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Active Tectonics: Studies in Geophysics 14 Seismic Hazards: New Trends in Analysis Using Geologic Data DAVID P.SCHWARTZ and KEVIN J.COPPERSMITH* Woodward-Clyde Consultants INTRODUCTION Where? When? How large? These are the most frequently asked questions in evaluating seismic hazards. The ability to answer these, whether estimating a maximum earthquake, the amount of potential surface displacement on an active fault, or the probability of exceeding a particular level of ground motion, rests on the ability to recognize and characterize seismic sources Seismic source characterization is the quantification of the size(s) of earthquakes that a fault can produce and the distribution of these earthquakes in space and time. As such, source characterization provides the basis for evaluating the long-term seismic potential at particular sites of interest. In the late 1960s and early 1970s—largely in response to expansion of nuclear power plant siting and the issuance of a code of federal regulations by the Nuclear Regulatory Commission referred to as Appendix A, 10CFR100—the need to characterize the earthquake potential of individual faults for seismic design took on greater importance. Appendix A established deterministic procedures for assessing the seismic hazard at nuclear power plant sites. Bonilla and Buchanan (1970), using data from historical surface-faulting earthquakes, developed a set of statistical correlations relating earthquake magnitude to surface rupture length and to surface displacement. These relationships, which have been refined and updated (Slemmons, 1977; Bonilla et al., 1984) along with the relationship between fault area and magnitude (Wyss, 1979) and seismic moment and moment magnitude (Hanks and Kanamori, 1979), have served as the basis for selecting maximum earthquakes in a wide variety of design situations (Schwartz et al., 1984). A related concept that developed at about the same time and that has also seen widespread use is the idea that a seismic source can produce two types of earthquakes, a “maximum credible” event or simply a “maximum” earthquake, which is the largest conceivable, and a “maximum probable” event, which is smaller and more frequent. It is clear that the correlations between earthquake magnitude and fault parameters can provide reasonable estimates of the magnitude or surface displacement associated with future earthquakes on a fault when appropriate values for the parameters are used. However, in applying these correlations to actual siting situations, there is often much uncertainty, and there has frequently been great controversy, in the selection of the parameters used. Perhaps no better example can be found than the diversity of conclusions regarding the seismic design parameters for the proposed Auburn Dam on the American River east of Sacramento, California. Reports on these were issued by the U.S. Bureau * David P.Schwartz’s present address is U.S. Geological Survey, Menlo Park, California; Kevin J.Coppersmith’s present address is Geomatrix Consultants, San Francisco, California.
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Active Tectonics: Studies in Geophysics of Reclamation, the U.S. Geological Survey, Woodward-Clyde Consultants, and five additional independent consultants to the Bureau of Reclamation. Estimates of the magnitude of the maximum earthquake on a fault in the vicinity of the dam ranged from 6.0 to 7.0; the closest approach of the source of the maximum earthquake ranged from less than 0.8 to 8 km; estimates of the focal depth of the maximum event varied from 5 to 10 km; the amount of the surface displacement expected during the maximum event varied from 25 cm to 3 m; and estimates of the recurrence interval of the maximum earthquake ranged from 10,000 to 85,000 yr. Characteristics of expectable faulting within the dam foundation similarly had a wide range of estimated values: the maximum earthquake was 5.0 to 7.0; displacement per event was less than 2.5 cm to 1 m; and the recurrence interval of an event in the foundation was 260,000 to about 1,000,000 yr. This clearly illustrates the differences in perception among the various consultants or groups regarding both the physical basis for quantifying a particular fault parameter and the general understanding of fault behavior. During the past 10 yr the integration of geologic, seismologic, and geophysical information has led to a much better, though still far from complete, understanding of the relationships between faults and earthquakes in space and time. Geologic studies, especially a few highly focused fault-specific studies, have shown that individual past large-magnitude earthquakes can be recognized in the geologic record and that the timing between events can be measured. Such investigations of prehistoric earthquakes have developed into a formal discipline called paleoseismology (Wallace, 1981). Additionally, they have yielded information on fault slip rate, the amount of displacement during individual events, and the elapsed time since the most recent event. These data can be used in a number of different ways and have led to the development of new approaches to quantifying seismic hazards. Specifically, they have allowed us to begin to develop models of fault zone segmentation, which can be used to evaluate both the size and potential location of future earthquakes on a fault zone, and also earthquake recurrence models, which provide information on the frequency of different size earthquakes on a fault. At the same time, significant advances have been made in developing earthquake hazard models that use probabilistic approaches. These are particularly suited to incorporating the uncertainties in seismic source characterization and our evolving understanding of the earthquake process. In the present paper we discuss new trends in seismic hazard analysis using geologic data, with special emphasis on fault-zone segmentation and recurrence models and the way in which they provide a basis for evaluating long-term earthquake potential. THE GEOLOGIC DATA BASE Figure 14.1 is a schematic diagram showing the types of geologic data that can be obtained for individual faults and the applications of each to the evaluation of seismic hazards. Slip Rate Slip rate is the net tectonic displacement on a fault during a measurable period of time. In recent years a great deal of emphasis has been placed on obtaining sliprate data, and published rates are available for many faults. Slip rates are an expression of the long term, or average, activity of a fault. In a general way, they can be used as an index to compare the relative activity of faults. Slip rates are not necessarily a direct expression of earthquake potential. Although faults with high slip rates generally generate large-magnitude earthquakes, those with low slip rates may do the same, but with longer periods of time between events. Slip rates reflect the rate of strain energy release on a fault, which can be expressed as seismic moment. Because of this they are now being used to estimate earthquake recurrence on individual faults, especially in probabilistic seismic hazard analyses. FIGURE 14.1 Relationship between geologic data and aspects of seismic hazard evaluation.
