Appendix R1, Distribution of Slip in Ruptures
Glenn Biasi, Ray J. Weldon, and Timothy E. Dawson
University of Nevada, Reno
University of Oregon, Eugene
California Geological Survey, Menlo Park, California
Introduction
We investigate the distribution of slip on ruptures in the Grand Inversion. In terms of the inversion itself, the distribution of slip on rupture r is divided among subsections s, and the individual subsection displacements are denoted Dsr. The frequency with which ruptures occur is roughly the slip rate divided by the average value for Dsr.
Candidate shapes for slip distribution include the uniform (“boxcar”), triangular, and empirical. Wesnousky (2008) fit a the triangular shape to observed ruptures, but did not find it predicted much of the data, plus it requires knowledge of the rupture direction to apply prospectively. Biasi and Weldon (2006) found that the functional form sin(x/2L) 1/2 (“sinesqrt”) fits surface ruptures once they are normalized by length and average displacement. This shape works well when all ruptures are considered, as well as for subsets such as ruptures < 30 km and >200 km. In addition it can be used without knowing the rupture direction. The general
“rainbow” shape of the net rupture profile across fault-to-fault interactions has been modeled using boundary element and finite-difference methods (Willemse et al.,
1996, Kase, 2010). They find general support for a flattened slip distribution, the specific shape of which depends on how the model is structured and how many elements are interacting. The set of normalized empirical ruptures seems to include similar degrees of variation without introducing complications of how it arises. As such it is the focus of proposed implementation of Dsr.
Model Rupture Shape
The distribution of slip in surface ruptures can be approached empirically or theoretically. The empirical approach seeks ways to generalize and apply observations of previous ground ruptures. The theoretical approach draws from studies of strain and displacement in elastic media. In general the two approaches agree quite well, suggesting that the essential properties of rupture displacement are being represented.
Empirical Rupture Shape: A basic problem for using observed ruptures is that the database of well-mapped ruptures is small and ruptures vary significantly from one another. This means that for any given rupture length there are too few past ruptures of similar size to develop a statistically meaningful representation.
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Hemphill-Haley and Weldon (1999) addressed this problem by first normalizing ruptures by length and average displacement. By giving all ruptures unit length, they can be compared to one another and investigated for systematic properties.
This approach does make the assumption that slip variability among small and large ruptures is similar, but to first order this seems satisfactory (Shaw, 2011; Biasi and
Weldon, 2006). An empirical shape for rupture profiles is obtained by stacking the normalized ruptures and using their averaged shape.
To develop an averaged rupture shape we used 21 strike-slip ruptures from
Wesnousky (2008). Two approaches are possible in developing the average. The first approach includes each rupture only once, either as plotted in the original paper, or otherwise, such as with the epicenter on one side, to look for systematics in rupture propagation. Wesnousky (2008) explored these possibilities at some length, but did not find any compelling directionality effects or reasons to adopt other rupture shapes such as triangles. The second approach is to consider the plotting convention for ruptures as arbitrary, and to include in the average each rupture and its left-to-right reflection. The plot of any given rupture would be reversed if plotted from the other side of the fault. By stacking ruptures and their reflections the result is less subject to an accident of presentation. Note that these measures to reflect and normalize are done because fault-by-fault particularized information on rupture is generally not available. If, on the other hand, a characteristic rupture is known to occur on a particular fault, using an averaged rupture profile for it would not be appropriate.
Figure 1 provides results of the averaging process for different subsets of
Wesnousky (2008) strike-slip ruptures. In each figure the average is shown for unreflected and reflected rupture stacks. Short ruptures are seen to have similar average shapes compared to longer subsets. The averaged shape for the longest ruptures is of interest to see whether the rupture shape flattens in the middle, perhaps because of a saturation in slip. There is some suggestion to this effect among the >200 km ruptures, but not so sufficiently strong a case that an additional parameter is required. Note that for normalized ruptures only the shape of the rupture is preserved, so that the question of whether slip saturates is not really being addressed in Figure 1. Two model shapes are drawn on each set of profiles, functionally sin(x/2L) and sin 1/2 (x/2L) (a.k.a, “sinesqrt”). The sinesqrt shape captures the averaged shape remarkably well considering that it is not fit to the data (or equally, plotted with no free parameters).
Figure 1: Strike-slip rupture profiles averaged in groups by length. (a) Blue line is the average of four rupture profiles shorter than 30 km. Upper panel is unreflected; lower each profile has been stacked with its reflection. Sinesqrt shape is in red, sin(x/2L) is in green. (b)
16 profiles < 75 km in length. (c) 7 profiles > 100 km. These ruptures would all be 6 or more times the thickness of the seismogenic zone. (d) 5 profiles > 200 km. The average shape emerges even without reflection.
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We looked briefly into why the sinesqrt shape might work as well as it does.
Eschelby (1957) found that a uniform stress drop patch in a homogeneous, isotropic, linear elastic space will be elliptical. The ellipse concentrates stress at the crack edge into an apparent singularity. Studies by Ingraffea (1987), Vermilye and
Scholz, (1998), Cowie and Scholz (1992), Okubo and Dieterich (1984), and Martel and Pollard (1989), among others, have examined this problem. A process zone of non-linear behavior, micro-fracture or off-fault failure of some sort is inferred at the crack tip. Wilkins and Schultz (2005) synthesized previous work into a model end of rupture they termed a “cohesive end zone” (CEZ). The CEZ is a zone near the crack tip in which resolved shear stress along the fault is matched by back shear stresses. The back stresses are modeled as a zone of increasing normal stresses that act with friction to react, and ultimately to counteract the shear stress and arrest rupture. In their model displacement on the rupture is tapered and decreases asymptotically to the end, instead of having a maximum displacement gradient at the crack tip. This taper reduces the displacement gradient and the singularity.
Without needing to endorse any specific model of processes at the ends, the cohesive end zone model flattens the displacement profile relative to an ellipse. It is also likely that the shear stresses on the fault are not uniform, but tapered, because faults have little or no intact material to fracture. It appears that relative to a model elliptical surface rupture, the more tapered sinesqrt shape better matches real ruptures because it represents more of the of the physics of what is happening at the ends of ground ruptures.
Normalizing measured surface rupture profiles by average displacement removes differences between ruptures caused by variations in stress drop and the thickness of the elastic crust. On the other hand, the spread of real data around a
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regression (e.g., Wells and Coppersmith 1994 AD vs. L) is caused by this variation.
Therefore, variability in average displacement can be preserved by sampling from the uncertainty in the average displacement vs. rupture length (AD(L)) relation.
Details of UCERF-3 regression relations and their uncertainties are in Appendix R2.
The Effect of Enveloping on Average Displacement
In W08 the average displacements of ruptures were taken from the point measurements of displacement reported in the individual studies. In some cases the average displacements almost certainly underestimate the slip at, say, a kilometer depth. The potential underestimation of AD was also raised as a possible explanation for why the geologic moment systematically underestimates instrumental Mw. To estimate the potential scale of underestimation of slip in rupture profiles, an envelope estimate of the displacement was developed for the strike-slip ruptures of W08. Figure 2 shows as an example the Hector Mine event, which had one of the larger discrepancies. Figure 3 shows the relative increase in displacement versus average displacement. On average enveloping the displacement profiles increases the average displacement by about 15%. The largest events are seen to have the least change from enveloping because little of their length is mapped in sufficient detail for a 1-2 km averaging function to have much effect.
