament. The work at this site was not completed due to heavy rain and flooding that forced the research team to close the trench. Both the Nancy 1 and Nancy 2 sites were confirmed to be sand blows of seismogenic origin (Figures 5, 6, and 7). Below is a description of the three trenches excavated through these sand blows: 506 Seismological Research Letters Volume 76, Number4 " " .- -- . -7: ,A Figure 4. Aerial photograph of a sand blow (Nancy 1) just east of Marianna, Arkansas. Dark solid line indicates the location of the trench shown in Figure 5. Nancy 1, T-1 A trench oriented approximately N38~ was excavated across the long axis of an elliptically shaped sand blow (Figure 4). The excavation was 59 m long and ranged from 1.85-2.25 m deep. The east wall was cleaned, gridded at a 50-cm spacing, logged in detail, and photographed. Important portions of the west wall were also cleaned and photographed. Logging revealed four distinct lithologic layers (Figure 5). The lowermost layer is a gray to brownish clay, which extended the entire length of the trench. The excavation exposed the upper 1.5 m of this layer, denoted as Unit A. The clay is plastic, is slightly iron-stained, and exhibits a moderately developed soil structure (blocky) with rootlet pores; small charcoal fragments were present. At least 45 vertical to near vertical sand dikes cutting across Unit A are connected to the overlying sand layers. The sand dikes range in width from < 1 cm to 20 cm. Radiocarbon dating of charcoal (Beta B-149264) collected 5 cm from the top of Unit A (Figure 5) yielded a twosigma calibrated date of 4850--4800 B.E Overlying the clay (Unit A) are two sand layers denoted as Units B and C, which are distinguished from one another by their degree of cementation. Unit B is moderately cemented, while Unit C is loose. Both units are a light gray, fine-medium-grained sand with yellowish brown iron staining or mottling throughout. Overlying both sand units is a plow zone of highly disturbed silty sand which ranges in thickness from 13-35 cm. Nancy 2, T-1 A 38-m-long trench oriented N66~ was excavated across a sand blow located at the Nancy 2 site (Figure 6). This excavation averaged 2.1 m in depth. The northwest wall was cleaned, gridded at a 50-cm spacing, logged, and photographed. Portions of the southeast wall were also cleaned and photographed to assist in interpretation. Four distinct layers were exposed in the wall, all of which extended the complete July/August2005 NE o . SW . . . . . . . . . . . . . . . . . 20 . . . . . . . . . 30 . . . . . . . . . 40 . . . . . . . . . so Meters . . . . . . . . . 0 L_ | IE 1 I Sao, lUn'. oI I San, lUn"'l A Figure 5. Log and photographs of the east wall of the trench excavated in the sand blow at site Nancy 1, T-1. See Figure 2 for location. The photographs show a number of nearly vertical dikes cutting through a thick clay layer (Unit A). length of the excavation. The oldest layer, denoted as Unit A, was exposed at the bottom of the trench wall and floor. Only the upper 15-75 cm of the lowermost layer were observed. Unit A is a light brown and light bluish mottled clay. This unit is plastic and heavily iron stained. Many charcoal fragments are present and the layer has a moderate blocky soil structure. Overlying this unit is Unit B. The contact between Units A and B is gradational. Unit B is also a clay, which ranges in thickness from 20-100 cm. The unit is plastic with a minor amount of charcoal and rootlet pores present. It has a moderate to well developed blocky soil structure. Radiocarbon dating of organic sediments (Beta 149266) collected 10 cm from the top of Unit B (Figure 6) yielded a two-sigma calibrated date of 5660-5580 B.P. Cutting across both clay units are five sand dikes feeding the overlying sand blow. These discordant features include one thin near-vertical dike, three shallowly dipping thin dikes, and one wide (15 cm) shallowly dipping (10-15~ dike striking N25~ All dikes dip to the northwest except one, which dips to the northeast at 30 ~ The overlying sand (Unit C) is from 22-118 cm thick. The sand was loose, light colored, and fine to medium grained with a minor amount of silt present. Charcoal fragments were scattered throughout the unit. Above the shallowly dipping dike numerous clay clasts of Unit A and several rounded pebbles (4 cm in diameter) occur in the lower portion of the sand blow unit. Clay clasts of Unit A were also observed in the near-horizontal dike. Overlying Unit C is a plow zone of highly disturbed silty sand that ranged in thickness from 7-18 cm. Nancy 2, T-2 A 34-m-long trench oriented N32~ was excavated across a second sand blow at the Nancy 2 site (Figure 7). This trench averaged 1.9 m deep. The east wall was cleaned, gridded at a 50-cm spacing, logged in detail, and photographed. Portions of the west wall were also cleaned and photographed to assist in interpretation. Exposed in the trench wall were four distinct