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Active Tectonics: Studies in Geophysics Recurrence Intervals A recurrence interval is the time period between successive geologically recognizable earthquakes. The excavation of trenches across faults has proven to be a tremendously successful technique for exposing stratigraphic and structural evidence of past individual earthquakes in the geologic record. The recognition of geomorphic features such as tectonic terraces and individual stream offsets, morphometric analysis of fault scarps, and evidence of past liquefaction also provide direct information on the number of past events for many faults. Where datable material is found, the actual intervals between successive events can be determined, although in many cases only average recurrence intervals can be estimated. Data on recurrence intervals can be combined with information on displacement during each event to develop fault-specific recurrence models. Elapsed Time Elapsed time is the amount of time that has passed since the most recent large earthquake on a fault. Many faults have experienced repeated late Pleistocene and Holocene surface-faulting earthquakes but have not ruptured historically. With trenching and geomorphic analysis it is possible to identify and estimate the timing of the most recent event. Information on elapsed time is desirable because, when combined with data on recurrence intervals, it provides the basis for calculating real-time probabilities of the occurrence of future events on a fault. Differences in the timing of the most recent surface rupture along the length of a fault zone are also extremely useful in identifying segments that may behave independently. Displacement per Event Displacement per event is the amount of coseismic slip that occurs at the surface during an individual earthquake. Geologic studies are providing this information for past earthquakes and assume that the measured displacement occurred coseismically, that is, simultaneously with seismic rupture rather than (to any significant extent) during a period of postseismic adjustment called afterslip. Displacements may be obtained, for example, from measurements of displaced stratigraphic horizons; the thickness of colluvial wedges observed in trenches, stream offsets, the heights of tectonic terraces on the upthrown side of faults; and inflections in fault scarp profiles. Displacement reflects the energy associated with an earthquake; displacement data can be used as input for calculating maximum earthquakes. Because the amount of coseismic slip generally varies in some systematic way along the length of a surface rupture, care must be taken to evaluate the degree to which a particular displacement value reflects a minimum, maximum, or average displacement for that event. Displacement per event data for repeated earthquakes at a point on a fault coupled with the timing of the events provide a basis for formulating recurrence models. Fault Geometry The geometry of a fault is defined by its surface orientation, its dip, and its down-dip extent. For many faults, and particularly dip-slip faults, changes in the strike of the fault at the surface, especially when coupled with major changes in lithology, may aid in assessing the location of fault segment boundaries. For strike-slip faults dips are generally vertical, but for dip-slip faults the dip at depth may vary considerably from the surface dip. Some normal faults may decrease in dip with depth (become listric), whereas seismogenic thrust or reverse faults often steepen with depth. Seismic reflection data and seismicity data such as focal mechanisms can provide constraints on dip. The thickness of the seismogenic or brittle crust in a region determined from the depth distribution of seismicity also places constraints on the down-dip extent of the part of a fault that exhibits brittle behavior. Fault dip and down-dip seismogenic extent define fault width, which, along with fault length, are the key parameters for quantifying the fault area that is used to estimate magnitude and seismic moment. FAULT-ZONE SEGMENTATION The Concept In evaluating the hazard posed by a specific fault or seismic source zone, a major concern is the location of future events on that zone. It is commonly observed that long fault zones do not rupture along their entire length during a single earthquake. Therefore, to what degree is the location of rupture random, or are there physical controls in the fault zone that define the location and extent of rupture and divide the zone into segments? If a zone is segmented, how long can segments persist as discrete units without overlap of rupture during successive faulting events? Even more importantly, can segments be recognized on the basis of geologic, seismologic, and geophysical data? Answers to these questions have the potential to provide new insights into understanding rupture propagation and also to provide a physical basis
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Active Tectonics: Studies in Geophysics for evaluating where along a fault the next rupture may occur. In addition, the ability to identify potential rupture segments places constraints on fault rupture length, which is a major geometric parameter used in the estimation of maximum earthquake magnitude. Inherent in the concept of segmentation is the idea of persistent barriers (Aki, 1979, 1984) that control rupture propagation. Examples of Segmentation Wasatch Fault Zone, Utah The Wasatch is a 370-km-long normal-slip fault that has not had a historical surface-faulting earthquake. Based on historical surface ruptures on normal faults in the Great Basin, which have ranged in length from about 35 to 65 km, only a part of the Wasatch Fault zone will be expected to rupture in future earthquakes with lengths comparable to the historical examples. A segmentation model for the Wasatch Fault zone (Schwartz and Coppersmith, 1984) is shown on Figure 14.2. Each Wasatch segment is identified using surface fault geometry, fault scarp morphology, slip rate, timing of the most recent and prior