Caption, Figure 2: Detailed field measurements of the Hector Mine rupture. AD using the measurements is 1.57 m. An envelope function was drawn by hand (stars) is used to interpolate assuming a more slowly varying slip function at 1-2 km depth. Note that local site conditions can act to hide surface motion or less commonly, to amplify them. Figure 3: Ratio of enveloped AD to AD from individual points. Enveloping increases AD on average by about 15%.
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Expanded Event Set
The surface rupture set in Wesnousky (2008) was limited by in scope to ruptures with readily available geologic mapping of nearby fault structures. The goal was to compile data to relate rupture stopping to fault ends, steps, and geometric discontinuities. The uniform presentation of ruptures in W08 made it relatively easy to import and apply to the problem of an average rupture profile shape. Limits on the selection of W08 events however, mean that they are not necessarily the best selection for alternative uses such as for developing length vs. displacement regressions (UCERF-3 Task R2). Recognizing the need for this data in
Task R2 and the overlap with Task R1, a wider net was cast to find additional ground ruptures with surface rupture measurements, especially as they would contribute to use in constructing AD vs. L relations.
Two classes of ground ruptures were sought for expansion of the data set. The first are long ruptures that can contribute to the asymptotic shape of the AD-L curve.
The second are any ruptures in California that might be developed to constrain the behavior of ruptures in California. These include the 1872 Owens Valley, 1906 San
Francisco, and 2010 El Mayor-Cucapah earthquakes and ruptures identified in the new LiDAR data set (Appendix P10).
Twenty-five earthquakes are added in Table R1. A narrative description of each earthquake with data sources is provided in Addendum R1. Some effort was
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expended to capture the uncertainties in length and AD. In many cases the uncertainty in length is not due to measurement uncertainty but reflects other sources such as when the rupture ends were estimated for lack of physical access.
Another case is how length of significant secondary co-seismic ruptures are included. In part for this reason uncertainties in length and average displacement are inversely related to one another. That is, the maximum estimates for length are associated with minimum estimates for AD, normally because the additional length is associated with rupture with lesser displacements. The inverse relation between
AD and length has the positive effect of stabilizing estimates of geologic moment.
Length and/or average displacement estimates were adjusted for four entries in
Wesnousky (2008). For the 1857 Ft Tejon and 2002 Denali earthquakes, new LiDAR measurements were used to adjust the rupture profile. For the 1857 rupture LiDAR
(Zielke et al., 2010) reduced the displacement estimates in the central part of the rupture. The rupture length was also shortened to remove contributions from the previous 1812 rupture on the southeast. For the Denali rupture LiDAR measurements were used to fill in displacements across the Denali-Totchunda intersection. Initially it appeared that displacements were small, giving the appearance of two nearly separate ruptures, but new data show that displacements were quite continuous across this boundary. The 1992 Landers rupture length was reduced and the average displacement slightly increased by removal of the Eureka
Peak and Burnt Mountain sections. Ground rupture on these sections was triggered by the main shock and occurred tens of seconds after it (Hough, 1994).
Figure 4. AD vs. Length for W08 and new events. Green line is Wells and Coppersmith (1994), shown for reference.
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Figure 5. Subset of earthquakes in Figure 4 that are from California. LiDAR ruptures are known from paleoseismological study and LiDAR measurements. Others are historical. The gray square shows an alternate, shorter length for the 1812 rupture.
Magnitudes for the compilation are Mw, generally from the latest available studies, unless marked otherwise. Geologic moment magnitudes were not used because of the circularity of using them subsequently to evaluate magnitude-length and magnitude-area regressions. Many early estimates of magnitude especially in the first half of the 20 th century were extremely high compared to later estimates, primarily because they relied on surface or shear waves well beyond the free period of the sensors. To the extent possible these estimates were replaced with later Mw values. The Engdahl and Villasenor (2002) Mw estimates were adopted for many events. They developed regressions to estimate modern Mw from early magnitudes such as Ms or surface waves that consider limitations in available measurements and methods. For some events (e.g., 1872 Owens Valley, 1911 Chon Kemin), magnitude uncertainties are large, reflecting the range of apparently credible estimates.
Depth estimates also varied among studies of a given rupture. Aftershock zones were used where available. Where seismologists could provide estimates from waveform modeling or depth phases (e.g., 2005 Pakistan), that depth was preferred. A depth greater than 25 km is listed only for the 1905 Mongolian earthquakes. The estimate (40 km best, 30-70 km range) is adopted from waveform modeling (Schlupp and Cisternas, 2007). Although instrumentation at the time was limited, they focused on on-scale body-wave waveforms recorded well within the instrumental free periods. For many earthquakes the depth controls are not well known.
The Length Scale for Multi-Fault Ruptures
The sinesqrt shape is seen to reasonably represent normalized slip in earthquake ruptures. For simple fault traces, a usable rupture is constructed by
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using the rupture length to scale the shape using a length-average displacement relationship.
For cases where rupture jumps from one fault to another, the displacement distribution might be done a couple of ways. The two ways reflect different possible ways that faults link in a multi-fault rupture. One way is to use the complete rupture length, which would scale to a larger AD, then distribute slip onto the linking fault sections in a way that makes the total slip add up. This method in effect views the total slip as the result of a similarly large stress field capable of larger slips. A second way is to view fault-to-fault rupture as a sequential triggering process where component faults are loaded individually, and produce fault-to-fault ruptures when one happens to trigger the next. In this situation, slip on individual faults scales with the individual fault lengths.
To resolve this question, slip in the W08 strike-slip ruptures is plotted versus their full rupture length in Figure 6. The regression of Wells and Coppersmith
(1994) is also shown. The bulk of the distribution points are reasonably distributed around the regression, indicating that the full rupture length and AD correspond reasonably. If the W08 ruptures are divided at step-overs into individual fault ruptures (Figure 7, a), the AD of the individual faults, perhaps not surprisingly, do not scale with their individual lengths. This means that while fault elements of a fault-to-fault rupture may occasionally be individually loaded in scale with their lengths and trigger sequentially, this situation would be the exception and not the rule. Similar conclusions apply to the non-strike-slip ruptures in W08 (Figure 7, b).
Caption: Figure 6. (Left) Average displacement is plotted vs. surface rupture length for strike-slip ruptures in W08. The W08 events are consistent in their trend and scatter with the original
L-AD data of Wells and Coppersmith (1994).
Figure 7. (Below) AD vs. L for segments of
W08 strike-slip ruptures. Segment AD consistently is greater than would be predicted by the segment length indicating that multi-fault ruptures are not simply individual faults that happen to trigger each other. (Right) Limited reverse and normal faulting data show a similar pattern.
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The sequential triggering model might be modified to include dynamic effects.
In this model once the second fault is triggered, a feedback condition results in which slip on the first fault increases because the second fault is also slipping.
Willemse et al. (1996) show with quasi-static models that fault interaction does increase slip, but the increase is relatively small. The dynamic interaction model requires information at the leading edge of ruptures somehow feed back to the successive sections behind. Dynamic models of multi-segment ruptures by Kase
(2010) indicate that AD does depend on how a rupture is segmented, but that slip does not continue to increase with rupture length as the sequential model would require. However this question is resolved, the conclusion is that full rupture length is most relevant for L-AD scaling of sinesqrt model displacements.
