The Shear Deformation Zone and the Smoothing of Faults with Displacement Clement Perrin, Felix Waldhauser, Christopher Scholz
The Shear Deformation Zone and the Smoothing of Faults With Displacement Clement Perrin, Felix Waldhauser, Christopher Scholz
To cite this version:
Clement Perrin, Felix Waldhauser, Christopher Scholz. The Shear Deformation Zone and the Smooth- ing of Faults With Displacement. Journal of Geophysical Research : Solid Earth, American Geophys- ical Union, 2021, 126 (5), pp.e2020JB020447. 10.1029/2020JB020447. hal-03284736
HAL Id: hal-03284736 https://hal.archives-ouvertes.fr/hal-03284736 Submitted on 12 Jul 2021
HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. 1 The Shear Deformation Zone and the Smoothing of Faults with Displacement
2
3 Clément Perrin1,2,*, Felix Waldhauser1 and Christopher H. Scholz1
4
5 1 Lamont Doherty Earth Observatory at Columbia University, New York, USA
6 2 Present address : Laboratoire de Planétologie et Géodynamique, UMR6112,
7 Observatoire des Sciences de l’Univers de Nantes Atlantique, UMS3281, Université de
8 Nantes, Université d’Angers, CNRS, 2 rue de la Houssinière - BP 92208, 44322 Nantes
9 Cedex 3, France
10 * Corresponding author: [email protected]
11
12 Keypoints:
13 Across strike distributions of aftershocks of large earthquakes describe the width of the
14 shear deformation zone around large faults.
15
16 The zone of active shear deformation scales with fault roughness and narrows as a
17 power law with fault displacement.
18
19 Earthquake stress drops decrease with fault displacement and hence fault roughness or
20 displacement rate.
21
22 Keywords:
23 Fault maturity; shear deformation zone; large earthquakes; aftershock distributions;
24 scaling laws.
25
1 26 Plain Language Summary
27 Active fault zones worldwide are 3D features made of a parent fault and secondary
28 faults and fractures that damaged the surrounding medium. During and soon after a
29 large earthquake, these structures are reactivated, highlighted by numerous smaller
30 events –aftershocks. Their distribution allows us to characterize the zone of shear
31 deformation around the fault plane. In this study, we show that the width of the shear
32 deformation zone is narrower around mature faults than around immature faults. It
33 decreases as a power law with cumulative fault displacement which we infer to be the
34 result of the smoothing of the fault with wear through geological times. We also find that
35 the stress-drop of mainshocks decrease with fault smoothness or slip rate, both of which
36 correlate with maturity. Our study provides some relations to better understand and
37 anticipate the size of off-fault deformation reactivated during and after an earthquake,
38 based on geological fault parameters.
39
40 Abstract
41 We use high-resolution earthquake locations to characterize the three-dimensional
42 structure of active faults in California and how it evolves with fault structural maturity.
43 We investigate the distribution of aftershocks of several recent large earthquakes that
44 occurred on continental strike slip faults of various structural maturity (i.e., various
45 cumulative fault displacement, length, initiation age and slip rate). Aftershocks define a
46 tabular zone of shear deformation surrounding the mainshock rupture plane.
47 Comparing this to geological observations, we conclude that this results from the re-
48 activation of secondary faults. We observe a rapid fall off of the number of aftershocks at
49 a distance range of 0.06–0.22 km from the main fault surface of mature faults, and 0.6-1
50 km from the fault surface of immature faults. The total width of the active shear
2 51 deformation zone surrounding the main fault plane reaches 1-2.5 km and 6-9 km for
52 mature and immature faults, respectively. We find that the width of the shear
53 deformation zone decreases as a power law with cumulative fault displacement.
54 Comparing with a dynamic rough fault model, we infer that the narrowing of the shear
55 deformation zone agrees quantitatively with earlier estimates of the smoothing of faults
56 with displacement, both of which are aspects of fault wear. We find that earthquake
57 stress drop decreases with fault displacement and hence with increased smoothness
58 and/or slip rate. This may result from fault healing or the effect of roughness on friction.
59
60 1. Introduction
61 A fault zone is a complex brittle-frictional system that wears as slip occurs on it. It is
62 formed of three main features, that evolve with fault growth (Fig. 1): (i) the cataclastic
63 core contains the cataclastic detritus of wear of the slipping surfaces of the fault. Its
64 width (WC in Fig. 1) increases linearly with fault displacement at a rate that depends on
65 the strength of the wall rock (Scholz, 1987, 2019, pp 132). For displacements greater
66 than a few hundred meters, growth of the fault core levels off at a thickness of a few tens
67 of meters (Scholz, 2019, pp 132); (ii) Beyond the fault core lies a region of pervasive
68 tensile fracturing which defines the “dilatant damage zone” (WD, Fig. 1; e.g. Faulkner et
69 al., 2011; Savage & Brodsky, 2011; Vermilye & Scholz, 1998). The fracture density in this
70 zone dies off as a power law with distance from the fault (e.g., Ostermeijer et al., 2020
71 and references therein). The dilatant damage zone width increases linearly with fault
72 displacement, and typically levels out at several hundred meters for fault displacements
73 exceeding several hundred meters (Savage & Brodsky, 2011); (iii) Including and
74 extending beyond the dilatant damage zone is what we call the “shear deformation
75 zone” (WS; Fig. 1) which is defined by a region of enhanced seismicity, first pointed out
3 76 by Powers & Jordan (2010). This zone shows a region of high seismic activity near the
77 fault with a power law fall-off beyond a corner at WS1 to a full half-width of WS2 (Fig. 1).
78
79 The above definitions allow us to distinguish two types of damage zones: the “dilatant
80 damage zone” dominated by volumetric strains, and the “shear deformation zone”
81 dominated by shear strains. The tensile (Mode I) cracks in the dilatant damage zone are
82 dilatant cracks that align parallel to the maximum compression direction and
83 perpendicular to the minimum principal stress. Hence the orientation of cracks provides
84 evidence for the several different mechanisms responsible for their formation (Wilson et
85 al., 2003). The shear deformation zone is characterized by secondary faults (Mode II and
86 III cracks) and hence are oriented parallel to the maximum Coulomb stress. For example,
87 in the case of a strike-slip fault, this zone is defined by a conjugate set of secondary faults
88 (Little, 1995), in which one set is parallel to the primary fault.
89
90 The evolution of these three zones in figure 1 defines what is called fault maturity. The
91 three zones can be viewed as regions controlled by wear processes, and the fault
92 structural maturity can hence be measured by its degree of wear, which depends
93 primarily on the net fault displacement, assuming a constant slip-vector throughout the
94 fault’s history. However, previous studies have shown that, in the absence of data on net
95 fault displacement, several other fault parameters such as the fault initiation age and the
96 geological slip rate can be also used as a proxy of net displacement in evaluating the
97 overall maturity of the fault (e.g. Choy et al., 2006; Choy & Kirby, 2004; Dolan &
98 Haravitch, 2014; Hecker et al., 2010; Ikari et al., 2011; Manighetti et al., 2007; Niemeijer
99 et al., 2010; Perrin, Manighetti, Ampuero, et al., 2016; Stirling et al., 1996; Wesnousky,
100 1988). As these parameters increase, the fault grows and becomes more “mature”. Prior
4 101 studies have suggested that the structural maturity may have a strong impact on
102 earthquake behavior, such as magnitude, stress drop, distribution of slip, rupture
103 velocity, ground motion amplitude, and number of ruptured segments (e.g., Cao & Aki,
104 1986; Dolan & Haravitch, 2014; Hecker et al., 2010; Malagnini et al., 2010; Manighetti et
105 al., 2007; Perrin, Manighetti, Ampuero, et al., 2016; Radiguet et al., 2009; Stirling et al.,
106 1996; Wesnousky, 1988).