events, gravity data, and geodetic data. From north to south, the length and orientation of the segments are (1) Collinston segment, 30 km, N20°W; (2) Ogden segment, 70 km, N10°W; (3) Salt Lake City segment, 35 km, convex east N20°E to N30°W; (4) Provo segment, 55 km, N25°W; (5) Nephi segment, 35 km, N11°E; and (6) Levan segment, 40 km, convex west. The Collinston segment has had no identifiable surface faulting during the past 13,500 yr. The Ogden segment has experienced multiple displacements, including two within the past 1580 14C yr before present (BP) and with the most recent of these within the past 500 yr. The Salt Lake City and Provo segments have each had repeated Holocene events; the timing of the most recent event along the Salt Lake City segment is not known, and the youngest event on the Provo segment appears to have occurred more than 1000 yr ago. Along the Nephi segment one event has occurred within the past 1100 14C yr BP and possibly as recently as 300 yr ago; two earlier events occurred on this segment between 4580 and 3640 14C yr BP, and this event occurred less than 1750 14C yr BP. The proposed segment boundaries may represent structurally complex transition zones ranging from a few to more than 10 km across. To varying degrees, boundaries selected on the basis of paleoseismic and geomorphic observations are coincident with changes in the surface trend of the fault zone; major salients in the range front; intersecting east-west or northeast structural trends observed in the bedrock geology of the Wasatch Range; cross faults and transverse structural FIGURE 14.2 Segmentation model for the Wasatch Fault zone, Utah. Stippled bands define segment boundaries (modified from Schwartz and Coppersmith, 1984). trends interpreted from gravity data (Zoback, 1983); and geodetic changes (Snay et al., 1984). Smith and Bruhn (1984) showed a strong spatial correlation between segment boundaries and the margins of major thrust faults of Late Jurassic to Early Tertiary age. Oued Fodda Fault, Algeria An excellent example of fault-zone segmentation is provided by the Oued Fodda Fault, which produced the El Asnam, Algeria, earthquake (MS=7.3) of October 10, 1980. Yielding et al. (1981) and King and Yielding (1984) described this earthquake in terms of fault geometry and rupture propagation and termination. Basic features of the surface rupture and segmentation are shown in Figure 14.3. Thirty kilometers of coseismic surface faulting occurred on a northeast trending thrust fault, with secondary normal faulting on the upper plate. This rupture is
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Active Tectonics: Studies in Geophysics FIGURE 14.3 Map showing coseismic surface rupture from the 1980 El Asnam, Algeria, earthquake and the segmentation model for the Oued Fodda fault (modified from King and Yielding, 1984). Fault segments A, B, and C are defined by differences in geomorphic expression, seismicity, coseismic slip, geometry, and long-term rates of deformation. composed of three distinct segments, referred to as A, B, and C. The southern segment contains two smaller segments, A1 and A2. Local and teleseismic data showed that the earthquake occurred at a depth of 10 to 15 km and was a complex rupture event. The main shock nucleated at the southwest end of segment A and propagated 12 km northeast, where a second rupture of equal seismic moment occurred and ruptured 12 km further northeast; a smaller third rupture occurred and propagated along segment C. Geologically, coseismic surface displacement during the 1980 earthquake decreases at each segment boundary, the strikes of the segments differ, and there is a gap in the main thrust rupture and an en echelon step between southern and central segments. There are also differences in long-term deformation along each as expressed by the degree of development of folds on the hanging wall of the thrust. A well-developed anticline with an amplitude of more than 200 m occurs along segment B, the amplitude of the anticline decreases to less than 100 m along A2, and the amplitude along A1 is less than 30 m before the anticline dies out toward the south end of segment. The slip distribution from the 1980 earthquake corresponds closely with the observed differences in the amount of long-term deformation. The average net slip in 1980 was greatest on segment B, decreased along A2, and decreased again along A1. Aftershocks show that strike-slip faulting normal to the trend of the surface rupture occurs at the segment boundaries, specifically between A1 and A2, and between A and B. In addition, aftershocks indicate differences in dip between segments, with segment A having a steeper dip than segment B. Based on these observations, Yielding et al. (1981) and King and Yielding (1984) concluded that the 1980 displacement pattern was similar to past surface ruptures and that features of fault geometry and barriers that control the nucleation and propagation of rupture on this fault have persisted through geologic time. Lost River Fault Zone, Idaho Surface faulting associated with the October 28, 1983, Borah Peak, Idaho, earthquake (MS=7.3) on the Lost River Fault zone provides another example for examining segmentation. The Lost River Fault is a normal-slip fault zone that extends for approximately 140 km from Arco to Challis. In 1983 it ruptured along 36 km of its length (Crone and Machette, 1984). Scott et al. (1985) suggested that the zone may be composed of five or six segments characterized by different geomorphic expression, structural relief, and timing of most recent displacement. The segmentation model for the fault zone is shown on Figure 14.4. At the southern end of the 1983 rupture zone, where surface rupture initiated, a 25-cm-high scarp that formed in 1983 is coincident with a fault scarp of approximately the same height that defines the pre-1983 event of this location. South of this point the strike of the range front changes sharply, transverse faults occur in the bedrock of the range, and a set of higher fault scarps