Alternative Rupture Shapes
Other slip profile shapes than the sinesqrt were considered in the rupture frequency inversion. The simplest is a uniform (boxcar) distribution. The differences were discussed in a June 2011 workshop. The conclusion from that discussion was that the shape should be matched to the slip rate gradients. If a tapered rupture shape such as the sinesqrt is applied, then slip rates should taper toward fault ends and major step-overs. If ruptures are assigned a uniform shape, the slip rates must continue to the end of the fault so that net slip can be matched. If slip rates are not tapered, but the rupture profile is, the inversion will seek to match the fault slip rate by adding extra small ruptures at the fault ends.
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Slip Distribution at Steps and Fault-to-Fault Jumps
Slip on ruptures such as the 1992 Landers event are seen to end on one fault and continue on another. The individual sections of the rupture have tapered ends suggesting that they should be represented by separate “rainbow” shapes.
However, in spite of tapers at steps the net shape of the rupture is similar to a rupture without steps. Slip increases on the contributing segments of the rupture, and tapers more rapidly where they overlap. Thus when displacement is totaled, the net AD is generally consistent with the length. Modeling results (Kase, 2010) indicate that AD should be larger for ruptures comprised of fewer, longer contributing segments. However, the differences are small compared to the variability in the empirical AD vs. L data, which includes data from short and long multi-segment ruptures. Future research may allow some reduction in AD vs. L uncertainty if a systematic effect of segment length can be demonstrated. For
UCERF-3 use the recommended strategy is to use the sinesqrt shape, and scale it based on its length with an L-AD relation and its uncertainties.
We investigated discordance among slip vectors of adjoining sections as a way of modulating displacements within a master shape applied to ruptures. Intuitively, displacement might decrease after negotiating a change in trend or a fault-to-fault jump to a different style of faulting. However, we found the empirical data of mapped ruptures give too few well-documented cases to use this information prescriptively in UCERF-3.
Applying the Model Rupture Shape
The sinesqrt function is continuous, while the ruptures in the inversion consist of sub-segments, each of which has constant slip within it. Section lengths are constructed to be half the thickness of the seismogenic crust, which varies spatially.
Constant slip within sub-sections leads to a coarse discretization of rupture profiles.
To discretize individual ruptures on a single fault, the sinesqrt shape is implemented by averaging displacement of the functional form within the section. For a rupture of N sections (N>=2), there are N+1 edges of sections. The value of the functional form is found at each edge. The unnormalized section displacement is the average of the two edge points. The average displacement for the full rupture is implemented by scaling the section average displacements higher or lower using an
L-AD relationship to achieve the desired average for the entire rupture.
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References
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Cowie, P A. and C. H. Scholz (1992). Physical explanation for the displacementlength relationship of faults using a post-yield fracture mechanics model,
Journal of Structural Geology, 14, 983-997.
Engdahl and Villasenor (2002) Global Seismicity: 1900-1999, in the International
Handbook of Earthquake Engineering and Seismology, W. H. K. Lee, H.
Kanamori, P. C. Jennings, and C. Kisslinger eds.
Eschelby, J. D. (1957). The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proceedings of the Royal Society of London, A,
241, 376-396.
Hemphill-Haley, M. A. and R. J. Weldon II (1999). Estimating prehistoric earthquake magnitude from point measurements of surface rupture, Bulletin of the
Seismological Society of America, 89, 1264-1279.
Hough, S. E. (1994). Southern surface rupture associated with the M 7.3 1992
Landers, California, Earthquake, Bulletin of the Seismological Society of America,
84, 817-825.
Ingraffea, A. R. (1987). Theory of crack initiation and propagation in rock, in
Fracture Mechanics of Rock, B. K. Atkinson (ed.), Academic Press, London, 71-
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Kase, Y. (2010). Slip-length scaling law for strike-slip multiple segment earthquakes based on dynamic rupture simulations, Bulletin of the Seismological Society of
America, 100, 473-481.
Okubo, P. G. and J. H. Dieterich (1984). Effects of fault properties on frictional instabilities produced on simulated faults, Journal of Geophysical Research, 89,
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Martel, S. J. and D. D. Pollard (1989). Mechanics of slip and fracture along small faults and and simple strike-slip fault zones in granitic rock, Journal of
Geophysical Research, 94, 9417-9428.
Shaw, B. E. (2011). Surface slip gradients of large earthquakes, Bulletin of the
Seismological Society of America, 101, 792-804, doi: 10:1785/0120100053.
Schlupp, A. and A. Cisternas (2007). Source history of the 1905 great Mongolian earthquakes, Geophysical Journal International, 169, 1115-1131.
Vermilye, J. M. and C. H. Scholz, (1998). The process zone: a microstructural view of fault growth, Journal of Geophysical Research, 103, 12,223-12,237.
Wells, D. L., and K. J. Coppersmith (1994). New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement, Bull. Seism. Soc. Am. 84, 974-1002.
Wesnousky, S. G. (2008). Displacement and geometrical characteristics of earthquake surface ruptures: Issues and implications for seismic-hazard analysis and the process of earthquake rupture, Bulletin of the Seismological
Society of America, 98, 1609-1632.
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Willemse, E. J., D. D. Pollard, and A. Aydin (1996). Three-dimensional analysis of slip distributions on normal fault arrays with consequences for fault scaling,
Journal of Structural Geology, 18, 295-309.
Wilkins, S.J. and R.A. Schultz (2005), 3-D cohesive end-zone model for source scaling of strike-slip interplate earthquakes, Bull. Seismol. Soc. Am., 95, 2232-2258.
Zielke, O., J. R. Arrowsmith, L. G. Ludwig, S. O. Akciz (2010). Slip in the 1857 and earlier large earthquakes along the Carrizo Plain, San Andreas fault, Science,
327, 1119-1122, DOI: 10.1126/science.1182781.
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Addendum to Appendix R2, Distribution of Slip in Ruptures
Glenn Biasi, Ray Weldon, Tim Dawson
Introduction
The event set used in magnitude-area relations of Hanks and Bakun (2002) differ from the smaller set examined by Wesnousky (2008; “W08”). Bruce Shaw showed in a March 2011 UCERF-3 workshop in Menlo Park that the difference would have consequences for the relationships recommended to UCERF-3 for magnitude-area scaling and for his proposed alternative, average displacement (AD) vs. surface rupture length (L) (UCERF-3 Report Appendix R2). The W08 events were recognized as well reviewed, but the collection was restricted to events with good mapping of the rupture and nearby faults and was limited in resources for data collection. The W08 data were not developed to constrain AD vs. L regressions.
From the workshop a review was recommended of the extra events in Hanks and
Bakun (2002), and of the literature at large for any additional events that could improve the L-AD curve, focusing particularly on events with large rupture lengths.
The list of largest events discussed in the March 2011 workshop included:
1872 Owens Valley
1905 Tsetserleg
1905 Bulnay
1906 San Francisco
1911 Chon-Kemin
1920 Haiyuan
1976 Motagua
1997 Manyi
2008 Wenchaun
2010 El Mayor Cucapah.
Other events with sufficient data were discovered in the course of the review. We also examined a few particular parameters in Table 1 of W08 where workshop attendees questioned particular entries. The discussion below covers all new events and any W08 events for which L, AD, or Mw were modified.
A review of available rupture maps indicates that ruptures often include overlapping and secondary traces that would not be counted in the main trace total length. Events that have overlapping rupture segments that contribute to moment release but not to total rupture length may create a bias in regression of displacement vs. rupture length. In light of this it seemed worthwhile for key events to estimate the length with overlaps as an alternative for regression purposes.
