Bends and Ends of Surface Ruptures

Transcription

1 Bulletin of the Seismological Society of America, Vol. 17, No. 6, pp , December 217, doi: / Bends and Ends of Surface Ruptures E by Glenn P. Biasi and Steven G. Wesnousky * Abstract To improve the empirical basis for estimating the likely length of future earthquake ruptures on mapped active faults, we measure map-scale complexities including fault bends, discontinuous rupture, overlaps, and fault-to-fault rupture from 67 historical ruptures and analyze the measurements for statistical relationships relevant to seismic hazard analysis. We observe that angles of bends at the ends of surface ruptures on strike-slip faults are systematically larger than interior bends (IBs), whereas corresponding interior and ending populations are similar for dip-slip events. The probability of a strike-slip rupture passing a bend decreases systematically with increasing bend angle roughly as PR 3:1 :83 A, in which PR is the passing ratio and A is the bend angle, with values ranging between 5 and 3. The regression shows the likelihood of a strike-slip rupture propagating through a bend of 25 is about 5%. The maximum IB angles through which ruptures propagate, and the net orientation differences of fault segments at the end of ruptures, may be explained to first order by changes in frictional resistance due to changes in fault strike in a locally constant orientation of regional stress. The average curvature of a fault rupture is defined by dividing the sum of absolute values of bends in the rupture by rupture length. Median and 95% curvatures of strike-slip ruptures are :5 =km and 1:5 =km, respectively; corresponding values for dip-slip ruptures are 1:6 =km and 5:6 =km, respectively. We find that most fault-to-fault rupture connections jump to a fault of like mechanism, such as strike slip to strike slip. Only two strike-slip ruptures out of a total of 42 jump to reverse structures and continue for a significant distance. Results here provide empirical data to support study of the dynamics of fault rupture and to improve rupture-length estimates for use in seismic hazard assessment. Electronic Supplement: Rupture maps annotated to show interpreted linear segments and measurements of bends in the ruptures. Introduction Probabilistic seismic hazard analysis (PSHA) depends directly on estimates of the rate and size of earthquakes on active faults. It is common practice in PSHA to develop an ensemble of potential ruptures that may occur on mapped active faults, based on fault geometry and length. Ruptures where slip jumps across discontinuities that appear as steps along a mapped fault trace are increasingly being considered in hazard analysis. PSHA thus requires assigning probabilities to the likelihood of a future rupture passing through these discontinuities. This motivates interest in acquiring further observations and developing methods to define and refine these probabilities. Previous studies focused on discontinuities in fault trace that appear as steps in a map view *Also at University of Nevada, Reno, Nevada Seismological Laboratory, MS-174, Reno, Nevada (e.g. Wesnousky, 1988, 26; Lettis et al., 22; Biasi and Wesnousky, 216; hereafter, BW16); we here develop similar empirical observations from bends in past earthquake ruptures. The use of empirical observations to suggest that bends in fault trace play a role in fault rupture is not new. For example, King and Nabelek (1985) suggested bends in a fault trace might correlate with the initiation or termination of earthquake ruptures. Fliss et al. (25) and Bhat et al. (27) used physical models to explore the possibility that bends leading to branches in a fault trace might reflect rupture directivity. Ando et al. (29) examined the San Andreas fault system of California to observe that the angles of splays bending from a fault trace are most commonly oriented about 17. From this, they suggest that fault-tip stress may play a role in splay formation. Klinger (21) considered a mix of both 2543

2 2544 G. P. Biasi and S. G. Wesnousky steps and bends in 1 historical continental strike-slip earthquake ruptures to suggest that the distance between such features along a fault trace is controlled by the thickness of the continental crust. Observations of bends in earthquake surface ruptures and active fault traces have also been used, along with criteria such as patterns in total fault offset, in attempts to explain the extent of past and future ruptures on dip-slip faults (DuRoss, 28; Manighetti et al., 215). In this article, we measure angles of bends within, and at the ends of, the surface traces of 67 historical earthquake ruptures, with an aim to assess whether or not there is a relationship between the angle of fault bends and the likelihood that a rupture will pass through it. Empirical and Dynamic Modeling Studies of Bends in Ruptures Empirical observations indicating that bends and steps in fault trace play a role in controlling the extent of earthquake ruptures are supported in physical models examining rupture propagation and fault growth (Harris et al., 1991; Harris and Day, 1993; Aochi et al., 22; Anderson et al., 23; Kame et al., 23; Fliss et al., 25; Duan and Oglesby, 26; Kase and Day, 26; Bhat et al., 27; Oglesby 28; Ando et al., 29; Scholz et al., 21; Lozos et al., 211, 215). Fault bends influence rupture propagation because they are associated with changes in fault friction, elastic and gravitational energy, and inelastic rock deformation (Scholz, 22). Saucier et al. (1992) relate the sinuosity of the fault trace to degrees of concentration of fault-perpendicular stresses, which at map scale relate to offfault topography and relative susceptibility of rupture to propagate. Duan and Oglesby (26) find that rupture propagation through a geometric offset also depends on the faultrupture history. Ruptures may be arrested for some number of cycles, but each rupture causes progressive damage that leads eventually to successful thoroughgoing rupture. Typically, how far a particular section of fault has progressed in this damage cycle is unknown, so for PSHA applications, the probability of through-propagation is considered in statistical terms. A passing ratio describing the likelihood of a rupture passing through a step of >1 km was developed for this purpose from empirical data (Biasi and Wesnousky, 216). In this passing ratio, the likelihood of a rupture passing through a fault step depends on step size. Step size is thus a faultgeometry measurement that can be used to improve seismic hazard estimates. Because of its relevance to the present effort, we describe in more detail the dynamic modeling of Lozos et al. (211). These authors conduct a comprehensive parametric study of strike-slip rupture propagation through fault steps of various widths connected by a relay fault segment taking off at some angle to the main fault strike. For step widths up to a few kilometers, the angle of the relay has little effect; rupture dynamic forces essentially overwhelm the resistance and push through the bend. As the separation between main sections increases, the relay fault becomes like a fault bend that the rupture must transfer onto in order to continue to the other side of the step. For relays of 4 5 km and longer, the bend angle is found to exert a systematic influence on rupture propagation. The authors also find that the alignment of the model driving stress relative to the bend section affects the possibility of rupture propagating through the bend. For stresses aligned to drive the main fault, compressional bends up to about 18 and extensional bends up to 34 are consistently passed. However, with a 1 rotation of the stress field in a direction favorable to the compressional step, threshold angles switch, and compressional bends up to 31 are passed by all ruptures, whereas extensional bends are passed only up to 18. Kame et al. (23) report similar sensitivity to stress orientation in the favorability of compressional versus extensional fault branches. Overall, the Lozos et al. (211) study predicts that once arms of a bend reach 5 7 km, strike-slip ruptures should rarely pass through bends larger than 34. It is also pertinent to this effort to consider the approach that was used recently to estimate earthquake probabilities for active faults in California by Field et al. (214) in the Uniform California Earthquake Rupture Forecast 3 (UCERF3). In UCERF3, faults are discretized into fault subsections that extend down to the base of the seismogenic zone, and half that, or about 7 km, in strike length. Fault ruptures are developed for all unique combinations of two or more contiguous subsections. On long, straight faults, this leads to a near continuum of rupture sizes. This discretization removed any need for an a priori model for fault segmentation. Two-subsection ruptures may be interpreted as the shortest ruptures in which the rupture patch is approximately equant in dimension and thus has a strong chance of causing displacement at the surface. Also new in UCERF3, the forecast includes earthquake ruptures that jump from one fault to another. An exact definition of fault-to-fault rupture was not proposed, but generally the term includes cases in which a rupture might continue on the same fault but instead deflects or jumps to a major splay or oblique connecting structure. Fault-to-fault rupture connection is allowed if the closest approach between the faults is less than 5 km and the junction satisfies certain geometric rules for compatibility (Wesnousky, 26; Milner et al., 213). As one rule, individual subsections can join only at included angles of 6 or less. An additional rule was introduced to control interconnections, such that the total absolute value of changes in rupture orientation (familiarly called squirreliness) was required to be less than 54. In addition, the orientation of ends of ruptures cannot differ by more than 6. Without these rules, the fault system connectivity is so great as to allow unphysical ruptures and even ruptures that could connect back on themselves. The limits in UCERF3 were chosen to be inclusive about possible ruptures, but remain to be independently validated with observational data. Although UCERF3 was highly tailored to the fault system in California, rules for fault-to-fault connectivity and the need to validate those rules

3 Bends and Ends of Surface Ruptures 2545 could be necessary for PSHA in many other regions with multiple and geometrically irregular active faults. Data and Methodology Biasi and Wesnousky (216) and Wesnousky (28; hereafter, W8) compiled maps describing the surface traces of 75 large continental earthquakes. Each map was based on the best field work available at the time of publication. Metadata including rupture length, earthquake magnitude, and rupture mechanism were provided with the maps. Readers are referred to these respective papers for details on map sources, decisions made in the syntheses, and references. The present study applies these same maps and assembled data to study the effect of bends on surface ruptures. Specifically, we 1. measure and tabulate angles of bends inside and at the ends of ruptures, 2. measure the total and net angular deviations of fault strike along the ruptures, 3. compile instances of Y- and T-branching ruptures and rupture mechanisms associated with fault-to-fault rupture, and 4. tabulate and analyze rupture overlap lengths. Of the original map set, 67 ruptures are sufficiently long and detailed to provide data on rupture behavior at fault bends. The maps we use are considered sufficiently detailed for interpretation of fault bends associated with linear fault sections of 5 7 km minimum length. In dynamic rupture studies, features of this length or longer generally define rupture behavior, whereas shorter features of any orientation can be overcome by local rupture dynamic effects. The 5 7 km length also conveniently corresponds approximately to the discretization of fault segments employed by UCERF3. Rupture maps with interpretive lines and bend measurements are provided in the E electronic supplement to this article. It should be recognized that our interpretations involve some degree of smoothing through small angle deviations of the longest ruptures in the data set. In all, 42 strike-slip, 11 reverse, and 14 normal mechanism ruptures are analyzed. Slip mechanism type was assigned on the basis of the dominant slip of the main rupture. For ruptures in which the slip sense changes along strike, assigning a single main-rupture mechanism can lead to apparent outlier bend-angle measurements, such as at the bend where strike slip on the Denali fault connects to dip slip on the Susitna Glacier fault (Haeussler et al.,24). Oblique slip may also lead apparent outliers in bend angle, but we have not attempted to adjust for 3D geometric effects. Rupture Bends and Ends Here, we describe measurement methods and empirical relationships among rupture bend angles and lengths. Figure 1 illustrates the manner and assumptions used in our measurements of fault bend angles along surface rupture traces. These include interior angles overcome in rupture, rupture-ending bends, net orientation change as measured by the strike difference between the main ending branches of the rupture, and total absolute angular deflection (TAAD; the sum of all measured bend angles interior to the observed rupture). All measurements are made on the basis of bends in the surface trace. We adopted this approach for two reasons. First, although it would be nice to have, little or no actual data are available for most ruptures about changes in dip or other 3D geometry affecting the surface trace. Second, map-view knowledge of faults provides the starting point for many types of analyses, including decisions about where investments to resolve 3D geometry would be most beneficial. In making measurements, a suitable scale length must be considered. Features smaller than a kilometer or so are inconsistently recorded in the original surface rupture maps, especially for the larger and older ruptures. Also, as noted earlier, steps in fault trace connected by linking faults of a few kilometers or less can be overwhelmed by dynamic rupture effects, making the bend angle incidental. These considerations lead us to set a minimum fault segment length of 5 7 km to summarize rupture orientation and bend angles. Most fault segments in the data set are significantly longer than the minimum (e.g., Fig. 1b). Strike-slip ruptures often end with some displacement on an oblique dip-slip structure. Short oblique terminations of a few kilometers or less with rapidly decaying slip are also observed in numerical models, apparently associated with dynamic effects (e.g., Lozos et al., 211, their fig. 3). Short, oblique extensions of this type are counted as ruptureending bends and not as interior bends (IBs) of a through rupture. Figures 1h and 2 together illustrate the measurement and tabulation of bend measurements. Figure 2 is from the 1 February 1944 Gerede-Bolu, Turkey, earthquake and illustrates the manner in which all maps are presented in the E electronic supplement. The base-rupture map and a brief summary of the Gerede-Bolu event are given in Wesnousky (28). In the annotated maps, straight lines are used to summarize the rupture trace and document our measurements of bend angles. Some lines extend beyond the surface rupture to facilitate the measurement of bend angles and to improve traceability for the motivated reader. Dashed lines are used to indicate mapped but unruptured faults that strike oblique to the rupture end (e.g., Fig. 1h). Bend angles are indicated in small numbers near line intersections. IBs are counted where sections of at least 5 7 km meet (Fig. 1h). Signs are reversed where bends change from clockwise to counterclockwise. The net deflection angle is the absolute value of the difference in orientation of ending summary section lines. Sq is the sum of absolute values of bends. Other observations made on each rupture map are shown in a text field with the map and defined in the caption of Figure 2. All measurements are summarized in Table 1.

4 2546 G. P. Biasi and S. G. Wesnousky (a) (c) (e) (g) (h) θ E A Ending bend θ E Oblique fault continuation not ruptured Simple trace - No bend Step but no bend Bend - with step A θ Complex trace with bend - with step θ Interior bend θ 1 Fault step - No bend (b) (d) (f) Segments of fault <~7.5 km - No bend Simple trace and bend Bend - with step 7.5 km Interior bend θ 2 N ~SCALE θ θ E Ending bend Short rupture continuation; dies out in a few km or less θ 15 km 1 km θ N Dashed line is strike of rupture at A-A, the other end of the rupture Maximum s Passed inside Ruptures IBs are angles through which a rupture succeeds in propagating (e.g., θ 1 and θ 2 in Fig. 1h). The largest absolute angle deflection (max IB) through which rupture propagated for each respective earthquake is tabulated in Table 1 and plotted in Figure 3. Figure 3a shows IBs for strike-slip and dip-slip ruptures as a function of surface rupture length. Longest strike-slip ruptures may show a weak trend toward smaller max IB, but overall, max IB does not obviously depend on rupture length. Figure 3b plots the same max-ib data in the form of a cumulative distribution. Dip-slip and strike-slip populations are seen to differ in terms of the observed values of max IB, with median values of 17 and 38, respectively. Over 95% of the largest bends in strikeslip ruptures are below 28, with only two exceptions above this: the 22 Denali rupture at the Denali-Susitna Glacier strike-slip-reverse junction (Haeussler et al., 24) and the 1957 Gobi-Altai rupture (Kurushin et al., 1997), where a 15 km salient projects out of strike with the main rupture. This apparent complexity in the 1957 event may relate to the unusual geometry of the main fault. Strikeslip rupture occurred on a 45 dipping plane (Choi et al., 212) and tens of kilometers of coseismic reverse faulting occurred off the main fault. Considering the other unusual features of rupture geometry of the 1957 earthquake, its extreme max IB value is interpreted as an outlier. For dip-slip ruptures, maximum IB measures concentrate below 5 and at all percentiles are larger than for strike-slip ruptures. Figure 1. Upper panel illustrates the measurement of bend angles θ. Bends occur at all scales, but measurements for this project are generally limited to those where fault branches on both sides of the bend are at least 7 km length or greater: (a) undeflected rupture trace; (b) bends in continuous trace and short misaligned sections; (c) rupture continues parallel or nearly so across a step. No bend is indicated. (d) Simple bend; (e,f) bends where rupture continues on a different trend across a step; (g) bend across a step where fault branches on either side of the bend are characterized by variations in strike at length scales less than 7 km. (h) Figure of schematic fault trace illustrates manner in which sums of bend angles are calculated and how bends associated with the ends of ruptures θ E are defined. In this representation, solid black lines represent the rupture trace, and dashed black lines represent the unruptured trace of the fault zone on which the earthquake occurred. In some instances, the ending branches defined by the dashed black line exhibit relatively minor amounts of surface rupture. Net deflection is the orientation difference between the main fault branches that define the respective ends of the fault rupture. Total absolute angle deviation is the sum of absolute values of interior bends (IBs) observed within a rupture jθ 1 j jθ 2 j, that is, the total of changes in rupture direction. The color version of this figure is available only in the electronic edition. Angular Deflections at Ends of (Stopping) Rupture Surface ruptures have been observed with field mapping to sometimes end at high-angle oblique structures or at significant bends in fault strike. To quantify the frequency of this phenomenon, angle deflections associated with rupture termination θ E are plotted in Figure 4. Ruptures may contribute, 1, or 2 end-angle measurements to the plot, depending on how the rupture terminated and whether or not mapping is sufficient to make the measurement at each end of the rupture. Largest fault deflections are concentrated among ruptures less than 15 km, but overall, there is little clear support for a trend of the size of bends at rupture terminations with rupture length among either dip-slip or strike-slip earthquakes. To quantify the relative incidence of ending deflections of various sizes, Figure 4b presents ending angles as cumulative fractions. For strike-slip ruptures, a smooth distribution of ending deflection angles is observed, with 9% being less than 6. Fewer data are available for dip-slip ruptures, but among our measurements, dip-slip ruptures are observed to have rarely