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Active Tectonics: Studies in Geophysics FIGURE 14.4 Segmentation model for the Lost River Fault zone, Idaho (modified from Scott et al., 1985). along which there was no slip in 1983 can be traced southward. These observations suggest that rupture may have initiated at the same point during the past two events and that a segment boundary occurs at the location of rupture initiation. Crone and Machette (1984) also suggested that a subsegment boundary may occur in association with a complex zone of bedrock structure near the northern end of the 1983 surface rupture. San Andreas Fault Zone, California The San Andreas Fault zone also provides an example for evaluating segmentation, primarily because most of the fault has ruptured in historical time and the amount and extent of slip are known. Allen (1968) recognized differences in the historical behavior of various parts of the San Andreas Fault zone and identified four segments (Figure 14.5): a northern segment that was the location of the 1906 rupture, a central segment that is currently creeping and has been the location of repeated moderate earthquakes during this century, a south-central segment that was the location of the 1857 rupture, and a southern segment that has not generated large earthquakes during the historical period. Recently developed historical and paleoseismicity data, particularly recurrence data developed from trenching studies and data on displacement per event gathered at different points along the zone (Sieh, 1978, 1984; Bakun and McEvilly, 1984; Hall, 1984; Sieh and Jahns, 1984), indicate that long-term differences in the behavior of individual segments do occur and that such behavior has remained relatively constant during the past few thousand years. This strongly suggests that the
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Active Tectonics: Studies in Geophysics FIGURE 14.5 Segmentation model for San Andreas Fault zone, California. The northern segment ruptured in 1906; the central segment has been the location of repeated moderate earthquakes during this century and is currently creeping; the south-central segment ruptured in 1857; and the southern segment has not generated large historical earthquakes. historically defined segments have persisted as distinct units through at least the past several seismic cycles (Schwartz and Coppersmith, 1984). Segmentation and Seismic Hazard Assessment Fault segmentation occurs on a variety of scales. Segments may represent the cumulative coseismic rupture during a single event on a long fault and be many tens of kilometers in length, they may represent a part of the rupture associated with an individual faulting event and be only a few kilometers long, or they may represent local inhomogeneities along a fault plane and be only a few tens or hundreds of meters in length. Because of their longer lengths, it is the first and second types of segments that have the most relevance to evaluating seismic hazards and are discussed here. The identification of segments is not particularly easy, and methods for doing so are in the early stages of development. As more segmented faults are observed and studied, the physical characteristics and controls of segmentation will become more readily identifiable and better understood. The best types of data that provide information on segmentation are those that quantify differences in behavior along the length of a fault during its most recent seismic cycle. The most definitive is the difference in the timing of the most recent event, followed by differences in the timing of older events as indicated by paleoseismological recurrence data. Differences in representative slip rates, major changes in the strike of the fault, the occurrence of significant lithologic changes, and the presence of transverse geologic structures may spply additional information that can be used to recognize fault segments. For many faults it appears that surface geology and changes in fault geometry frequently have a one-to-one correlation with, and are an expression of, rupture processes occurring at seismogenic depths. As a result, geologic, seismologic, and geophysical data can be used to define fault-specific segmentation models for individual faults. Implicit in segmentation modeling is the concept that segments can persist as generally discrete units through significant periods of time and, therefore, that each segment ruptures separately. There are no geologic data that currently preclude the possibility that some ruptures may cross segment boundaries or that adjacent segments may rupture completely during the same event. However, in instances where the amount of surface slip during a historical event can be compared with that from previous events at the same location it is observed often that displacement during successive events has been essentially the same. This indicates that the slip distribution along the fault, and by inferences the rupture length, has remained relatively constant. When the amount and rate of short-term (i.e., Holocene) deformation on a fault segment can be compared with the amount of long-term deformation, there is often a good correspondence. For example, Schwartz and Coppersmith (1984) showed that Wasatch Fault segments defined on the basis of paleoseismicity data are also reflected by systematic changes in the elevation of the Wasatch Range. The elevation of the range is highest where late Quaternary slip rates are fastest and recurrence intervals are shortest, the elevation of the range decreases at segment boundaries and where Holocene scarps die out, and the elevation of the range is lowest at each end where paleoseismicity data reveal the lowest Holocene slip rates and the longest recurrence intervals along the fault zone. Along the south-central segment of the San Andreas Fault, the parts of the segment that had the largest amounts of coseismic slip in 1857 also have the higher long-term slip rates. Aki (1979, 1984) suggested that strong, stable barriers to rupture propagation persist through many repeated earthquakes, and the observations noted above are consistent with this.