107
108 The widths of the fault core and dilatant damage zones saturate at fault lengths
109 comparable to the seismogenic thickness, due to the switch from crack like to pulse like
110 earthquake propagation (Ampuero & Mao, 2017). For larger faults, the evolution of fault
111 maturity involves only changes in the shear deformation zone. In this paper we are
112 concerned with the scaling of large faults (i.e., which breach the brittle seismogenic
113 width) and their associated large earthquakes, so we are only concerned with the shear
114 deformation zone. There is evidence that indicates that large faults become smoother
115 with net displacement (Stirling et al., 1996; Wesnousky, 1988). This smoothing is
116 probably the prime attribute of fault maturity. Here we show that the width of the shear
117 deformation zone of large faults decreases with fault displacement, as a consequence of
118 this smoothing.
119
120 Precise earthquake locations can be used to image the internal structure of fault and the
121 zone of brittle deformation, often at a resolution similar to field observations (e.g.
122 Powers & Jordan, 2010; Hauksson, 2010; Valoroso et al., 2014). Powers & Jordan (2010)
123 studied the association of small earthquakes with large faults in California. They found
124 that the frequency of small earthquakes is highest in a narrow region surrounding faults
125 and then falls off as a power law at greater distances. They modeled this behavior with a
5 126 fault model with rough (fractal) topography (Dieterich & Smith, 2009), showing that
127 such a rough fault model would produce high stresses near the fault that could account
128 for the seismicity. The earthquakes they used was from the interseismic period of the
129 faults. Although stacked profiles from many fault sections show the association of
130 seismicity with the faults, individual sections and map views, both in Powers & Jordan
131 (2010) and Hauksson (2010) show that such a tight correlation with the fault is not
132 typical for individual fault segments, which often display a wide variability in
133 distributions. As Hauksson (2010) observed, this variability is likely due to many
134 factors, such as heterogeneity in lithology, the effect of nearby faults both mapped and
135 unmapped, and fault offsets and bends.
136
137 As Hauksson (2010) observed further, aftershocks of large earthquakes, in contrast,
138 mostly show a tight clustering around the main fault. At depth, they are mainly
139 distributed at the edges of regions experiencing high coseismic slip and in surrounding
140 areas of low coseismic slip (e.g., Mendoza & Hartzell, 1988). Also, earthquakes that occur
141 during interseismic periods often delineate the edges of stuck patches sometimes
142 surrounded by creeping areas, and potential rupture surfaces at depth (e.g., Perrin et al.,
143 2019; Schaff et al., 2002; Waldhauser et al., 2004). In both cases, the majority of
144 aftershocks of large earthquakes sample a portion of the main fault zone structure at
145 depth at the edge of the rupture surface, and are often used to delineate it. In an
146 earthquake model with a smooth rupture surface, stress-drop increases to a maximum
147 near the fault surface, thus precluding aftershocks in the near-fault region (Kostrov &
148 Das, 1984). Near-fault aftershocks therefore are an indication of a rough fault, as near-
149 fault stresses are generated by dynamic slip on rough topography. They are greatest
150 right after the mainshock, after which they are relaxed by aftershocks and other
6 151 relaxation mechanisms. In this study, in order to estimate the roughness of active faults,
152 and how they evolve with displacement, we use high-precision aftershock locations of
153 large earthquakes on faults with different net displacements.
154
155 2. Data analysis
156 2.1 Width of the shear deformation zone from aftershock locations
157 We use high-resolution earthquake catalogs available in the literature to analyze the
158 aftershock distribution of seven large (Mw≥6) continental strike slip earthquakes that
159 occurred on faults with a wide range of net displacement: the 1984 Morgan Hill, 2004
160 Parkfield, and 2014 South Napa earthquakes in northern and central California
161 (Waldhauser, 2009; Waldhauser & Schaff, 2008), and the 1987 Superstition Hills, 1992
162 Landers, 1999 Hector Mine, and 2010 El Mayor Cucapah earthquakes in Southern
163 California/Mexico (Hauksson et al., 2012). These earthquakes were selected because
164 high-precision aftershock catalogues, relocated by the double difference method
165 (Waldhauser & Ellsworth, 2000) and with relative lateral location errors derived from
166 bootstrap analysis that are typically less than ≤ 0.03 km on average (Supp. Fig. S1). In
167 order to perform a homogeneous analysis of all sequences, we selected all aftershocks
168 with ML≥1 that occurred within 2 months of each mainshock.
169
170 For each aftershock sequence we determine the three-dimensional fault geometry by
171 applying a principal component analysis (PCA) to all events within boxes that are
172 between 3 and 10 km long along strike and between 3 and 20 km wide across strike (i.e.
173 centered on the surface fault trace), stepping at 1 km intervals along the fault trace
174 (Perrin et al., 2019). For each box, we obtain a plane that best fits the locations of
175 aftershocks. For simplicity, we assume a constant dip of the calculated planes in each
7 176 box (see also Perrin et al., 2019). In general, the calculated fault plane parameters are in
177 good agreement with existing fault parameters derived from source inversion models
178 (Mai & Thingbaijam, 2014 and references therein; see details in Supp. Table 1 and Supp.
179 Fig. S2).
180
181 We then compute the orthogonal distance between each hypocenter and the calculated
182 fault plane segment, count the number of aftershocks as a function of distance from the
183 fault plane within bins of 0.03 km, and normalize the results by the total number of
184 aftershocks in each box (gray lines in Fig. 2b, d, e, f, g and Supp. Fig. S3). Finally, we
185 compute the mean of these normalized counts for each distance bin (black line in Fig. 2
186 and Supp. Fig. S3) to describe the smoothed distribution of aftershocks as a function of
187 distance from the fault plane for each of the seven earthquake sequences.
188
189 We use a power law function to fit the mean normalized aftershock distribution (red
190 curve in Fig. 3 and Supp. Fig. S4) to find the two parameters that describe the width of
191 the shear deformation zone. WS1 is the distance from the fault plane where the fall-off in
nd 192 number of events exhibits the maximum curvature (i.e., maximum in 2 derivative). WS2
193 is the distance from the fault plane where the number of events departs from the power
194 law fit and either flatten out (see Fig. 3a) or drop towards zero (see Fig. 3e). Both
195 parameters represent significant changes in event density, with WS2 indicating the
196 transition from the zone of active faulting to a largely undeformed crustal host rock (see
197 section 4.3 for a comparison with Powers and Jordan, 2010). This transition generally
198 occurs when less than 20% of all boxes used to count aftershocks include events (grey
199 circles in figure 3 and Supp. Fig. S4). We use this criterion to define WS2 for all aftershock
200 distributions considered here.