layers, all of which extend the complete length of the excavation. Only the upper 20-50 cm of the lowermost layer, denoted as Unit A, was exposed. Unit A is a light brown and light bluish mottled clay. This unit is plastic and heavily iron stained. Overlying this unit is Unit B. The contact between Seismological Research Letters July/August2005 Volume 76, Number4 507 ~ Meters 10 0 9.8 20 5 2 4 5 6 7 8 9 I I I I I I "! IE - 7? , " o . _ ~_~ v'~[ ,i Figure 6. Log and photographs of the trench at Nancy 2 T-1. The top panel represents the log of the entire length of the trench. The lower panel represents a close-up view of the first 10 m of the trench. $1 indicates the location of the sample collected for dating. The two photographs are of the two largest dikes observed in the trench. Units A and B is gradational. Unit B is also a clay that ranged in thickness from 30-75 cm. This unit is light bluish gray with white zones in the upper 4 cm for most of its exposure. In the southern 12 m of the trench, the white zone extends throughout the thickness of Unit B. Cutting across both clay units are three sand dikes feeding the overlying sand blow. These disconcordant features include two thin vertical dikes dike strikand one wide (20 cm) shallowly dipping (44~ ing N35~ The sand blow (Unit C) is from 65-130 cm thick. The sand is pale yellow, loose fine to medium grained with a minor amount of silt present. Radiocarbon dating of charcoal (Beta 149267) collected 15 cm from the top of Unit B (Figure 7) yielded a two-sigma calibrated date of 5590-5450 and 5410-5330 B.P. At the northern end of the trench a tree-root cavity in Unit B is filled with sand. Above the shallowly dipping dike numerous clay clasts of Unit A occur in the sand blow. Overlying Unit C is a plow zone of highly disturbed silty sand that ranged in thickness from 7-15 cm. 508 Seismological Research Letters Volume 76, Number4 Geophysical Investigation (GPR) Geophysical techniques have already proven to be a powerful tool to study earthquake-related features such as sand blows (Wolf el:. al., 1998; Tuttle et al., 1999) and faults (Sexton et al., 1992). Ground-penetrating radar (GPR) technology is known to work well in dry, sandy conditions. It is widely utilized in environmental and engineering sciences. We conducted GPR surveys at several sites near Marianna, including Nancy 1 and Nancy 2. Because sand thickness in most of the features is no more than 2 m, we used a 400-MHz antenna in all of the GPR surveys. This antenna is designed to give the best resolution in the upper 5 m of soil, similar to that in the study area. Data acquisition was along parallel profiles 5 m apart. These profiles were run normal to the long axes of the sand deposits in all three sites. The data reduction procedure included removal of the direct and ground-surface effects; band-pass, high-pass, and low-pass filtration to remove noise; gaining control to enhance the signal of desired reflectors; profile migration to remove high July/August2005 SE N_W 80 Meters 0 20 10 30 L Plow Zone Sand (C) Clay (A & B) ,:i,~,:~:i i:,~:i:::~ i~ii[[:i): ?~ ,A, Figure 7. Trench log and GPR profile at Nancy 2 T-2. Top panel represents a ground-penetrating radar profile run parallel but at about 10 m west of the trench. A 400-MHz antenna was used to collect the GPR data. Second panel represents the log of the east wall of the trench. $1 indicates the location of the sample collected for dating. The photographs at the right and center show low-angle sand dikes. The photograph to the left shows clay clasts within the sand blow that were ripped from the underlying clay layer during venting of sand-bearing water. The dashed line represents the contact between Unit A and Unit B. parabolas and improve depth determination; and threedimensional visualization for signal enhancement and identification. The upper panel of Figure 7 shows a GPR profile from site Nancy 2. This profile is parallel and about 4 m to the west of trench 2 of this site. In this profile, the contact between the yellow and the purple represents the contact between the sand and the clay. Note the similarities in the morphology of this contact between the GPR profile and the trench log. Note also the disruption to this contact in the area of the sand dikes. trench at Parkin 1 was excavated for the purpose of studying a 1.5-km-long linear feature identified through interpretation of aerial photography and land survey. The lineament trends N56~ and the ground surface on the southeast side of the lineament is 2.75 m higher in elevation. No fault was discovered in the trench, but sand and clay layers tilt to the northwest, suggesting possible subsurface faulting. Geophysical work (GPR) was conducted at three sites near Marianna. Results indicate that GPR is a very promising, cost-effective tool for sand-blow studies. SUMMARY AND CONCLUSIONS Due to the paucity of radiocarbon dates of the liquefaction features discovered in this study, it is possible to suggest three viable earthquake sources: (1) The liquefaction features are the result of an earthquake generated by a local source that might not be directly relatedto NMSZ seismicity. (2) The liquefaction features are due to major New Madrid events. (3) These features formed as a result of aftershocks near the study area possibly triggered by mainshocks within the NMSZ. Due to the lack of a complete record of earthquake activity in Source Region Scenarios Four trenches at three sites were excavated during the summer and fall of 2000. Two of these sites were near Marianna, Arkansas (Nancy 1 and Nancy 2), and one was near Parkin, Arkansas (Parkin 1). Each of the trenches exposed a fine- to medium-grained sand overlying a thick clay unit. The surficial sand deposit was found to be connected to numerous vertical- to shallow-dipping sand dikes up to 20 cm wide. The Seismological Research Letters July/August2005 Volume 76, Number4 509 the central United States, and the difficulty of precisely dating these features, it might be difficult to isolate a single scenario as the most likely one. The sizes of these features (some more than 100 m in diameter) and the aerial extent of the liquefaction field (which has a minimum radius of approximately 5 km) may indicate that no matter what the source region or the epicentral distance is, severe ground shaking has taken place in the area. In reference to the first case scenario, Cox et al. (2004) studied earthquake-related liquefaction features approximately 100 km to the south and southwest of our study area. That study described multiple episodes of ground shaking in the last 6,000 years and suggested that some episodes of liquefaction correlate with the chronology of the NMSZ events, while other episodes may not. Although it is focused on an area at a considerable distance from Marianna, the study raises the possibility that significant earthquake sources may occur outside the NMSZ. Although inconclusive, the dating of some of the sand blows discovered in this research (-5500 B.P.) does not match with any event within the NMSZ. This increases the possibility that the source region might be closer to the study area. There is strong evidence that major earthquakes may cause liquefaction features at considerable distances from their epicenters. The 1811-1812 New Madrid earthquakes induced liquefaction about 240 krn from their inferred epicenters, including areas near the mouth of the Arkansas River (Johnston and Schweig, 1996). More recently, the M w 7.6 2001 Bhuj, India earthquake induced liquefaction up to 250 km from its epicenter (Rajendran and Rajendran, 2002; Tuttle et al., 2002). The features discovered near Marianna, Arkansas are only about 100 km from the present-day seismicity of the NMSZ. This makes it impossible to rule out the second scenario, that a major NMSZ earthquake may by the energy source that caused these features. One observation that is not in favor of this scenario is the lack of large liquefaction features between Marianna and the NMSZ. Aerial and repeated ground-reconnaissance surveys failed to find sand blows as large and as concentrated as the ones discovered in the study area. This, however, might be attributed to burial by repeated flooding or to soil conditions, site amplifications, and other factors that can influence soil liquefaction. There is increasing evidence that supports the hypothesis that triggered earthquakes (afiershocks) may be generated at considerable epicentral distances from a major earthquake. Recent research in the central United States (Hough, 2001; Hough and Martin, 2002; Hough et al., 2004) suggested or concluded that damaging earthquakes occurred at considerable distances (200-500 km) from the NMSZ. Hough and Martin (2002) stated that one aftershock (17 December 1811) of the 16 December 1811 earthquake had a M w of approximately 6.1. They presented accounts suggesting that the epicenter for this aftershock might be beyond the southern end of the NMSZ, possibly close to the modern city of Memphis, Tennessee. Given the margin of error in constrain- ing the epicentral region, especially to the south, this aftershock might have taken place much closer to the liquefaction field near Marianna, Arkansas. An earthquake of this magnitude has, without a doubt, the energy to cause local liquefaction and sand blows. El ACKNOWLEDGMENTS We thank M. Egan, C. Clegg-Scala, and S. Eyuboglu for field assistance; and Mrs. Nancy Apple and Mr. Mike Ragsdale for providing their farmland for trenching. The research was partially supported by the U.S. Geological Survey /NEHRP (Award # 00-HQ-GR-0066) and the Arkansas Science & Technology Authority (Award # 00-B-38). Eugene Schweig and Martitia P. Tuttle contributed greatly to improve this article. REFERENCES AI-Shukri, H. J., R. Lemmer, J. Connelly, H. Mahdi, and M. Egan (2000). 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