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Active Tectonics: Studies in Geophysics For dip-slip faults these barriers appear to be mainly transverse geologic structures inherited from previous stress regimes that permit decoupling of adjacent segments. The controls of segmentation on strike-slip faults are not so clear, and, because these faults propagate laterally, the longevity of individual segments may be shorter than for dip-slip faults. The independent behavior of fault segments has important implications for seismic hazard evaluation. Segment identification provides a physical basis for the selection of rupture lengths used in the calculation of maximum earthquakes. Also, if a fault is segmented, the potential hazard posed by each segment may be different. For example, variability in segment length will mean variability in the size of the maximum earthquake. Moreover, recognition of segments and of the differences in the behavior of each will be extremely important for long-range earthquake forecasting. Information on the difference in the elapsed time and on the recurrence interval for each segment can be used to assess where along a fault zone the next major event will most likely occur and to calculate the probability of that event. This provides a basis for selecting parts of a fault zone for more intensive investigation for purposes of short-term earthquake prediction. THE CHARACTERISTIC EARTHQUAKE MODEL Recent fault-specific geologic investigations have shown that many individual faults and fault segments tend to generate essentially the same size or characteristic earthquakes having a relatively narrow range of magnitudes at or near the maximum (Schwartz and Coppersmith, 1984). The characteristic earthquake model was developed from geologic observations that, at a point along a fault, the displacement during successive surface-faulting earthquakes remained essentially constant. This was observed in trenches along the Wasatch Fault zone, where past displacements could be measured using colluvial deposits derived from erosion of fault scarps. Similar behavior is observed along the south-central segment of the San Andreas Fault, where location-specific displacement during the 1857 earthquake appears to repeat the amount of displacement of at least the two previous events. This has been shown to be the case at Wallace Creek (Sieh and Jahns, 1984) as well as at other sites along the fault segment. The 1983 Borah Peak, Idaho, Earthquake—A Characteristic Event Comparisons of observations of the October 28, 1983, Borah Peak, Idaho, earthquake (MS=7.3) with paleoseismic observations provide strong support for the characteristic earthquake model. In 1976 a trench was excavated across a fault scarp of the Lost River Fault zone that was developed in a Pinedale-age outwash fan (approximately 15,000 yr old) at Doublespring Pass Road (Figure 14.4). Relationships in this trench suggested that only one major surface faulting event had occurred since formation of the fan surface and that this event was mid-Holocene (about 6000 yr) in age (Hait and Scott, 1978). As part of the evaluation of the 1983 earthquake, a parallel trench was excavated to re-expose the pre-1983 earthquake relationships and observe the changes that occurred in 1983. A generalized log of the 1984 trench is shown on Figure 14.6. Within this trench, correlative stratigraphic marker horizons occur on both sides of the main fault and can be traced across the graben. Because of this, the complete postfan faulting history is exposed, and measurement of pre-1983 displacements can be made and compared with those of 1983 displacements. Mapping and analysis of the stratigraphic and structural relationships in the trench (Schwartz and Crone, 1985) indicate the following sequence of events: Pre-1983 surface faulting. The fan surface was displaced, and a series of graben and a horst were produced across a 40-m-wide zone west of the main scarp. The amount of displacement on individual faults formed during this event is the same across the base of a pedogenic carbonate horizon (Ck) that was near the surface of the fan and lithologic contacts at the base of the trench (for example, the top of the distinctive silty gravel). Deposition of scarp-derived colluvium. This occurred at and west of the main fault (meters 5 through 10) and in graben (meters 15 through 19; 24 through 27). Fissure infills also developed (meters 24 and 39). These deposits are shown by the gray stippled pattern in Figure 14.6. Continued colluviation and the development of an organic A-horizon (slanted pattern) at the pre-1983 ground surface. 1983 surface faulting. All pre-1983 faults were reactivated, one new trace developed, and the existing colluvial wedge at the main fault was backtilted to the east. Deposition of scarp-derived colluvium. Postfaulting colluvial deposits (dashed pattern) buried fault scarp free faces and are prominently developed at the main fault (meter 5) and in a graben (meters 15 and 19). Important conclusions can be drawn from the new Doublespring Pass trench regarding the number and size of past events. Only one pre-1983 surface faulting earthquake occurred along this segment of the Lost
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Active Tectonics: Studies in Geophysics FIGURE 14.6 Generalized log of trench across the Lost River Fault and surface rupture from the 1983, Borah Peak, Idaho, earthquake at Doublespring Pass Road (from Schwartz and Crone, 1985). The trench location is shown on Figure 14.4.