8 201
202 As examples of our approach, analyses of the 2004 Parkfield and 1999 Hector Mine
203 aftershocks are presented in figure 2 and 3 (see Supp. Fig. S3 and S4 for all earthquake
204 cases). The power law fit to the near-fault aftershock data at Parkfield (red curve, Fig.
205 3a) has a maximum curvature at about 0.06 km away from the fault plane (WS1). Beyond
206 WS2 = 0.56 km, the distribution departs from the red fit, implying that no significant
207 additional aftershock activity (ML≥1) related to the active fault zone is detected. In cases
208 with multiple ruptures on sub-parallel or sub-perpendicular faults such as Hector Mine,
209 Landers, Superstition Hills and El Mayor Cucapah, we estimated WS1 and WS2 for the
210 individual fault segments that broke during the earthquake (Fig. 2c, d, e, f, g, 3b, c, d, e
211 and Supp. Fig. S3 and S4) and then averaged the values so that a single value could be
212 assigned to each aftershock sequence. The variance in the parameters obtained for
213 individual segments is typically small. Table 1 lists WS1 and WS2 we obtained for the
214 seven earthquakes.
215
216 Also listed in Table 1 are data from the immature Awatere fault. This right-lateral strike-
217 slip fault is a first order splay of the Alpine fault of New Zealand. It crosses the coast at a
218 sea-cliff that offers an almost complete exposure of the entire fault zone from the fault
219 core through the shear deformation zone. This was mapped by Little (1995), who
220 showed that the shear deformation zone consists of a set of right-lateral and conjugate
221 left-lateral secondary faults that decreased in frequency with distance from the primary
222 fault in the same manner as the aftershocks do in our study. The right-lateral set of the
223 secondary faults is nearly sub-parallel to the main fault and the left-lateral set about 60°
224 from that. Values of WS1 and WS2 obtained from that data are indicated in Table 1. An
225 exposure at mid-crustal depths of a strike-slip fault in Austria shows just the same
9 226 orientation of secondary faults (Frost et al., 2009). These observations provide the
227 ‘ground truth’ for the structures upon which the near-fault aftershocks occur.
228
229 2.2 Fault parameters
230 We collect key parameters describing the degree of evolution of the faults that broke
231 during the selected earthquakes. Since faults propagate laterally through time, their
232 structural maturity varies also along strike (Perrin, Manighetti, & Gaudemer, 2016;
233 Perrin, Manighetti, Ampuero, et al., 2016). Thus, it is necessary to use fault parameters
234 that describe the local fault maturity where the rupture occurred. This is particularly
235 true for long faults, such as the San Andreas Fault, for which fault initiation age varies
236 greatly along the fault, from ancient fault sections in Central California (24 to 29 Ma at
237 Parkfield; e.g. Atwater & Stock, 1998; Liu et al., 2010) to younger fault sections in
238 Southern California (<12Ma, e.g. Powell & Weldon, 1992; Sims, 1993), and which
239 therefore have different local net displacements. Table 1 presents the fault parameters
240 used in this study. The seven fault sections span a wide range of structural maturity,
241 with various initiation ages (1.1 to 29 Ma), cumulative displacements (1 to 315 km) and
242 geological slip rates (0.2 to 26 mm/yr).
243
244 Some fault parameters are not fully constrained, especially for the fault associated with
245 the South Napa earthquake. The West Napa fault corresponds to the northern extension
246 of the Calaveras fault, which transfers its slip northwards via the Contra Costa shear
247 zone (Brossy et al., 2010; Catchings et al., 2016; Unruh et al., 2002). We estimated its
248 cumulative slip using a linear fault tip model (Scholz & Lawler, 2004). The West Napa
249 Fault terminates about 35 km north of the South Napa earthquake, and the tip taper for
250 interacting faults is 0.1-0.8 (Scholz & Lawler, 2004). Combining these values give a total
10 251 slip range of 3.5-28 km (Table 1). As the West Napa Fault is genetically linked to the
252 Calaveras fault and situated at its northern tip, we assume that it formed after the
253 formation of the main Calaveras fault (about 12 Ma; Wakabayashi, 1999) and before the
254 younger surrounded Greenville and Green Valley faults situated to the east (about 6 Ma
255 ago; Wakabayashi, 1999). The slip rate on the West Napa fault is estimated to exceed 1
256 mm/yr, based on geomorphic evidence (Wesling & Hanson, 2008) and to be 4±3 mm/yr
257 as derived from geodetic data (d’Alessio, 2005; Field et al., 2015). For clarity, the
258 estimated geological parameters of the West Napa fault are represented as open
259 symbols in figure 5.
260
261 3. Results
262 We investigate the relationship between the aftershock distributions, as characterized
263 by WS1 and WS2, and the various, independently derived fault parameters (Table 1). Our
264 first observation is that WS1 (i.e., the half distance from the calculated fault plane where
265 the aftershock rate saturates) and WS2 (i.e., the full half-width of the shear deformation
266 zone) correlate with each other (Fig. 4), indicating that these two parameters are not
267 independent and that the shape of the shear deformation zone grows in a self-similar
268 way as
269 WS1=(0.2±0.1)*WS2
270 In figure 5 we plot WS1 and WS2 as a function of various fault parameters. When plotted
271 against cumulative fault displacement (Fig. 5a and 5b), they both indicate that the width
272 of the shear deformation zone (as characterized by WS1 and WS2) decreases with net
273 displacement as a power law with an exponent of -0.54 and -0.39 for WS1 and WS2,
274 respectively. We note that the field measurements across the Awatere fault (red symbol
275 in Fig. 5) are in good agreement with the trends highlighted from seismological data.
11 276 This supports the interpretation that the shear deformation zone defined by the width of
277 the aftershock zone corresponds to the width of the zone of active secondary faulting.
278
279 Furthermore, we observe a decrease of WS1 and WS2 with increasing fault initiation age
280 (fig. 5c and 5d) and geological slip rate (fig. 5e and 5f), showing a wider shear
281 deformation zone for younger fault sections and slower slip rates. This is also in good
282 agreement with geological observations across the Awatere fault. We note that the
283 power law exponents in figure 5 should be used with caution given the occasionally
284 large uncertainties in the fault parameters.
285
286 Figure 6a shows the near-fault aftershock distribution as a function of fault
287 perpendicular distance for each of the seven earthquake sequences (see also black
288 curves in Fig. 2 and Supp. Fig. S3). These curves show a clear pattern: intermediate to
289 mature fault sections (warm colors in fig. 6) are characterized by aftershocks
290 concentrated close to the fault plane. The rapid fall-off in activity away from the fault
291 plane describes a narrow deformation zone at the scale of hundreds of meters. In
292 contrast, intermediate to immature faults (cold colors in fig. 6) exhibit a wider
293 deformation zone at the kilometer scale where events are more widely distributed
294 within the surrounding medium (fig. 6a and b). The distributions remain proportional to
295 one another, indicating that the shape of the shear deformation zone remains constant.
296 Field measurements of the cumulative number of faults across the Awatere fault (black
297 squares, fig. 6a; Little, 1995) show a similar trend and corroborate our seismological
298 observations.
299
300
12 301 4. Discussion
302 4.1. The nature of the shear deformation zone and the smoothing of faults
303 In this study we show that, for fault displacements greater than 1 km, the width of the
304 shear deformation zone (defined by WS1 and WS2) decreases with fault displacement. So,
305 what determines the width of the zone of near-fault aftershocks that define the shear
306 deformation zone? If the fault is smooth, the mainshock would produce a stress shadow
307 centered at the fault and there would be no near-fault aftershocks (Kostrov & Das,
308 1984). Slip on a rough fault, on the other hand, would result in high stresses in a narrow
309 region adjacent to the fault, within which earthquakes could be generated. This was the
310 explanation used by Powers & Jordan (2010) to explain near-fault seismicity during the
311 interseismic period. There they used the static rough fault model of Dieterich & Smith
312 (2009).
313
314 Here we use instead the model of Aslam & Daub (2018) which calculates the stresses
315 resulting from dynamic ruptures propagating on a rough surface. They characterized the
316 fault as a self-affine fractal with Hurst exponent H and fault roughness measured by the
317 RMS of the ratios between the amplitude and the wavelength of the fault surface
318 topography (. This is a fairly realistic rendition of the observed topography of faults
319 (e.g. Candela et al., 2012). Their model predicts large changes in the Coulomb Failure
320 Function (CFF= ; of more than 20 MPa) within a well-defined narrow region, Wnf
321 close to the fault. The modeled receiver faults they assumed are parallel to the primary
322 fault, which is consistent with the orientation of most of the secondary faults observed
323 by Little (1995) and Frost et al. (2009). They find that the width of this near-fault region
324 of high stresses is insensitive to H but decreases with . Assuming that our observed
325 shear deformation zone represents the near-fault region of high stresses, this suggests
13 326 that the observed decrease of WS2 with fault displacement is the result of smoothing of
327 the fault with slip, similarly to observations made during laboratory experiments
328 (Goebel et al., 2017)
329
330 Aslam & Daub (2018) found that the half width of the near fault zone Wnf is ~ 2.7 km and
331 ~ 0.9 km for profiles with fault roughness RMS values of 0.01 and 0.001, respectively.
332 Comparing these results with the range of WS2 in figure 5 indicates that more than an
333 order of magnitude of roughness change will be required to explain these observations.
334 This indicates a wear rate far greater than that observed for the roughness of individual
335 fault segments measured in the outcrop scale range for fault displacements in the range
336 10-1-103 m (Brodsky et al., 2011). Similar measurements made on fault segments in the
337 high porosity and friable Navajo and Entrada sandstones of Utah (Dascher-Cousineau et
338 al., 2018) indicate greater smoothing rates but predict fault roughness at our scales
339 orders of magnitude smoother than indicated by our results as interpreted with Aslam &
340 Daub (2018). However, faults are composed of many segments or sub-faults at many
341 scales (Ferrill et al., 1999; Klinger, 2010; Manighetti et al., 2015; Scholz, 1998; Wallace,
342 1989) and of nested sub-faults offset from one another (Ben-Zion & Sammis, 2003; de
343 Joussineau & Aydin, 2009; Segall & Pollard, 1980). The length distribution of sub-faults
344 follows a power law (Scholz, 1998) and they are offset by jogs that are self-similar (de
345 Joussineau & Aydin, 2009). The combination of the latter relations would produce a
346 fractal topography at a hierarchy higher than that of the roughness of the individual sub-
347 fault. A fault smoothing relationship based on roughness at this supra-segment level,
348 measured as fault step spacing, shows an approximately inverse linear reduction of fault
349 roughness with fault displacement (Stirling et al., 1996). This is a much higher rate of
350 smoothing than that of individual fault segment surfaces, and is comparable to that we
14 351 infer from the narrowing of the shear deformation zone. Converting the roughness
352 parameter step frequency of Stirling et al. (1996) to using the typical step width 1-2
353 km (Wesnousky, 1988) and their smoothing curve allows us to recast the two fiducial
354 points of Aslam & Daub, 2018 from (Wnf ,to (Wnf , D) coordinates (i.e. values of 0.001
355 and 0.01 corresponding to fault displacements “D” of 100 and 10 km, respectively).
356 These are plotted in Figure 7 (blue circles) where they are compared with our WS2
357 measurements from figure 5b (squares). The good agreement supports the hypothesis
358 that narrowing of the shear deformation zone with fault displacement is the
359 consequence of the smoothing of the fault with wear (see also discussion in section 4.3).
360
361 4.2. The effect of fault maturity on earthquake properties
362 Once a fault reaches the seismogenic thickness, with a length of ~ 10 km and slip ~ 100
363 m, its core and dilatant damage zones are fully formed and further maturation occurs by
364 the fault becoming smoother through the processes of frictional wear. It follows that the
365 characteristics of earthquakes may also evolve with the smoothing of the fault. It has
366 been suggested, for example, that earthquake stress drop, apparent stress, and radiation
367 efficiency vary with fault maturity (Choy et al., 2006; Hecker et al., 2010; Ross et al.,
368 2018). These are not entirely independent parameters. The radiation efficiency, 휂푅, is
369 given by:
퐸푅 2휇퐸푅 2휎푎 370 휂푅 = = = , 퐸푅+퐸퐺 Δ휎푀표 Δ휎
371 where 퐸푅 is radiated energy, 퐸퐺 is energy dissipated in damage, Δ휎 is (static) stress
372 drop, 휎푎is apparent stress, 푀표is seismic moment, and 휇 is shear modulus. Here we focus
373 on stress drop, which is the most commonly reported of these properties.
15 374 Five of the earthquakes in our study have three or more estimates of stress drop (Δ휎).
375 Following the procedure of Hardebeck (2020), we assume that log10(Δ휎) has a normal
376 distribution (Baltay et al., 2011) and calculate its mean and the standard error of the
377 mean, as reported in Table 2. The corresponding values of mean Δ휎 are plotted vs. the
378 cumulative fault slip in figure 8. The correlation Δ휎 D-0.23, compared to our earlier
−0.39 379 finding that 푊푆2 ∝ 퐷 implies that stress drop scales with 푊푆2 and hence, from figure
380 7, that stress drop scales with fault roughness. Hecker et al. (2010) measured the
381 maximum slip to length ratio of prehistoric earthquake scarps on intraplate dip-slip
382 faults in the western U.S. They found that this ratio, an indicator of stress drop, tends to
383 decrease with net fault displacement, consistent with our finding.
384
385 However, net fault slip usually correlates with slip rate (see Fig. 5), so we also find a
386 similar correlation between stress drop and that parameter, as shown in figure 9a (the
387 relation between stress drop and fault initiation age is shown in Supp. Fig. S5). This is
388 shown also in log-linear coordinates in figure 9b to compare it with the form expected
389 from fault healing. The correlation of stress drop with the log of slip rate or its inverse,
390 the recurrence time, is well known (Kanamori & Allen, 1986; Scholz et al., 1986) as is its
391 correlation with strain rate (Hauksson, 2015). The size of the effect seen in figure 9b is
392 about -2 MPa/decade in slip rate, in rough agreement with the other studies.