Adjusted lengths and displacements may improve the degree of agreement between geologic and seismic moments.
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Events to Supplement the Wesnousky (2008) Collection
Owens Valley, 26 March 1872
Style: SSR
Length: 110 (107-140)
AD: 2.8 (2.6-3.4)
Depth: 17.5 (15-20)
Dip: 80 (65-105)
Instrumental Magnitude: N/A.
Discussion: Beanland and Clark (1994) mapped the rupture in the field and integrated earlier observations. Only a limited number of offsets were obtained because much of the evidence was lost to erosion. Some of the most important reported displacements are internally inconsistent (e.g., 6.1 m of strike-slip on a trace a few hundred meters long). The length estimate of 110 (107-140) uses the early known length of 90 km plus an accepted extension from low-angle sun photos by Vittori et al. (2003) to the southern end of Owens Lake, plus 3 km for trace lost over time. One meter strike slip and 0.5 m is added to the AD calculation to give the southern 8.7 km of extension enough displacement to be found in low angle sun photographs. Upper bound length is from Hough and Hutton (2008); if used, AD would be decreased as surface rupture, if present, was apparently small. The AD computed for horizontal component offset, 2.6 m, is from the LiDAR observations for UCERF-3 Task P10 (Appendix P10). The AD estimate in the table combines 2.6 m horizontal with 1 m average vertical displacement from Beanland and Clark
(1994) in the square-root of sum of squares. Depth is averaged from doubledifference relocations of Hauksson and Shearer (2005), as cited in Hough and
Hutton (2008). Dip is from Beanland and Clark (1994). No instrumental magnitude exists; Hough and Hutton estimate M7.6-7.8 from intensity measures and comparison with the 1906 earthquake.
Tsetserleg, Mongolia, July 1905
Style: SS Left Oblique
Length: 177 (130-190) km
AD: 2.3 (2.3-3.8) m
Depth: 40 (30-70) km
Dip: 65 (55-75)
Instrumental Magnitude: Mw 8.0
Discussion:
The 1905 Tsetserleg earthquake was reviewed using data from Baljinnyam et al.
(1993) and Schlupp and Cisternas (2007). The few mapped displacements for the
July 9, 1905 Tsetserleg earthquake were relatively small – 2 meters or less, and averaged to 2.3 m by Baljinnyam et al. Upper AD estimate 3.78 m = 2.3m * 130 km for the mapped trace + 6 m over 60 km from waveform modeling. Length of 177 km from Vergnollee et al. (2003), weighting instrumental results. Minimum is the mapped length of 130 km; maximum = 190 km, from waveform modeling. Dip from mapping is 65 +-10 degrees over 80 km, and subvertical in the southern 50 km
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where it approaches the Bulnay rupture. Depth 40 (30-70) km is from waveform modeling, weighting the Bulnay rupture results where it is better resolved. The
Richter (1958) magnitude estimate (M 8.4) would have used clipped body waves or surface waves well beyond the free period of available sensors. The Schlupp and
Cisternas (2007) magnitude estimate, Mw 8.0, used waveform modeling of portions of on-scale instrumental records within their free periods, with a clear source-time function 65 s long and a fitting-based length of 190 km. The preferred magnitude reflects a 60 km extension beyond the mapped end of the rupture that has an average displacement of 6 meters. There is conventional satellite evidence for a continuing rupture, but not field or metric satellite confirmation so far. The majority of the Tsetserleg earthquake seismic moment release is thus where mapping has not yet reported surface rupture. The extra moment would create a major difference between the geologic and instrumental magnitudes. The event is included with parameters in the table, but not recommended for AD-L or magnitude-area use.
Bulnay, Mongolia, July 1905
Style: SSL
Length: 375 (350-395) km main trace; 475 (450-495) km with major secondary traces.
AD: 6.5 (6.5-6.7) m, main trace only; 5.7 (5.7-5.8) with secondary traces.
Depth: 40 (30-70) km
Dip: 87 (84-90)
Instrumental Magnitude: Mw 8.4 (8.3-8.5)
Discussion:
The July 23, 1905 Bulnay rupture has multiple displacement measurements from field mapping in 1914 through 1991, plus spot checks of offsets by USGS personnel.
Photographic evidence is clear that this event was huge. The surface rupture and moment release for this event apparently included significant secondary ruptures that contributed to the total seismic moment.
The main trace is 375 (350-395) km. The upper estimate includes minor secondary traces from mapping. The lower length estimate is from D. Schwartz (pers. comm.).
Major secondary ruptures occurred on the Teregtiyn and Dungen faults; rupture total about 100 km in length. The Teregtiyn rupture is 80 km, 20 km with 3.2+-1 reverse faulting on a 50-70 degree NE-dipping plane, and 60 km of en-echelon faults, with 3.0+-1 m strike-slip. The association of the Teregtiyn rupture with the main Bulnay rupture is strongly suggested from modeling of horizontal component seismograms that require significant moment release at a high angle to the main rupture trace. The evidence against it being co-seismic with the Bulnay main rupture is primarily from silence, it not being mentioned in Russian fieldwork from
1914 and only first reported in 1959. The Dungen rupture is 20-22 km in length, and estimated to have 1.5+-0.5 m slip on a vertical plane. Many other shorter scarps were recognized in the field but not included in the summary mapping. With
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principal secondary structures the rupture length is 475 (450-495) km. This is considered the most representative length for the 1905 Bulnay rupture.
AD was developed from the rupture profile using displacement measurements of D.
Schwartz (personal comm., UCERF-3 March 2011 workshop). Where measurements disagreed, the later work that included USGS personnel was used. The USGS field work did not confirm either end of the main trace, so a range of lengths centered on the Baljinnyam et al. (1993) estimate was adopted. Average displacement estimates use linear extrapolation between field measurements, and linear extension to the ends of the fault. The average displacement on the main trace is 6.7, 6.5, and 6.5 m for 350, 375, and 395 km lengths, resp.). With the secondary traces, AD estimates are 5.8, 5.7, and 5.7 m, for 450, 475, and 495 km main trace lengths.
Dip is from Schlupp and Cisternas (2007). Main trace dips are well constrained by the seismic data, and differ by about a degree between the west and east sections of the main trace.
Depth: Estimate of 40 km adopted from Schlupp and Cisternas (p. 1128) based on waveform modeling and comparison with Kokoxili (Kunlun) 2001. For the main trace, fault rupture depths from 30 km to 70 km lead to reasonable waveform fits.
Magnitude: Source-time function was 120 s. Waveform fits give Mo 3.97*10^21 to
7.27 *10^21 Nm, Mw 8.34 to 8.51; table values Mw 8.4 (8.3-8.5) reflect realistic precision. Earlier magnitude estimates using Ms or surface waves (e.g., Richter,
1958) rely on instrument corrections well beyond the free period of the sensors.
April 18, 1906, San Francisco
Style: RL SS
Length: 497 (483-517) km.
AD: 4.3 (3.7 – 5.0) m
Depth: 15 (12-18) km
Dip: 90 (85-95) degrees
Instrumental Magnitude: Mw 7.9 (7.8-8.0)
Discussion: The primary resources for study of the full rupture profile are Thatcher et al., (1997), Wald et al., (1993), and Song et al. (2008). Thatcher et al. invert survey-based geodetic data, with some lines not resurveyed until substantially after
1906. Their rupture profile ends to the NW at Shelter Cove with 8.5 meters of slip and no controls north of that point. Geodetic offsets south of San Francisco are generally 1-2 m larger than point offset measurements in the Lawson (1908) report.
Wald et al. (1993) attempted to invert the few available seismic records for a slip distribution. Sensor bandwidth limitations prevented their estimate from being widely accepted. Song et al. (2008) conducted a joint inversion of seismic and geodetic data. Their estimate is considered here as most reliable.
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Length of 497 (483-517) is based on the documented surface rupture (477 km) plus a taper from 6 m to 0 on the north end at a taper rate of 3.3x10-3/km, twice the most rapid internal taper of the Song et al. model. The lower L estimate tapers from
6 m to 0 at 10-3/km; the upper L estimate tapers at 6.7x10-3, and extends the rupture to the Mendocino Triple Junction. Average displacement is from the Song et al. slip profile, with linear tapers on the ends described above. Uncertainties assigned at +-15%. Depth of rupture assigned at 15 +- 3 km, corresponding to a
20% uncertainty. Magnitude is from Song et al. (2008) with 0.1 unit uncertainties.
1911 Chon-Kemin (Kyrgyzstan)
Style: R60
Length: 177 (169-260) km
AD: 3.6 (3.5-4.1) m
Depth: 25 (20-30) km
Dip: 60 (50-70)
Instrumental Magnitude: 7.7 (7.6-7.9)
Discussion:
Reverse faulting occurred on multiple sub-parallel strands. The surface rupture was studied shortly after it occurred in a major Russian effort. Recent extensive field study includes Delveaux et al. (2001) primarily on geomorphology, and Arrowsmith et al. (2005) and Crosby and Arrowsmith (in prep) focusing on surface rupture and on separating the 1911 rupture from earlier ruptures.
Length of 177 km was obtained by digitizing the location map in Arrowsmith et al.
(2005), generalizing the rupture as two simple strands with ~8 km overlap.
Minimum length = 177 minus the 8 km of overlap = 169 km. The maximum length,
260 km, includes the more significant sub-parallel secondary strands. Average displacement of 3.6 m is based on Arrowsmith et al. (2005) estimates of the displacement made on individual reaches of the fault, with linear connections where gaps are shown. The length for this AD is 160 km. AD range is 3.5 to 4.1 m.
Displacement estimate at 260 km length: (160*3.6 + 100*1.5+-0.5)/260 = 2.8 (2.6-
3.0) m. The 1.5 +-0.5 m displacement is assigned, based on it being large enough for reconnaissance mapping but not large enough to merit field work to develop details.
The depth is the down-dip extent is based in seismicity extending to 20 km vertical depth. Average dip ~60 degrees (Crosby and Arrowsmith mapping) +-10 degrees based on their narrative description and geometric considerations for projecting faults to depth.
Engdahl and Villesenor (2002) estimate Mw 7.8 from their recalculated catalog.
This agrees reasonably with the geologic moment of Arrowsmith et al. (2005), Mo =
3.86e+20, and Mw 7.72.; Mw 7.89 max) Mw minimum is set at 7.6 based on an approximate estimate of the consequences if displacements are systematically smaller than the section means used in the estimate.
Haiyuan, China, December 16, 1920
17

Style: SSL, SSLO
Length: 237 (220-260) km
AD: 3.3 (3.0 – 5.0) m
Depth: 25 km
Dip: 90 (80 – 100)
Instrumental Magnitude: 8.25 (8.0 – 8.6) See discussion.
Discussion:
This rupture occurred on the Haiyuan (Nanxihuashan) fault zone.
Length: The Dec 16, 1920 Haiyuan earthquake was 237 km long, adopted from
Liu-Zeng et al., 2007. Mapping was not located to permit estimation of off-fault and secondary ruptures.
Deng et al. (1986) present displacements measured at 168 points along the central ~170 km of the rupture. Rupture was primarily left-lateral and left oblique, with most sections of the fault trending 10-15 degrees NW of the net slip of the main trace. Pull-apart structures developed in several left steps between sections, presumably to accommodate this obliquity. Deng et al. give strike-slip displacement averages by fault segment. Most averages are over 10 or more measurements, with a few likely outliers removed. Strike-slip measurements were made on cultural structures (e.g., walls) and some small gullies.
The western ~60 km was not mapped by Deng et al., so displacement was assigned at the level of the westernmost displacements. Small tapers were applied to the ends, at a rate of 5*10^-4 (1 meter in 5 km). The Deng et al. length was 220 km, with ~10 km uncertainty in the western end and an inequality length given for the eastern-most section. Six km was added to each end, consistent with the uncertainties in their estimate, to bring the total to 237 km. Displacements for the
Deng et al. (1986) section SF7 (12 km length) were not given. A displacement of 2 meters was assigned to offsets on the argument that it was large enough to make the section mappable. Displacements in tensile-shear basins totaled at least 30.5 km.
The authors state that off-fault displacements could have been missed. For the minimum AD, replace western 60 km at 2 meters with 1.0 instead: (237*3.3 – 60*2
+ 60*1 )/ 237 = 3.0 m AD.
Using the Deng et al. average displacements and section lengths modified as described above gives an average rupture displacement of 3.28 m for the main trace of 237 km. Including normal faulting in pull-aparts and overlaps gives L=268 and
AD=3.32 m. The average depends somewhat on displacements assigned to the western unmapped region. An upper estimate of 5.0 m allows for 50% of the rupture being unrecognized, either being off the main trace or otherwise obscured by landslides or erosion. AD estimates here are relatively low compared with other values ascribed to this rupture.
Depth of seismicity: 25 km, from Engdahl and Villasenor (2002). Dip was subvertical.
18

Magnitude: No revised instrumental magnitude was found in the literature review. Chen and Molnar (1977) give Mo=3.0*10^28 dyn-cm with a 200 km rupture and 10 m slip (Mw=8.25). The range in table 8.0-8.25-8.6. Liu-zeng et al. (2007) cite
M 8.6. Klinger (2010) lists Ms=8.0, which may understate the M w
because M
S
is estimated at a 20 second period. Engdahl and Villasenor (2002) list it at Mw 8.3.
Luoho-Qiajiao (Daofu), 24 March 1923
Style: SSL
Length: 80 (60 – 100) km
AD: 2.5 (2.3 – 3.0)
Depth: 20 km
Dip: 90 (80-100).
Instrumental Magnitude: 7.2.
Discussion:
Rupture is on the Xianshuihe fault. Allen et al. (1991) refer to this as the Sharato earthquake at one point. Papadimitriou et al. (2004) surveyed measurements in central part, a rough maximum, based on rice paddy offsets, tree lines. This survey produced the best offsets. Co-author Weldon participated in this study.
Papadimitriou et al. (2004, p. 1693) uses 3 m as an average, based on measurements of 2.3 to 4.2 m in the central 10-20 km. Applying a sinesqrt with 3 m average across this section gives an AD of ~2.5 m. The minimum AD assumes that 3 m in the measured area is the maximum of a sinesqrt shape. AD max = 3.0 m assumes a maximum of ~4 m and the sinesqrt shape. Length estimate is 80 (60-100). The maximum length of 100 km is from Papadimitriou et al. (2004, p. 1695), citing mapping done in 1934. Allen et al. (1991) list the event only as “>60 km”. The dip is approximately vertical according to Papadimitriou et al. (2004). Depth of seismicity is assumed to be ~20 km. Instrumental magnitude of 7.2 (M o
0.62*10 20 ) N-m is from Papadimitriou.
Fuyun, 10 August 1931
Style: SSL/R
Length: 160 (160-176) km
AD: 5.2 (4.9 – 5.6) m
Depth: 20 km
Dip: 90
Instrumental Magnitude: 7.9
Discussion:
Left-lateral strike slip occurred on a sub-vertical fault plane. Some oblique slip is indicated by the fault style in the unmapped NW 40 km of the rupture. The key data set is from Klinger et al. (2011) using SPOT/Quick Bird satellite imagery, which covers the eastern 120 km. Ruptures are strikingly characteristic. Several offsets were benchmarked in the field. Secondary ruptures on Klinger’s map total about 38 km. Length estimate and minimum of 160 km are from Klinger et al., (2011). The
19

maximum length of 171 km is from Vergnolle et al. (2003) With secondary traces the potential full length is 160+38 = 198 km.
Klinger et al. (2011) give hundreds of estimates of the MRE displacement along the central 110 km of the rupture. In the 8 km from the end of the SPOT data to the SE end of the rupture, a linear gradient was applied. For the 40 km NW not covered by
SPOT measurements, a tapered end was formed by copying the SE 40 km and reflecting it. Clearly the actual shape of the NW 40 km is speculative. Note that the average of 6.2 meters in the 110 km measured does not translate directly to 6.2 m for the whole rupture. The AD 5.2 m is found from the net rupture profile.
Minimum AD = 4.9 m is found by replacing the 40 km NW taper with 2 m constant value. The maximum AD = 5.6 m is found by replacing 40 km NW taper with 20 km full amplitude (6.5 m) and a linear taper from there.
Depth of 25 km, based on focal depth of 19 km in the AGI Map Volume. Rupture at this depth would imply that some slip was actually deeper. D min
: 20 km from
Vergnolle et al. (2003). Magnitude M w
= 7.9 in Klinger et al. (2011) and Engdahl and
Villasenor (2002).
Tuosuo Lake (Dongxi), 7 January 1937
Style: LL SS
Length: 150 (140 – 160) km
AD: 4.1 (3.2 – 4.1) m
Depth: 20 km
Dip: 90 (80 – 100)
Instrumental Magnitude: 7.5
Discussion:
This rupture is variously called the Tuosuo Lake, Dongxi, or Huashixia earthquake.
It ruptured the eastern Kunlun fault in northern Tibet with nearly pure left-lateral strike slip motion. Most recent published data are in Guo et al. (2007). New data in that study include air photos from 1963-1966, field mapping, displacement measurements at 9 locations, and trenching. Displacement sites are distributed along the rupture. Air photos resolve some uncertainties in field studies from the
1980’s including the boundary with the 1963 Alake Lake rupture and the (lack of) overlap with the Tuosuo Lake. Magnitude is from Guo et al, (2007), citing the
International Seismological Centre (2001) On-line bulletin, www.isc.ac.uk/Bull
(accessed June 2007).
Length of 150 +- 10 km and average displacement of 4.1 m are from Guo et al.
(2007). The minimum AD = 3.2 m recognizes that SE displacements are not known.
AD max = 4.1 m. Note: at the March 2011 workshop Klinger summarized it as Mw
7.5, based on a 15 km seismic width, 120 km length, and average slip of 3 m, but did not address why the Guo et al. results should not be accepted. Dip is vertical, with minor variation.
20

Gobi-Altay, Mongolia, 4 December 1957
Style: SSL
Length: 259 (240 – 361) km
AD: 3.1 (3.0 – 4.0) m
Depth: 25 (20-30) km
Dip: 55 (45 – 65)
Instrumental Magnitude: 8.1
Discussion:
The primary source for displacement measurements of the 1957 Gobi-Altay earthquake is Kurushin et al. (1997). Ground rupture was mapped in remarkable detail to a distance of several tens of km from the main trace. The 1957 Gobi-Altay rupture main trace is 259 km long with rupture displacements of 3-4 meters on much of it, but locally 5-7 meters, of left-lateral strike slip. Average main trace displacement is 3.1 m. This modest average displacement might be anticipated from the table of 46 measured displacements - only two exceeded 5.8 m. AD min = 3.0 m;
AD max of 4.0 m. L_min = 240 km discounts minor normal faulting on the east end and reverse structures at the west termination. This earthquake also included several tens of km of secondary ruptures, many with reverse mechanisms that would have contributed to moment release. Including larger secondary structures,
L_max = 361 (AD ~3 m). Total mapped off-main rupture was ~256 km, with an average displacement of 1.5 m. This comes to about half the main trace moment.
Length considering all mapped secondary faulting = 515 km, with AD: 2.3 m.
Dip on the main trace = 55 degrees from Kurushin et al. (1997) field mapping. 10 degree range (45 – 65) is a generic uncertainty.
Depth is estimated to be 25 km, and could be greater. Adjoining the main trace is a mechanically coherent plateau-like named Il Bogd. Secondary reverse fault rupture skirts much of the way around this structure, but internally it is relatively undeformed, as though rooted at depth. Kurushin used 20 km in moment estimates.
Engdahl and Villasenor (2002) also use depth = 25 km with their M w
=8.1 estimate.
Alake Lake, 19 April 1963
Style: SSL
Length: 40 (30-50) km
AD: 1.9+-0.5 m
Depth: 20 km
Dip: 90 (80-100)
Instrumental Magnitude: 7.0
Discussion:
Left-lateral strike slip on the Kunlun fault west of the 1937 Tuosuo Lake rupture. It is distinguished from the latter and from older ruptures to the west based on the freshness of scarp and faulting surface evidence in 1963-1966 air photos (Guo et al.
2007). Length: 40+-10 km. Displacement: AD=1.9 (1.5-2.4) m. Two displacement
21

measurements (1.6+-0.5 and 2.3+-0.5 m) were taken near the center of the rupture.
Depth value is a default.
Tonghai, China, 4 January 1970.
Style: SSR
Length: 60 (48-90) km
AD: 1.54 (1.54 – 2.1) m
Depth: 15 km
Dip: 90 (80-100)
Instrumental Magnitude: 7.2
Discussion:
Right-lateral slip on the Qujiang fault, part of the Honghe (Red River) fault system.
Length of 60 is from Hu (2002). Length minimum of 48 is from the mapped rupture trace, the maximum = 90 km from modeling of Zhou et al, 1983. AD = 1.54 from slip measurements in Zhou et al. (1983). Upper value of AD = 2.1 is +20% uncertainty, reflecting potential underestimates of geologic offsets. M w
=7.2 in Engdahl and
Villasenor (2002) Table 1, with depth = 14 km.
Luhou, China, 6 February 1973
Style: SSL
Length: 90 (90-105) km
AD: 3.0 (2.5 – 3.6) m
Depth: 15 (12 – 20) km
Dip: 90 (80 – 100)
Instrumental Magnitude: 7.4
Discussion:
Earthquake occurred on the Xianshuihe fault. Papadimitriou et al. (2004) noted several displacement measurements in the central ~10 km of the rupture.
Discussion says the length of 90 km was exceptionally well mapped, but lists 105 km in one table. AD of 4 m in Papadimitriou is too high based on field checks by
Weldon (unpublished). Weldon (unpublished) work on this rupture put the central
10-15 km at about 4 m. If 4 m is the approximate maximum of a sinesqrt rupture shape, AD = 4/1.31 = 3 m as the rupture average (Dmax/AD = 1.31 for the sinesqrt shape). Dmax = 3.6 from Zhou et al. 1983, backcalculating from seismic data with depth = 20 km. Dip and depth from Papadimitriou et al. (2004). Magnitude M w
7.4
(M o
= 1.70*10 20 Nm) from E&V (2002).
Motagua, February 4, 1976
Style: SSL
Length: 230 (230-251) km
AD: 1.1 (1.0 – 1.1) m
Depth: 15 (10-15) km
Dip: 90 (80-100)
22

Instrumental Magnitude: 7.5
Discussion:
Rupture was almost pure sinistral displacement on a vertical, N65E to N80W trending fault. Length is 230 km, from Plafker (1976) and 1978 Bucknam et al.
(1978) articles. Secondary fault ruptures include the Mixco zone >10 km long with
~13 cm oblique slip, the Villa Linda-Castanas zone ~8 km long; and the Incienso-
Santa Rosa at 7 km long, for a total of 25 km. Minimum = 230 km. L_max = 251 km is obtained by summing the main and secondary traces. Aftershocks and damage span 300 km. The maximum displacement was 325 cm. AD = 1.0 m is from the
Bucknam et al. (1978) rupture profile. The upper AD estimate of 1.1 m includes a small amount of afterslip. Mw=7.5 is from E&V (2002), with depth=13 km.
Manyi, China, 8 November 1997
Style: SSL
Length: 173 (160-180km)
AD: 3.4 (2.9-3.7) m
Depth: 15 (15-24) km
Dip: 70 (60 – 80)
Instrumental Magnitude: Mw 7.5
Discussion:
Mw 7.5 on the western-most Kunlun fault. The sense of motion was mostly leftlateral strike slip. Three model length and slip estimates were constructed from two papers, primarily from InSAR (Funning et al., 2007; Wen and Ma (2010). AD and range reflect three InSAR modeled displacements. AD agreement among the models is good. Funning et al. (2007) show the aftershock distribution, which matches the coseismic extent.
Depth: 15 km (hypocenter at 15 km). The Peltzer et al. (1999) model includes slip to 20 km. Dmax=24 is from the E&V02 CMT depth.
Magnitude Mw 7.5 is from Wen and Ma (2010). E&V02 also have Mw 7.5, with depth =24.
Sakhalen Island, 27 May 1995
Length: 35.5 (35-36) km
AD: 3.9 (3.8-4.0) m
Depth: 15 (12-18) km
Dip: 70 (60-80) degrees
Instrumental Magnitude: Mw 7.0
Discussion:
The fault plane dips west at approximately 70 degrees on a trend N15E on the
Gyrgylan’i-Ossoy fault. Surface rupture length is 35.5 km from Shimamoto et al.
(1996) mapping. Tight bounds (35-36 km) assigned because the rupture was mapped promptly by strong teams of geologists. Shimamoto et al. (1996) give a detailed slip distribution of both strike-slip and vertical displacement components.
23

Vertical average displacement is 3.8 m. With the vector horizontal it increases to 3.9 m. Estimate +-0.1 m uncertainty, as it was mapped thoroughly and not long after the earthquake. Dip 70 (60-80) is from Shimamoto et al. (1996).
Magnitude was studied by Katsumata et al. (1994). M o
4.2x10
19 N-m, and M w
= 7.0.
E&V02 have Mw 7.1 at 18 km. The Katsumata et al. (1994) study is more detailed than the Harvard CMT.
Seismicity depth: 15 km (est. +-3) is based on aftershock studies.
Altai, Mongolia, 27 September 2003
Length: 50 (40 – 70) km
AD: 1.8 (1.5 – 2.2) m
Depth: 12 (10-15) km
Dip: 76 (71-82)
Instrumental Magnitude: Mw 7.2
Discussion:
Rupture properties for this earthquake include some field observation but primarily
InSAR imaging and inversion. In all, the relevant parameters are not that well resolved.
Length: Nissen et al. (2007) used mapping plus InSAR to estimate a rupture length of 50 km, with models from 45 to 55 km (their Table 4). Surface rupture is highly distributed, and likely includes the effects of a triggered M6.7 or subsequent M6+ aftershocks. Splays were noted, but not well mapped and their association with the main shock is not clear. Total system length is ~70 km (Barbot et al., 2008) For the table, length = 50 (45-70) km.
Average displacement, from InSAR model: 1.8 (1.5-2.2) m. Displacements on west end of InSAR model (west 10 km) look like they could be artifacts, estimate lower displacement of 1.5 m. Nissen et al. (2007) note the problems of tracing fractures and en-echelon tears in forested terrain, so 25% was added as an upper bound (2.2 m).
Depth: InSAR places most of the slip is in the upper 9 km. Depth estimate 12 km
(10-15).
Dip: 71-82 degrees (Barbot et al., 2008, quoting seismic studies)
Mw 7.2, right-lateral slip (Barbot et al., 2008 ).
Pakistan, 4 October 2005
Length: 70 km
AD: 5.0 (4.5-5.5) m
Depth: 26 km (from surface)
Dip: 39 (30 – 45)
Instrumental Magnitude: Mw 7.6
Discussion:
24

Three faults or fault segments combined in the Balakot-Bagh fault. Rupture length =
70 km from field mapping. AD estimated from enveloped profile of Kaneda et al.
(2008). AD=2.74 m. After dip and slope corrections, Kaneda et al. (2008) estimate
5.0 m net displacement. +-10% used as bounds.
Dip: Kaneda et al. (2008, p. 541) report dips of 30+-10 degrees for near surface features. For instrumental moment estimation, dip =39 degrees on the relevant plane of the moment tensor solution. Dip range: min: 30, from near-surface estimates, max = 45 from errors on the CMT. Epicentral depth=26 km from the
USGS hypocentral solution. Magnitude Mw 7.6 cited from Kaneda et al. (2008).
Wenchuan, 12 May 2008
Style: Reverse Oblique
Length: 240 (232 – 330) km
AD: 3.85 (3.48 – 4.2) m
Depth: 20 km (vertical)
Dip: 50 (42-60) degrees
Instrumental Magnitude: Mw 7.9
Discussion:
Main trace surface rupture of the Longmen Shan system was 240 km long. Rupture was duplexed over 72 km of that distance on the Pengguan fault. Modeling of InSAR and GPS indicate the coseismic rupture continued northward another 90 km (Qi et al., 2011; X. Xu et al., 2009). Sense of slip and coseismic rupture extent from G. Yu et al. (2009); slip from surface rupture, InSAR, and GPS joint inversion in C. Xu et al.
(2010).
Dip: 42-60 degrees from InSAR + GPS (C. Xu et al. 2010; Qi et al., 2011). Depth estimate is from Qi et al. (2011) modeling 20 (18-24) km of the base of the reverse fault; slip on sub-horizontal plane may continue. Qi et al. (2011) modeling puts some slip 70-80 km down-dip.
AD on the main trace: 3.48 minimum from measurements. AD on the sub-parallel
Pengguan fault is 1.09 m, from displacement measurements. The Pengguan rupture could be counted as a main trace extension or as an increase to the AD of the main trace. Put end-to-end with the main trace gives 312 km length, AD 2.95, and a best
AD = 3.3 m that includes 10% in enveloping of the main trace measurements. The shortest surface rupture and largest AD would add Pengguan to main trace displacements since the sense of the motion is similar, giving 3.84 length averaged over 240 km; upper AD estimate of 4.2 m is 10% more, from approximate enveloping of the rupture profile. AD over the whole rupture is likely to be smaller if the northern 90 km is included.