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Active Tectonics: Studies in Geophysics River Fault zone between the time of formation of the surface of the Pinedale-age outwash fan and the 1983 event. Surface displacement that occurred in 1983 closely mimicked displacement from the previous event in both style and amount. All individual pre-1983 faults in the trench were reactivated, including small graben and the well-defined horst. Displacement across the main fault was similar for both events, as was displacement on many of the synthetic and antithetic faults. Crone and Machette (1984) showed the distribution of displacement along the length of the 1983 surface rupture. Although measurements of pre-1983 displacements have not been made systematically, mapping suggests that scarp heights from 1983 were extremely similar to heights developed during the one pre-1983 event; small 1983 scarps are associated with small pre-1983 scarps and large 1983 scarps are associated with large pre-1983 scarps. The pattern of faulting is also remarkably consistent. This is shown not only in the trench but also at other locations along the fault where other graben and existing en echelon scarps were all reactivated in 1983. Therefore, it appears that point-specific displacement is essentially the same for the past two events. These observations, coupled with those of segmentation, support the characteristic earthquake model and imply that the 1983 earthquake was a characteristic event for this segment of the Lost River Fault zone. EARTHQUAKE RECURRENCE MODELS An earthquake recurrence model describes the rate or frequency of occurrence of earthquakes of various magnitudes, up to the maximum, on a fault or in a region. We distinguish this from an earthquake hazard model, which describes the likelihood or probability of future earthquake occurrence. Statistical studies of the historical seismicity of large regions have shown that the number of earthquakes is exponentially distributed with earthquake magnitude. The general form of this recurrence model is the familiar Gutenberg-Richter exponential frequency magnitude relationship (14.1) where N(m) is the cumulative number of earthquakes of magnitude m or greater and a and b are constants. This is often termed a “constant b-value” model. In the general absence of fault-specific seismicity data, it has commonly been assumed that the exponential recurrence model is as appropriate to individual faults as it is to regions. Recent geologic studies of late Quaternary faults strongly suggest that the exponential recurrence model is not appropriate for expressing earthquake recurrence FIGURE 14.7 Diagrammatic cumulative frequency-magnitude recurrence relationship for an individual fault or fault segment. A low b value is required to reconcile the small-magnitude recurrence with geologic recurrence, which is represented by the box (from Schwartz and Coppersmith, 1984). on individual faults. The evaluation of geologic recurrence rests on the ability to recognize past events, date the interval between events, and evaluate the size of each event. By combining the recurrence intervals for large-magnitude earthquakes developed from geologic data with the recurrence for smaller-magnitude events developed from seismicity data, a characteristic earthquake recurrence model is derived that has the general form shown in Figure 14.7. Notice that the geologic data represented by the box on Figure 14.7 include the uncertainty in both the recurrence intervals and the magnitude of the paleoseismic events. The model has a distinctive nonlinear b value that changes from values of about 1.0 in the small-magnitude range to lower values of about 0.2–0.4 in the moderate- to large-magnitude range. The low b value reflects a recurrence curve anchored at the large-magnitude events and having relatively fewer moderate-magnitude earthquakes than would be expected for b of about 1.0 (Schwartz and Coppersmith, 1984). The implications of this are that for an individual fault, estimates of the frequency of occurrence of large earthquakes based on extrapolation of the frequency of occurrence of small earthquakes may be subject to considerable error. Likewise, the concept
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Active Tectonics: Studies in Geophysics of a “probable” earthquake that is somewhat more likely to occur than the maximum event, and is therefore usually assumed to be somewhat smaller, is probably erroneous. Although it may be argued that the nonlinear slope of the recurrence curve in Figure 14.7 results from too short a sampling period of historical seismicity data, the distinctive nonlinear recurrence relationship suggested by the characteristic earthquake model has been observed solely from historical seismicity data along fault zones that historically have had repeated characteristic events. Examples are the Alaskan subduction zone (Utsu, 1971), the Mexican subduction zone (Singh et al., 1983), Greece (Bath, 1983), Japan (Wesnousky et al., 1983), and Turkey (Bath, 1981). These observations suggest that the nonlinear slope is real and not merely the result of an inadequate data base. From these data, Youngs and Coppersmith (1985) developed a recurrence density function for the characteristic earthquake model. This relationship is essentially a refinement of the generalized characteristic earthquake recurrence model and, unlike the exponential model, is appropriate for describing fault-specific recurrence. Slip Rate and Earthquake Recurrence As discussed, geologic studies have been successful at identifying prehistoric earthquakes in the geologic record and at estimating recurrence intervals between surface-faulting earthquakes. Unfortunately, these types of paleoseismicity data are not currently available for most faults. The late Quaternary geologic slip rate, however, can frequently be obtained and is being used to constrain fault-specific earthquake recurrence relationships for seismic hazard analysis. Fault slip rates offer the advantage over historical seismicity data of spanning several seismic cycles of large-magnitude earthquakes on a fault, and they can be used to estimate average earthquake frequency. Their use, however, requires a number of assumptions, and each of these must be carefully considered when using a slip rate to calculate recurrence on a specific fault. These assumptions are (1) all slip measured across the fault is seismic slip, unless fault creep has been recognized; (2) surface measurements of slip rate are representative of slip at seismogenic depths; (3) the slip rate is an average, which does not allow for short-term fluctuations in rate to be recognized; (4) the slip rate measured at a point is representative of the fault; and (5) the slip rate is applicable to the future time period of interest. Two basic approaches have been developed for using geologic slip rates. The first, proposed by Wallace (1970), allows average earthquake recurrence intervals to be calculated by dividing the slip rate into the displacement per event. Slemmons (1977) developed this