393 Scholz et al. (1986) pointed out that this behavior could either reflect a rate effect due to
394 fault healing as predicted by the rate- and state-dependent friction laws (Dieterich,
395 1972) or a roughness effect in which friction increases with surface roughness, as
396 indicated by several experimental rock friction studies (Biegel et al., 1992; Byerlee,
397 1967), or some combination of the two.
398
16 399 Observations of repeating earthquakes in which seismic moment increased with
400 recurrence time promised a separation of these effects (Marone et al., 1995; Vidale et al.,
401 1994). Simulations with one dimensional spring-slider models with rate-state friction
402 indicated that these data could be explained with fault healing at a rate of 1-3
403 MPa/decade. However, subsequent studies using a 3D model of a repeating earthquake
404 occurring on a velocity-weakening patch imbedded within a creeping velocity-
405 strengthening fault showed that the recurrence time – moment scaling could occur
406 without any increase in stress drop (Chen & Lapusta, 2009). Observations at Parkfield,
407 California, showed both positive and negative moment-recurrence time scaling of
408 repeating earthquakes (Chen et al., 2010). Both types of scaling can be predicted with
409 the Chen & Lapusta, (2009) model by varying the ratio of nucleation to patch size.
410
411 In the Chen & Lapusta, (2009) model, aseismic slip propagates from the external
412 creeping region into the velocity-weakening patch such that only a fraction of its slip is
413 seismic. The ratio of seismic to aseismic slip in the velocity-weakening patch is sensitive
414 to parameters such as the radius of the velocity-weakening patch and its ratio to the
415 nucleation radius. As a result, it behaves very differently from a simple velocity-
416 weakening block slider model in which the slip is entirely seismic. The recurrence time –
417 moment scaling can be reproduced by varying the patch radius without varying stress
418 drop. In our problem, however, we are considering the fault to be fully coupled
419 seismically so that its slip is entirely seismic. In that case, the simple spring slider model
420 should be more applicable. If so, the analysis of Beeler et al. (2001) finds that stress drop
421 should increase logarithmically with recurrence time at about 0.5 to 1.5 MPa per decade,
422 assuming typical laboratory values for the friction parameters a and b. This is in
17 423 reasonable agreement with the slope in Fig. 9b of -2 MPa/decade in slip rate, although,
424 as we said earlier, the effect of fault roughness on stress drop cannot be ruled out.
425
426 4.3. Strengths, limitations and comparison with other studies.
427 In our study, we use aftershock distributions to study how the early postseismic events
428 are reactivating the long-term damage zone around active faults. We define WS2 as the
429 distance from the fault plane where the mean aftershock distributions start to flatten
430 out or drop abruptly (Fig. 3 and Supp. Fig. S4). Either the flattening or the abrupt
431 termination of the number of events with distance away from the fault would indicate
432 that there are no faults or fractures big enough to accommodate a large number of
433 events. Powers and Jordan (2010) observed a flattening of the interseismic event
434 distribution away from the fault which they attributed to background seismicity. Since
435 we are only using 2 months long aftershock sequences, with significantly larger number
436 of events compared to the interseismic period, we don’t systematically observe the
437 curve flattening and cannot reliably estimate the off-fault background seismicity level as
438 Powers & Jordan (2010) did for interseismic periods. If significant off-fault seismicity
439 exists during our observational period, then it may have occurred shortly after the
440 mainshock, and went undetected due to the low signal to noise ratio in the coda of the
441 mainshocks. However, a few of our aftershock distributions show curve flattening (e.g.
442 Parkfield, South Napa, Morgan Hill). These sequences occurred on intermediate to
443 mature faults where creep has been observed (e.g. Harris & Segall, 1987; Schaff et al.,
444 2002; Xu et al., 2018). Our hypothesis is that these aftershock distributions have fewer
445 absolute number of events because they are related to smaller mainshocks (M~6), and
446 also lower stress drops (see Fig. 8). Moreover, the presence of creeping sections might
447 increase the regional background seismicity level.
18 448
449 In this study, we selected aftershocks of Ml>1, thus including events with magnitudes
450 that are below magnitudes of completeness, Mc, levels for most aftershock sequences,
451 especially in southern California. Assuming that small events are randomly distributed
452 in the stress field, recovering and including all small events in our analysis would
453 increase the number of events in all boxes. This would result in shifts along the y axis in
454 figure 6a, but would not change the shape of the curves. It might lead to slight increases
455 in the WS2 values, which therefore should be considered here as lower bounds of our
456 shear deformation zone widths. This is in good agreement with figure 7, where some
457 measurements corresponding to southern California sequences seem to be under-
458 estimated compared to the expected theoretical models.
459
460 Our estimates of the shear deformation zone width might also be affected by the
461 aftershock productivity, which depends on the magnitude of the mainshock. The number
462 of aftershocks does increase with magnitude, but also linearly with fault area (Wetzler et
463 al., 2016; Yamanaka & Shimazaki, 1990), and therefore the density of aftershocks per
464 unit area is constant. This is what we show in supplementary figure S6, where the mean
465 number of events in boxes per km2 are quite similar and do not show any magnitude
466 dependency (Parkfield and Morgan Hill being slightly off because of the creeping areas
467 that bound the rupture zones, which produce abundant interseismic earthquakes on the
468 fault, contaminating the data at small distances). The apparent correlation between
469 mainshock magnitude and WS2 in our study results rather from the happenstance that
470 the larger earthquakes happen to have occurred on low maturity intraplate faults
471 whereas the smaller ones occurred on mature faults.
472
19 473 As mentioned earlier, Powers & Jordan (2010) estimated the normal distance of the
474 earthquakes away from a single vertical fault plane inferred from the surface trace of the
475 fault. They defined the zone of shear deformation from the near fault seismicity during
476 the interseismic period and averaged over the entire fault length, possibly neglecting
477 local variations in fault plane orientation and dip, leading to wider zones compared to
478 our results. In addition, geological heterogeneity over long distances along the fault and
479 other effects (such as triggering or regional stress release caused by other earthquakes)
480 may play a role, as pointed out by Hauksson (2010). Finally, our approach of fitting a
481 single fault plane to the local aftershock distribution as we step along the fault assumes
482 that the rupture occurred mainly on one fault strand and that aftershocks are
483 homogeneously distributed in the surrounded medium. While individual secondary
484 faults are distinguishable around mature fault sections (see for instance oblique linear
485 faults around Morgan Hill in Supp. Fig. S3), it is more difficult to identify them around
486 immature fault sections, within the broader zone of deformation, especially near the
487 rupture tips (see the northern part of the El Mayor Cucapah earthquake for instance;
488 Supp. Fig. S3).
489
490 Previous studies have estimated damage zone width or low velocity zones across several
491 faults in California using various seismic and/or geodetic methods (see Yang, 2015 for a
492 review). We compare some measurements with our results in Supp. Table S2. First, we
493 note that, different methods result in different estimates of “damage zone” widths.