5 Bends and Ends of Surface Ruptures February 1944 Gerede-Bolu, Turkey 1 2 km releasing step 1957 and 1967 Bolu rupture trace 13 Abant Lake Gerede 5 km E12 Gerede-Bolu: Max IB: 19 Sq: = > 34; Net deflection: 4; Rupture end deflections West: 13, 8 km; east: fault continues across step but on same alignment; F2F: No. Complexity: no Overlaps: 4 km Ismetpasa Cerkes 2 km releasing step 1951 rupture 1943 rupture ended at a deflection less than 2. It is not clear why this might be so. Net Angular Deflection The net angular deflection (NAD) is defined here as the absolute difference in map orientation between the two ending sections (branches) of a surface rupture (Fig. 1h). In circumstances in which the regional stresses are approximately constant in orientation, fault bends measured by the NAD should be limited to the difference between maximum and minimum orientations at which fault slip can be driven. The NAD can also be used to screen out pathological cases that can arise from fault-to-fault linking algorithms in a complicated fault network (e.g., Milner et al., 213). Figure 5 shows the NAD for the combined surface rupture set. Minor normal or reverse terminal structures on primary strike-slip ruptures are not included in the NAD (Fig. 1h). The four NAD measurements greater than 5 (Fig. 5a) are all associated with dip-slip ruptures. The largest of these occurred in the 11 April 211 Fukushima-ken Hamadori earthquake, in which rupture proceeded north on the Itozawa fault and then continued southeast through a net angle of 147 on the Yunodake fault (Tanaka et al., 214). If rupture direction is ignored, NAD for this event would be 33. Only 3 of 42 strike-slip ruptures have an NAD greater than 31. Of these, only one, the 1943 Tosya, Turkey, event is associated with bending on a relatively simple fault trace. NAD for the other two (1992 Landers and 22 Denali) earthquakes are large due to fault-to-fault complexities. By comparison, 3% of dip-slip ruptures have ends that strike 3 or more from each other. Two ruptures, both dip slip, exceed the upper NAD limit of 6 used to remove ruptures in UCERF3 (Milner et al., 213) parallel across step Figure 2. Example surface rupture map for the 1 February 1944 Gerede-Bolu, Turkey, earthquake, with bend angles and other measurements. Base fault summary map from Wesnousky (28). Long straight lines extending beyond the surface rupture summarize the trace for purposes of measuring interior and ending bend angles. Dashed lines indicate unruptured end structures. Numbers near line intersections are bend angles. The signs of angles indicate turns clockwise or counterclockwise, as considered in a traverse from one end. Measurements and overlap lengths are summarized in text blocks. Max IB, maximum IB; Sq, sum of IB angles; net deflection, difference in direction between last sections inside rupture, neglecting ending deflections associated with rupture termination; F2F, rupture considered to contain fault-to-fault connections; complexity, yes if rupture contains T or Y connections; overlaps, mapped overlapping rupture (km). The color version of this figure is available only in the electronic edition. Total Deflections The TAAD is a measure of rupture complexity. TAAD is measured as the sum of the absolute value of angular deflections interior to a rupture trace (TAAD jθ 1 j jθ 2 j in Fig. 1h). TAAD was referred to unofficially by developers of UCERF3 as squirreliness after an image for how ruptures could jump back and forth from one fault to another under automated rules for fault connection. As noted earlier, our measurements of TAAD use the longest linear sections that would fit the rupture. Had we used only 5 7 km sections as in UCERF3 and had adequate supporting map detail, misalignments of 1 or a few degrees between sections could accumulate on long ruptures and lead to TAAD values somewhat greater than our estimates. We summarize observations of TAAD in Figure 6. The TAAD increases with rupture length at first because of the 5 7 km minimum length of sections defining a bend (Fig. 6a). Continued growth of TAAD with rupture length might be expected if ruptures gain length by breaking past more bends, but this pattern is not observed. The one exceptional event among strike-slip ruptures, with a TAAD of 257, is the 1957 Gobi-Altai earthquake (Kurushin et al., 1997). In this case the TAAD seems to be due to the strong oblique component of rupture. Systematic differences between the dip-slip and strike-slip populations are clear when plotted as complimentary cumulative distributions (Fig. 6b), with TAADs for dip-slip ruptures being roughly twice the corresponding values for strike slip. TAAD can also be recast into a measure of average curvature by dividing TAAD by the rupture length (Fig. 6c,d). Measured in this way, the dip-slip rupture population strongly separates from the strike-slip set, with median curvatures of 1:6 =km versus :5 =km, respectively. The greater curvature of dip-slip ruptures is not unexpected, but Figure 6 nonetheless provides a quantitative view of how complexity measured in terms of bend angles compares between strike-slip and dip-slip faults. Because the TAAD sums the absolute values of orientation changes, the average curvature in ruptures will not, in general, apply to the full rupture length. Effect of Uncertainty in Bend Measurements With the types of measurements introduced in Figures 3 6, we are in a position to evaluate the effects of uncertainty in bend measurements. A review of the annotated rupture maps (Fig. 2; complete set in the E electronic supplement) would find hand-fit lines that might be adjusted a bit, but in most cases even a few degrees change could be difficult. Klinger (21) found this to be the case when evaluating rupture traces for evidence of segmentation. He found that changes

6 2548 G. P. Biasi and S. G. Wesnousky Table 1 Earthquake Parameters, Bend Measurements, and Complexities Event Number Date (yyyy/mm/dd) Location Mechanism* Y, T Complexity Flag Length (km) M Distance (km) Distance Fault (km) to Fault Total Overlap (km) Squirrel Net Deflection Maximum Internal Bend Interior Bends Complexities and Notes /1/9 Fort Tejon, California /5/3 Sonora (Pitaycachi), Mexico S O No , 8, 7, 14, 14, 1, 17, 17, 4, 3, 3, 7 N X N N , 25, 43, 22, 45, 12, /1/28 Neodani, Japan S O , 28, 6, 25, 23, 11 5 km step, 7 km gap to Otates fault Neodani on strike with Umehara fault; not included as fault to fault /8/31 Rikuu, Japan R X R R , 36 R R across 12 km step to opposite vergence rupture; R R across 8 km step /1/2 Pleasant Valley, Nevada N X N N, N N , 12, 2 4, 7 km steps; fractured hanging wall 6 193/11/2 Kita-Izu, Japan S O No Terminal rupture /12/26 Erzincan, Turkey S O No , 8, 8, 2, 12, /5/19 Imperial, California /12/2 Erbaa-Niksar, Turkey occurs on conjugate fault S O No , 15, 7 S O No , /11/26 Tosya, Turkey S O No , 16, 9, 8, /2/1 Gerede-Bolu, Turkey /12/16 Dixie Valley, Nevada /12/16 Fairview Peak, Nevada /8/18 Hebgen Lake, Montana /7/22 Mudurnu Valley, Turkey S O No , 19 N O No , 35, 96, 48 6 Shattered hanging-wall piedmont N O No Total deflection much larger at smaller length scale; slip comparable to N N X N N , 64 5 km step, Y topology S O No , 13 (continued)

7 Bends and Ends of Surface Ruptures 2549 Event Number Date (yyyy/mm/dd) Location Mechanism* Y, T Complexity Flag Length (km) M Table 1 (Continued) Distance (km) Distance Fault (km) to Fault Total Overlap (km) Squirrel Net Deflection Maximum Internal Bend Interior Bends Complexities and Notes /4/9 Borrego Mountain, California /2/1 San Fernando, California /1/15 Imperial Valley, California S O No , 18, 21 R O No S O No km splay on northwest end at /1/1 El Asnam, Algeria R O No /7/29 Sirch, Iran S O No , 27 Extensive parallel ruptures off main trace /1/28 Borah Peak. Idaho N O No , 1, 24 Y topology, 2 arms 13 km; overlap is 1 arm of Y /3/3 Marryat, Australia R O No Conjugate ruptures /3/2 Edgecumbe, New Zealand /11/23 Superstition Hills, California /1/22 Tennant Creek, Australia N X N N, N N 6 ND ND ND N N across 8 and 3 km; hanging wall widely fractured; retained as 15 km rupture with main phase stopping at a bend S O No , 8 R O R R Y topology; 6 km step, vergence reversal /7/16 Luzon, Philippines S O No , 18, 11, 22, /6/28 Landers, California S X ,, , 28, 21, 15, jumps; extensive shear overlap /3/14 Fandoqa, Iran S O No /9/21 Chi-Chi, Taiwan R O No , 3, 46, 46, 19, 19, /11/12 Duzce, Turkey S O No , /8/17 İzmit, Turkey S O No , /1/16 Hector Mine, S O No , 27, 26 Parallel secondary California zones on southeast end of rupture (continued)

8 255 G. P. Biasi and S. G. Wesnousky Event Number Date (yyyy/mm/dd) Location Mechanism* Y, T Complexity Flag Length (km) M Table 1 (Continued) Distance (km) Distance Fault (km) to Fault Total Overlap (km) Squirrel Net Deflection Maximum Internal Bend Interior Bends Complexities and Notes 36 21/11/14 Kunlun, China S O , 11, 9, 6, 8, 5, 6, 9, /11/3 Denali, Alaska S X R, /2/2 Laguna-Salada, Baja, California , 4, 17, 8, 9, 26, 9, 6 TAAD is minimum because of map scale R at Susitna Glacier-Denali fault intersection; at Denali- Totschunda fault S O No , 4 3-km prominent normal-fault terminal ending /7/23 Bulnay, Mongolia S O , /1/3 Chon-Kemin (Kebin), Kyrgyzstan , 11, 4, 7, 4, 4, 5 R X R R , 13, 16, /1/13 Avezzano, Italy N X N N, N N Y topology to for 82 km, conjugate for 2 km; in Y's is not in squirrel or IB 1 km step; extensive overlaps , 7 km steps; hanging wall fractured /12/16 Haiyuan, China S O No , 21, 2, 28, 13, 21 TAAD is minimum /3/7 Tango, Japan S O No km gap; 8.5 km at right angles separated from main rupture /1/6 Laikipia-Subukia Kenya N O No /8/1 Fuyun, China S O No , 12, 12, 17, 8, 12, 16, 24, 18, /12/25 Changma, China S X No , 13 Oblique normal and reverse terminations at high angles; very complex surface rupture /3/18 Yenice-Gonen, S X No , 13, 25 Y structure at east end, Turkey arms 6 and 7 km (continued)

9 Bends and Ends of Surface Ruptures 2551 Event Number Date (yyyy/mm/dd) Location Mechanism* Y, T Complexity Flag Length (km) M Table 1 (Continued) Distance (km) Distance Fault (km) to Fault Total Overlap (km) Squirrel Net Deflection Maximum Internal Bend Interior Bends Complexities and Notes /2/9 San Miguel, Mexico /12/4 Gobi-Altai, Mongolia /9/1 Buyin Zara (Ipak fault), Iran S O No S O R, , 23, 19, 15, 38, 55, 24, 19, 36, 1, km+ in Gurvan Bulag thrust, Y-topo (2 ), 2 km on conjugate fault S O No , 22 Steps, reverse, and normal structures at <5 km scale /1/5 Mogod, Mongolia S X No , 1 Southern-end reverse structure interpreted as ending rupture /8/31 Dasht-e-bayaz, Iran S O No , 17 East end: conjugate slip on syncline /3/28 Gediz, Turkey N O N N , 57, km of hanging-wall offsets and overlapping rupture /12/19 Bob-Tangol, Iran S O No /9/16 Tabas, Iran R O R , 22, 6, 44, /11/27 Khuli-Buniabad, Iran 2 gaps, 6, 7 km; southend hanging wall broken in 4 reverse tiers; transition to on north end S O No , /11/23 Irpinia, Italy N O No , 4 km gaps, southeast end deflection same if San Gregorio section used /2/ Gulf of Corinth, Greece /3/4 Gulf of Corinth, Greece /11/6 Gengma, Yunnan, China N O No 5 N O No , 3 Rupture short; retained because rupture well described by bends S O No Interpreted from more detailed map of Zhou et al. (199) /12/7 Spitak, Armenia R O No , /6/2 Rudbar, Iran S O No , 6, 11, 8 (continued)

10 2552 G. P. Biasi and S. G. Wesnousky Event Number Date (yyyy/mm/dd) Location Mechanism* Y, T Complexity Flag Length (km) M Table 1 (Continued) Distance (km) Distance Fault (km) to Fault Total Overlap (km) Squirrel Net Deflection Maximum Internal Bend Interior Bends Complexities and Notes /5/27 Neftegorsk (Sakhalin), Russia S O No /5/1 Zirkuh, Iran S X R , 23, 24, 17, km of paired reverse structures 68 25/1/8 Kashmir, Pakistan R O No , 14, /5/12 Wenchuan, China R O R R , 21, 8, 85 km overlap on 43, 41, Penguan fault 19, 4, 35, 34, 14, /4/4 Sierra Mayor- Cucapah, Mexico S O , 14, 1, 13 Northeast dip transition on southwest end; 8 1 km internal gap/wrench structure 72 21/4/14 Yushu, China-1 S O No , /9/4 Darfield, New S X No Zealand /4/11 Iwaki, (Fukushima-ken Hamadori), Japan N X N N , 141, 6 Outer angle between faults chosen to follow line of rupture north on Itozawa then south on Yunodake IB, interior band; TAAD, total absolute angular deflection. *Mechanism: S, strike slip; R, reverse; N, normal. Flag for Y or T rupture shape complexity, X = present, O means not observed., refer to ends of rupture. is bend made from previous trace to terminal section, in degrees. End dist is distance rupture continues before ending, in kilometers. Observations of fault-to-fault rupture., strike slip, R, reverse, N, normal.

11 Bends and Ends of Surface Ruptures 2553 (a) Max IB (a) End angle (b) Fraction passing Length (km) Medians, : 18., Dip: Max interior bend Figure 3. (a) Largest IBs (max IB) overcome in strike-slip () and dip-slip ruptures as a function of rupture length. If rupture dynamic or momentum terms increase with magnitude, larger IBs might be found in longer ruptures. No strong trend of maximum bends with magnitude is indicated. Strike-slip ruptures rarely pass bends >28. (b) Maximum IBs for strike slip and dip slip are sorted by size and plotted as fractions greater than the horizontal axis bend angle. To preserve plot scale, the three largest dip-slip points from (a) are not repeated in (b). The color version of this figure is available only in the electronic edition. of a few degrees are readily detected and used many such trend changes to define segments in his model. In addition, examination of Figures 3 6 shows that the signals we interpret do not depend on individual measurements but on aggregate properties of the ensemble of measurements. The ensemble can be moved only by a systematic error of a single sign. Also, a property of cumulative distributions (e.g., Figs. 3b, 4b, 5b, and 6b) is that the data are sorted first and then plotted in order. If there are many data, a random error may increase one measurement but may decrease another, with offsetting net effect. When individual measurements are sparse (e.g., Fig. 5b, measurements > 3 ) we note the values as extremes but otherwise do not use them in interpretations. We also note that bend angle uncertainties are correlated. For example, the net deflection angle of rupture ends in Figure 5 is measured from compass orientation differences of ending segments. The sum of all IBs with their signs and uncertainties has to yield the same net deflection. As a result, errors overestimating one bend have to be compensated for by underestimates elsewhere. The total absolute angle deviation might be inflated if an angle of θ δθ is matched to a compensating j θ δθj, but realistic uncertainties should not change fundamentals, such as the signal in Figure 6. Thus, the measurement types and the cumulative distribution function presentation insulate the resulting interpretations from the first-order sensitivity to measurement uncertainty. (b) Fraction Length (km) End angle Figure 4. (a) Deflection angles θ E at rupture ends. No clear trend is observed relative to rupture length. (b) Rupture-ending angles are sorted and shown as the fraction greater than the horizontal angle axis. The color version of this figure is available only in the electronic edition. Ending versus Passed Deflections For estimating fault hazards, it would be useful to know the relative effectiveness of fault bends to stop ruptures. This can be developed by comparing the relative incidence of a bend angle in the sample from the ends of ruptures to its frequency among IBs passed during rupture. For example, if bends of 15 form a large fraction of IBs but a small fraction of those stopping rupture, then we would conclude that a 15 bend is not a strong barrier to rupture. Data for this comparison are shown in Figure 7, again as cumulative distributions. For strike-slip ruptures, basic differences are evident. The median rupture-ending bend is 26, compared to median and maximum IBs of 13 and 18, respectively. The maximum IBs have been overcome in rupture and thus are preferred for comparison to rupture-ending bends. The corresponding data for dip-slip ruptures in Figure 7b do not exhibit a similar degree of separation between ending and maximum bend angles. For example, the maximum IBs in dip-slip ruptures are systematically larger than the bends ending rupture. At face value, this has the improbable meaning that, when examining a dip-slip fault for candidate ruptures, a sharp bend in the fault trace is more often passed than it stops a rupture. To evaluate the effectiveness of bends to stop ruptures, using the absolute numbers of bends is inappropriate because the numbers of interior and ending bend measurements are not the same. Instead, we compare the fraction of a given angle range among ending bends to the corresponding fraction among IBs. Figure 8a,b compares these fractions as a function of angle for strike-slip and dip-slip faults, respectively. The data for the plot are provided in Table 1. Because the sample sizes are relatively small, interior and ending bend angles are binned. In Figure 8a,b, bins are 5 wide with

12 2554 G. P. Biasi and S. G. Wesnousky (a) Net deflection (b) Fraction greater all Rupture length (km) 1.5 Median : 11., Dip: Net deflection all Figure 5. Net deflection angle is the absolute difference in map orientation between ends of ruptures. In (a), net deflection is plotted versus rupture length, with symbols distinguishing dip-slip and strike-slip ruptures. (b) Complimentary cumulative distribution of net deflection angles. To preserve plot scale, two dip-slip points in (a) are not repeated in (b). Median net deflections are 11 and 19.5 for strike-slip and dip-slip cases, respectively. Only one simple strike-slip rupture exceeds 31 net deflection. The color version of this figure is available only in the electronic edition. (a) TAAD (squirrel) (c) TAAD (squirrel) ( /km) Length (km) Gobi-Altai 2 4 Length (km) (b) Fraction (d) Fraction Squirrel centers at 7.5, 12.5, etc. Figure 8c and 8d is derived from Figure 8a and 8b. They are plots of the ratio of IBs passed to those not passed as a function of bend angle. We refer to this value as the passing ratio and interpret it as a measure of the relative resistance of a bend to rupture propagation. For strike-slip ruptures, it is observed that bends of 13 are passed by a ratio of 2:1 compared to stopping rupture, when the data are binned at 5. For a bend of 31, the ratio is reversed, and rupture stops twice as often as it continues. The passing ratio does not vary much with the choice of bin width; results for bins of 4, 5, 6, 8, and 1 are shown in Figure 8c. A clear trend is seen of declining passing ratio with increasing bend angle. Using data from 5 to 3, a linear trend PR 3:1 :83A is found, in which PR is the passing ratio and A is the bend angle. A similar trend is found if the bin centers are offset by half their widths. The passing ratio relationship is intended only to summarize the main features of the observations. The linear trend cannot apply for all angles, because it predicts meaningless negative passing ratios for bends greater than about 4. It is also not clear whether the relative flatness of the passing ratio of 1:2 from 17 to 28 is a real feature or derives from some idiosyncrasy of the data. Dip-slip data do not yield as simple a trend for passing ratio. For example, bends greater than 4 are passed at higher ratios than they stop rupture. However, if we use the data in Figure 8d to summarize more coarsely, bends in the three bins less than 2 are passed as a group by a ratio of 4.5:1, whereas Squirrel ( /km) Figure 6. Total absolute angular deflection (TAAD), or squirreliness, as a (a) function of length, (b) complimentary cumulative distribution showing data fractions greater than a given TAAD, (c) TAAD interpreted as average curvature in units of degrees/km of length, and (d) complimentary cumulative distribution of curvature in units of degrees/ km. Dip-slip ruptures change direction by a factor of 3 more than strike-slip ruptures. The color version of this figure is available only in the electronic edition. bends from 2 to 35 stop rupture by about 2:1. At this extreme level of simplification, the dip-slip passing ratio is grossly similar to the strike-slip relationship. A larger sample size will be needed to be sure that this coincidence is not an accident of the small sample size. Other Rupture Complexities The state of practice in PSHA has advanced such that hazard analysts are considering the incidence and frequency of more complex rupture possibilities, including splays and branching shapes. The collected surface-rupture maps of BW16 and W8 give some basis to evaluate how common these complexities are in nature. Overlapping lengths in surface rupture are generally associated with the release of fault-normal stresses. In the 21 Kunlun rupture, Klinger et al. (25) report a 7-km length of normal faulting subparallel along a broad releasing bend in the main strike-slip rupture trace. In reverse and normal mechanism

13 Bends and Ends of Surface Ruptures 2555 (a) Fraction (b) Fraction 1.5 ending max int. all int Ending and interior bends 1.5 ending Dip max int. Dip all int Ending and interior bends Figure 7. Interior and rupture-ending bend angles for (a) strikeslip and (b) dip-slip ruptures. Data are repeated from Figures 3 and 4. Ending bends (triangles) for a distinct population for strike-slip ruptures but not for dip-slip ruptures. Fractions (y axis) refer to the portion of data with a bend larger than the angle on the abscissa. The color version of this figure is available only in the electronic edition. (a) Fraction (c) Passing ratio Bin width: 5 Int End Bend angle Bend angle w: 1 w: 8 w: 6 w: 5 w: 4 (b) Fraction (d) Passing ratio Bin width: Bend angle ruptures, overlapping rupture commonly occur as subparallel secondary failures of the hanging wall (e.g., Arrowsmith et al., 216). In the 28 Wenchuan, China, earthquake (see the E electronic supplement), secondary failure on the Penguan fault extended for tens of kilometers, with a maximum displacement of 3.5 m (Xu et al., 29). Overlap lengths for the combined rupture set are plotted in Figure 9a and 9b as a function of length and rupture magnitude, respectively. To preserve the plotting scale, three overlap estimates greater than 1 km (Table 1) are not shown. Long strike-slip ruptures generally have smaller fractional overlap compared with shorter ruptures (Fig. 9c). The prominent exception, the 1957 Gobi-Altai rupture, had a main trace length of 245 km and a fractional overlap of.8 (Kurushin et al., 1997). Much of the overlap occurs in the extensive system of reverse-faulting offsets southwest of the main trace that apparently relieved significant fault-normal stresses (Choi et al., 212). Dip-slip ruptures have fractional overlaps somewhat larger, on average, than that of strike-slip ruptures (Fig. 9d). The possibility of rupture jumping from one fault to another is increasingly being included in high-level seismic hazard assessments (Field et al., 214; Senior Seismic Hazard Analysis Committee [HAC] Level 3 Technical Integration (TI) Team, 215). Well-known Int DI End DI Bend angle Figure 8. Comparison of data fractions of interior and ending bends for dip-slip and strike-slip ruptures. (a) Strike-slip bend data, gathered in 5 bins. The number of measurements in each bin is divided by the total to get the plotted bin fractions. Bends passed inside the ruptures are concentrated below 2, whereas bends ending ruptures are more evenly distributed. One IB and many ending bends larger than 45 are not shown (see Fig. 7). (b) Dip-slip binned data and (c) ratio of passed to ending bin fractions for strike slip. The ratio shows how frequently, as a fraction of its respective type, a bend of a given size is passed. Bends <15 are passed over twice as often as they stop rupture. Bends of 31 are twice as likely to stop rupture as to be passed. Multiple lines show how the passing ratio would vary with different bin widths. (d) Dip-slip passing ratios are more variable because of small sample size. The color version of this figure is available only in the electronic edition. DI fault-to-fault examples include the 1992 Landers, California, earthquake, which jumped in strike slip across steps or shear zones to connect the Johnson Valley, Homestead Valley, Emerson, and Camp Rock faults, and the previously described 22 Denali rupture. We use the combined set of rupture maps to evaluate how frequently fault-to-fault ruptures occur. Instances of fault-to-fault rupture are listed in Table 1 and summarized by mechanism type in Table 2. Map relations for all are provided in the E electronic supplement. In general, instances of fault-to-fault rupture were counted when rupture left a main fault trace to continue as a viable rupture on a splay or higher-angle structure or through a substantial step or gap onto another fault. As with rupture terminal bends, we did not count fault-to-fault cases in which a short rupture termination could readily be explained by dynamic rupture effects. A reader interested in how the compilation might change using shorter length criteria is referred to compilations of end distances and end bends in Table 1 and to the maps provided in the E electronic supplement. We find (Table 2) that fault-to-fault rupture cases tend not to change mechanism, but that among ruptures that do change type, strike-slip transitioning to reverse (events 37, 49, 55, and