further and arrived at relationships between recurrence intervals, magnitude, and slip rate. This general approach assumes that only one size earthquake, usually the maximum, occurs and that the displacement per event used represents this event. However, because earthquakes with magnitudes less than the maximum also occur on the fault, less of the total slip rate is available for the maximum event. Therefore the maximum event may have a longer recurrence interval than would be calculated assuming that no other slip events occur. The second approach is based on the assumption that the slip rate reflects the rate at which strain energy (seismic moment) accumulates along the fault and is available for release. Seismic moment, M0, is the most physically meaningful way to describe the size of an earthquake in terms of static fault parameters: (14.2) where µ is the rigidity or shear modulus (usually taken to about 3×1011 dyne/cm2), A is the area of fault plane undergoing slip during the earthquake, and D is the average displacement over the slip surface (Aki, 1966). The seismic moment rate which is the rate of energy release along a fault, is estimated by (Brune, 1968) (14.3) where S is the average slip rate along the fault (in centimeters per year). The seismic moment rate provides an important link between geologic and seismicity data. For example, seismic moment rates determined from fault slip rates in a region may be directly compared with seismic moment rates based on seismicity data (Doser and Smith, 1982). Once a seismic moment rate has been calculated for a fault, it must be partitioned into various magnitude earthquakes according to an assumed recurrence model. Most commonly, an exponential magnitude distribution is used. Several authors (Smith, 1976; Campbell, 1977; Anderson, 1979; Molnar, 1979; Papastamatiou, 1980) have developed relationships between earthquake recurrence and fault or crustal deformation rates, assuming an exponential magnitude distribution. As discussed, there is increasing evidence that, at least for some faults, a recurrence model based on the characteristic earthquake may be more appropriate than the exponential model for individual faults and fault segments. Youngs and Coppersmith (1985) developed a generalized recurrence density function for this model that can be used when fault slip rate data are available. The choice of either the exponential model or the characteristic earthquake model can have a significant im-
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Active Tectonics: Studies in Geophysics pact on the resulting recurrence relationship. Figure 14.8 compares the earthquake recurrence relationship for a single fault developed using an exponential magnitude distribution (solid curve) with that developed using the characteristic magnitude distribution (dashed curve). Both relationships were developed using the same maximum magnitude, b value (for the exponential distribution magnitude range), and fault slip rate. As shown in Figure 14.8, for the same slip rate, use of the characteristic earthquake model rather than a constant b-value model results in a significant reduction in the rate of occurrence of moderate-magnitude earthquakes and a modest increase in the rate of the largest events. This difference can have a significant impact on seismic hazard assessment at a site, depending on whether the moderate-magnitude events or the large events contribute most to the hazard. One final consideration that is important in assessing earthquake recurrence from fault slip rate (moment rate) is sensitivity to the choice of maximum magnitude used in the analysis. As shown in Figure 14.9, for the same slip rate (constant moment rate), increasing the maximum magnitude from 6 to 8 results in a dramatic decrease in the recurrence rate for smaller events. This is FIGURE 14.8 Comparison of recurrence relationships based on an exponential magnitude distribution (solid curve) and a characteristic earthquake distribution (dashed curve). Both relationships assume the same maximum magnitude, b value, and fault slip rate (from Youngs and Coppersmith, 1985). FIGURE 14.9 Effect of variations in maximum magnitude on the recurrence relationship for a fault when fault slip rate (moment rate) is held constant (from Youngs and Coppersmith, 1985). because the largest earthquakes account for the major part of the total seismic moment rate and adding a single large earthquake requires the subtraction of many smaller events to maintain the same moment rate. EARTHQUAKE HAZARD MODELS One primary goal of a seismic hazard analysis is to quantify the hazard in such a way that it can be used for engineering decisions regarding seismic design. For the seismic design of dams, power plants, hospitals, and schools it has been common practice to use deterministic design criteria. That is, the design is based on the assumption that a particular earthquake magnitude, level of ground motion, or amount of displacement on a fault will occur during the life of the facility. In recent years, probabilistic models have become increasingly used in evaluating seismic hazards. Estimates of the likelihood or probability of future earthquake occurrence are quantified into probabilities through the use of earthquake hazard models. These models express assumptions regarding the timing and size of earthquake occurrence based on a physical and statistical understanding of the earthquake process. As
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Active Tectonics: Studies in Geophysics our understanding of fault behavior advances, the use of forecast models and the quantification of probabilities based on more refined geologic input will take on greater importance in guiding judgments regarding seismic design parameters. Some of the more common models are discussed below. They range from simple models that require few data constraints to complex models that, because of their large number of data constraints, have rarely been applied. It is expected that, with our evolving understanding of fault behavior and earthquake generation, increasingly sophisticated models will be put into more frequent use. Poisson-Exponential Model The most commonly used hazard model (see Cornell, 1968) is based on the assumption that earthquakes follow a Poisson process. That is, along a fault or within a seismic source zone, earthquakes are assumed to occur randomly in time and space. Coupled with this assumption is the exponential distribution of earthquake magnitudes. The Poisson-exponential model assumes that the times between earthquake occurrences are exponentially distributed and there is some time between occurrences of particular magnitudes. Therefore, the time of occurrence of the next earthquake is independent of the elapsed time since the previous one. Also, the Poisson process has no “memory” in that the magnitude of the next earthquake will not depend on the magnitude of any past events. Finally, the magnitude, locations, and times of occurrence of earthquakes along the fault are independent. This means, for example, that a long period