494 Secondly, all studies using seismic fault zone trapped waves (FZTW) techniques find a
495 similar low velocity zone that is 100-200 m wide, regardless the fault structural
496 maturity. The FZTW derived width correspond to the constant width of dilatant damage
497 zones around large faults, already described by geological studies (e.g., Faulkner et al.,
20 498 2011; Savage & Brodsky, 2011; also called the inner damage zone in Perrin, Manighetti,
499 Ampuero, et al., 2016). However, other seismic and geodetic studies (sometimes used
500 together; see Cochran et al., 2009), find greater damage zone widths, that are in general
501 agreement with our results. This discrepancy between results from different methods
502 was also pointed out by Spudich & Olsen (2001). We tested the relations found in Figure
503 5a and 5b to deduce the size of the shear damage zone of the San Jacinto fault, for which
504 both a narrow damage zone using FZTW methods (e.g., Lewis et al., 2005) and wider
505 damage zone using tomography (e.g., Allam et al., 2014) have been described. Assuming
506 a cumulative slip of 24 km (Sharp, 1967), we obtain a half width of the shear
507 deformation zone ranging from 0.2 (i.e. WS1) to 1.5 km (i.e. WS2), which is in better
508 agreement with tomographic studies (half width of 1.5 to 2.5 km; Allam et al., 2014).
509 Thus, we believe that the studies using FZTW are mainly sensitive to the most damaged
510 inner part of the fault zone, also called the dilatant damage zone, which we don’t seem to
511 be able to resolve with our aftershock data. The other seismic and geodetic studies
512 found damage zone widths that are between 2(WS1) and 2(WS2), which we define as the
513 inner and outer bounds of the shear deformation zone.
514
515 A recent geodetic study from Scott et al. (2018) has shown that the dilatant damage zone
516 is equivalent to slightly wider than the shear deformation zone. These results come from
517 surface measurements (i.e., LiDAR) along the active fault zone responsible for the 2016
518 Kumamoto earthquake. It is possible that extensional strains are greater at the surface
519 than at depth. As cracks close down rapidly under pressure, dilatant strains in the
520 dilatant damage zone will decrease more rapidly with depth (Yoshioka & Scholz, 1989)
521 than the shear strains. This may explain why their results from surface measurements
522 differ from ours measured at depth.
21 523
524 In our study we average the near-fault aftershock distributions assuming that the degree
525 of fault maturity is locally constant along each broken fault sections we investigate.
526 However, it has been shown that the fault maturity can vary along strike and this can
527 affect the heterogeneity of fracture density around the fault core (Ostermeijer et al.,
528 2020), the distribution of secondary faults at greater distances away from the fault
529 (Perrin, Manighetti, & Gaudemer, 2016) and finally the behavior of earthquakes (e.g.,
530 Cappa et al., 2014; Huang, 2018; Perrin, Manighetti, Ampuero, et al., 2016).
531 Consequently, for long or multiple-fault earthquake ruptures, the fault normal
532 distribution of aftershocks could change along strike, and present a shear deformation
533 zone that widens towards the most immature parts of the rupture. Such a behavior
534 would be in good agreement with mapped faults at the surface showing that the off-fault
535 damage zone widens in the direction of long-term fault propagation (e.g., Manighetti et
536 al., 2001; Perrin, Manighetti, & Gaudemer, 2016). Future work is needed to relate such
537 observations to the occurrence of seismicity.
538
539 5. Conclusion
540 Our study presents strong correlations between independent datasets that describe the
541 near-fault distribution of aftershocks following large earthquakes and geological fault
542 parameters such as cumulative displacement, initiation age and slip rate. We find that
543 for large faults, defined as those that have ruptured the entire brittle crust, the zone of
544 active shear deformation narrows as a power law with cumulative fault displacement,
545 hence with fault maturity. This result is predicted by a dynamic rough fault model
546 combined with an empirical roughness/displacement relation, indicating that the
547 narrowing of the shear deformation zone is the result of fault smoothing with
22 548 cumulative displacement. Earthquake stress-drop also decreases with fault
549 displacement and hence fault smoothness or slip rate.
550
551 ACKNOWLEDMENTS
552 This work is supported by the Brinson Foundation (CP) and the National Science
553 Foundation (NSF-EAR #1520680). Earthquake catalog data are available at
554 http://ddrt.ldeo.columbia.edu and https://scedc.caltech.edu/research-
555 tools/altcatalogs.html. We thank the editor R. Abercrombie, associate editor M. Cooke
556 and reviewers E. Nissen, N. Abolfathian and K. Dascher-Cousineau for their fruitful
557 comments that greatly improved the manuscript. This paper is LDEO contribution 8477.
558
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1135
1136
46 1137 Figures and figure captions:
1138
1139 Figure 1: Simplified view of the architecture of a fault zone and the density of
1140 fractures (red) and seismicity (blue) away from the fault core.
1141
47 1142
1143
48 1144 Figure 2: Aftershocks distribution of the (a, b) 2004 Parkfield and (c, d, e, f, g)
1145 1999 Hector Mine earthquakes (see Supp. Fig. S3 for all cases). (a) Map view showing
1146 the San Andreas fault (black lines) and the surface rupture (thick grey line) of the 2004
1147 Parkfield earthquake (epicenter indicated by the red star). Red dots are aftershocks that
1148 occurred within 2 months after the mainshock (Waldhauser & Schaff, 2008; Perrin et al.,
1149 2019). (b) Gray profiles are fault-normal earthquake distributions measured from the
1150 best fitting plane in each moving box along the rupture trace (see text for explanations).
1151 Black curve is the mean of the gray profiles. Inset: cross section going through the
1152 hypocenter area. Depth in y-axis; across strike distance in x-axis. Black line is best fitting
1153 plane minimizing fault-normal distance to aftershock hypocenters (red dots); (c) same
1154 as (a) but for the 1999 Hector Mine earthquake (earthquake catalog from Hauksson et
1155 al., 2012). Boxes include earthquakes used in d-g. (d-g) Same as (b) but for the 1999
1156 Hector Mine earthquake. The four sub-figures are based on earthquakes included in
1157 boxes shown in (c).
1158
49 1159
1160 Figure 3: Determination of WS1 and WS2 parameters from the aftershocks
1161 distribution of the (a) Parkfield 2004 and (b, c, d, e) Hector Mine 1999
1162 earthquakes (see Supp. Fig. S4 for all cases). Blue circles represent the mean
1163 hypocenter distances from each fault section within 0.03 km wide bins (see black curve
1164 in Fig. 2 and Supp. Fig. S3). Grey circles represent the mean distances of events that are
1165 only included in less than 20% of all boxes. The red curve is the best (power law) fit to
1166 the blue circles, taking into account the power law singularity on the fault (see Supp. Fig.
1167 S4 for details). The vertical gray dashed lines labeled WS1 and WS2 point out the locations
1168 where the power law fit shows the maximum curvature and where the data (blue
50 1169 circles) deviate from the power law fit by dropping or flattening (i.e., the transition
1170 between seismically active fault damage zone and the undeformed crustal medium),
1171 respectively.
