1998 statistics of paleoseismic data - geo-haz consulting inc

STATISTICS OF PALEOSEISMIC DATA

Program Element III: Understanding earthquake processes

Final Technical Report Contract 1434-HQ-96-GR-02752

National Earthquake Hazards Reduction Program U.S. Geological Survey

Principal Investigator: James P. McCalpin

GEO-HAZ Consulting, Inc. P.O. Box 1377

1221 Graves Ave. Estes Park, CO 80517

OFFICE: (970) 586-3217 FAX: (970) 577-0041

This report was prepared under contract to the U.S. Geological Survey and has not been reviewed for conformity with USGS editorial standards and stratigraphic nomenclature. Opinions and conclusions expressed herein do not necessarily represent those of the USGS. Any use of trade names is for descriptive purposes only and does not imply endorsement by the USGS.

GEO-HAZ Consulting, Inc. ________________________________________________________________________

USGS-NEHRP Contract 1434-HQ-96-GR-02752

NON-TECHNICAL SUMMARY Compiled data from numerous neotectonic-geomorphic and trench studies reveals patterns in the spatial and temporal variation of coseismic fault displacement. Recurrence intervals between successive large earthquakes on faults define a near-symmetrical probability distribution with a coefficient of variance of 0.36. Normal faults have the most regular recurrence, and subduction zones the most variable. Variability in recurrence times at a site is not dependent on the number of recurrence intervals dated at that site. During historic surface-rupturing earthquakes slip has varied widely along strike. Based on 56 ruptures where more than 15 displacement measurements were made, the generic pattern is for average displacement (Davg) to equal 0.35 of maximum displacement (Dmax). The frequency of smaller-than-average displacements is much greater than larger-than-average ones, with less than 5% of displacements being larger than 90% of the maximum. The frequency distributions permit one to estimate Dmax or Davg from one or more random measurements of displacement, which then permits an estimate of paleoearthquake magnitude. INTRODUCTION This project aims to increase the utility of results from many years of paleoseismic investigations for use in Seismic Hazard Assessments (SHAs). Most paleoseismic studies have been able to characterize only a few (2-4) large (M>7) paleoearthquakes on a given structure for displacement patterns and timing. Particular characteristics derived are: 1) slip per event, 2) slip gradients, 3) slip rates, and 4) recurrence intervals. For any particular fault the low number of "characterizable" paleoearthquakes precludes any rigorous statistical definition of the four characteristics mentioned above. Modern probabalistic SHAs depend heavily on the use of logic trees to estimate hazards (e.g. Reiter, 1990). Branches within the logic trees for each seismic source are devoted to slip per event, slip rates, and recurrence intervals; often these are the key parameters that drive estimates of hazard. To date, estimating the mean value and range of some of these characteristics has been performed in an ad-hoc manner, which is not surprising given the paucity of paleoseismic data for each seismic source. However, by combining data from many faults of similar type we can begin to define the typical frequency distributions for these characteristics. Such an ability allows us to replace the current procedures with procedures based on definable probability density functions. This change would decrease the current reliance on "expert opinion" for choosing the values and probabilities for logic trees, and replace it with data that are more reproducible and justifiable. At the same time, it allows analysis in a unified data set of results of many NEHRP paleoseismic studies that have hitherto been considered only as isolated data. Current SHAs in progress for critical facilities (e.g. Yucca Mountain nuclear waste repository) still rely heavily on "expert opinion". At the same time the results of 20



years of paleoseismic studies (many funded by NEHRP) have not been collated and analyzed sufficiently to look for behavioral patterns. These data sets hold an invaluable key for replacing expert opinion with statistically robust and defendable probability distributions. PROJECT PLAN Our basic premise is that the long-term behavior of a given type of fault (e.g., normal, intracontinetal, or strike-slip, plate-boundary) can be characterized by observing the aggregate short-term behavior of many faults of the same type or in the same region. This premise underlies the ergodic substitution of space for time that is widely used in geology, geomorphology, and hydrology (e.g. Hunter and Mann, 1992). The ergodic hypothesis states that "under certain circumstances sampling in space can be equivalent to sampling through time, and that space-time transformations are permissible as a working tool" (Chorley et al, 1984, p. 32). For each of the paleoseismic parameters listed below, we describe the current knowledge and the questions that will be posed by our analysis. Displacement per event Paleoearthquake magnitudes are estimated in logic trees by applying estimates of displacement (and rupture length) per event to empirical equations relating magnitude to displacement. Displacement estimates are also used to estimate seismic moments of paleoearthquakes. These displacement measurements are made at points along the fault from offset landforms or from displacements observed in trenches (e.g. Sieh, 1978; Schwartz and Coppersmith, 1984; Machette et al, 1992; McCalpin et al, 1994). In many studies the displacements attributed to events before the most recent event (MRE) are derived solely from trenches. Trenches are often sited where displacements are inferred to have been larger than average, although in other cases trenches are sited to maximize the potential for dating earthquakes. Whereas the observed offsets of landforms may allow us to estimate where slip was greatest in the latest one (or two) events, the slip pattern in previous events usually cannot be discerned from surface evidence. From this perspective, almost all trenches are located "blindly" with respect to the minima and maxima of slip during pre-MRE earthquakes. Before 1994, the only published empirical equations related earthquake magnitude to maximum displacement (e.g. Slemmons, 1977, 1982; Slemmons et al, 1989; Bonilla et al, 1984). Paleoseismologists would reason (understandably) that since their trench displacements were measured in reaches of the fault where slip was larger than average, displacements could reasonably be construed to be essentially equal to maximum displacement for that event. This justification then allowed the use of equations that related the maximum displacement to magnitude. This procedure was necessitated by the general lack of studies relating average displacement to maximum displacement. In 1994 Wells and Coppersmith published equations relating earthquake magnitude to both maximum and average displacement. Many paleoseismologists then began to wonder whether the "blind" spot measurements of displacement made in previous studies were more likely to have been nearer to the average than to the



maximum displacement for that particular paleoearthquake. Mason (1992) noticed this problem and proposed a novel (if drastic) solution. He reasoned that it was much more likely (from a probabalistic standpoint) that a randomly-located trench (or measured landform) would coincide with an average displacement rather than a maximum displacement. Examination of many graphs of slip along strike in historic ruptures (e.g. Fig. 1) shows that maximum slip is attained in only one short reach of the fault, whereas many reaches display slip near the average. Both Mason (1992) and Wells and Coppersmith (1994) calculated the typical ratio between maximum:average displacement in historic ruptures as 2.7:1 and 2.0:1, respectively. Accordingly, Mason (1992) proposed that trench-derived values of displacement (being likely closer to average) should be multiplied by 2.0-2.7 to approximate maximum displacement. The resulting value should be entered into equations relating maximum displacement to magnitude. With the advent of equations using average displacement, these "randomly located" displacement values could also be directly input into those equations. The dilemma remains, however, how to determine the probability that a spot displacement measurement on a fault segment is closer to the average than to the maximum. The practical implications are large; the magnitude associated with an average displacement of 3 m is much larger than that associated with a maximum displacement of 3 m. The best way to solve this dilemma is to examine the statistical nature of slip variations along strike in well-documented historic ruptures. Fig. 2 shows how we propose to do this. First, displacements (in this case throws) are normalized in relation to the maximum observed displacement. Normalization is a key component of the ergodic approach because it allows ruptures with different values of displacement to be grouped. The throws are binned (in 5% classes) and both incremental and cumulative frequency distributions are generated. Due to the 10 km of small throws at the north end of the example rupture (Figs. 1 and 2), both the mean (94.6 cm) and the median (99.0 cm) are less than half of the maximum throw. Because most trenches to date have been placed in the central halves of faults or fault segments (where offsets are large, but still variable; Fig. 1), we also show the cumulative frequency distribution of throws in the central half of the Borah Peak rupture (solid line in Fig. 2). This curve shows the effect of removing the very small end throws from the data set; the median throw is now about equal to 50% of the maximum throw. From statistics, there is a 50% chance that a throw measured at a randomly located point on such a rupture will be either larger or smaller than the median; this statistical property presumably underlies Mason's speculations. The median normalized throws for the whole rupture and central half are 0.367 and 0.50, respectively. If the median is the most likely value to measure randomly, then the maximum throw could be calculated by multiplying the median throw by the inverse of those two numbers (2.7 and 2.0, respectively). Thus, Mason's suggestion to multiply randomly-measured throw values on normal faults by about 2.5 has some statistical justification. Conversely, the cumulative frequency curves also demonstrate that the probability of randomly measuring a throw near to the maximum is quite small. For example, throws greater than or equal to 90% of the maximum throw comprise only 3-6% of the entire distribution. Thus, by random choice one has only a 3-6% chance of measuring a throw that is within