14 2556 G. P. Biasi and S. G. Wesnousky (a) Overlap length (km) (c) Overlap/rupture length Length (km) Gobi-Altai 2 4 Rupture length (km) Overlap length (km) 1 66) are most common. Examination of the rupture maps indicates that, for at least events 49, 55, and 66, strike-slip transition to reverse structures had the effect of preserving the slip direction through a change in rake angle onto the reverse fault. Strike-slip to normal transfers occur, but none propagated far enough to be included in our compilation. Another type of complexity arising in seismic hazard estimation is the rupture with coseismic motion in a Y (both sides of a splay) or T shape (primary and conjugate fault planes). We use the combined rupture map set to ask how commonly these rupture shapes occur and whether patterns are suggested in where they occur. In Table 1, events 16, 21, 24, 28, 39, 47, and 49 include coseismic rupture on two or more arms. Of these, four of 42 total involve strike slip only (events 21, 39, 47, and 49), three of 25 total (events 16, 24, and 28) are purely dip slip, and one (event 49, 1957 Gobi- Altai) involves simultaneous strike-slip and reverse motion. Recognizing that the sample size is small, it appears that (b) (d) Overlap/rupture length Magnitude Wenchuan 1 2 Rupture length (km) Figure 9. Overlapping rupture length (a) as a function of rupture length, (b) overlap length as a function of magnitude, (c) fraction of overlap to total length, strike-slip ruptures, and (d) overlap in dip-slip ruptures as a fraction of total length. Three overlap totals longer than 1 km from Table 1 are not shown in (a) and (b) to preserve plot scale for the majority of the data. The color version of this figure is available only in the electronic edition. Table 2 Fault-to-Fault Rupture Cases Mechanism Reverse Normal Any Reverse Normal 1 1, strike slip. fewer than 1% of strike-slip ruptures in our collection have significant Y- or T- shaped ruptures, while slightly more than 1% of dip-slip ruptures include them. If the criteria for complexity is extended to include extensive fracturing and/or discontinuous rupture of the hanging wall, 6 of 14 normal events (events 5, 14, 16, 41, 53, and 75) and 5 of 11 reverse ruptures (events 4, 28, 4, 55, and 69) would be included. Thus, almost half of dip-slip ruptures in our compilation have significant complexity expressed as secondary fault offsets in the hanging wall. Results in Table 2 summarize our map interpretations at the project scale length of > 7 km. Readers with interests at other scales are referred to the original map data. Discussion Empirical measurements from past surface ruptures provide fundamental data for comparison with numerical simulations and fault theoretical models. We have attempted only a first-order synthesis. For almost all of these events, more might be learned from an in-depth analysis. For example, plotting the rupture on a digital elevation map would show where slip is producing positive or negative topography and improve the interpretation of rupture bends. In the meantime, the first-order map observations may nonetheless be useful to those modeling the earthquake source or to those who are using fault data to assess seismic hazard. The largest IBs passed in rupture (Fig. 3) provide a direct empirical test of allowable fault misalignment relative to fault driving stress. Regional stress inversions from geodetic data and focal mechanisms typically find that the strain field varies smoothly on the scale of tens of kilometers (e.g., Becker et al., 25). At some small length scale, this smoothness may break down (Bailey et al., 29; Yang and Hauksson, 213), but at the scale considered here (bend arms > 5 7 km), a nearly constant stress orientation appears appropriate. For rupture to propagate, both arms of the bend must be at least minimally favorable in orientation. Modeling results of Lozos et al. (211) suggest an upper limit for strike slip between 32 and 34. Our empirical data (Fig. 3) suggest a somewhat smaller limit near 28, a value very similar to the upper range found by Ando et al. (29, their fig. 4) for splays from a main fault. Two apparent exceptional points are associated with strike-slip transitions to reverse-faulting structures. The dips of the reverse faults have the geometric effect of reducing the IB angle in 3D. Neither exceptional max IB case would be well represented by the strike-slip model of Lozos et al. (211). Our study also suggests that dip-slip ruptures have a nominal IB limit near 5. For such a