El Mayor-Cucapah, 4 April 2010
Style: SSRO
Length: 117 (115 – 120) km
AD: 1.88 (1.7 – 2.1) m
25

Depth:10 (9 – 17) km
Dip: 65 (55-75) degrees
Instrumental Magnitude: Mw 7.17
Discussion:
Rupture was right-lateral on the Borrego and Pescadores faults within the Sierra
Cucapah. A linking normal fault joins the two. Dips are in opposite senses, dipping east to the south, and west to the north of the join. Mo: 7.28*10^19 N-m, Mw 7.17.
Length is 117 km from SAR and SPOT airborne observations. Minimum and maximum (115, 120 km, resp.) from possible extrapolations of the displacement profile in Wei et al. (2011). AD from measurements: 1.88 m. With 10% increase by enveloping, upper estimate: 2.1 m. Low estimate is -10%, or 1.7 m.
Dip: 65 (55-75) degrees. Wei et al. (2011) give dips by rupture section: 51 km dips
75 E, 60 km dips 60W, 18 km dips 50E.
Depth: Wei et al. (2011) report, “Overall, most of the energy release occurred at depths of less than 9 km…” Depth estimate from this: 9 as a minimum, 10 best, 17 allowed because some energy does radiate from deeper in the models.
Darfield, New Zealand, September 2010
Style: SSR
Length: 29.4 (29.4 – 31.5) km
AD: 2.5 (2.4 – 2.7) m
Depth: 15 (12 – 18) km
Dip: 90 (67 – 100)
Instrumental Magnitude: 7.1
Discussion:
Length: 29.5 km linear, 31.5 counting overlap of rupture in profile.
AD: 2.54 m computed from Quigley et al. (2012). Range of 2.4-2.7 is estimate of the effect of enveloping or running average method of computing AD from the scattered field points.
Dip: sub-vertical SS from seismic indications, but GPS field is fit best by a plane at
67 degrees.
Magnitude from van Dissen et al. (2011).
Sources:
Adjustments to Earthquakes in Wesnousky (2008)
Length and/or average displacement were adjusted for four ruptures in W08.
Fort Tejon, January 9, 1857
Style: SSR
Length: 339 km (330-345). Range in length interpreted from the plot of Zielke et al.
(2010).
26

AD: 4.45 m. Estimate from digitizing the displacement profile in Zielke et al.
Measurements were considered sufficient that uncertainties were not assigned.
Depth: 15 km (not revised from W08).
Dip: 90 (85-95) degrees.
Discussion: Wesnousky (2008) lists this rupture at 360 km in length. This total almost certainly includes 20+ km of the 1812 rupture on its south end. Zielke et al.
(2010) give an updated slip distribution for the 1857 rupture based on abundant
LiDAR measurements of most recent event offsets.
Landers, June 28, 1992
Style: SSR
Length: 63.2 km
AD: 2.8 m
Depth: Unchanged
Dip: 90 Unchanged.
Discussion: The W08 length of the Landers rupture includes displacements on the
Burnt Mountain and Eureka Peak faults. Hough (1994) shows that displacement on these faults occurred after the Landers main shock as triggered slip and coseismic slip of an M 5.6 aftershock. Thus for ground motion prediction purposes the net length of the Landers rupture should not include these southern components. The table length of 63.2 km considers the southern end of the Johnson Valley rupture to also be the end of the Landers rupture. The average displacement was recalculated with the remaining rupture.
Hector Mine, October 16, 1999
Style: SSR
Length: 44 km, unchanged
AD: 2.0 m
Depth: Unchanged
Dip: 90 Unchanged.
Discussion: The AD estimate for the Hector Mine event in W08 was disputed at the
March 2011 UCERF-3 Workshop The Hector Mine rupture profile exhibits extreme spatial variation that must be related to surficial conditions. To approximate slip at a depth below these effects, the displacement profile was enveloped. Surficial properties can also exaggerate displacements, so the envelope attempted to smooth considering both the number of points and the spatial extent of the highs and lows.
Denali, Alaska, 3 November 2002
Style: SSR
Length: 341 km
AD: 4.2 (4.0 – 4.4) m
Discussion:
Length: 341.
27

In Haeussler et al. (2004) the full earthquake is 341 km long. The additional 39 km compared to the W08 length of 302 km is from LiDAR measurements. Haeussler does not show a rupture profile for it, which seems to be why it is not in the W08 length. LiDAR imaging post-dating Haeussler et al. (D. Schwarz, pers. comm.) also led to revised mapping near the Denali-Totschunda transition. The under-estimate there averaged 2 meters over 15 km. This increases AD to 4.2 (4.0-4.4) m. Other parameters from W08 are unchanged.
Other SAF and Southern California Ruptures from LiDAR
Event displacement profiles were extracted from the southern San Andreas fault
LiDAR data (Weldon et al., UCERF-3 Appendix P10). The 1857 rupture profile is based on a 13 event averaged shape (ref. Hemphill-Haley and Weldon, 1999). Lines were drawn by hand through clusters of LiDAR displacement points representing earlier events. The displacements under the curves and above any lower event line were used for previous event displacements. Two events are identified in this manner, the historical 1812 rupture and a more northerly event thought to have occurred in the 1700's. It is called 1700 arbitrarily. The purpose for listing these events is to try to represent as much as possible about known major surface ruptures on California faults.
The 1812 AD = 2.31 m, length = 230 km. The end points are inferred from the freehand line drawing. The rupture extent of 1812 to the north could be 30 km more. If it extends farther north it (with some evidence in the LiDAR data) would do so with
~1 m displacement. As a minimum length, consider it to stop short of Plunge Creek in San Bernardino, for a total extent of 190 km. At this length the average displacement would be 2.4 m. To the south, Yule suggests 1812 displacements of
~0.5 m at Burro Flats. If so, the southern end of 1812 must be near; 10 km is allowed. This gives an upper length estimate of 270 km. Length: 230 (190-270).
Uncertainty in AD could be half a meter more or less, but not a meter for most of the rupture length, allowing different opinions for how to draw the event line through fuzzy LiDAR points. Also, the rupture displacements are pinned at Burro Flats,
Cajon Pass, and Wrightwood. Net range: 1.8 - 2.8m.
The 1700 rupture is estimated to be 230 (210 – 280) km long. The maximum length comes from the north end potentially being 20 longer than the preferred estimate, beyond which it gets into creeping section of the fault. The southern extent could be
30 km greater; were it any more, there would be more evidence for it in the central part of the rupture trace. The total length could be 20 km shorter within LiDAR uncertainties. AD for the respective length estimates is 3.5 (2.5 – 3.8) m.
A 1690 southernmost SAF event is inferred from Mojave and San Bernardino LiDAR south to Burro Flats, plus limited additional measurements farther south. This
28

event appears to have been 235 (220-250) km long with an average displacement of
4 (3.5-4.5) m.
The most recent large San Jacinto fault rupture is also evident in the LiDAR data
(Weldon et al., Appendix P10; _______ et al., in prep.). This event was 80 (76-85) km long with 2 (1.8-2.2) m average displacement.
References
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