51 Half width of Earthquake Half width of Long-term the shear Name of fault Initiation Cumulative References Location name, date, seismicity fall slip rate deformation section(s) age (Ma) slip (km) for fault parameters magnitude off WS1 (km) (mm/yr) zone WS2 (km) El Mayor Elsinore (southern Dorsey et al., 2012; K. E. K. Fletcher USA Cucapah, 0.6 0.03 4.51 0.03 ~ 1.1 1 to 2 1 to 2 section) et al., 2011 and references therein 2010, Mw 7.2 Dibblee, 1961; Dokka, 1983; Dokka 0.86 Hector Mine, & Travis, 1990; Garfunkel, 1974; USA +0.26/-0.13 3.36 0.03 Lavic Lake-Bullion < 10 10 to 20 ~ 0.8 1999, M 7.1 Jachens et al., 2002; Oskin et al., w (mean value) 2007 Dibblee, 1961; Dokka, 1983; Dokka 0.96 Emerson-Camp Rock- Landers, & Travis, 1990; Garfunkel, 1974; USA +0.16/-0.27 3.96 0.03 Homestead Valley- < 10 3.5 to 4.6 0.2 to 0.7 1992, M 7.3 Jachens et al., 2002; Rockwell et w (mean value) Johnson Valley al., 2000; Rubin & Sieh, 1997 Morgan Hill, Stirling et al., 1996; Wakabayashi, USA 0.12 0.03 1.32 0.03 Calaveras ~ 12 60 to 70 3 to 25 1984, Mw 6.1 1999 and references therein Atwater & Stock, 1998; Critelli & Nilsen, 2000; Crowell, 1979; Parkfield, San Andreas (central Graham et al., 1989; Liu et al., USA 0.06 0.03 0.56 0.075 24 to 29 ~ 315 ~ 26 2004, Mw 6.0 section) 2010; Matthews, 1976; Revenaugh & Reasoner, 1997; Toké et al., 2011 West Napa (considered d’Alessio, 2005; Field et al., 2015; South Napa, USA 0.22 0.03 0.90 0.06 as a splay of the 6 to 12† 3.8 to 28† 1 to 7 Wakabayashi, 1999; Wesling & 2014, M 6.1 w Calaveras fault zone) Hanson, 2008; Zeng & Shen, 2016 Blisniuk et al., 2010; Dorsey et al., Superstition San Jacinto (southern 2012; Gurrola & Rockwell, 1996; USA Hills, 1987, 0.78 0.03 > 3 < 2 ~ 4 ~ 4 section) Hudnut & Sieh, 1989; Kirby et al., M 6.6 w 2007; Lutz et al., 2006 0.12 to 1.83 ~2.80 New - (field (field Awatere < 4 < 2 ~ 5 Little, 1995 and references therein Zealand measurements) measurements)
52 1172
1173 Table 1: Fault and aftershock distribution parameters for the seven earthquake sequences analyzed in this study. Uncertainties in WS1
1174 and WS2 correspond to size of bin (0.03 km) used in this analysis. For multiple broken fault sections (Hector Mine, Landers, El Mayor Cucapah),
1175 WS1 and WS2 are mean values, when possible, and the uncertainties represent the minimum and maximum range of values (see detailed
1176 measurements in Supp. Figure S3). Field measurements of the Awatere fault from Little et al. (1995) are also indicated (see text for details).
1177 * available at: https://gbank.gsj.jp/activefault/
1178 † cumulative slip deduced from scaling relations in Scholz & Lawler, 2004 (West Napa fault). Initiation age of the West Napa fault is estimated
1179 from
1180 the age of surrounding faults in California. See text for details
53 1181
1182 Figure 4: Relations between WS1 and WS2 for the seven earthquakes analyzed in
1183 this study. Grey lines indicate two affine functions between WS1 and WS2 that bound our
1184 data. Uncertainties are reported in Table 1.
1185
54 1186
1187 Figure 5: Relations between WS1 (circles; a, c, e), WS2 (squares; b, d, f) of seven
1188 earthquake sequences and the cumulative slip (a, b), initiation age (c, d) and
1189 geological slip rate (e, f) of their host fault taken from literature (solid symbols)
55 1190 and estimated from scaling relations (open symbols for fault parameters
1191 associated with the South Napa earthquakes) (see Table 1 and text for details).
1192 Power laws are indicated by grey lines. For comparison, red symbols indicate geological
1193 surface measurements along the Awatere fault (from Little, 1995). D is cumulative fault
1194 displacement, A is initiation age of the fault, SR is slip rate, k is a different constant in
1195 each relation.
1196
56 1197
1198 Figure 6: (a) Normalized distribution of the mean number of aftershocks as a
1199 function of normal distance from the fault (see also black curves in Fig. 2 and Supp.
1200 Fig. S3). Each colored curve represents one earthquake sequence. Curves with the same
1201 color are distinct fault sections that broke during one earthquake. Colors are warmer as
1202 the structural maturity of the broken fault sections increases. For comparison, black
1203 squares indicate the cumulative number of faults (right y axis) measured at surface from
1204 the Awatere fault (modified from Little, 1995). (b) Sketch summarizing the fault-normal
57 1205 distributions of aftershocks for immature (blue curve) and mature (red curve) fault
1206 sections. (c) Interpretative cross-section describing the structural makeup of immature
1207 (blue) and mature (red) faults. As fault structural maturity increases, inner and outer
1208 bounds of the shear deformation zone (WS1 and WS2, respectively) decrease, as
1209 expressed by a decreasing width of the fault-normal aftershock distribution. See text for
1210 more discussion.
1211
58 1212
1213 Figure 7: Comparison between the outer bound of the shear deformation zone (WS2;
1214 data from fig. 5b) and the predictions of the model of Aslam & Daub, 2018 that were
1215 calibrated to fault displacement with roughness-displacement relation of Stirling et al.,
1216 1996 (blue circles, dashed lines and shaded area). See text for explanation of the latter.
1217 Blue circles are for step widths of 1 and 2 km, which are typical step width range
1218 (Wesnousky, 1988).
1219
1220
59 1221
Earthquake Number of Mean Mean Mean References name measurements log10() standard stress drop error (in MPa) Hector Mine, 8 0.672 0.011 4.7 ± 1 Allmann & Shearer, 2009; 1999 Ancheta et al., 2014; Baltay et al., 2019; Hanks & Bakun, 2008; Hauksson et al., 2002; Kaverina et al., 2002; Price & Burgmann, 2002 Landers, 6 0.792 0.016 6.2 ± 1 Allmann & Shearer, 2009; 1992 Ancheta et al., 2014; Baltay et al., 2019; J. B. Fletcher & McGarr, 2006; Peyrat et al., 2001; Price & Burgmann, 2002 Morgan Hill, 3 0.447 0.032 2.8 ± 1 Mikumo & Miyatake, 1995 1984 Parkfield, 4 0.362 0.011 2.3 ± 1 Allmann & Shearer, 2009; 2004 Kim & Dreger, 2008; Ma et al., 2008; Twardzik et al., 2014 Superstition 3 0.763 0.011 5.8 ± 1 Ancheta et al., 2014; Hills, 1987 Baltay et al., 2019; Wald et al., 1990 1222 1223 Table 2: Mean stress drop values available from the literature for five of the seven
1224 earthquakes analyzed in this study.
1225
1226
60 1227
1228 Figure 8: Earthquake stress drop (Δ휎) as a function of cumulative displacement of the
1229 broken fault section (D) for earthquakes listed in Table 2.
1230
1231
1232
61 1233
1234 1235 Figure 9: Earthquake stress drop (Δ휎) as a function of geological slip rate (SR) for
1236 earthquakes listed in Table 2, represented in (a) log-log and (b) semi-log coordinates.
1237
62 Figure 1. log fracture and seismicity density
WS1
3 2 1
log 1 cataclasite core Wc distance W from fault 2 dilatant damage zone d W 3 shear deformation zone S2 Figure 2. N A’ 2 a 0 −2 2004 Across strike Across distance [km] distance A −20 −15 −10 −5 0 5 10 15 20 Along strike distance [km] 10 0 A A’ b 0 10 −1
10 −2 −10 [km]
10 −3 −20 −5 0 5 −4 10 [km]
Number of events (normalized) Number of events −5 10 1 10 −2 10 −1 10 0 10 Normal distance from the best fitting plane [km]
d D’ g c 5 E’ 1999 G’ f F’ 0 D e N Across strike Across E distance [km] distance -5 F G
-30 -20 -10 0 10 20 30 10 -1 10 -1 d D D’ e E E’ 0 0 10 -2 -10 -10
-2 [km]
[km] 10 -20 -20 10 -3 The Blind -5 0 5 The Lavic -5 0 5 section [km] Lake section [km]
10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 -2 10 -1 10 0 10 1 -1 10 -1 10 f g G G’ F F’ 0 0 10 -2 -10 [km] Number of events (normalized) Number of events -10
10 -2 [km] 10 -3 -20 -20 -5 0 5 -5 0 5 10 -4 The South [km] The Bend [km] Bullion section section 10 -3 10 -5 10 -2 10 -1 10 0 10 1 10 -2 10 -1 10 0 10 1 Normal distance from the best fitting plane [km] Figure 3. 10 0 WS1 Parkfield 2004 WS1 : 0.06 km 10 -1 WS2 : 0.56 km
-2 10 WS2
10 -3
10 -4 a Mean number of events (normalized) Mean number of events 10 -5 10 -2 10 -1 10 0 10 1 Normal distance from the fault plane [km]
10 -1 10 -1
WS1 WS1
10 -2 10 -2 Hector Mine 1999 Hector Mine 1999 WS2 ? Blind WS2 ? Lavic Lake fault section fault section WS1 : 0.86 km WS1 : 1.12 km WS2 : - WS2 : - b c Mean number of events (normalized) Mean number of events 10 -3 10 -3 10 -2 10 -1 10 0 10 1 10 -2 10 -1 10 0 10 1
10 -1 10 -1 WS1
WS1
10 -2
WS2 Hector Mine 1999 10 -2 Hector Mine 1999 10 -3 The Bend WS2 ? South Bullion fault section fault section WS1 : 0.73 km WS1 : 0.74 km -4 WS2 : - 10 WS2 : 3.36 km d e Mean number of events (normalized) Mean number of events 10 -3 10 -5 10 -2 10 -1 10 0 10 1 10 -2 10 -1 10 0 10 1 Normal distance from the fault plane [km] Normal distance from the fault plane [km] Figure 4. 10
Hector Mine Sup. Landers 1 Hills El Mayor South Cucapah (km) Napa S1
2 W S Morgan =0.3W 0.1 W S1 Hill S2 Parkfield =0.1W W S1
0.01 0.1 1 10 WS2 (km) Figure 5. 10 a b El Mayor 5 Cucapah Awatere Landers Hector Landers 1 Mine Hector El Mayor Awatere Mine Cucapah Sup. Hills Sup. (km)
(km) Hills S1 South S2
W Morgan 0.1 Napa W Hill Morgan South Napa Hill -0.54 Parkfield -0.39 WS1 = k*D WS2 = k*D 0.01 0.5 Parkfield 0.1 1 10 100 1000 0.1 1 10 100 1000 Cumulative fault displacement (km) Cumulative fault displacement (km) 10 c d
5 El Mayor Landers Cucapah 1 El Mayor Awatere Landers Cucapah Hector Mine Sup. Hills Hector Sup. Awatere Mine (km) Hills South (km) S1 Napa S2 Morgan W 0.1 W Hill Morgan Hill Parkfield -0.80 -0.62 W =k*A W =k*A South S1 S2 Napa Parkfield 0.01 0.5 0.1 1 10 100 0.1 1 10 100 Fault initiation age (Ma) Fault initiation age (Ma) 10 e f El Mayor 5 Cucapah Hector Landers 1 Landers Mine Awatere Sup.Hills Sup. Hector El Mayor Mine Awatere (km) Hills Cucapah (km) S1 Morgan S2
W Morgan South Hill W 0.1 Napa Hill
Parkfield -0.71 -0.46 South W =k*SR Parkfield S1 WS2 =k*SR Napa 0.01 0.5 0.11 10 100 0.1 1 10 100 Geological fault slip rate (mm/yr) Geological fault slip rate (mm/yr) Figure 6. 10 0 Field measurements across 100 a the Awatere fault (Little, 1995)
10 -1 Number of faults (%)
10 10 -2
10 -3 Parkfield 1 Increasing Morgan Hill South Napa -4 structural 10 maturity of Hector Mine fault sections Landers El Mayor Cucapah Superstition Hills Mean number of events (normalized) Mean number of events 10 -5 10 -2 10 -1 10 0 10 1 Normal distance from the fault plane [km]
b c WS2 Immature Immature fault
fault section crust section Undeformed Damage intensity Mature fault WS1 - + section
Increasing time Mature Mean number of EQs fault and slip crust section
Distance from the fault plane Undeformed Cataclasite fault core Figure 7. Data from this study 5 (km) S2 W
Theoretical models j=1.0 j=2.0 0.5 0.1 1 10 100 1000 Cumulative fault displacement (km) Figure 8. Earthquake stress drop (MPa) 10 1 1 Landers Sup. Hills Cumulative displacement of the the of displacement Cumulative broken fault section (km) section fault broken Hector Hector Mine 10 Morgan Hill 100 ∆σ=8.3*D Parkeld -0.23 1000 Figure 9. Earthquake stress drop (MPa) 10 1 . 10 0.1 a Landers Hector Hector Mine Geological slip rate (mm/yr) Geological slip rate (m rate slip Geological (mm/yr) rate slip Geological 1 Sup. Hills Morgan Hill ∆σ=5.4*SR Parkfield -0.22 100
Earthquake stress drop (MPa) 10 2 4 6 8 0 . 10 0.1 b Landers Hector Hector Mine 1 Sup. Hills ∆σ=-2*log(SR)+5.5 Morgan Hill m/yr) Parkfield 100