90% of the maximum throw. Although this analysis is based on only a single rupture, the results strongly suggest that throws measured in randomly-located trenches are unlikely to approach the maximum in each paleoearthquake. We can transfer the probabilities from the EDF in Fig. 2 directly into the logic tree branches for representing maximum throw (Tmax). For example, a tree with 5 branches of equal probability (0.2) for Tmax can be approximated from the 10%, 30%, 50%, 70%, and 90% cumulative frequency values from the EDF. For the top 20% probability branch (10% cumulative frequency), T/Tmax=0.21 (from the solid line in Fig. 2), therefore Tmax= T/0.21. The other four branches are calculated in the same way. The numbers at right in Fig. 3 show probablistic values for Tmax that correspond to "randomly-located" throw measurements of 1, 2, and 3 m. The median Tmax value is 2T in each case, which follows from Fig. 2 where the median value of T/Tmax= 0.5. The logic tree in Fig. 3 thus shows how a randomly-located throw measurement is likely to correlate to Tmax for a given faulting event. We analyze frequency of throw by normalizing all throw values to the value T/Taverage. We took this approach further by examining the slip patterns of 56 historic ruptures for which at least 15 measurements of slip along strike are available (29 strike-slip, 15 reverse, and 12 normal faults; see Wells and Coppersmith, 1994, table 2B). Questions we asked are: 1) what type of frequency distribution characterizes most faults?, 2) is it the same distribution of SS, R, and N faults?, 3) is the distribution dependent on magnitude or maximum slip?, i.e. are small ruptures more or less variable than large ruptures. Until we can answer these questions, we will not know how to relate displacements measured in paleoseismic studies to paleomagnitudes. Most of this compilation was done by co-PI Slemmons. Recurrence Intervals Knowing recurrence intervals between large (characteristic) earthquakes has become a critical component of earthquake forecasting (Working Group, 1988, 1993). If recurrence were perfectly regular, earthquake forecasting would be a simple matter of comparing the time since the last earthquake to the recurrence interval. The fact that recurrence is irregular explains why earthquake forecasts must be couched in terms of probability, and why forecasts such as at Parkfield, California, can fail (often spectacularly). Two studies (Nishenko and Buland, 1987; Goes, 1996) inventoried recurrence data from worldwide faults where three or more large (M>7) earthquakes have occurred on the same fault or fault segment. These studies concluded that the variability of recurrence times (T), compared to mean recurrence (Tavg), was a relatively constant value for many faults. For example, Nishenko and Buland (1987) normalized their historic data and concluded that the probability distribution was lognormal, with a mean ln T/Tavg=0.21. In the past two decades enough paleoseismic trenching studies have been performed and published to allow a parallel analysis of paleoseismic recurrence intervals. Our data set is derived from published papers that contain sequences of three or more paleoearthquakes, each of which is dated by one-sided or two-sided age constraints.



METHODS Slip Along Strike This collection of data for fault slip distribution along historical surface fault ruptures (Appendix 1, Appendix 2) is based on Wells and Coppersmith (1994) and their spiral bound preprint, which lists the main publications summarizing fault slip distributions and seismological data for the events. Their study, which is herein referred to as the W&C report, improved upon the earlier studies of Tocher, Bonilla, Slemmons, and their colleagues by adding estimated average displacement (MD) to the usual maximum displacement (MD) regressions. They concluded from the data that AD is about one-half MD. To quantitatively assess this important relationship, and compile the available statistical basis for part of our analysis, we reevaluated slip distribution data for 56 surface faulting events that had 14, or more displacement measurements. The fault ruptures are from 8 to 333 km in length, and have moment magnitudes of M = 6- to 8+. The data base measurements are divided into the main surface rupture types: normal-slip (11), strike-slip (22), reverse-slip (5), reverse-oblique-slip (11), and normal-oblique-slip (5). Our study was greatly facilitated by Donald Wells and Kevin Coppersmith, who made all of their reprints available, and by A. Strom and Andrei Nikonov, who provided excellent data for Russian, Mongolian, and Chinese events. Most events are referred by W&C earthquake number (EQN), unless the event we add a new rupture event to the data base, with the listing by date and fault location. The slip distribution values are by location of a specific site on the fault, but some listings are for an small area or traverse across the main fault, where there are branches or en echelon faults zone, with the displacements summarize measurements across more than one branch in a distributed or imbricate zone. The arithmetic average displacement is the average of all displacement measurements along the fault, excluding zero measurements at the ends of the main fault, with end points of zero displacement shown primarily to bound the surface rupture length (SRL). The surface rupture length (SRL) listed in the previous literature may be less than the SRL of this report, since the primary purpose of this study is to summarize the statistical distribution of displacement values along the rupture, and SRL is the cumulative distance along the rupture and commonly bends along the trace. The lengths are taken along the trace of the fault, rather than the shorter distance taken directly between the ends of the trace. This is done primarily to make it easier to correlate observations with scarp morphology or exploratory trenching study of a paleoseismic fault . The average displacement (AD) is calculated from all measurements along the fault rupture, dividing the displacement values, which are weighted by their distance from adjoining points by the maximum displacement (MD). The cumulative length along the traces includes significant gaps for may events. For example, the 62 km length of the 1954 Pleasant Valley earthquake rupture is divided into four main subparallel traces, that includes a 7.2 km gap between the Tobin and China Mountain Scarps. Other gaps include the 5 km gap in 1954 Fairview Peak faulting near the north end of the West Gate



fault and a 4 km gap near the southern end of 1954 Dixie Valley scarp, which has large gaps between a few minor displacements. The surface faulting events used for this study are divided into five main fault types: normal, strike-slip, reverse, normal-oblique, and reverse-oblique faults. For oblique-slip events, where data was available for only one component, this component was tabulated and shown for the oblique-slip event. Within each of these categories, events are designated either as “Reference Events, RE”, or “Other Events, OE”, generally with magnitude values, M (moment magnitude) compiled by Wells and Coppersmith (1994). The RE events have a sufficiently large data base to give good to excellent values for AD, and the small number of measurements, makes AD determination from OE events more unreliable. (1) REFERENCE EVENTS (RE) include faults with more than 14 well-located

measurements of surface displacement (AD) along the main surface rupture, and the average displacement from these measurements is considered to be representative of the rupture event. Most tabulations are for the main seismogenic fault rupture, but also some tabulated faults with more than 14 measurements are on distributed or branch faults in the epicentral region. These faults are indicated by fault name as a separate listing under the causative earthquake event, but without a magnitude value. For example, in addition to the listing for the main 1954 Fairview Peak rupture, there are listings for the Gold King, West Gate, Eastern Monte Cristo Mountains and Phillips Wash faults. Except for the more recently available data for events not included in Wells and Coppersmith (1994), the earthquake number is from Wells and Coppersmith (1994). Added rupture events are indicated by a letter rather than number designation. The Maximum Displacement (MD) value is usually observed only with a few percent of all measurements, but the Average Displacement (AD) can generally be determined from a much smaller number of observations. The tabulation uses net (total) slip for combinations of normal-slip, strike-slip, and reverse-slip components, or for fault are not vertical.

(2) Other events have fewer than 15 measurements of the surface displacement along

the fault, or part of the fault. Although the measurements do not always give a good indications of the MD, they provide a better estimate of the AD.

Recurrence Intervals The recurrence data set was derived from either raw dates published in papers, or from the author's distillation of these dates (added to their best judgement) to estimate the most likely timing of the earthquake. Constraining ages were dominantly radiocarbon dates, with analytical errors cited as 1 or 2 sigma. Provenance errors (errors in relating the dated sample to the exact time of the earthquake) were generally not quantified, but were often included in author's "best-guess" estimates for the time of a particular earthquake.



Several basic questions must be answered during the data collection phase. The first, and probably the most serious, concerns the magnitudes of the paleoearthquakes detected and dated in these trench investigations. For example, should we assume that the paleoearthquakes thus dated are: 1) all the same magnitude, 2) characteristic earthquakes that vary +/- 1/2 magnitude unit, or 3) any threshold-exceeding event, which might cover 2 or more units of magnitude. If the recurrence intervals between earthquakes of a given magnitude (say M 7.5) are fairly regular, this regularity would be detected if in fact all the surface-rupturing earthquakes were M=7.5. However, if the trench contains physical evidence from earthquakes over the entire range of morphogenic earthquakes (M 6 to Mmax for that fault), then one might obtain an exponential-type distribution of recurrence, since a range of magnitudes are being dated. The wider the range of magnitudes sampled, the harder it would be to detect regularity in recurrence of any one magnitude event. Some studies contained magnitude estimates for dated earthquakes, but most did not. Even those magnitude estimates that were based on site-specific displacement cannot be relied upon, because: 1) the displacement at the site for each event cannot usually be related to either Davg or Dmax for that event, thus empirical estimates of M cannot be made, and 2) many recurrence studies deliberately choose locations where displacement is complex and partitioned on multiple strands. As a result, we assumed in this study that the detected and dated paleoearthquakes were "characteristic" events, and although not of exactly the same magnitude, were restricted to some magnitude range smaller than Mthreshold>M>Mmax. The second problem is dealing with the dating uncertainties for each paleoearthquake. This was not a problem with the historic data sets analyzed by Nishenko & Buland (1987) and Goes (1996), but is certainly an issue with a paleoearthquake data set, or when comparing the paleoearthquake frequency distributions to those derived from historic data. Our approach was to weight the dates based on their uncertainty (sigma). RESULTS Slip Along Strike Altogether we found 56 historic surface ruptures where post-faulting investigations had yielded at least 15 high-quality measurements of one or more components of slip. Ruptures with 15-30 slip measurements were most common, with a decreasing frequency for more measurements (Fig. 4). The largest number of slip measurements was made on the 1920 Haiyun, China earthquake. The frequency distribution of slip along strike can be characterized in two ways. First, we can compare the average displacement (AD) to the maximum displacement (MD). As seen below (Table 1) this ratio ranges from 0.29 to 0.39 for various fault types, with an overall average of about 0.35. Thus, the average displacement tends to be about 35% of the maximum displacement, or put another way, the maximum displacement tends to be about 2.9 times larger than the average displacement. This finding contrasts with the conclusion of Wells and Coppersmith (1994), who concluded that AD averaged about 50% of MD. Our results indicate that the maximum displacement on a rupture is



even more anomalous than previously suspected. A more detailed summary of each surface rupture is given in Appendix 1. Table 1. Ratio of Length-Weighted Average Displacement (AD) to Maximum Displacement (MD), for Various Fault Types AD/MD Component of Displacement Fault Type Dvert (N) Dss (N) Dnet (N) Strike-slip 0.38±0.08 (18) - - Normal 0.33±0.09 (11) - - Normal-oblique 0.31±0.07 (6) 0.37±0.11 (2) 0.42±0.11 (2) Reverse 0.38±0.09 (6) - - Reverse-oblique 0.33±0.12 (16) 0.30±0.11 (14) 0.35±0.10 (11) The second way to characterize the frequency distribution of displacement along strike is to plot the individual and cumulative frequency distributions of 10%-ile classes of normalized displacement (D/Dmax). An example is shown in Fig. 5 for the 1857 Ft. Tejon earthquake on the San Andreas fault. Fig. 5a shows the 93 normalized displacements measured by Sieh (1978) plotted along the normalized rupture length (surface rupture length, SRL, was 330 km). Fig. 5b shows the individual and cumulative frequencies of normalized displacements, both for the whole rupture (black) and the central half only (white). In this particular rupture, displacements that covered the most length of the rupture (affected length) were 50-60% of Dmax, and 20-30% of Dmax. As is typical of most ruptures, very small and very large normalized displacements have small frequencies. An unusual aspect of this rupture is the low frequencies for displacements of 30-50% of Dmax. Composite Frequency Distributions of Slip for Various Fault Types For each type of faulting event (normal, reverse, strike-slip, reverse-oblique, and normal oblique) we combined all the normalized displacement measurements into a single data set. The composite frequency distributions of slip for each fault type appear as Figs 6 to 14. In each graph we display the frequency of slip calculated in two ways. If faulting events were equally weighted, the slip frequencies were calculated as the mean of the slip frequencies for each 10%-ile bin for all the component ruptures of a given type. If measurements were weighted equally, we weighted the 10%-ile of slip bin frequencies by the number of slip measurements in each event, as a fraction of the total slip measurements in that fault category. The former approach treats all events as equal contributors to the composite curve, without regard to the number of slip measurements made on each rupture. One might prefer this approach if he assumed that variations in slip along strike had a relatively long wavelength, and thus the density of measurements along strike would affect the frequency content. The latter approach assumes that events with more, closely-spaced slip measurements are more important than events with fewer measurements. This assumption would be necessary if one thought slip variations along strike had a short wavelength, such that infrequent sampling would miss much of the variation in slip.



For normal fault ruptures (10 events, 559 displacement measurements), there is a near-exponential decrease in slip frequency for increasing normalized slips (Fig. 6). For both methods of weighting the data, the most common normalized displacements are from 0-10% Dmax, affecting about 25% of the rupture length. The next most common displacements are 10-20% Dmax and 20-30% Dmax. Altogether, 60% of the rupture lengths of normal faulting events have displacements of Less than or equal to 30% of Dmax. The larger (normalized) displacements are increasingly rare, with displacements greater than or equal to 90% Dmax covering only 2-3% of the rutpure length. The length-weighted average displacement is 0.33 ± 0.09 Dmax (1 sigma range). This frequency pattern has important implications for estimating the surface rupture length of normal-fault paleoearthquakes. Displacements less than or equal to 10% Dmax will be small enough to be eradicated by surface erosion and weathering processes, perhaps in only a few hundred or thousand years. Thus, if one measures a mid-Holocene paleoearthquake rupture after all D less than or equal to 10% Dmax displacements have been eradicated, one would underestimate the length of the original rupture bu ca. 25%. As weathering and erosion continue woth time, displacements of 10-20% Dmax and 20-30% Dmax will also become hard to see in the field. Thus, normal fault ruptures appear to be very sensitive to erosion eradicating large proportions of the original rupture length. Zollweg (1998) noted this problem and suggested that paleoseismic displacements should be used to estimate magnitudes, but of course the spatial variability of displacements makes that assumption flawed. For reverse fault ruptures (6 events, 193 displacement measurements) the most common displacements ranged from 20-40% Dmax (Fig. 7). The number of events (6) and data points (192) is considerably smaller than for normal and strike-slip ruptures, so we are uncertain about this statistical validity of this result. One rather odd pattern is the increase in frequency of displacements of 90-100% Dmax, in contrast to the decline in frequency of slips greater than or equal to 40% Dmax. This increase appears regardless of the weighting method, so it cannot be ascribed to a single rupture in the 6-event set. Examination of the frequencies of the 6 component earthquakes (Appendix 4b) shows that 5 of the 6 events show this tendency. It is possible that workers did not make many measurements on either side of the maximum displacement, in which case that displacement value would have been assigned to a long affected length of the rupture. However, workers typically make dense measurements as displacement increases toward Dmax, and if anything they omit measurements where displacements are smaller than average. So, we do not know the exact reason for this anomalous frequency pattern. The length-weighted average displacement is 0.38 ± 0.009 Dmax, or some 15% higher than that of normal faults, which contain a larger proportion of small displacements. For strike-slip ruptures, the frequencies of various normalized displacements are much more uniform than for normal or reverse faults (Fig. 8). The length-weighted frequencies of displacements of 0-10%, 10-20%, 20-30%, 30-40%, and 40-50% of Dmax are essentially identical at 12-15% of total rupture length. Only displacements greater than or equal to 50% Dmax became rarer with increasing size. This is the largest data set (18 events, 1088 displacements measurements) so we have confidence in its statistical validity. Due to the relatively small frequency of small displacements (less than or equal to 10% Dmax), strike-slip ruptures should not be eradicated by erosion as quickly as



normal fault ruptures are. Conversely, displacements of 90-100% Dmax affect 4-6% of rupture length, as opposed to only 2-3% in normal faults, so it should be easier to find and measure Dmax on a strike-slip rupture (Appendix 4c). For reverse-oblique ruptures we made separate analysis for the three components of displacements (vertical, horizontal, and net). These data sets have different numbers of measurements because not every site had measurements of both vertical and horizontal slip. Included in this data set are events that had much larger strike-slip component than vertical component (e.g. Fuyan, China, 1931, Dmax-ss= 6m, Dmax-vert= 0.64m; Gobr Altai, 1957, Dmax-ss= 8.8m, Dmax-vert= 3.25m), and events where the reverse was true (e.g. Kern County, USA, 1952, Dmax-vert= 1.2m, Dmax-ss= 0.75m). The overall frequency pattern for all three displacement components is a steady decline in the frequency as normalized displacements increase (Figs. 9 and 10). The 556 vertical displacements and the 511 strike-slip displacements show very similar trends. The trend for the 427 net displacements (Fig. 11) is not a strong a decline in the lower normalized displacements. The probable reason for the discrepancy between the frequency curves of the two components, versus net slip, is that at many locations where a slip component was very small, it was not measured by field workers. These locations would thus have a measured value for one component, and no value for the second component, rather than a record of zero displacement for that component. Because we cannot compute a net displacement for such sites, net displacements could not be computed at 120 sites (23% of the total), even though at these sites net displacement was probably essentially equal to the displacement component that was measured. Thus, the net displacement data set has lost 23% of the measurement sites, and many of those must have been where even the displacement component measured was less than or equal to 10% Dmax. The AD/MD ratio of the components ranges from 0.30 ± 0.11 (Dss) to 0.35 ± 0.10 (Dnet). For normal-oblique ruptures we have little data, and it is from quite dissimiliar faults. For example, Owens Valley 1872 has larger Dmax-ss (9.1m) than Dmax-vert (4.4m), whereas Fairview Peak 1954 has larger Dmax-vert (3.4m) than Dmax-ss (2.7m). Most geologist would classify the Owens Valley fault as strike-slip and the Fairview Peak fault as normal. Given this mixed population of ruptures, it is not surprising that the frequency patterns are not clear-cut. Horizontal displacement has a steeply declining pattern similar to that of normal faults (Fig. 12), vertical displacement has a pattern similar to that of reverse faults (Fig. 13), and the net displacement frequencies go up and down in a nearly random fashion (Fig. 14). These results suggest that perhaps this category of six events should be abandoned, and the events added to other fault type data sets. The AD/MD ratios are likewise widely variable, from 0.31 ± 0.07 to 0.42 ± 0.11, the latter being the largest value for any fault type or component. Recurrence Intervals The variability in recurrence is assessed by normalizing the recurrence time T to the average recurrence of the local sequence (Tavg). This analysis follows the conventions of Nishenko and Buland (1987) who analyzed a large data set of historic recurrence data. Each fault type has been analyzed separately. The frequency distributions all have a



mean=1 (since the data were all normalized), and thus the sigma value is also the Coefficient of Variation. Table 2. COV of T/Tavg for Various Types of Faults Fault Type No. of RIs COV of T/Tavg Strike-slip 44 0.39 Subduction 36 0.43 Normal 20 0.16 Reverse 11 0.31 ALL TYPES 94 0.36 Results From published and unpublished sources we discovered 41 local paleoseismic chronologies where at least three consecutive paleoearthquakes were constrained by numerical ages (Appendix 3). By far most of these local sequences contained 3 or 4 dated paleo-earthquakes, i.e. 2 to 3 dated recurrence intervals (Fig. 15). Normal Faults On normal faults we inventorized 19 local paleoearthquake sequences containing a total of 56 recurrence intervals. Individual sequences contained between 3 and 8 earthquakes, yielding 2 to 7 recurrence intervals (mean of 2.9 recurrence intervals) Fig. 16. This low number of intervals per sequence is due to two factors. First, most normal faults studied have long recurrence intervals (several ka to 10's of ka), so age dating is difficult more than 2-3 events back into the past, since those events are often beyond the range of radiocarbon dating. Second, per-event vertical displacements on the faults studied tend to be 2-4m, so after three events cumulative vertical displacement can equal 6-12m. Stratigraphic evidence for earthquakes beyond 3 events is often too deep to be reached by backhoes, so most normal fault paleoearthquake records contain 4 or fewer recognized events. The frequency distribution of the 56 normalized recurrence intervals (T/Tavg) is slightly asymmetrical (Fig. 17) with the mode (1.1) slightly higher than the mean (1.0), and more RIs smaller than the mode than larger. The standard deviation (and also, by definition, the coefficient of variance) is 0.32. Individual sequences have COV's ranging from 0.04 to 0.79, with a mean of 0.39. Strike-Slip Faults On strike-slip faults we inventorized 9 local paleoearthquake sequences containing a total of 44 reccurnece intervals. Individual sequences contained between 3 and 12 earthquakes, yielding 2 to 11 recurrence intervals (mean of 4.9 recuurence intervals per sequence, Fig. 16). This relatively high number of intervals per sequence results from tow factors. First, most strike-slip faults studied have short recurrence intervals, so that even earthquakes 7-10 events prior to the latest one are still within the range of radiocarbon dating. Second, repeated surface rupture on a strike-slip fault does not create large vertical relief, so the stratigraphic evidence of events does not become deeply buried. Thus 3-4m-deep backhoe trenches can often expose evidence of up to 10



paleoearthquakes (e.g. the Pallette Creek- Wrightwood record on the San Andreas fault, with 12 dated paleoearthquakes). The frequency distibution of the 44 normalized recurrence intervals (Fig. 18) is slightly asymmetrical, with a mode of 1.1, with more intervals shorter than the mode than larger than the mode. The COV of the grouped data is 0.39. Individual paleoearthquake chronologies have recurrence COV's of 0.16 to 0.96, with a mean of 0.44. Reverse Faults On reverse faults we only found six published site studies where at least three consecutive paleoearthquakes had been dated. These sequences 3 to 6 earthquakes (2 to 5 recurrence intervals), with a mean of 2.7 intervals per sequence. This was the smallest number for any fault type. In other words, the dated paleoseismic chronologies for on-land reverse faults mainly contained either two or three recurrence intervals. The small number of studied sites reflects the poor geomorphic expression of reverse fault traces; they are often expressed as folds, and the fault trace can be observed by landslides a the base of steep range fronts. The frequency distribution of the 16 normalized recurrence intervals (Fig. 19) has an opposite symmetry than that for normal and strike slip faults, The mode (0.9) is smaller than the mean (1.0), and there are more data points larger than the mode than smaller. Despite this difference in symmetry, the COV of the grouped data set (0.37) is very similar to that of the normal and strik-slip group data (0.32 and 0.39, respectively). Individual paleoearthquake chronologies have recurrence COV's of 0.10 to 0.64, with a mean COV of 0.38. Subduction Zones For subduction zones we found seven published site studies with dates on at least three consecutive paleoearthquakes. Several of these sequences (Prince William Sound, Alaska; Petrolia, California) include a historic earthquake as the youngest event. However, this is the limit of overlap with the historic recurrence data sets of Nishenko and Buland (1987) and Goes (1996). Among the seven site studies are two pairs of studies from the same segment of the subduction zonee. In each pair are study dated a series of emergent marine terraces, while the other dated rapid subsidence emergence events in a marsh setting. The marine terrace chronologies always have fewer inferred paleoearthquakes than do the marsh chronologies, over the same time period. There are two possible factors responsible for this discrepency: 10 the marine terrace records are missing closely-spaced events, as suggested by Plafker (1994) for the Middleton Island, Alaska record, or 2) the peat-mud marsh records contain non-earthquake submergence (or emergence) events. The first factor woul lead to underestimating the true number of paleoearthquakes, and the second factor to overestimating the number. Due to the ambiguities described above, the present data base retains both types of records, if they exist for a single segment. Both records cannot be correct. In fact, both may be incorrect for the reasons outlined above, such that the true number of paleoearthquakes lies between their estimates.



All Fault Types Grouping all the 161 normalized recurrence intervals ogether, the frequency distribution is slightly asymmetric, with a mode of 1.0- 1.1, and more intervals smaller than Tavg than larger (Fig. 21). The extremes are T/Tavg= 0.2 and 2.0. Thus, if a fault had a long term mean recurrence interval of 1000 years, and it obeyed the frequency distribution shown in Fig. 21, its recurrence intervals would range from 200 years to 2000 years, with recurrence intervals shorter than the mode being slightly more common than the larger intervals. This latter tendency implies weak clustering of earthquakes in time. Clustering results in more short (intra-cluster) recurrence intervals and fewer long (inter-cluster) recurrence intervals. Reduction of Variance with More Paleoearthquakes The COV of local sequences does not change consistently with the number of paleoearthquakes (and thus recurrence intervals) in the local sequence (Fig. 22). Instead, the COVs of sequences containing few recurrence intervals vary the most among local sequences, but this spread decreases as longer sequences are examined. For example, the 13 local sequences containing only three dated paleoearthquakes (two recurrence intervals) had COVs ranging from 0.02 to 0.96. As the number of recurrence intervals in the sequences increases, the spread of COV values decreases, converging on a value of ca. 0.3. One interpretation of this pattern is that all the sampled faults have a long term COV of recurrence of ca. 0.3, and that the larger a portion of their complete recurrence history is sampled, the closer the estimated COV is to the real COV. Conversely, picking a random 3 consecutive events (two recurrence intervals) out of an infinitely long series of events with a recurrence COV=0.3, can result in two recurrence number that may not be representative of the entire series. The two recurrence intervals might fall in a cluster, in which case they would be very similar, and result in a low estimated COV. Conversely, the two recurrence intervals might include one short intra-cluster interval and one long inter-cluster interval, yielding very different values and thus a high estimated COV. However, as more consecutive events are dated in a sequence, the chances are that the record will include both clusters and gaps, and that the estimated COV will approach the true COV of the series. In fact, given enough local sequences, the plot in Fig. 22 could determine the typical clustering content of paleoseismic records. Imagine for example an earthquake series in which clusters of three earthquakes were separated by long time spans centered on oneearthquake. If pieces of this record were extracted containing three consecutive events (two recurrence intervals), there are three possible outcomes: 1)all three events are in a cluster, so the two recurrence times are short and uniform, 2) the three events are the last in one cluster, the intercluster eartquake, and the first one in the next cluster, so the two recurrence times are long and uniform, or 3) the three events include the last tow in a cluster and the intercluster earthquake, yielding one short and one long recurrence interval. Thus, if this series was sampled in 3-earthquake sections, estimated COV would be high because some sections would yield uniform recurrence times and some greatly different recurrence times. Note, however, the result of sampling this same sequence in sections containg 4 consecutive events (3 recurrence intervals). Each sampled section now must contain both



inter-cluster and intracluster recurrenc times, so the COVs of various local sequences will start to resemble one another. The big drop in the spread of COV values between local sequences thus comes when no sampled section can contain only intercluster, or intracluster, recurrence intervals. Looking at Fig. 22, there is no single conspicuous drop in the spread of COVs as the number of recuurence intervals sampled increases. The most conspicuous drop is from 2 to 3 intervals, but that is based on a single data point (COV=0.96 for 2 intervals). However, if this drop persisted as more data were added to Fig. 22, it would imply that the inventoried faults tended to have earthquakes in clusters of threes, separated by longer gaps. REFERENCES Adams, John and Weichert, D., 1994, Near-term probability of the future Cascadia megaquake: USGS Open-File Report 94-568, p. 5-7. Atwater, B. , pers. comm., 1998. Biasi, G.P. and Weldon, R. III, 1997, Paleoseismic event dating and the conditional probability of large earthquakes on the southern San Andreas fault, California: unpub. manuscript. Bonilla, M.G., Mark, R.K. and Lienkaemper, J.J., 1984, Statistical relations among earthquake magnitude, surface rupture length, and surface fault displacement: Bulletin of the Seismological Society of America, v. 74, n. 6, p. 2379-2411. Goes, S.D.B., 1996, Irregular recurrence of large earthquakes; an analysis of historic and paleoseismic catalogs: Jour. Geophys Res. 101 (B3): 5739-5750. Gurrola, L.D. and Rockwell, T.K., 1996, Timing and slip for prehistoric earthquakes on the Superstition Mountain fault, Imperial Valley, southern California: Jour. Geophys. Res., 101 (B3): 5977-5986. Hunter, R.L. and Mann, C.J. (eds.), 1992, Techniques for determining probabilities of geologic events and processes: International Association for Mathematical Geology, Studies in Mathematical Geology, no. 4, Oxford University Press, Oxford, UK, 364 p. Kelson, K.I., Simpson, G.D., Lettis, W.R., and Haraden, C.C., 1996a, Holocene slip rate and earthquake recurrence of the northern Calaveras fault at Leyden Creek, northern California: Jour. Geophys. Res., 101 (B3): 5961-5976. Kelson, K.I., Simpson, G.D., VanArsdale, R.B., Haraden, C.C. and Lettis, W.R., 1996b, Multiple late Holocene earthquakes along the Reelfoot fault, central New Madrid seismic zone: Jour. Geophys. Res., 101 (B3):6151-6170.



Machette, M.N., Personius, S.F. & Nelson, A.R. 1992. Paleoseimology of the wasatch fault zone: a summary of recent investigations, interpretations, and conclusions, in Gori, P.L & Hays, W.W. (eds.) Assessment of Regional Earthquake Hazards and Risk Along the Wasatch Front, Utah. U.S. Geological Survey Professional Paper 1500, p. A1-A71. Mason, D.B., 1992, Earthquake magnitude potential of active faults in the Intermountain Seismic Belt from surface parameter scaling: unpublished M.S. thesis (Geophysics), University of Utah, Salt Lake City, UT, 110 p. McCalpin, J.P., 1993, Neotectonics of the northeastern Basin and Range margin, western USA: Zeitschrift fur Geomorphologie, Supplement Bd. 94, p. 137-157. McCalpin, James, Forman, S.L. and Lowe, M., 1994, Reevaluation of Holocene faulting at the Kaysville site, Weber segment of the Wasatch fault zone, Utah: Tectonics, v. 13, no. 1, p.1-16. McCalpin, J.P. and Khromovskikh, V.S., 1995, Holocene paleoseismicity of the Tunka Fault, Baikal Rift Zone, Russia: Tectonics, v. 14, p. 594-605. McCalpin, J.P. and Niskenko, S.P., 1996, Holocene paleoseismicity, temporal clustering, and probabilities of future large (M>7) earthquakes on the Wasatch fault zone, Utah: Jour. Geophys. Res., 101 (B3): 6233-6254. Merritts, D.J., 1996, The Mendocino riple junction; active faults, episodic coastal emergence, and rapid uplift: Jour. Geophys. Res., 101 (B3): 6051-6070. Michetti, A.S., Brunamonte, F., Serva, L. and Vittori, E., 1996, Trench investigations of the 1915 Fucino earthquake fault scarps (Abruzzo, central Italy); Geological evidence of large historical events: Jour. Geophys. Res., 101 (B3):5921-5936. Nishenko, S. and Buland, R., 1987, A generic recurrence interval distribution for earthquake forecasting: Bulletin of the Seismological Society of America, v.77, p.1382-1399. Okada, A. and Ikeda, Y., 1991, Active faults and neotectonics in Japan: The Quaternary Research (Daiyonki-Kenkyu), v. 30, p. 161-174. Okada, A. and 11 others, 1989, Trenching study of the Atotsugawa Fault at Nokubi, Miyagawa Village, Gifu Prefecture, central Japan: Journal of Geography, v. 98, p. 62-85. Okumura, K., Shimokawa, K., Yamazaki, H. and Tsukuda, E., 1994, Recent surface faulting events along the middle section of the Itoigawa-Shizuoka Tectonic Line: Journal of the Seismological Society of Japan, v. 46, p. 425-438.



Ota, Y. and Chappell, J., 1996, Late Quaternary coseismic uplift events on the Huon Peninsula, Papua New Guinea, deduced from coral terrace data: Jour. Geophys. Res. 101 (B3): 6071-6082. Pantosti, D., Schwartz, D.P. and Valensise, G., 1993, Paleoseismology along the 1980 surface rupture of the Irpina fault; implications for earthquake recurrence in the southern Appennines, Italy: Journal of Geophysical Research, v. 98, p. 6561-6577 Pantosti, D., D'Addezio, G. and Cinti, F., 1996, Paleoseismicity of the Ovindoli-Pezza fault, central Appenines, Italy; A history including a large, previously unrecorded earthquake in the Middle Ages (860-1300 A.D.): Jour. geophys. Res., 101 (B3): 5937-5960. Pezzopane, S.K., Whitney, J.W., and Dawson, T.E., 1996, Models of earthquake recurrence and preliminary paleoearthquake magnitudes at Yucca Mountain, in Whitney, J.W. (coordinator), Seismotectonic framework and characterization of faulting at Yucca Mountain, Nevada: submitted by U.S. Geological Survey, Denver, CO to U.S. Dept. of Energy, Contract DE-AC04-94AL85000. Plafker, G. and Rubin, M., 1994, Paleoseismic evidence for "Yo-yo" tectonics above the eastern Aleutian subduction zone; coseismic uplift alternating with even larger interseismic subsidence: U.S. Geol. Survey Open-File Rept. 94-568, p. 155-157. Plafker, G., 1987, Application of marine-terrace data to paleoseismic studies: U.S. Geol. Survey Open-File Rept. 87-92, p. 146-156. Qidong, D. and Yuhua, L., 1996, Paleoseismology along the range-front fault of Helan Mountains, north central China: Jour. Geophys. Res., 101 (B3): 5873-5894. Qidong, D., Zhang, Peizhen, Xu, Xiwei, Yang, Xiaoping, Peng, Sizhen and Feng, Xianyue, 1996, Paleoseismology of the northern piedmont of Tianshan Mountains, northwestern China: Jour. Geophys. Res., 101 (B3): 5895-5920. Reiter, L., 1990, Earthquake hazard analysis; issues and insights: Columbia University Press, New York, 254 p. Rockwell, T.K., and Pinnault, C.T., 1986, Holocene slip events on the southern Elsinore Fault, Coyote Mountains, southern California, in Ehlig, P. (ed.), Neotectonics and faulting in southern California: Geological Society of America Guidebook for the Cordilleran Section Meeting in Los Angeles, p. 193-196. Sarna-Wojcicki, A.M., LaJoie, K.R. and Yerkes, R.F., 1988, Recurrent Holocene displacement on the Javon Canyon fault- a comparison of fault-movement history with calculated average recurrence intervals: U.S. Geological Survey Professional Paper 1339, p.125-136.



Schwartz, D.P. and Coppersmith, K.J., 1984, Fault behavior and characteristic earthquakes--Examples from the Wasatch and San Andreas fault zones: Journal of Geophysical Research, v. 89, p. 5681-5698. Sieh, K.E., 1978, Slip along the San Andreas fault associated with the great 1857 earthquake: Bulletin of the Seismological Society of America, v. 68, p. 1421-1448. Sieh, K.E., Stuiver, M., and Brillinger, D., 1989, A more precise chronology of earthquakes produced by the San Andreas fault in southern California: Journal of Geophysical Research, v. 94, P. 603-623. Sims, J.D., 1995, A 200-year average recurrence interval of earthquakes on the San Andreas fault at Phelan Creeks, Carrizo Plain, California; reconstruction from paired offset channels: unpub. manuscript. Slemmons, D.B., 1977, State-of-the-art for assessing earthquake hazards in the US- Report 6, Faults and Earthquake Magnitude: U.S. Army Corps of Engineers, Waterways Experiment Station, Vicksburg, Mississippi, Miscellaneous Paper S-73-1, 129 p. Slemmons, D.B., 1982, Determination of design earthquakes magnitudes for microzonation: Proceedings of the Third International Earthquake Microzonation Conference, Seattle, WA; Earthquake Engineering Research Institute, v. 1, p. 110-130. Slemmons, D. B., Bodin, P., and Zhang, X., 1989, Determination of earthquake size for active faults: Intl. Seminar Seismic Zonation, Guangzhou, China, p. 157-169. Swan, F.H., 1988, Temporal clustering of paleoseismic events on the Oued Fodda fault, Algeria: Geology, 16: 1092-1095. Valentine, D., Vick, G., Carver, G. and Manhan, C.S., 1992, Late Holocene stratigraphy and paleoseismicity, Humboldt Bay, California: Pacific Cell, Friends of the Pleistocene Guidebook for the Field trip to Northern Coastal California, June 5-7, 1992. Wells, D.L. and K.J. Coppersmith, 1994, Empirical relationships among magnitude, rupture length, rupture area, and surface displacement: Bulletin of the Seismological Society of America, v. 84, p. 974-1002. Working Group on California Earthquake Probabilities, 1988, Probabilities of large earthquakes occurring in California on the San Andreas fault: U.S. Geological Survey Open File Report 88-398, 62 p. Working Group on California Earthquake Probabilities, 1990, Probabilities of large earthquakes in the San Francisco Bay region, California: U.S. Geological Survey Circular 1053, 51 p.



Zollweg, J. E., 1998, On the use of surface rupture lengths to determine paleoseismic avent magnitudes: Seismol. Res. Letters 69(2): 140.



List of Figures Fig. 1. Surface net throws associated with the 1983 M 7.3 Borah Peak, Idaho earthquake. Fig. 2. Frequency characterization of the net throws at Borah Peak, as shown in Fig. 1. Fig. 3. Example of a logic tree branch structure for maximum throw (Tmax). Fig. 4. Frequency of inventoried surface ruptures used in this study that contain various numbers of displacement measurement points. Note that most ruptures have <50 displacement measurements. Fig. 5. Surface fault displacement data for the 1857 Ft. Tejon earthquake on the San Andreas fault, California. (a) normalized strike-slip displacement plotted along normalized strike; (b) Frequency of normalized fault displacements. Fig. 6. Composite normalized frequency data for surface displacements during 10 normal faulting events. Average displacement (AD) of the 559 measurements is 0.33+/-0.09 of the maximum displacement (MD, or Dmax). Note the abundance of small displacements. Fig. 7. Composite normalized frequency data for surface displacements during 6 reverse faulting events. Average displacement (AD) of the 192 measurements is 0.38+/-0.09 of the maximum displacement (MD, or Dmax). Small displacements are less abundant than for normal faulting events. Fig. 8. Composite normalized frequency data for surface displacements during 18 strike-slip faulting events. Average displacement (AD) of the 1088 measurements is 0.38+/-0.08 of the maximum displacement (MD, or Dmax). Note the relatively uniform abundance of displacements smaller than the 50%-ile. Fig. 9. Composite normalized frequency data for vertical surface displacements during 15 reverse-oblique faulting events. Average displacement (AD) of the 556 measurements is 0.33+/-0.12 of the maximum displacement (MD, or Dmax). Note the abundance of small displacements. Fig. 10. Composite normalized frequency data for horizontal surface displacements during 15 reverse-oblique faulting events. Average displacement (AD) of the 556 measurements is 0.30+/-0.11 of the maximum displacement (MD, or Dmax). Note the abundance of small displacements. Fig. 11. Composite normalized frequency data for net surface displacements during 15 reverse-oblique faulting events. Average displacement (AD) of the 427 measurements is 0.35+/-0.10 of the maximum displacement (MD, or Dmax). Note the abundance of small displacements.



Fig. 12. Composite normalized frequency data for vertical surface displacements during 6 normal-oblique faulting events. Average displacement (AD) of the 312 measurements is 0.31+/-0.07 of the maximum displacement (MD, or Dmax). Most common displacements are 10-30% of Dmax. Fig. 13. Composite normalized frequency data for horizontal surface displacements during 6 normal-oblique faulting events. Average displacement (AD) of the 76 measurements is 0.37+/-0.11 of the maximum displacement (MD, or Dmax). Note the abundance of small displacements. Fig. 14. Composite normalized frequency data for net surface displacements during 6 normal-oblique faulting events. Average displacement (AD) of the 76 measurements is 0.42+/-0.11 of the maximum displacement (MD, or Dmax). Note the scarcity of small displacements, and the irregular frequency trend. Fig. 15. Frequency of consecutive recurrence intervals (RIs) contained in inventoried paleoearthquake sequences (chronologies) used in this study. Note that most local chronologies have only 2 or 3 consecutive recurrence intervals. Fig. 16. Frequency of consecutive recurrence intervals contained in inventoried paleoearthquake sequences (chronologies) used in this study, separated by fault type. Note that subduction zones have the most RIs per record, and normal and reverse faults the fewest. Fig. 17. Frequency of normalized recurrence times (T/Tavg) contained in 19 paleoearthquake chronologies from normal faults. The coefficient of variance of the 56 RIs is 0.32. Fig. 18. Frequency of normalized recurrence times (T/Tavg) contained in 9 paleoearthquake chronologies from strike-slip faults. The coefficient of variance of the 44 RIs is 0.39. Fig. 19. Frequency of normalized recurrence times (T/Tavg) contained in 6 paleoearthquake chronologies from reverse faults. The coefficient of variance of the 16 RIs is 0.37. Fig. 20. Frequency of normalized recurrence times (T/Tavg) contained in 7 paleoearthquake chronologies from subduction zone megathrusts. The coefficient of variance of the 45 RIs is 0.39. Fig. 21. Frequency of normalized recurrence times (T/Tavg) contained in 41 paleoearthquake chronologies from all fault types. The coefficient of variance of the 161 RIs is 0.36.



Fig. 22. COV of normalized recurrence for 41 local paleoearthquake sequences, as a function of the number of recurrence intervals in each sequence. The convergence of COVs to ca. 0.3 with increasing number of consecutive RIs suggests that COV=0.3 may be a fundamental characteristic of long-term fault behavior.



1983 Borah Peak, Dvert

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1983 Borah Peak, Dvert

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Fig. 2. Frequency characterization of the net throws at Borah Peak, as shown in Fig. 1.



Fig. 3. Example of a logic tree branch structure for maximum throw (Tmax). The five values on the branches and their associated probabilities come from the empirical distribution of frequencies of 10%-ile values of T/Tmax. They were arbitrarily binned in probability bins of 0.2, although many other choices exist. The three columns at right show various predicted values for Tmax during a paleoearthquake (each value having a probability of 0.2), given single-point measurements of T somewhere along the paleoearthquake rupture. For example, if the random measurement of T was 2.0 m, then Tmax during that same rupture could have drawn from a continuous probability distribution approximated by these disctrete values (and probabilities): 2.6 m (0.2), 3.3 m (0.2), 4.0 m (0.2), 5.0 m (0.2), or 9.5 m (0.2). Note that the distribution is bounded by T on the lower end (Tmax cannot be less than the random T), and is asymmetrical with a long “tail” of higher values of predicted Tmax. The median value of the distribution is approximately 2T. That means that, given a random T of 2.0 m, 50% of the values of predicted Tmax lie between 2.0 and 4.0 m, and 50% lie between 4.0m and infinity. The implications of this distribution are rather staggering for deciding how to use displacement measurements from randomly-located single trenches on a fault trace. For estimating paleoearthquake magnitude using an empirical equation based on Tmax (or maximum displacement, in the terminology of Wells and Coppersmith, 1994), use of this approach will predict much larger paleomagnitudes than simply assuming (as was often done in the past) that the random T value EQUALS Tmax.



Fig. 4. Frequency of inventoried surface ruptures used in this study that contain various numbers of displacement measurement points. Note that most ruptures have <50 displacement measurements.



1857 Ft. Tejon Earthquake: San Andreas fault, Dss

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1857 Ft. Tejon Earthquake: SanAndreas fault, Dss

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Fig. 6. Composite normalized frequency data for surface displacements during 10 normal faulting events. Average displacement (AD) of the 559 measurements is 0.33+/-0.09 of the maximum displacement (MD, or Dmax). Note the abundance of small displacements.



Fig. 7. Composite normalized frequency data for surface displacements during 6 reverse faulting events. Average displacement (AD) of the 192 measurements is 0.38+/-0.09 of the maximum displacement (MD, or Dmax). Small displacements are less abundant than for normal faulting events.



Fig. 8. Composite normalized frequency data for surface displacements during 18 strike-slip faulting events. Average displacement (AD) of the 1088 measurements is 0.38+/-0.08 of the maximum displacement (MD, or Dmax). Note the relatively uniform abundance of displacements smaller than the 50%-ile.



Fig. 9. Composite normalized frequency data for vertical surface displacements during 15 reverse-oblique faulting events. Average displacement (AD) of the 556 measurements is 0.33+/-0.12 of the maximum displacement (MD, or Dmax). Note the abundance of small displacements.



Fig. 10. Composite normalized frequency data for horizontal surface displacements during 15 reverse-oblique faulting events. Average displacement (AD) of the 556 measurements is 0.30+/-0.11 of the maximum displacement (MD, or Dmax). Note the abundance of small displacements.



Fig. 11. Composite normalized frequency data for net surface displacements during 15 reverse-oblique faulting events. Average displacement (AD) of the 427 measurements is 0.35+/-0.10 of the maximum displacement (MD, or Dmax). Note the abundance of small displacements.



Fig. 12. Composite normalized frequency data for vertical surface displacements during 6 normal-oblique faulting events. Average displacement (AD) of the 312 measurements is 0.31+/-0.07 of the maximum displacement (MD, or Dmax). Most common displacements are 10-30% of Dmax.



Fig. 13. Composite normalized frequency data for horizontal surface displacements during 6 normal-oblique faulting events. Average displacement (AD) of the 76 measurements is 0.37+/-0.11 of the maximum displacement (MD, or Dmax). Note the abundance of small displacements.



Fig. 14. Composite normalized frequency data for net surface displacements during 6 normal-oblique faulting events. Average displacement (AD) of the 76 measurements is 0.42+/-0.11 of the maximum displacement (MD, or Dmax). Note the scarcity of small displacements, and the irregular frequency trend.



Fig. 15. Frequency of consecutive recurrence intervals (RIs) contained in inventoried paleoearthquake sequences (chronologies) used in this study. Note that most local chronologies have only 2 or 3 consecutive recurrence intervals.



Fig. 16. Frequency of consecutive recurrence intervals contained in inventoried paleoearthquake sequences (chronologies) used in this study, separated by fault type. Note that subduction zones have the most RIs per record, and normal and reverse faults the fewest.



Fig. 17. Frequency of normalized recurrence times (T/Tavg) contained in 19 paleoearthquake chronologies from normal faults. The coefficient of variance of the 56 RIs is 0.32.



Fig. 18. Frequency of normalized recurrence times (T/Tavg) contained in 9 paleoearthquake chronologies from strike-slip faults. The coefficient of variance of the 44 RIs is 0.39.



Fig. 19. Frequency of normalized recurrence times (T/Tavg) contained in 6 paleoearthquake chronologies from reverse faults. The coefficient of variance of the 16 RIs is 0.37.



Fig. 20. Frequency of normalized recurrence times (T/Tavg) contained in 7 paleoearthquake chronologies from subduction zone megathrusts. The coefficient of variance of the 45 RIs is 0.39.



Fig. 21. Frequency of normalized recurrence times (T/Tavg) contained in 41 paleoearthquake chronologies from all fault types. The coefficient of variance of the 161 RIs is 0.36.

Fig. 22. COV of normalized recurrence for 41 local paleoearthquake sequences, as a function of the number of recurrence intervals in each sequence. The convergence of COVs to ca. 0.3 with increasing number of consecutive RIs suggests that COV=0.3 may be a fundamental characteristic of long-term fault behavior.



APPENDIX 1-- Summary of Surface Ruptures Analyzed



APPENDIX 2-- Specific Comments by Event: Normal-Slip Faults EQN 4 Pitaycachi, Mexico. Poor data base, with some scarp height inferred to be the

Dvert. The southern ~32 km (43%) of the main 75 km fault rupture has no displacement measurements, and the northern 43 km (57%) section has only 11 measurements. Some measurements are of scarp height, rather than vertical, strike-slip, or net displacement, and may overestimate the AD and MD.

EQN 9 Pleasant Valley, Nevada, Note that there is a gap between the tobin and china

mountain scarps of 7.2 km, or an increase in the average fault displacement of 13.4 %. Caskey et al (1996) have 1.9 m average SO-vert, and (2.2 m) for 60 and we have 0.27339*5.80 = 1.58, or 1.58/5.80 = 0.27. , or 1.83 if 15% is added for the gaps between the two main faults-China Mountain and Mt. Tobin. Slemmons earlier estimate, using a less precise method was an average displacement of 1.74/5.80 m = 0.30. The real displacements are about 15.5% higher for a 60 degree dip, or AD=1.84, and 2.12 m.

EQN 45 Rainbow Mountain. Note that the unpublished work of John Caskey

shows that there may be as Dss = l meter in one or two localities. EQN 47 Fairview Peak. This linear fault zone is mainly a right-oblique fault, with

the part south of Chalk Mountain (Fairview Peak Fault) dipping east, and the part north of Chalk Mountain (Louderback Fault) dipping west, with a bend near the point of change, but the fault is a narrow, nearly continuous zone, which does not have a position above the down-dip, seismogenic location. In addition to the main zone several other normal-slip and normal-oblique-slip faults were activated. The scarps assocated with the Eastern Monte Cristo Mountains fault are of uncertain age, and may be either from the 1932 Cedar Mountain earthquake, or the 1954 earthquake.

EQN 47 Gold King Fault. Dvert = 1.0 m from Table 1 of Caskey et al. (1996).

Comparison of Caskey et al (1996) and Slemmons et al. (1959) showed no systematic differences in measured VS measurements, although their highest scarp was 1.21 m (4 ft). Caskey’s measurements were used for this fault.

EQN 54 Hebgen Lake Faulting. The main fault zone is very short, about 26 km,

which includes several main overlapping branches. This analysis is based on showing this as a single fault that is much longer than the total length of the zone.



APPENDIX 3—Recurrence Data from Local Paleoearthquake Chronologies



APPENDIX 4—Frequency Data for Normalized Displacements for Various Fault Types. 4a—Normal Faulting Events 4b—Reverse Faulting Events 4c—Strike-Slip Faulting Events 4d—Reverse Oblique Faulting Events 4e—Normal-Oblique Faulting Events

1998 statistics of paleoseismic data - geo-haz consulting inc

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