of quiescence does not imply anything about the size of the next earthquake. Also, the next event is just as likely to occur on a segment of a fault that recently ruptured as on any other segment. Where data on faults and fault behavior are lacking, the Poisson-exponential model may be necessary and useful. However, in many cases the assumptions of the model may not be compatible with our understanding of the physical processes of earthquake generation. For the Poisson-exponential model few data constraints are required. The probability of occurrence of x number of events during time t is only a function of the rate v (the average number of events per unit time or the average recurrence interval): (14.4) The rate v may come directly from geologically derived estimates of earthquake recurrence. Time-Predictable Model The time-predictable model, as proposed by Shimazaki and Nakata (1980), is based on assumptions of constant rates of stress and strain accumulation and that stress accumulates to some relatively constant threshold at which failure occurs. From these assumptions, given the size of the most recent strain release (usually expressed as coseismic fault slip) and the rate of strain accumulation (slip rate), one can predict the time to the next earthquake Figure 14.10). In this regard, the time-predictable model is relatively deterministic, although some uncertainty may be introduced in the model parameters. For example, stochastic models of earthquake occurrence have been developed based on the time-predictable model (Anagnos and Kiremidjian, 1984). The evaluation of seismic hazards would be greatly simplified if all faults followed a time-predictable behavior. However, it is likely that this is not the case. Rather, time-predictable behavior may be strongly dependent on tectonic environment. Along plate boundaries, such as major transform fault zones like the San Andreas, or subduction zones, where the rate and source of stress are relatively constant and the rate of strain accumulation is high, major faults and fault segments may approach a generally uniform behavior. In these cases, a time-predictable model may provide a reasonable approach to quantifying hazard, even if there is some uncertainty in the precision regarding the regularity of recurrence. Geodetic observations in Japan suggest that the rate of strain accumulation between large earthquakes is not constant, but if the true variations in rate can be measured, the time-predictable model may still be applicable (Thatcher, 1984). However, the time-predictable model does not appear to be applicable to interplate environments, where repeat times for the same-size earthquake on a fault can be highly variable. FIGURE 14.10 The time-predictable recurrence model. With information on the amount of the most recent coseismic fault slip (heavy line) and the assumption of linear strain accumulation (thin line), the time to the next earthquake (dashed line) can be estimated (from Shimazaki and Nakata, 1980).
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Active Tectonics: Studies in Geophysics Renewal Models Renewal models, which are also referred to as real-time models, also imply a time-dependent accumulation of energy between major earthquakes. As opposed to the Poisson model, renewal models have a one-step “memory” that considers the time since the most recent event (Figure 14.11). That is, the likelihood of earthquake occurrence during a particular future period of interest, which is referred to as conditional probability, is related to the elapsed time since the most recent event and the average recurrence interval between major earthquakes. To use this model, the parameters required are the elapsed time, the average recurrence interval, and the uncertainty of dispersion about the average recurrence. Renewal models and variations thereof have been widely used to describe earthquake occurrence (Veneziano and Cornell, 1976; Kameda and Ozaki, 1979; Savy et al., 1980; Grandori et al., 1984). More complex FIGURE 14.11 Schematic diagram of simple renewal model. A, The distribution of earthquake repeat times (recurrence intervals) is represented by the probability density function. The future period of interest is shown from present, t to (t+Δt). The conditional probability of earthquake occurrence is defined as area under the density function (stippled area) divided by the area under the curve to the right of the present. B, For the renewal model the conditional probability varies as a function of the elapsed time since the most recent earthquake, whereas the Poisson estimate is independent of the elapsed time. models that are based on an assumed renewal process have also been proposed. However, additional parameters are required to specify these models, for example, the semi-Markov two-step memory that relates the probability of future earthquakes of particular sizes to both the elapsed time since the most recent event and the magnitude of the prior event. This model has been used to assess probabilities of earthquake occurrence in Alaska (Patwardhan et al., 1980), the Wasatch Fault zone (Cluff et al., 1980), and the San Andreas Fault (Coppersmith, 1981). In many instances, renewal models have the potential to provide the most realistic estimates of seismic hazard. Therefore, it should be the goal of hazard evaluation studies to provide the fault behavior data that best characterize seismic sources. SOME FINAL THOUGHTS In recent years there has been an evolution in the approach toward the evaluation of seismic hazards. Deterministic estimates of maximum earthquake size and associated ground motion that are based on a restricted data base are gradually being replaced by probabilistic assessments of future earthquake potential that incorporate information on earthquake recurrence intervals, displacement per event, fault slip rate, fault segmentation, and the uncertainties in these parameters. This is occurring, in large part, because of the progress that has been made in obtaining and using geologic data to quantify fault behavior and earthquake processes. We are optimistic that future geologic investigations, especially of faults or seismic sources associated with historical events that can be used for calibration, will provide even greater insights into understanding the space-time relationship between faults and earthquakes. Characterization of hazards in greater detail will increase our ability to make better informed and more realistic engineering decisions regarding seismic design. ACKNOWLEDGMENT We thank Walter J.Arabasz and Robert D.Brown for their insightful and constructive reviews. REFERENCES Aki, K. (1966). Generation and propagation of G-waves from the Niigata earthquake of June 19, 1964. 2. Estimation of earthquake movement, released energy, and stress-strain drop from G-wave spectrum, Bull. Earthquake Res. Inst. (Tokyo Univ.) 44, 23–88. Aki, K. (1979). Characterization of barriers on an earthquake fault, J. Geophys. Res. 84, 6140–6148.
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Representative terms from entire chapter: