Geophys. J. Int. (2001) 147, 272–293
Aftershock zones of large shallow earthquakes: fault dimensions, aftershock area expansion and scaling relations
C. Henry and S. Das Department of Earth Sciences, University of Oxford, Parks Road, Oxford, OX1 3PR, UK. E-mail: [email protected]
Accepted 2001 May 22. Received 2001 May 5; in original form 2000 August 23
SUMMARY We determine the aftershock areas from relocated hypocentres for 64 dip-slip and eight strike-slip earthquakes in the period 1977–1996 together with those for three recent earthquakes, the 1998 Antarctic plate earthquake, the 1999 Izmit, Turkey earthquake and the 2000 Wharton Basin earthquake. We also include the data for 27 strike-slip earthquakes from Pegler & Das (1996). We find that the location of the hypocentre is essentially random along strike for both strike-slip and dip-slip earthquakes. Subduction zone earthquakes appear to initiate more frequently towards the down-dip edge of the fault, whereas the non-subduction zone dip-slip earthquakes do not have any preferred depth of initiation. The aftershock zones of subduction zone earthquakes often expand substantially along strike and up dip but far less in the down-dip direction, whereas those for non-subduction zone earthquakes do not expand significantly in either the up- or the down-dip direction. Subduction zone thrust earthquakes have larger and more numerous aftershocks than earthquakes in all other tectonic settings. For strike- slip earthquakes, we find that slip increases at least linearly with length. For dip-slip earthquakes, we find that the ratio of length to width increases systematically with length for lengths >40 km, indicating that there is some restriction on fault width; slip is found 17 21 to be proportional to length over the moment range 10 Nm the fitting of seismograms. Locating aftershocks is relatively 1 INTRODUCTION reliable and the methods to do this have been well established The 1952 Kern County, California earthquake was the first one for several decades. On the other hand, the inverse problem for for which portable seismometers were set up in the field within the earthquake source is intrinsically very unstable (Kostrov hours of the main shock in order to record the aftershocks, with & Das 1988), and until very recently, sufficiently high-quality Gutenberg, Richter and Benioff all being involved in this project. seismograms and with sufficiently good spatial coverage were Richter (1955) was the first to associate clearly the location of not available for a reliable estimate of the fault dimensions of the aftershocks with the fault rupture area. Richter (1995) demon- the main shock. Even for an Mw=8.0 earthquake as recently as strated the spatial complexity of the aftershock distribution and 1989 (the Macquarie Ridge earthquake), Das (1993) showed noted a slight expansion of the rupture area with time. Since that the teleseismic seismograms were unable to constrain the then, one of the most widely used methods of obtaining the fault area, and aftershocks had to be used to constrain it rupture dimensions is by using aftershocks. The expansion of the a priori. The 1998 Antarctic earthquake is the first one for rupture area with time has been noted for many earthquakes, which the seismograms did constrain the fault rupture area and it is considered that if a short time period after the main (Henry et al. 2000), and hence this is a very promising tool for shock is selected, the aftershock area gives a good estimate of future global studies. Previously, only in land areas with a very the rupture area of the main earthquake. Although the total dense local network had it been possible to constrain rupture moment of the aftershocks is usually only a few per cent of the areas by inverting seismograms. A recent study by Mai & Beroza main shock moment, aftershocks have been disproportionately (2000) using this latter method included mainly Californian well studied due to the possibility of deployment of arrays after earthquakes. the main earthquake. In fact, for several reasons, this method The main purpose of this paper is to obtain the aftershock may be more reliable than trying to find the fault dimensions by areas of many earthquakes worldwide using teleseismic data, 272 # 2001 RAS Aftershock zones of large shallow earthquakes 273 and to discuss the properties of the aftershock areas and the (Ly60), favouring a W model for large events. This was implications of the aftershock dimensions for the problem of disputed by Scholz (1994a) and further discussed by Romanowicz earthquake scaling. (1994) and Scholz (1994b). There is more of a consensus, based on the limited available data, that at least the very largest strike-slip earthquakes (L>200 km) have some restriction on 2 EARTHQUAKE SCALING slip and tend towards M0 3 L scaling (Scholz 1994b; Bodin & How earthquakes scale with size is a problem of great Brune 1996; Fujii & Matsu’ura 2000). Most empirical studies of importance. Without knowing the relationship between fault earthquake scaling, including all of those cited above, have size and other source parameters, it would be impossible to been based on compilations of earthquake parameters from the make ground motion predictions, essential for the construction literature, in some cases using measurements made using very of earthquake-resistant structures, for large, infrequent earth- different methodologies. Pegler & Das (1996) have argued that in quakes based on the recordings from smaller, more frequent the observational study of scaling relationships it is important ones in the same region. Scaling relations are also often used to to analyse all earthquakes in a uniform manner. They com- estimate seismic moment from length or vice versa, a very recent pared Harvard CMT (centroid moment tensor) moments to example being Parsons et al. (2000). Finally, scaling relations fault lengths measured from relocated aftershock distributions provide insight into the mechanics of earthquake rupture. The for large crustal strike-slip earthquakes from 1977–1992. They 2 17 problem was first considered by Aki (1967), and has been a found that M0 3 L over the moment range 5r10 Nm 21 subject of vigorous research since. The seismic moment M0 is to 1.4r10 N m, with no indication of a break in slope mu¯A, where m is the rigidity, u¯ is the mean slip and A is the fault at y7r1019 N m as observed by Romanowicz (1992), and area. The rupture area on any planar fault can be approxi- thereby supporting the original finding of Scholz (1982). mated either by a rectangle or by an ellipse (a circle being a No study comparable to Pegler & Das (1996) has been special case of this). For a rectangular fault of length L and carried out for dip-slip earthquakes. The recent compilation of width W, M0=mu¯LW. For an elliptical fault, M0=(p/4)mu¯LW, earthquake data by Wells & Coppersmith (1994) uses sub- where L and W are now the lengths of the axes of the ellipse. surface length (primarily determined from aftershocks occur- Thus, in general, M0=Cmu¯LW, where C is a geometrical factor ring from a few hours to a few days after the main shock) and lying between about 0.75 and 1. Empirical scaling relations the seismically determined scalar moment for 50 thrust and found between M0 and fault dimensions can be used to make 24 normal earthquakes from 1952–1993 in the moment range 16 20 inferences regarding the factors that control mean slip. For 2r10 Nm # 2001 RAS, GJI 147, 272–293 274 C. Henry and S. Das another earthquake of similar or greater moment prevents the sampling of the underlying rupture area by aftershocks, and determination of the aftershock dimensions. For smaller earth- also assumes that we have correctly identified the aftershocks quakes we include only those for which we have a sufficient that are directly associated with the main fault. number of aftershocks to be truly representative of the fault In the JHD relocations, the main shock is used as the length, usually with a few mbj4.0 aftershocks reported by the calibration event and although it is fixed during the calculation ISC, so as not to underestimate the lengths of small earth- of station corrections, it can later be relocated using the station quakes. Throughout this study, we shall always call L the fault corrections evaluated during the relocation process. In most dimension along the strike of the aftershock zone, even for cases the main shock hypocentre does not move significantly, the small number of cases for which the other dimension, W,is which is expected since the station corrections are evaluated longer. relative to the main shock hypocentre. This does not necessarily Following Pegler & Das (1996), we use relocated 1 day indicate that the original location is correct, but that a set aftershock lengths as our preferred measure of fault length. of station corrections for the whole aftershock sequence was For almost all the earthquakes studied here, high aftershock found that is consistent with the original location. In a few activity continues for significantly longer than 1 day, and thus cases, the main shock location does change, indicating that no our measurements represent an early phase of the evolution of consistent set of station corrections exists using the original the aftershock distribution. Although for some earthquakes in location, and we regard the relocated main shock hypocentre as this study there are sufficient early aftershocks to permit the an improvement on the original location. In every such case in determination of the length after a shorter time period, say a this study, the relocated main shock hypocentre lies, within its few hours, this is not possible for all earthquakes and we prefer 90 per cent confidence ellipsoid, on the plane of the relocated to use a uniform time period of 1 day for all earthquakes. We aftershocks, although often the unrelocated position does not, determine also 7 day and 30 day lengths in order to examine confirming that the relocated main shock hypocentre and the the expansion of aftershock areas with time. We relocate relocated aftershocks are self-consistent. Note that we will not aftershock sequences using primarily P arrivals, with some S use any absolute location information in this study, except in a arrivals, other reported phase types being too few to be useable. single case where we shall discuss the seismogenic depth. In particular, for the shallow earthquakes under consideration We use seismic moments from the Harvard CMT catalogue. here, reliable depth phase arrival times are not available. For The formal errors in the Harvard moment tensors are small most earthquakes, we perform relocations using the method of (typically 2 per cent error in the seismic moment), and systematic joint hypocentre determination (JHD) (Douglas 1967; Dewey errors are likely to be much greater than this. However, we 1971, 1983), using the algorithm JHD89, with modifications have no means of reliably estimating the magnitude of these to improve stability (discussed in the Appendix). We use the errors and do not attempt to do so. P-wave traveltime tables determined by Herrin (1968), and the Jeffreys–Bullen S-wave tables; we note that since the JHD 3.1 Dip-slip earthquakes method evaluates corrections to these tables, the exact choice of traveltime tables has little impact on the solutions, as any Since a major goal of this study is to consider the scaling systematic errors within one traveltime table, or any inconsist- relations for dip-slip earthquakes, and since we also wish to encies between P and S tables are absorbed into the corrections consider differences in aftershock behaviour between dip-slip and (Dewey 1971, 1983). First we relocate a subset of the best- strike-slip earthquakes, we consider only pure dip-slip earth- recorded aftershocks, preferably using only those recorded by quakes. Whilst it is clear that earthquakes with large strike-slip 30 or more stations, and typically using 20 such earthquakes, components should not be included as they are not directly and then we use the station corrections determined for these comparable to pure dip-slip earthquakes, the selection of a earthquakes to relocate the smaller aftershocks. When 10 or criterion for inclusion is somewhat arbitrary. The large numbers fewer aftershocks are recorded by 20 or more stations each, the of earthquakes for which ISC and Harvard CMT data are master event relocation method (Evernden 1969; Dewey 1971, available allow us to adopt the fairly conservative criterion that 1983) is used instead. the rakes of both fault planes must be within 15u of pure Fig. 1(a) shows a sample measurement of length. The strike dip-slip. An increase in our tolerance to 20u would have used for measurements of length is determined from com- resulted in the inclusion of about 15 additional earthquakes. Of parison of the CMT strike, the orientation of the aftershock the five shallow dip-slip earthquakes from 1997–1996 with 21 distribution and the trend of features in the local marine gravity M0i10 N m that do not meet this strict criterion, we include field (Sandwell & Smith 1997) or land topography (Gesch four, for each of which the shallow-dipping nodal plane has an et al. 1999). The exact choice of strike does not significantly oblique component. These are the 1977 Sumba normal earth- affect determinations of fault length. We select aftershocks by quake, and the 1979 Colombia, 1985 Chile and 1996 Biak sub- magnitude, using different selection criteria for the measure- duction zone thrust earthquakes. The fifth is the 1994 Kurile ment of aftershock lengths of dip-slip and strike-slip earth- Islands thrust earthquake, which has a large oblique com- quakes, as is explained below. For the determination of length, ponent on both nodal planes. We consider only crustal and we use only aftershocks located with epicentral location errors shallow subduction zone earthquakes with centroid depths of <25 km, and in addition exclude any single aftershock with from the Harvard CMT catalogue in the range 0–70 km. Many a relatively large error if the end of the fault is well defined by of the thrust earthquakes in this study are located in sub- better-located earthquakes. We determine errors in the 1 day duction zones with high levels of background seismicity, in length by finding the range of lengths consistent with the 90 per some cases recorded by regional networks capable of detecting cent confidence ellipses of aftershocks near the edges of the faults. earthquakes of mb<3. At this magnitude level, the aftershock This takes into account the uncertainties in our relocations, area is not clearly distinct from background seismicity for but does not take into account the possibility of incomplete some earthquakes, particularly at longer time periods. For this # 2001 RAS, GJI 147, 272–293 Aftershock zones of large shallow earthquakes 275 Figure 1. Example of measurement of L and W for the 1995 December 3 Kurile Islands earthquake. (a) Map view. The epicentre is shown by an open star, with the Harvard CMT mechanism also shown. Aftershocks occurring within 1 day of the main shock are shown by solid circles with error ellipses, and aftershocks occurring between 1 and 30 days are shown by crosses without error ellipses. Only aftershocks with mb<4 and with 90 per cent epicentral confidence ellipses <25 km are shown. The 1 day aftershock length of 185 km is measured along an azimuth of 45u, the strike of the NW-dipping nodal plane of the Harvard CMT solution. This strike is confirmed by the good alignment of the aftershocks at the up-dip (SE) edge of the aftershock distribution. (b) Cross-section looking from the direction of the open arrow in (a). Same symbols as (a), but now showing only aftershocks with 90 per cent hypocentral confidence ellipsoid <20 km, with less well-located aftershocks being rejected for this earthquake, as they are not reliably associated with the fault plane. The 1 day aftershock width of 80 km is measured along the dip (12u) of the Harvard CMT solution, which is confirmed by the aftershocks. reason only aftershocks with mbi4.0 are used in the deter- geographical regions and time periods. For 1 day lengths, the mination of fault length for dip-slip earthquakes. In addition aftershock region can usually be clearly distinguished from the we consider this common choice of cut-off magnitude to pro- background seismicity, and the length is usually insensitive to vide more consistent measurements of length between different the precise choice of cut-off magnitude. # 2001 RAS, GJI 147, 272–293 276 C. Henry and S. Das For dip-slip earthquakes we also estimate the fault width, as earthquakes of Table 1. The parameters of three such earth- this allows the influences of length and width on mean slip to be quakes are listed in Table 2, with references. For the 1957 examined separately. A sample measurement of width is shown Aleutian Islands, Alaska earthquake and the 1960 Chile earth- in Fig. 1(b). To determine the down-dip width of the quake, modern redeterminations of the moments are available. aftershock zone, the fault plane of the earthquake must be Dimensions of these two earthquakes are measured for this unambiguously identified. For many earthquakes, the best- study from published aftershock relocations. For the 1964 located aftershocks are clearly aligned, when looked at in cross- Prince William Sound, Alaska earthquake, no recent redeter- section, with one of the nodal planes of the Harvard CMT mination of the moment is available, but two independent solution. For a few cases, all but one dating from 1982 or determinations from the early 1970s are in broad agreement, earlier, the aftershocks are clearly aligned but differ by up to and the dimensions are determined from ISC aftershocks. 20u in dip from the nearest CMT nodal plane; in these cases the Thus the parameters of these three earthquakes are obtained by dip of the aftershock zone is adopted in preference to the CMT methods similar to those used for the post-1977 earthquakes of nodal plane. For some other earthquakes, the aftershocks are this study. not sufficiently well located or are too few in number for the dip to be accurately determined from the aftershocks alone, but are 3.2 Strike-slip earthquakes compatible with only one of the nodal planes of the CMT; in these cases the dip of that nodal plane is adopted. When the For strike-slip earthquakes we do not attempt to obtain the aftershocks cannot be used to distinguish between the two nodal rupture areas, but only determine the lengths. This is because planes no measurement of width is made. In some cases after- we are unable to obtain the earthquake depths accurately shocks occur on more than one plane; if one of these can be enough for the shallow earthquakes (with ISC main shock identified as the main shock fault plane, by the location of the depth between 3 and 40 km) in this study. We determine L hypocentre, by the extension of only one of the planes along following the method of Pegler & Das (1996) to maintain the whole length of the earthquake or by the occurrence of comparability with that study. However, we note that several early aftershocks, then the width of only this plane is measured. earthquakes were included that did not meet the mechanism If the identification is not clear, no measurement of width is selection criterion stated in the text of Pegler & Das (1996), so made. The different qualities of reliability are clearly indicated that this criterion had not been strictly adhered to. We use a for each dip-slip earthquake in this study. Overall, the fault revised criterion that the dip of both nodal planes must be plane can be identified, and the width measured, for 48 of the greater than 60u, but only one nodal plane is required to have a 64 dip-slip earthquakes of this study. For the 16 earthquakes rake within 15u of x180u,0u or 180u. This criterion is chosen to for which it is not possible to determine the fault plane, there is include both earthquakes with strike-slip motion on steeply no ambiguity in the determination of the fault length. dipping planes and also strike-slip earthquakes on near-vertical Once the fault plane has been identified, aftershocks with fault planes with a small component of dip-slip motion, but uncertainties in depth sufficiently great that it is not clear to exclude oblique thrust or normal earthquakes. We discard whether or not they lie on the fault plane are excluded from the earthquakes from Pegler & Das (1996) that do not meet this measurement of fault width. We also use only earthquakes that revised criterion. These are earthquakes 3, 8, 9, 10, 18, 23 and have an uncertainty of <25 km in their location along the 27 of that study. We restrict the study to crustal earthquakes, down-dip direction. We determine errors in the measured width mostly with depths reported by the ISC as less than 33 km. from the uncertainties in the aftershock locations in the same For the three earthquakes from 1998–2000, we use aftershocks way as for the aftershock lengths. The errors in aftershock reported by the National Earthquake Information Center width are in general greater than those for the aftershock (NEIC) and relocated by us using their phase data. Following length, because small subduction zone aftershocks are in Pegler & Das (1996), we use all well-located aftershocks reported general located better along strike than down dip, due to poor by the ISC in the determination of length. For the 11 new azimuthal distribution of stations. In addition, for earthquakes strike-slip earthquakes studied here, the lengths obtained using with few aftershocks, the measurement of width is more all the aftershocks were in most cases not significantly greater sensitive than the measurement of length to the selection of than the lengths that would have been obtained using only fault strike. the aftershocks with mbi4.0, as was used for the dip-slip The dip-slip earthquakes in this study are classified by ‘type’, earthquakes. The parameters of strike-slip earthquakes from based upon the moment tensor, a consideration of the after- 1993–2000 are tabulated in Table 3. We determine errors for shock distribution in relation to the historic seismicity and the 1 day length measurements of Pegler & Das (1996) using known tectonics of their location, and in some cases on studies the results of the original JHD relocations performed for that of individual earthquakes taken from the literature. For sub- study. duction zone thrust earthquakes, we distinguish between ‘simple’ subduction interface earthquakes and those earthquakes that 4 AFTERSHOCK DIMENSIONS FOR occur in regions of more complex tectonics or whose aftershock DIP-SLIP EARTHQUAKES patterns are not well described by a single fault plane. The parameters of dip-slip earthquakes are listed in Table 1, with The aftershock extents of the dip-slip earthquakes along strike, details on earthquake ‘type’ and quality of measured fault dip and depth are shown in Fig. 2. The data summarized in width. Fig. 2(a) shows that the hypocentres are located on average The greatest thrust earthquakes of this century have moments 26 per cent of the 1 day length along strike from the nearest end up to 2 orders of magnitude greater than those of the largest of the 1 day aftershock zone; this number is 23 per cent for earthquakes since 1977, and where reliable determinations ‘simple’ subduction earthquakes and 22 per cent for ‘simple’ of their parameters are available, we compare them with the subduction earthquakes with L>W. If the hypocentre is equally # 2001 RAS, GJI 147, 272–293 # 01RAS, 2001 Table 1. Parameters of dip-slip earthquakes 1977–1996. No. Date Location Type Lat. Long. Depth No. Aftershocks Length (km) Width (km) QM0 Mw (mm/dd/yyyy) (km) (1020 Nm) 1 7 30 1 7 30 1 7 30 GJI 147, 01 03/21/1977 S. Iran T 27.59 56.38 19 21 048 0070 33+10x4 040 050 c 0.140 6.7 02 06/22/1977 S. of Tonga Isl. NIa x22.91 x175.74 61 2 017 0031 75+10x10 100 115 c 13.900 8.0 272–293 03 08/19/1977 SW. of Sumba Is. NI* x11.16 118.41 23 38 115 0197 160+14x14 200 240 37+19x9 037 037 b 35.900 8.3 04 11/23/1977 San Juan, Argentina SI x31.04 x67.76 21 47 164 0263 70+13x4 080 090 c 1.860 7.4 05 03/23/1978 Kurile Isl. S 44.70 148.17 28 69 231 0208 100+10x10 145 145 45+9x7 070 070 a 2.690 7.6 06 02/28/1979 SE. Alaska Tb 60.74 x141.55 19 54 089 0138 85+5x2 085 085 25+15x6 025 025 b 1.880 7.5 07 10/23/1979 Solomon Islands SIc x10.68 161.35 31 16 024 0032 37+8x8 065 065 36+15x7 036 036 b 0.349 7.0 08 12/12/1979 Off Colombia S* 1.62 x79.34 20 20 069 0111 260+23x16 260 265 c 16.900 8.1 09 02/23/1980 Kuril Isl. Sxd 43.47 146.59 34 13 040 0053 25+10x10 100 100 55+15x13 075 100 a 0.559 7.1 10 07/08/1980 Santa Cruz Isl. S x12.49 166.37 44 19 036 . 50+20x4115. 65+8x8 090 . a 1.970 7.5 11 07/17/1980 Santa Cruz Isl. S x12.48 166.06 34 17 029 0051 150+23x14 150 205 80+28x28 090 120 a 4.840 7.7 12 10/10/1980 Algeria T 36.16 1.40 10 19 038 0052 40+9x5 045 060 17+15x10 017 017 b 0.507 7.1 13 10/25/1980 Loyalty Isl. S x21.78 169.60 29 43 117 0140 95+10x8 185 185 60+19x6 085 085 a 1.860 7.4 14 11/23/1980 S. Italy N 40.86 15.33 14 48 122 0163 65+8x5 075 075 21+6x3 026 026 b 0.247 6.9 15 04/24/1981 Vanuatu Isl. S x13.40 166.44 44 13 021 0023 75+23x19 105 105 c 0.225 6.8 16 07/15/1981 Vanuatu Isl. S x17.29 167.59 30 43 080 0107 100+16x10 115 150 40+17x8 070 070 a 0.576 7.1 17 03/21/1982 Hokkaido, Japan SI 42.23 142.46 37 66 131 0174 21+7x3 024 031 21+9x6 033 033 a 0.264 6.9 18 07/23/1982 Off Honshu, Japan S 36.36 141.63 27 61 094 0124 38+11x11 050 050 50+7x5 065 065 a 0.392 7.0 19 05/26/1983 Off Honshu, Japan SI 40.48 139.09 13 160 319 0509 130+9x5 145 160 50+17x12 050 050 a 4.550 7.7 20 03/19/1984 Uzbekistan TI 40.35 63.36 15 21 041 0057 36+18x18 036 045 cw 0.347 7.0 21 03/03/1985 Central Chile S* x33.08 x71.72 41 49 254 0679 174+25x15 195 200 34+15x11 055 060 a 10.310 7.9 22 09/19/1985 Michoacan, Mexico S 18.54 x102.32 21 18 045 0084 140+15x13 145 225 35+27x10 035 045 b 10.990 8.0 23 10/05/1985 NW. Terr., Canada TI 62.22 x124.26 10 20 047 0065 34+17x7 034 039 c 0.084 6.6 24 12/21/1985 Vanuatu Isl. S x13.98 166.51 46 15 033 0055 30+15x9 070 075 50+18x15 050 050 b 0.569 7.1 25 12/23/1985 NW. Terr., Canada TI 62.19 x124.27 15 29 066 0091 40+12x8 040 050 c 0.152 6.7 earthquakes shallow large of zones Aftershock 26 05/07/1986 Andreanof Isl. Sxe 51.54 x174.84 31 96 181 0267 4210+7x4 245 245 c 10.360 7.9 27 10/23/1986 Santa Cruz Isl. Sxf x11.04 165.19 15 20 031 0033 60+19x15 060 060 36+8x8 036 036 b 0.143 6.7 28 11/14/1986 Off Taiwan SI 23.95 121.76 33 28 052 0074 65+9x9 080 080 39+14x11 039 039 b 1.300 7.3 29 03/02/1987 N. Is. New Zealand NI x37.93 176.78 15 373 585 0661 45+26x13 045 055 23+32x15 023 023 b 0.064 6.5 30 04/22/1987 Off Honshu, Japan S 37.14 141.44 33 13 026 0060 20+4x4 027 027 14+13x10 014 055 a 0.108 6.6 31 10/16/1987 Off New Britain S x6.21 149.06 48 14 022 0027 37+13x13 037 037 29+12x10 035 035 b 1.260 7.3 32 01/10/1989 Ceram S x3.15 130.61 29 9 019 0027 45+28x28 045 050 cw 0.116 6.6 33 02/10/1989 Molucca Passage Sxg 2.29 126.78 44 39 052 0069 45+20x9 060 060 30+14x2 030 034 a 0.545 7.1 34 03/25/1990 Costa Rica S 9.96 x84.78 18 4 009 0013 26+9x6 036 055 14+5x5 014 019 a 1.101 7.3 35 03/08/1991 N. Kamchatka TI 60.86 167.02 15 26 045 0050 29+8x8 045 050 c 0.101 6.6 36 06/20/1991 Off Minahassa Pen. Sxg 1.19 122.82 15 9 011 0013 40+22x16 050 050 c 2.310 7.5 37 11/19/1991 Colombia S 4.60 x77.41 19 5 016 0029 25+9x5 025 025 26+18x18 030 030 a 0.732 7.2 38 05/15/1992 Papua New Guinea S x6.09 147.57 40 15 033 0056 50+28x23 070 080 27+23x9 032 050 b 0.809 7.2 39 07/10/1992 Kuril Isl. S 44.62 149.48 31 9 018 0027 12+12x4 012 013 15+20x9 045 045 a 0.074 6.5 40 09/02/1992 Off Nicaragua S 11.75 x87.37 15 75 149 0231 250+27x27 280 280 70+12x9 080 085 a 3.400 7.6 41 12/12/1992 Flores Is. SI x8.47 121.90 20 66 100 0133 150+22x16 170 170 c 5.060 7.7 42 06/08/1993 Off S. Kamchatka S 51.18 157.82 46 3 017 0023 55+3x3 095 095 27+14x12 110 120 a 2.020 7.5 43 07/12/1993 Off Hokkaido, Japan SI 42.89 139.23 17 246 900 1608 165+14x8 180 180 40+13x5 045 045 b 4.650 7.7 44 09/03/1993 Off Chiapas, Mexico S 14.57 x92.81 27 13 022 . 30+13x13 050 . 37+17x3 055 . a 0.149 6.7 45 09/10/1993 Off Chiapas, Mexico S 14.74 x92.69 29 33 066 0112 55+10x10 060 155 40+24x11 040 065 a 0.834 7.2 46 06/02/1994 Off Java S x10.41 112.93 15 35 137 0228 80+17x7 125 145 50+21x13 070 070 a 5.340 7.8 47 01/19/1995 Colombia T 5.09 x72.94 16 5 014 0015 20+9x9 021 021 9+19x8 012 027 b 0.071 6.5 48 02/05/1995 Off N. Is., New Z. NI x37.66 178.89 15 286 678 0808 55+24x11 100 100 15+9x4 023 023 b 0.584 7.1 277 49 05/13/1995 N. Greece N 40.17 21.69 15 177 446 0735 45+5x4 045 045 17+8x4 021 022 b 0.076 6.5 278 .HnyadS Das S. and Henry C. Table 1. (Continued.) No. Date Location Type Lat. Long. Depth No. Aftershocks Length (km) Width (km) QM0 Mw (mm/dd/yyyy) (km) (1020 Nm) 1 7 30 1 7 30 1 7 30 50 05/16/1995 Loyalty Isl. N x22.98 169.89 25 142 204 0232 135+32x13 160 185 75+12x7 075 075 a 3.900 7.7 51 06/15/1995 N. Greece N 38.40 22.27 15 244 271 0468 9+4x4 012 020 13+8x5 013 013 b 0.060 6.5 52 07/30/1995 N. Chile S x23.30 x70.21 29 107 177 0204 205+23x23 240 240 85+21x10 085 085 b 12.150 8.0 53 08/16/1995 Solomon Isl. Sxh x5.82 154.17 46 72 199 0281 135+22x12 135 135 c 4.620 7.7 54 09/14/1995 Guerrero, Mexico S 16.88 x98.60 22 11 021 0035 32+16x10 032 040 37+24x15 040 050 a 1.310 7.3 55 10/09/1995 Jalisco, Mexico S 19.12 x104.20 15 19 034 0045 140+12x5 145 160 39+20x17 040 040 a 11.470 8.0 56 11/24/1995 Kurile Isl. S 44.43 149.11 34 3 020 . 18+5x5 030 . 033 . a 0.081 6.5 57 12/02/1995 Kurile Isl. S 44.29 149.21 16 67 ..31+14x5 ..55+12x8 ..a 0.088 6.6 58 12/03/1995 Kurile Isl. S 44.53 149.31 26 219 330 0439 185+15x8 185 195 80+12x7 085 085 a 8.240 7.9 59 02/17/1996 Biak Is. S* x0.94 136.95 15 301 570 0682 290+20x20 315 315 50+14x13 050 050 a 24.100 8.2 60 02/21/1996 Off Peru Sxi x9.69 x79.77 15 11 025 0034 125+20x20 125 125 c 2.230 7.5 j 61 04/29/1996 Solomon Isl. Sx x6.54 155.04 54 22 087 0129 39+20x13 095 095 cw 0.755 7.2 62 06/10/1996 Andreanof Isl. S 51.55 x177.61 29 157 255 0304 150+12x8 160 160 65+9x7 065 070 a 8.050 7.9 63 06/21/1996 Off Kamchatka S 51.55 159.08 24 27 146 0200 30+7x5 060 075 24+10x6 040 052 a 0.146 6.7 64 07/15/1996 Guerrero, Mexico S 17.57 x101.05 22 6 008 0010 13+5x5 013 013 27+12x9 031 031 b 0.099 6.6 ‘Off’ in place name means ‘Off the coast of’. Earthquake types: S=simple interplate subduction zone thrust earthquake, defined here to be an earthquake that, based on its focal mechanism and aftershocks, occurs on a plane within, and parallel to, a Wadati–Benioff zone; Sx=complex interplate subduction earthquake, with the reason for its classification as complex given in a footnote; T=other interplate thrust earthquake; SI=subduction-related intraplate thrust earthquake; TI=other thrust intraplate earthquake; N=normal interplate earthquake (including regions of continuous deformation); NI=normal intraplate earthquake. Asterisks denote earthquakes that do not meet the strict rake criterion discussed in the text. Epicentral coordinates are from the ISC bulletin, centroid depths are from the Harvard CMT catalogue. Numbers of aftershocks and aftershock area dimensions are given after time periods of 1, 7 and 30 days, as indicated. Uncertainties in the 1 day dimensions are given as the maximum increase(+) followed by the maximum decrease(x) in the best value. Q is width quality: a=dipping zone clearly visible in aftershocks, b=correct nodal plane of CMT can be identified from aftershocks, c=fault plane could not be identified; cw indicates that the width of the aftershock zone is greater than its length. ‘ . ’ indicates that a measurement could not be made, either because a subsequent event of similar size precludes measurements at later times or because there are insufficient well-located early aftershocks. a Cuts across a subducting slab, with aftershocks mostly in the plane of the Wadati–Benioff zone. b Length is measured along the trend of the aftershocks, 40u from the CMT strike. c Cuts across a subducting slab. d Length is measured along the trend of the aftershocks, 30u from the CMT strike, which lie on a subducting feature of the ocean floor. e The hypocentre is at the upper limit of the Wadati–Benioff zone, and the aftershocks do not lie on a single plane. # f At the junction of a subduction zone and a transform fault. 01RAS, 2001 g Both in complex regions with multiple subduction zones. h At the junction of two subduction zones. i 1 day aftershocks cut across subducting slab, which conflicts with other studies of this earthquake; see text for details. j Aftershocks lie on two intersecting planes, one of which, containing the hypocentre, coincides with the Wadati–Benioff Zone. GJI 147, 272–293 Aftershock zones of large shallow earthquakes 279 Table 2. Parameters of great pre-1977 thrust earthquakes. Date Location No. aftershocks Length (km) Width (km) M0 Mw (mm/dd/yyyy) (1020 Nm) 1 7 3017301730 03/09/1957 Aleutian Isl., Alaska 023a 083 127 790 1000 1000 090 145 145 0088b 8.6 05/22/1960 Chile 011c 019 028 700 0930 0930 240 240 240 3200d 9.6 03/28/1964 Prince Wm. Sound, Alaska 195e 489 775 845 0855 0855 190 190 200 0750f 9.2 All aftershock lengths and widths were remeasured for this study, using the aftershock data from the sources indicated. a Aftershock data from Boyd et al. (1995). They estimate their magnitude of completeness as MS=5.5, although a small number of aftershocks have much lower magnitudes. Note that the length of the aftershock zone until 22 hr after the main shock is 590 km. b Johnson et al. (1994), from inversion of tsunami data. A seismological determination using the only available non-nodal surface wave seismogram gives 50r1020 Nm. c Aftershock data from Cifuentes (1989). The smallest aftershocks for which magnitudes are given have MS=5.8 d Cifuentes & Silver (1989), from inversion of normal modes. This moment does not include the inferred slow precursor to this event. e Aftershock data from the ISC, with dimensions measured using only those aftershocks with mbi4. Aftershocks were not relocated, since the spatial extent of the aftershock zone is large in comparison to typical distances to stations, and the assumptions underlying JHD are therefore not valid. f Kanamori (1970), from inversion of surface waves. Ben-Menahem et al. (1972) obtain 1000r1020 N m from analysis of normal modes; this result is independent of their later choice of the vertical nodal plane as the rupture plane of the event. This difference in moment is not significant on the scale of Fig. 7(b). likely to occur at any position along strike, then the hypocentre directly comparable to the ‘simple’ subduction zone earth- has uniform probability of occurring at any distance between 0 quakes, but it is unclear whether they should be grouped with and 50 per cent from the closest end; thus the mean distance the other dip-slip earthquakes. The 7 day length of ‘simple’ sub- from the closest end will be 25 per cent, very close to the values duction zone earthquakes is on average 31 per cent greater we observe. For the six great subduction earthquakes, with than the 1 day length, with the 30 day length being 43 per Mw<8.5, studied by Pe´rez & Scholz (1997), which include the cent greater. For non-subduction zone earthquakes the length three great earthquakes of Table 2, the hypocentres occur on increases by an average of 20 and 37 per cent over the same average 20 per cent of the rupture length from the nearest end time periods, respectively. Earthquakes in Fig. 2(a) are oriented of the rupture zone defined by aftershocks. Pe´rez & Scholz so that the end of the 1 day aftershock zone that is furthest (1997) comment that the hypocentres of these great earth- from the hypocentre along strike lies in the positive direction quakes occur near the ends of the rupture. The data do support along the ordinate. This direction corresponds to the principal this, but the difference between this and the mean location horizontal direction of propagation of each earthquake. We predicted from an assumption of random hypocentre location may consider earthquakes with L>W and with their hypo- is small. centres lying outside the central third of the 1 day aftershock The patterns of aftershock area expansion of subduction and zone to be earthquakes unilaterally propagating in the hori- non-subduction zone earthquakes are found to be different. zontal direction. The expansion of aftershock zones is seen to Since the numbers of earthquakes of each type of non- be strongly asymmetric for non-subduction zone unilateral subduction earthquake (SI, T, TI, N and NI) are too few to earthquakes. For these earthquakes, between 1 and 30 days, draw firm conclusions about each individual type, we shall the aftershock zone extends by an average 23 per cent of discuss them collectively as non-subduction zone earthquakes. the 1 day length in the direction opposite to the propagation Some of the earthquakes classified as ‘complex’ may not be direction, but only 8 per cent in the propagation direction. This Table 3. Parameters of strike-slip earthquakes 1993–1996 No. Date Location Lat. Long. ISC Depth. No. Aftershocks Length (km) M0 Mw (mm/dd/yyyy) (km) (1020 Nm) 1 7 30 1 7 30 65 06/05/1994 Off Taiwan 24.46 121.86 20 21 41 60 17+12x8 17 20 0.038 6.3 66 12/15/1994 Off N. Is., New Z. x37.46 177.59 11 104 190 239 34+14x7 34 34 0.033 6.3 67 01/16/1995 Honshu, Japan 34.55 135.04 19 394 596 721 55+6x3 55 60 0.243 6.9 68 03/19/1995 W Irian x4.16 135.09 39 34 49 55 80+11x11 80 80 0.225 6.8 69 05/27/1995 Sakhalin Is. 52.60 142.85 8 20 40 48 65+12x10 65 70 0.432 7.0 70 10/23/1995 Szechwan, China 25.99 102.24 3 16 33 42 28+11x8 28 29 0.022 6.2 71 07/16/1996 Off Kamchatcka 56.05 165.00 37 12 13 15 40+18x6 40 40 0.072 6.5 72 07/23/1996 Off Kermadec Isl. x26.91 x177.18 44 8 11 15 30+25x18 30 30 0.059 6.5 *73 03/25/1998 NW of Balleny Is. x62.88 149.53 10 25 43 54 315+5x5 315 325 17.000 8.1 *74 08/17/1999 Turkey 40.75 29.86 17 59 84 122 90+9x3 105 105 2.880 7.6 *75 06/18/2000 Wharton Basin 13.80 97.45 10 11 19 20 100+25x25 105 105 7.910 7.9 Aftershock numbers and fault lengths are given as for Table 1. * For these earthquakes, no ISC data were available at the time the study was carried out. Hypocentre given is from NEIC, and lengths are measured from aftershocks relocated using NEIC phase data. # 2001 RAS, GJI 147, 272–293 280 C. Henry and S. Das Figure 2. Aftershock extents of dip-slip earthquakes, labelled along the abscissa with their index number from Table 1. Earthquakes are grouped according to the tectonic ‘types’ defined in Table 1, as indicated along the base of the figure. 1 day dimensions are shown by shaded bars and 30 day dimensions are shown by open bars. Hypocentre locations are shown by open circles. The three pre-1977 earthquakes are labelled with their year of occurrence, and the 22 hr aftershock dimensions of the 1957 earthquake are shown by a solid line. (a) Extent of aftershock zone along strike from hypocentre, with each earthquake oriented so that the end of the 1 day aftershock zone that is furthest from the hypocentre is in the positive distance direction. (b) Extent of aftershock zone up dip from hypocentre for those earthquakes for which width was determinable. (c) Absolute depth extent of aftershock zones, determined from up-dip extent of aftershock zone and fault dip. # 2001 RAS, GJI 147, 272–293 Aftershock zones of large shallow earthquakes 281 asymmetry could reflect either differences in the pattern of Most ‘simple’ subduction earthquakes are seen to have their stress change beyond the edges of the main shock rupture zone lower edges at or above y50 km depth. Some exceptions are due to differing slip distributions at the two ends of a unilateral discussed next. For earthquake 38 the CMT depth is 40 km, rupture, or different material properties, since the termination it has a large depth extent, and two well-located aftershocks of the rupture in the forward direction has presumably been occur 20 km above the upper termination of the fault plane, so subjected to, and resisted, greater dynamic stresses than the its lower edge must be at a depth of at least 50 km, and possibly termination in the reverse direction. For unilateral ‘simple’ more. For earthquake 42, the CMT depth of this earthquake is subduction zone earthquakes the asymmetry has the opposite 46 km, and it has a depth extent of 60 km, providing additional sense, but is very slight and may not be significant: between 1 evidence for a relatively deep initiation. For earthquake 5, the and 30 days, aftershock zones expand by an average of 13 per CMT depth is 28 km, suggesting that the ISC depth of 56 km, cent in the direction opposite to propagation and 18 per cent in which was not significantly altered by relocation, is too large. the direction of propagation. Fig. 2(b) shows that the ‘simple’ For the three pre-1977 great subduction earthquakes of Table 2, subduction earthquakes mostly initiate at or near the base neither the dip nor the depths of aftershocks are very well of the aftershock zone, with some initiating in the middle of known; the extents shown in Fig. 2(c) are based, for the 1957 the depth range of the fault. No ‘simple’ subduction zone and 1960 earthquakes, on dips taken from the references earthquakes initiate at the top edge of the fault, although a few to Table 2, which were assigned on the basis of the regional initiate in the upper quarter of the depth range. This reconfirms seismicity, and for the 1964 earthquake on a dip consistent the observation of Kelleher et al. (1973) that subduction earth- with the ISC aftershocks. The absolute depths shown in quakes usually initiate on the landward side of their aftershock Fig. 2(c) for these three earthquakes are consistent with the zones. Das & Scholz (1983) have explained this using the fact regional tectonics. The base of the rupture area for most non- that both stress drop and fault strength increase with depth subduction earthquakes is significantly shallower than 50 km. in the Earth. They showed, using numerical modelling, that Of those approaching or exceeding 50 km, earthquake 7 cuts ruptures can propagate up dip easily due to the greater release across a subducting slab (as mentioned earlier), and initiates at of strain energy at deeper regions but are inhibited from its upper edge. For the normal earthquake 50 occurring at the propagating into higher stress drop regions down dip, and thus junction between a subduction zone and a transform fault, small shallow earthquakes cannot generally develop into great the depth extent is clear from its relocated aftershocks. For earthquakes. Our results show that most of the subduction zone earthquake 3, the 1977 Sumba earthquake, the ISC hypocentral earthquakes do propagate upwards, but with some initiating at depth is 78 km. Lynnes & Lay (1988) give a hypocentral depth mid-range and propagating both up and down dip. Many of of 25–30 km for this earthquake, and also presented evidence the largest subduction earthquakes fall in the latter category. from body wave modelling for a rupture extending from the The aftershock width is seen in most cases to expand signi- surface to a maximum depth of 30–50 km. The largest after- ficantly only in the up-dip direction (Fig. 2b), with a notable shocks have also been shown to have depths of less than 30 km exception being earthquake 13. The aftershocks of several (Fitch et al. 1981; Spence 1986). The earthquake generated a earthquakes with very small 1 day depth extents later expand large tsunami and thus must have extended close to the surface. significantly up dip. It is interesting to note that for the majority On the basis of these studies we consider the ISC hypocentral of the subduction earthquakes with 1 day widths >60 km, the depth and our relocated hypocentral depth of 67 km to be too width of the aftershock zone does not increase substantially large. in the time period 1–30 days. For earthquakes with lower 1 day The observation in Fig. 2(c) that for most subduction earth- widths, the width often increases substantially in this time period. quakes the maximum depth of rupture is at or shallower than For most non-subduction earthquakes, the aftershock zone 50 km may suggest that this limit is related to the subduction does not expand in width between 1 and 30 days. This may interface seismogenic depth. It is interesting to note that had indicate that most of these earthquakes extend across the whole we used a cut-off in centroid depth of 150 km rather than of the local seismogenic zone. Other than type S, earthquakes 70 km when choosing earthquakes for analysis, we would have initiate at a range of depths, with a few initiating at the up-dip obtained only two more earthquakes satisfying our other edge of the aftershock zone. The latter include earthquake 27, a selection criteria (such as mechanism, number of aftershocks, ‘complex’ subduction zone earthquake occurring in the ‘double etc.) in the 20 yr time period covered by this study; thus this subduction zone’ of the Molucca passage, and earthquake 7, depth limit is not an artefact of our event selection. the only thrust earthquake of this study identified as cutting Earthquake 60 (Mw=7.5), which occurred in 1996 off the across a subducting slab. coast of northern Peru, deserves special mention. Due to the In Fig. 2(c), depth extents are calculated from the down-dip location of this earthquake, the station distribution used in widths of the aftershock zones and plotted at their absolute the relocations is much worse than most other earthquakes of depths. These ranges represent the depth extent of the identified this study. By analysing broad-band body waves, Ihmle´ et al. fault plane for each earthquake. This is preferable to making a (1998) obtained a centroid depth of 7t2 km for this earth- direct measurement of the depth extent of the aftershock zone, quake. The earthquake generated a fairly large tsunami for its especially for shallow-dipping subduction zone earthquakes, moment (Ihmle´ et al. 1998; Heinrich et al. 1998), indicating since vertical errors are large (on average t30 km at 90 per significant slip at shallow depths. The ISC hypocentre is located cent confidence) in comparison to the depth extents of most at 13 km but the poor azimuthal distribution does not allow earthquakes. We plot the depth extents relative to the relocated reliable relocation of it using the JHD method. Even though we main shock hypocentral depths in Fig. 2(c); this is the only do not know the absolute depth of the hypocentre, we can still use of absolute location information in this study, all other consider its position relative to the aftershocks. The relocated measurements being relative to the location of the main shock 1 day aftershocks extend 70 km below the hypocentre, with hypocentre. depth errors of t20 km for the best-located aftershocks. The # 2001 RAS, GJI 147, 272–293 282 C. Henry and S. Das 30 day aftershocks form a diffuse cloud, with all well-located 6 NUMBER AND MAGNITUDE OF aftershocks lying below the hypocentre. This strongly suggests AFTERSHOCKS mainly downward rupture propagation. According to our criterion of identifying the fault plane from the early after- It has been noted before that the number and magnitude of shocks, we would select as the fault plane that nodal plane of aftershocks can be very variable for different earthquakes. the CMT solution that dips 76uE. This is opposite to the dip of Here we carry out a comprehensive study of the aftershock the subduction zone. Ihmle´ et al. (1998) used the nodal plane magnitude and number for the 102 post-1977 earthquakes in consistent with the subduction zone dip as the fault plane in this study in order to determine if such differences depend on their study. The surface wave fits to the data are not reported by the tectonic regime in which the earthquake occurs. We only them and the P waves are poorly modelled. Most importantly, consider aftershocks with Mwi5.0, with Mw taken from the no analysis attempting to use the vertically dipping nodal plane Harvard CMT catalogue. In particular, we do not use the body as the plane of faulting is reported by them. Our experience wave magnitudes assigned to aftershocks by the ISC as they are with the 1998 Antarctic earthquake (Henry et al. 2000) showed less reliable. Tables 4 and 5 give the number of aftershocks with that reasonably good fits can be obtained mistakenly using the Mwi5.0 for the 1, 7 and 30 day periods, as well as the number auxiliary plane as the fault plane. Moreover, Ihmle´ et al. (1998) of aftershocks for the 30 day period in the magnitude ranges find mainly up-dip propagation, which contradicts our earlier 5.0jMw<6.0, 6.0jMwj7.0 and Mwi7.0 for dip-slip and suggestion based on the position of the hypocentre relative to strike-slip earthquakes, respectively. However, we note that the aftershocks that the rupture propagated mainly down- the annual number of shallow (<70 km) earthquakes in the wards. Further work on this earthquake is clearly beyond magnitude range 5.0jMw<6.0 for which a Harvard CMT the scope of this study, and a more thorough analysis such as solution was obtainable has more than doubled between 1977 that carried out by Henry et al. (2000) for the 1998 Antarctic and 1999. For the other magnitude ranges the number has earthquake would be necessary to resolve this. remained steady with time, indicating that the CMT catalogue is complete for Mwi6.0. The most rigorous comparison can therefore only be made for aftershocks with Mwi6.0. The number of aftershocks with Mwi6.0 for the 30 day 5 AFTERSHOCK LENGTHS FOR period following the main shock is plotted against M in Fig. 4. SHALLOW STRIKE-SLIP 0 We see that subduction zone earthquakes have larger and more EARTHQUAKES numerous aftershocks than all other types of earthquakes. The extents along strike of the strike-slip earthquakes from this We see no distinction between non-subduction interplate and (Table 3) and from Pegler & Das (1996) are shown in Fig. 3. intraplate earthquakes, nor between non-subduction oceanic or On average, the hypocentre is 26 per cent of the 1 day after- continental earthquakes, nor between non-subduction dip-slip shock length from the nearest end of the fault, which is the and strike-slip earthquakes. The same pattern is also seen when same result as that obtained above for dip-slip earthquakes. the aftershocks with 5.0jMw<6.0 are included (not shown). The difference between the three lengths determined after 1, 7 The largest subduction zone earthquakes have a large variability and 30 days is insignificant for most of these earthquakes. in numbers of Mwi6 aftershocks. A majority have one or two such aftershocks, but several have more. The 1985 Chile earthquake (earthquake 21 of Table 1) has seven Mwi6 after- shocks, the greatest number for any earthquake in this study, its largest aftershock having Mw=7.4. The 1977 Sumba normal intraplate earthquake (earthquake 3 of Table 1) has five after- shocks with Mw<6, all other non-subduction earthquakes having two or fewer. 7 IMPLICATIONS FOR EARTHQUAKE SCALING 7.1 Strike-slip earthquakes The 1 day length L is plotted against M0 for the strike-slip earthquakes of this study in Fig. 5(a), together with the data of Pegler & Das (1996). Since we have shown that aftershock lengths of strike-slip earthquakes do not expand substantially over time, the choice of time period has essentially no impact on our results. Fig. 5(b) shows the uncertainties in the data, together with the line of best fit, which has a slope of 0.37, close to 1/3. Lines of slope 1, 1/2 and 1/3 are shown for reference. Lines of slope 1 are clearly not consistent with the data, and there is no sign of a change in slope within the range of the data, ruling out the scaling M0 3 L, which has been proposed Figure 3. Same as Fig. 2(a) but for strike-slip earthquakes, labelled by Romanowicz (1992) on the basis of non-uniform data sets with their index number from Table 3. Selected data from Pegler & Das compiled from the literature. The data are probably not sufficient (1996), using hypocentral locations from Pegler (1995), are also shown. to distinguish slopes in the range 1/2–1/3, allowing an exponent # 2001 RAS, GJI 147, 272–293 Aftershock zones of large shallow earthquakes 283 Table 4. Numbers of aftershocks of dip-slip earthquakes. Table 5. Numbers of aftershocks of strike-slip earthquakes. 5 6677 5 6677 Date Mw n1 n7 n30 n n n Date Mw n1 n7 n30 n n n (mm/dd/yyyy) (mm/dd/yyyy) 1 03/21/1977 6.7 2 3 04 0310 1993–2000 2 06/22/1977 8.0 0 2 03 0300 65 06/05/1994 6.3 0 0 0 0 0 0 3 08/19/1977 8.3 2 9 14 0950 66 12/15/1994 6.3 0 0 0 0 0 0 4 11/23/1977 7.4 0 2 04 0400 67 01/16/1995 6.9 0 0 0 0 0 0 5 03/23/1978 7.6 2 5 05 0311 68 03/19/1995 6.8 1 3 4 4 0 0 6 02/28/1979 7.5 0 1 01 0100 69 05/27/1995 7.0 1 1 3 3 0 0 7 10/23/1979 7.0 0 1 01 0100 70 10/23/1995 6.2 0 0 0 0 0 0 8 12/12/1979 8.1 1 1 03 0120 71 07/16/1996 6.5 0 0 0 0 0 0 9 02/23/1980 7.1 1 2 03 0210 72 07/23/1996 6.5 2 2 3 2 1 0 10 07/08/1980 7.5 3 3 .... 73 03/25/1998 8.1 1 4 5 4 1 0 11 07/17/1980 7.7 0 2 03 0120 M73 0 2 2 2 0 0 12 10/10/1980 7.1 1 2 03 0210 74 08/17/1999 7.6 0 1 3 3 0 0 13 10/25/1980 7.4 3 9 09 0630 75 06/18/2000 7.9 0 2 2 2 0 0 14 11/23/1980 6.9 0 1 01 0100 1977–1992 15 04/24/1981 6.8 1 1 01 0100 1 08/06/1979 5.7 0 0 0 0 0 0 16 07/15/1981 7.1 1 2 02 0200 2 09/12/1979 7.5 0 1 1 0 1 0 17 03/21/1982 6.9 1 3 03 0300 M2 0 0 0 0 0 0 18 07/23/1982 7.0 1 2 04 0310 4 06/09/1980 6.3 0 0 0 0 0 0 19 05/26/1983 7.7 0 1 05 0410 5 11/08/1980 7.3 0 0 0 0 0 0 20 03/19/1984 7.0 1 1 01 0100 6 05/25/1981 7.6 0 2 3 3 0 0 21 03/03/1985 7.9 5 7 14 0761 7 12/19/1981 6.8 0 0 2 1 1 0 22 09/19/1985 8.0 0 2 03 0201 11 08/06/1983 6.6 0 0 1 1 0 0 23 10/05/1985 6.6 0 0 00 0000 12 04/24/1984 6.2 0 0 0 0 0 0 24 12/21/1985 7.1 3 5 06 0420 13 09/10/1984 6.6 0 0 0 0 0 0 25 12/23/1985 6.7 1 1 01 0100 14 03/09/1985 6.1 1 1 1 1 0 0 26 05/07/1986 7.9 1 8 09 0810 15 05/10/1985 7.2 0 1 2 2 0 0 27 10/23/1986 6.7 4 4 04 0220 16 11/17/1985 7.1 1 1 2 1 1 0 28 11/14/1986 7.3 1 1 01 0000 17 02/08/1987 7.3 4 6 11 10 1 0 30 04/22/1987 6.6 0 0 01 0100 19 11/30/1987 7.8 1 3 4 4 0 0 31 10/16/1987 7.3 0 1 01 0100 20 03/06/1988 7.7 0 1 1 1 0 0 32 01/10/1989 6.6 0 0 00 0000 21 11/06/1988 7.0 1 1 4 3 1 0 33 02/10/1989 7.1 5 7 09 0900 22 05/23/1989 8.0 0 7 9 9 0 0 34 03/25/1990 7.3 1 1 01 0100 M22 0 3 3 3 0 0 35 03/08/1991 6.6 0 0 00 0000 24 03/03/1990 7.6 0 0 1 1 0 0 36 06/20/1991 7.5 0 2 02 0200 25 05/20/1990 7.1 0 2 2 0 1 1 37 11/19/1991 7.2 0 0 01 0100 26 06/14/1990 7.1 1 1 2 2 0 0 38 05/15/1992 7.2 0 2 03 0300 28 07/16/1990 7.7 2 9 12 10 2 0 39 07/10/1992 6.5 0 1 01 0100 29 08/17/1991 7.0 0 0 0 0 0 0 40 09/02/1992 7.6 2 5 11 10 1 0 30 03/13/1992 6.6 0 1 1 1 0 0 41 12/12/1992 7.7 1 2 02 0200 31 04/06/1992 6.7 2 2 3 3 0 0 42 06/08/1993 7.5 0 3 04 0310 32 06/28/1992 7.3 1 4 5 4 1 0 43 07/12/1993 7.7 0 2 02 0200 M32 0 3 3 3 0 0 44 09/03/1993 6.7 1 1 .... 33 08/07/1992 6.8 0 0 0 0 0 0 45 09/10/1993 7.2 0 2 06 0510 34 11/06/1992 6.0 0 0 0 0 0 0 46 06/02/1994 7.8 2 13 19 14 5 0 47 01/19/1995 6.5 1 2 02 0200 48 02/05/1995 7.1 4 10 14 13 1 0 Numbers in the first column refer to Table 3 of this study for the period 49 05/13/1995 6.5 0 2 02 0200 1993–1996 and to Table 1 of Pegler & Das (1996) for 1977–1992. Other 50 05/16/1995 7.7 2 8 08 0620 columns are the same as in Table 4. For earthquakes that have many 51 06/15/1995 6.5 0 0 00 0000 aftershocks on a feature that is clearly distinct from the main fault plane, the 52 07/30/1995 8.0 1 9 12 10 2 0 aftershocks on the main plane only are also counted and listed separately 53 08/16/1995 7.7 4 12 16 12 3 1 with an ‘M’ prefixed to the index number. 54 09/14/1995 7.3 0 0 00 0000 55 10/09/1995 8.0 0 1 02 0200 .... 56 11/24/1995 6.5 0 2 of 2–3 in the scaling relation of L to M . For the large strike- 57 12/02/1995 6.6 2 ..... 0 58 12/03/1995 7.9 0 6 09 0720 slip earthquakes, the saturation of fault width at 10–15 km 59 02/17/1996 8.2 4 9 14 10 4 0 allows inferences about slip to be made directly from the 60 02/21/1996 7.5 0 0 00 0000 observed scaling of length with moment. Then, our rejection 61 04/29/1996 7.2 1 10 12 0840 of M0 3 L implies a rejection of fault models where slip is 62 06/10/1996 7.9 1 9 10 0901 2 63 06/21/1996 6.7 0 8 10 0820 independent of length. If M0 3 L , this would imply that slip 64 07/15/1996 6.6 0 1 01 0100 is proportional to length. If the exponent in the scaling relation is in fact greater than 2, as indicated by the best fit to the data, then Numbers in the first column refer to Table 1 of this study. Mw is listed for this may indicate that the increase of slip with length is faster the main shock. n1, n7 and n30 are the numbers of aftershocks with Mwi5 than linear, or a slight increase in fault width for the largest occurring in 1, 7 and 30 days, respectively. 5n6, 6n7 and 7n are the numbers of strike-slip earthquakes, beyond the 10–15 km widths observed aftershocks occurring in 30 days with 5jMw<6, 6jMw<7 and 7jMw, respectively. ‘ . ’ indicates that a subsequent event of similar size precludes for smaller earthquakes (Scholz 1982; Wells & Coppersmith counting the aftershocks at later times. 1994). We do not favour the latter explanation due to the fact # 2001 RAS, GJI 147, 272–293 284 C. Henry and S. Das Figure 4. Plot of number of Mwi6 aftershocks occurring in a 30 day time period against main shock Mw for both strike-slip and dip-slip earthquakes. Symbols refer to different types of earthquakes, as shown in the key. Earthquakes with one or more aftershocks of this magnitude are numbered: for dip-slip earthquakes, bold numbers refer to Tables 1 and 4; for strike-slip earthquakes after 1993, bold numbers refer to Tables 3 and 5; for strike-slip earthquakes before 1993, italic numbers refer to Table 5 and to Table 1 of Pegler & Das (1996). that recent well-studied earthquakes do not appear to exceed Subduction earthquakes with L<50 km have L=2W, with some the normal seismogenic width. For the 1998 Antarctic intra- having L # 2001 RAS, GJI 147, 272–293 Aftershock zones of large shallow earthquakes 285 Figure 5. (a) Plot of 1 day aftershock length against moment for strike-slip earthquakes. Squares show data from this study, with bold numbers referring to Table 3. Circles show selected data from Pegler & Das (1996), with numbers in italics referring to Table 1 of that study. Interplate earthquakes, including earthquakes in regions of continuous deformation, are shown by solid symbols. Intraplate earthquakes are shown by open symbols. (b) Same data, with uncertainties (discussed in the text) shown by solid lines. The line of best fit to all the data, determined using the uncertainties in the lengths to weight the data (Press et al. 1992), is shown. Lines of slope 1, 1/2 and 1/3 are also shown separately for reference. describe the data over the whole magnitude range, lying below different for different tectonic environments, it is not surprising 20 most of the earthquakes with M0i3r10 N m. As discussed that the data are not described well by a single power law. We above, dip-slip earthquakes often undergo substantial expan- argue that W must be taken into account in any discussion sion of aftershock area with time. When the 7 and 30 day of the scaling of L with M0. Examination of Table 1 shows 20 lengths are plotted against M0 (not shown), they are found to that earthquakes with M0<10 N m, including most of the have greater scatter than the 1 day lengths, suggesting that they subduction earthquakes of this study, have widths in the range are less closely related to the rupture length, and we regard the 30–80 km, but that below this magnitude, widths are in the 1 day aftershock dimensions as the best estimate of the rupture range 10–40 km. Since L=M0/(Cmu¯W), this can account for length. After 7 and 30 days, the step change in length at M0 of the observed change in length. 0.8–1.0r 1020 N m is preserved, but lower-magnitude earth- Since, for reasons mentioned earlier, the errors in the quakes expand on average by a greater fraction of their 1 day determination of fault width are greater than those for fault lengths than larger earthquakes, leading to lesser slopes for the length, we shall adopt two approaches for the consideration of lines of best fit. the effect of fault width. For subduction zone earthquakes, by Since we have shown that, for large dip-slip earthquakes, W far the largest group of earthquakes of a single type in this is neither constant nor proportional to L, and since W may be study, we shall first discuss the observed scaling of moment # 2001 RAS, GJI 147, 272–293 286 C. Henry and S. Das Figure 6. Plot of 1 day aftershock width W (km) against 1 day aftershock length for dip-slip earthquakes. Symbols refer to different types of earthquake, as shown in key. (a) Numbers refer to Table 1, with asterisks indicating the earthquakes that do not meet the strict rake criterion discussed in the text. The 22 hr dimensions of the 1957 Aleutian earthquake are indicated by an open square. (b) Same data, with uncertainties shown by lines. The three large subduction earthquakes of Table 2 are also shown, labelled by their year of occurrence. Diagonal lines show L/W values of 1, 2, 4 and 8. with length, interpreted using the estimated widths, but without Cmu¯ for all earthquakes for which we have been able to obtain direct inclusion of these width values in the comparison. For the fault width, and examine its variation with width and non-subduction earthquakes we have too few examples of each with length. The latter will allow comparison of earthquakes of type to draw individual conclusions. We shall then determine different types and over a wide range of length scales. # 2001 RAS, GJI 147, 272–293 Aftershock zones of large shallow earthquakes 287 Figure 7. Plot of 1 day aftershock length L (km) against moment M0 for dip-slip earthquakes. Only earthquakes with L>W are plotted. (a) Symbols same as in Fig. 6(a). (b) Symbols same as Fig. 6(b). The line of best fit to the post-1977 thrust earthquake data, determined using the uncertainties in the lengths to weight the data, is shown. Lines of slope 1, 1/2 and 1/3 are shown for reference. expand progressively over the first 24 hr, suggesting that 7.3 Scaling relations for subduction earthquakes the 1 day aftershock lengths are significantly greater than the without explicit consideration of W true rupture lengths. This is confirmed for earthquake 16 by For the subduction earthquakes with 70 km # 2001 RAS, GJI 147, 272–293 288 C. Henry and S. Das during the rupture of shallow-dipping earthquakes which break the Earth’s surface can lead to a breakdown of the relation M0=mu¯A, and propose a corrected relationship M0=mu¯A/c, where c>1. The four earthquakes of Fig. 8 with L<70 km are worth consideration here. Earthquake 31 and the ‘complex’ sub- duction earthquake 36 have sufficient aftershocks that the 1 day lengths are likely to be a good estimate of the true rupture length. It is interesting to note that earthquakes 22 and 31 have the lowest measured widths of the earthquakes of Fig. 8. This would lead us to expect them to have high lengths for their moments, the opposite of the observed anomaly, indicating that they have very high slips. Earthquakes 34 and 42 have very few 1 day aftershocks, and the 1 day lengths are probably an underestimate of their true rupture lengths. 7.4 Scaling relations taking W explicitly into account We now consider the subduction earthquakes discussed above together with the three great subduction earthquakes of Table 2, and with earthquakes of other types. To extend the range of our data to lower moments we combine our data with data for pure dip-slip earthquakes given by Wells & Coppersmith (1994). For the eight dip-slip earthquakes in common between the two studies, we use the values of Table 1. Comparing the two data sets, in general the moments are in very good agreement, and the lengths agree within 25 per cent for six out of eight Figure 8. Same as Fig. 7(b), showing only the post-1977 subduction earthquakes, with the worst disagreement being 50 per cent. 20 zone thrust earthquakes with M0<10 N m of this study. The For the four of these eight for which we have been able to earthquakes individually discussed in the text are numbered. Lines of measure widths, they agree within 50 per cent. Fig. 9 shows L slope 1 (dotted), 1/2 (solid) and 1/3 (dashed) are superimposed. against M0 for the earthquakes of the combined data set with L>W; the line of best fit for the thrust earthquakes of the combined data set is shown, and has slope y1/3. The line of 20 main band of data is best described by lines with slope 1/2, best fit to only the thrust earthquakes with M0<10 Nmis with lines of slope 1/3 describing the data across the full range shown by a dashed line, and the step change in length at this of moments slightly less well, although the difference rests on magnitude and the deviation of the largest post-1977 earth- 3 relatively few earthquakes. The lines of slope 1 are clearly not quakes from M0 3 L scaling are clearly seen. Fig. 10 shows compatible with the earthquakes of L>70 km, with the lines of the relationship of L to W for the combined data set. For slope 1/2 or 1/3 clearly providing a much better fit to the data. L<40 km, L/W is fairly constant in the range 0.7–3. Above this Since the widths of these longest earthquakes are independent length, L/W is seen to increase systematically with length. This of length, this indicates that for these earthquakes we can reject reconfirms the necessity of taking fault width into account in categorically the possibility that u¯ is independent of length. The the analysis of these data. good fit of the lines of slope 1/2 indicates that u¯ 3 L, with a Again selecting only those earthquakes with L>W,we greater than linear increase also being consistent with the data. calculate M0/LW, here denoted U¯ , for those earthquakes for Earthquakes 22 and 55, the 1985 and 1995 Mexican earth- which width could be determined. Since M0/LW=Cmu¯, the quakes, respectively, fall just below the main band of data, and range of C is small, and rigidity is nearly constant across earthquake 46 falls substantially below the band. All three have the range of hypocentral depths of the earthquakes of this sufficient 1 day aftershocks that the 1 day aftershock lengths study, U¯ may be treated as a direct measure of fault slip. In may be considered reliable estimates of the true rupture length. Fig. 11(a), U¯ is plotted against length, with lines of slope 1 The only earthquake significantly above the general trend of superimposed. We see that the majority of earthquakes of the the data is earthquake 40, the 1992 Nicaragua earthquake, with combined data set lie within a broad band of slope 1. The post- a length three times that of other earthquakes of its magnitude. 1977 earthquakes with the greatest lengths are seen also to have This was a slow earthquake with a source duration of y100 s the greatest values of U¯ . Thus we conclude that u¯ 3 L over the 17 22 (Kanamori & Kikuchi 1993) associated with the subduction of range 10 Nm # 2001 RAS, GJI 147, 272–293 Aftershock zones of large shallow earthquakes 289 Figure 9. Plot of length against moment for the same earthquakes as Fig. 7. Symbols refer to different types of earthquakes and to data source, as indicated in the key. Also shown are those dip-slip earthquakes of Wells & Coppersmith (1994) that have L>W, which have no strike-slip component of slip, and for which there were no measurements in our data set (Table 1), marked by W&C. The line of best fit to the thrust earthquakes of the 21 20 21 combined data set with M0<5r10 N m is shown by a solid line. The best fit to only the thrust earthquakes with 10 Nm 29 are large; aftershock locations using local data (Anderson aftershock length were to be used instead the earthquake would et al. 1990) give a width of 12 km, which should be regarded as fall at the upper edge of the extrapolated band (not shown). a more reliable value. We have previously discussed reasons for These three large earthquakes, with fairly similar lengths, have considering the 1 day aftershock dimensions of earthquakes 16 values of U¯ that span an order of magnitude and broadly agree and 34 unrepresentative of the corresponding ruptures. with the band extrapolated from smaller earthquakes. The value of U¯ for the 1957 Aleutian earthquake is seen to be U¯ is plotted against aftershock width in Fig. 11(b) for the below the extrapolated bounds for smaller earthquakes, or just same earthquakes. For widths up to y30 km, the data are seen within the bounds if its 22 hr length of 590 km is taken as more to be well described by a broad band with slope 1. This reflects 3 representative of the true rupture length. The 1964 Alaskan the well-known M0 3 L scaling of small earthquakes (Hanks earthquake has U¯ in the middle of the extrapolated bounds. 1977). Above this width, earthquakes still occur across the U¯ for the 1960 Chile earthquake lies above the extrapolated whole of the marked band, but several subduction thrust bounds. The low detection threshold of the time could have earthquakes occur at the very top of the band, or just above caused the length to be underestimated, and if the 30 day it, with slip being independent of width for the subduction earthquakes of this study. The earthquakes with greatest U¯ are not those with the greatest width, and there are a sufficient number of earthquakes with high U¯ to be confident that this is not an artefact of the inverse relationship between errors in W and errors in M0/LW. The 1957 Aleutian earthquake plots in the centre of the marked band, and the 1964 Alaskan earth- quake plots in the upper part. The 1960 Chile earthquake plots clearly above the band, even if the 30 day length is used instead (not shown), and if the width used is reliable, this implies that the slip is not limited by its fault width. Thus both our study of subduction zone earthquakes with 20 20 10 Nm # 2001 RAS, GJI 147, 272–293 290 C. Henry and S. Das Figure 11. Plot of U¯ against (a) length and (b) width for the same earthquakes as Fig. 9. The 22 hr parameters of the 1957 Aleutian earthquake are indicated by an open square. Solid lines of slope 1, chosen to delimit the majority of the data, are shown. up to 1020 N m, above this magnitude there is a step change 8CONCLUSIONS in length (Fig. 9). This may be due to a change in the tectonic environments represented in the available data. This step change We have estimated the rupture dimensions of 64 dip-slip earth- is followed by a change to slope 1/2 over the magnitude range quakes from 1977–1997 by relocating their aftershocks, and the 20 20 2r10 Nm # 2001 RAS, GJI 147, 272–293 Aftershock zones of large shallow earthquakes 291 seismogenic part of the subduction zone plate interface. The Anderson, H.J. & Zhang, J., 1991. Long-period seismic radiation aftershock zones of subduction zone earthquakes often expand from the May 23, 1989, Macquarie Ridge earthquake; evidence for substantially up dip, but not down dip, which again could be coseismic slip in the mantle?, J. geophys. Res., 96, 19 853–19 863. explained in terms of increasing strength with depth. Subduction Anderson, H., Smith, E. & Robinson, R., 1990. Normal faulting in a back arc basin; seismological characteristics of the March 2, zone earthquakes show no asymmetry in along-strike expansion. 1987, Edgecumbe, New Zealand, earthquake, J. geophys. Res., 95, Most non-subduction dip-slip earthquakes occur at depths 4709–4723. significantly less than 50 km, and show no preferred nucleation Archuleta, R.J. & Day, S.M., 1980. Dynamic rupture in a layered position along the dip direction. The aftershock zones of these medium; the 1966 Parkfield earthquake, Bull. seism. Soc. Am., 70, earthquakes do not expand significantly up or down dip, which 671–689. may suggest that many of the earthquakes in this study have Benioff, H., 1955. Mechanism and strain characteristics of the White ruptured the entire seismogenic thickness of the region in which Wolf Fault as indicated by the aftershock sequence, in Earthquakes in they occurred. For unilateral non-subduction dip-slip earth- Kern County, California during 1952, Div. Mines, Bull., 171, 199–202. quakes, a strong preference is seen for expansion along strike in Ben-Menahem, A., Rosenman, M. & Israel, M., 1972. Source the direction opposite to the direction of rupture propagation. mechanism of the Alaskan earthquake of 1964 from amplitudes of free oscillations and surface waves, Phys. Earth planet. Inter., 5, 1–29. Subduction zone thrust earthquakes have larger and more Bodin, P. & Brune, J.N., 1996. On the scaling of slip with rupture length numerous aftershocks than earthquakes in all other tectonic for shallow strike-slip earthquakes: quasi-static models and dynamic settings. rupture propagation, Bull. seism. Soc. Am., 86, 1292–1299. For dip-slip earthquakes, the M0–L relationship for Boyd, T.M., Engdahl, E. & Spencer, W., 1995. Seismic cycles along 20 M0<10 N m is not adequately described by a single power the Aleutian arc; analysis of seismicity from 1957 through 1991, law. We show that to explain the observed relationship, fault J. geophys. Res., 100, 621–644. width must be taken into account explicitly. By consideration Brune, J.N. & Anooshehpoor, R., 2000. Failure of the standard 20 formula relating fault slip to seismic moment for thrust faults: results of only subduction zone earthquakes with 10 Nm # 2001 RAS, GJI 147, 272–293 292 C. Henry and S. Das Gesch, D.B., Verdin, K.L. & Greenlee, S.K., 1999. New land surface Scholz, C.H., 1994a. A reappraisal of large earthquake scaling, Bull. digital elevation model covers the Earth, EOS, Trans. Am. geophys. seism. Soc. Am., 84, 215–218. Un., 80, 69–70. Scholz, C.H., 1994b. Reply to comments on ‘A reappraisal of large Hanks, T.C., 1977. Earthquake stress drops, ambient tectonic stresses earthquake scaling’, Bull. seism. Soc. Am., 84, 1677–1678. and stresses that drive plate motions, Pure appl. Geophys., 115, Shaw, B.E. & Scholz, C.H., 2001. Slip-length scaling in large 441–458. earthquakes: observations and theory and implications for earth- Heinrich, P., Schindele, F., Guibourg, S. & Ihmle´, P.F., 1998. Modeling quake physics, Geophys. Res. Lett., 28, 2995–2998. of the February 1996 Peruvian Tsunami, Geophys. Res. Lett., 25, Shimazaki, K., 1986. Small and large earthquakes; the effects of the 2687–2690. thickness of seismogenic layer and the free surface, in Earthquake Henry, C., Das, S. & Woodhouse, J.H., 2000. The great March 25, Source Mechanics, eds Das, S., Boatwright, J. & Scholz, C.H., AGU 1998, Antarctic Plate earthquake: moment tensor and rupture history, geophys. Monogr., 37, 209–216. J. geophys. Res., 105, 16 097–16 119. Spence, W., 1986. The 1977 Sumba earthquake series; evidence for slab Herrin, E., 1968. Seismological tables for P phases, Bull. seism. Soc. pull force acting at a subduction, J. geophys. Res., 91, 7225–7239. Am., 58, 1193–1241. Sykes, L.R. & Quittmeyer, R.C., 1981. Repeat times of great Ihmle´, P.F., Gomez, J., Heinrich, P. & Guibourg, S., 1998. The 1996 earthquakes along simple plate boundaries, Earthquake Prediction; Peru tsunamigenic earthquake: broadband source process, Geophys. an International Review, Maurice Ewing Ser. 4, pp. 217–247, eds Res. Lett., 25, 2691–2694. Simpson, D.W. & Richards, P.G., AGU, Washington, DC. Johnson, J.M., Tanioka, Y., Ruff, L.J., Satake, K., Kanamori, H. & Wells, D.L. & Coppersmith, K.J., 1994. New empirical relationships Sykes, L.R., 1994. The 1957 Great Aleutian earthquake, Pure appl. among magnitude, rupture length, rupture width, rupture area, and Geophys., 142, 3–28. surface displacement, Bull. seism. Soc. Am., 84, 974–1002. Kanamori, H., 1970. The Alaska earthquake of 1964—radiation of long-period surface waves and source mechanism, J. geophys. Res., 75, 5029–5040. Kanamori, H. & Kikuchi, M., 1993. The 1992 Nicaragua earthquake; APPENDIX A: STABILITY OF JOINT a slow tsunami earthquake associated with subducted sediments, HYPOCENTRE DETERMINATION Nature, 361, 714–716. ALGORITHMS Kelleher, J., Sykes, L. & Oliver, J., 1973. Possible criteria for pre- dicting earthquake locations and their application to major plate For several of the aftershock sequences relocated for this study, boundaries of the Pacific and the Caribbean, J. geophys. Res., 78, the joint hypocentre determination algorithm JHD89 diverged. 2547–2585. This indicates that either the data could not adequately con- Kostrov, B.V. & Das, S., 1988. Principles of Earthquake Source strain the aftershock locations, or the starting locations were Mechanics, Cambridge University Press, Cambridge. insufficiently close to the solution, or that there were numerical Lynnes, C.S. & Lay, T., 1988. Source process of the great 1977 Sumba problems with the algorithm. In this appendix we investigate earthquake, J. geophys. Res., 93, 13 407–13 420. Mai, P.M. & Beroza, G.C., 2000. Source scaling properties from finite- the latter possibility. fault-rupture models, Bull. seism. Soc. Am., 90, 605–615. Here we briefly describe the method of joint hypocentre Parsons, T., Toda, S., Stein, R.S., Barka, A. & Dieterich, J.H., 2000. (JHD), following Douglas (1967). The equation of condition Heightened odds of large earthquakes near Istanbul: an interaction- for the location of a single earthquake is based probability calculation, Science, 288, 661–665. LT LT LT Pegler, G., 1995. Studies in seismotectonics, D.Phil thesis, University of dtzdh {dx cos aj {dy sin aj ~dTj , Oxford, Oxford. Lh j L* j L* j Pegler, G. & Das, S., 1996. Analysis of the relationship between seismic moment and fault length for large crustal strike-slip earthquakes (A1) between 1977–92, Geophys. Res. Lett., 23, 905–908. Pe´rez, O.J. & Scholz, C.H., 1997. Long-term seismic behavior of the where dt, dx, dy and dh are corrections to initial estimates of the focal and adjacent regions of great earthquakes during the time time, latitude, longitude and depth of the earthquake, Dj and between two successive shocks, J. geophys. Res., 102, 8203–8216. aj are the distance and azimuth of the jth station from the Press, W.H., Teukolsky, S.A., Vetterling, T.V. & Flannery, P.F., epicentre, Tj is the traveltime to the jth station, and dTj is 1992. Numerical Recipes in FORTRAN 77: The Art of Scientific the traveltime residual at the jth station. Computing., 2nd edn, Cambridge University Press, Cambridge. In JHD, eq. (A1) is generalized to the case of multiple Purcaru, G. & Berckhemer, H., 1982. Quantitative relations of earthquakes from a small physical region and includes, for each seismic source parameters and a classification of earthquakes, station, a correction to the traveltime table used, which is Tectonophysics, 84, 57–128. assumed to be the same for all earthquakes, and which is deter- Robinson, D.P., Henry, C., Das, S. & Woodhouse, J.H., 2001. mined as part of the solution. This may be expressed as a Simultaneous rupture along two conjugate planes of the Wharton Basin earthquake, Science, 292, 1145–1148. matrix equation: Romanowicz, B., 1992. Strike-slip earthquakes on quasi-vertical trans- Ax&b ,(A2) current faults; inferences for general scaling relations, Geophys. Res. Lett., 19, 481–484. where x is the vector of changes to the hypocentres and station Romanowicz, B., 1994. Comments on ‘A reappraisal of large earth- corrections, b is the vector of traveltime residuals and A is the quake scaling’, Bull. seism. Soc. Am., 84, 1675–1676. matrix of traveltime derivatives. Sandwell, D.T. & Smith, W.H.F., 1997. Marine gravity anomaly This equation is solved for x in the least-squares sense, from Geosat and ERS 1 satellite altimetry, J. geophys. Res., 102, and the new hypocentres are used to recalculate A and b for 10 039–10 054. Satake, K., 1994. Mechanism of the 1992 Nicaragua tsunami earth- the iteration. In the algorithm JHD89 (Dewey 1971, 1983) the quake, Geophys. Res. Lett., 21, 2519–2522. equation is first solved n1 times with depth constrained, to Scholz, C.H., 1982. Scaling laws for large earthquakes; consequences obtain initial estimates of the epicentres and station corrections, for physical models, Bull. seism. Soc. Am., 72, 1–14. and then solved a further n2 times with depth free. In this study # 2001 RAS, GJI 147, 272–293 Aftershock zones of large shallow earthquakes 293 } Figure A1. (a) Relocation of an aftershock (1996 February 22, 10:58:46) of earthquake 56 of Table 1. Cross shows ISC location of aftershock, used as the initial location. The solid line shows the path taken by the aftershock during relocation using JHD89-SVD, the solid circle shows the relocated position obtained, and the 90 per cent confidence ellipse is shown. Dashed line shows the path taken by the aftershock during unsuccessful relocation using JHD89, for which division by zero occurred on the seventh iteration. The location of the aftershock after each iteration is indicated by a number corresponding to the iteration. (b) Same as (a) for the aftershock (1995 February 15, 23:36:12) of earthquake 45 of Table 1. Symbols same as (a), except that dashed line shows path taken by aftershock during successful relocation using JHD89, the open circle shows the relocated position obtained, and the 90 per cent confidence ellipse obtained using JHD89 is shown dashed. we use n1=4 and n2=6. In the algorithm JHD89, eq. (A2) is compared the results of JHD89 and JHD89-SVD for after- solved by forming the matrix of normal equations (Press et al. shock sequences that had not diverged under JHD89. In most 1992), and using Gaussian elimination for the first n1+n2x1 cases, the two solutions followed identical or near-identical paths. iterations. In the last iteration, Gauss–Jordan elimination is However, for a few cases such as the aftershocks of earth- used, which simultaneously determines both x and the inverse quake 45 of Table 1, of which an example is shown in Fig. A1(b), of the matrix of normal equations, which is used in the the two solutions do differ after the fourth iteration, but the determination of error ellipses. In this study, the algorithm is numerical error is sufficiently small that JHD89 remains con- implemented at 32-bit precision. vergent, and regains numerical stability as it approaches the To assess the stability of JHD89, a we used a modified solution. The two algorithms JHD89 and JHD89-SVD arrive algorithm JHD89-SVD, which solved eq. (A2) directly using at the same solution by two different paths, and the small the method of singular value decomposition (SVD) (Press et al. difference seen between the locations, representing incomplete 1992), implemented at 64-bit precision. Direct solution of convergence, is insignificant in comparison to the formal location eq. (A2) is intrinsically more stable than solution of the normal errors. equations, and SVD allows the identification of null and near- The greater stability of Gauss–Jordan elimination in com- null vectors in the solution space, which can then be excluded parisontoGaussianelimination(e.g.Presset al. 1992) motivates from the solution if necessary. Its only drawback is that it is us to investigate a third algorithm, JHD89-M, which solved the significantly slower than Gaussian elimination or Gauss–Jordan normal equations using Gaussian elimination for the first n1 elimination. inversions, with depth fixed, and Gauss–Jordan elimination for It was found that all cases that had diverged when all subsequent inversions, implemented at 32-bit precision. This solved using JHD89 converged when solved using JHD89- produces identical solutions to JHD89-SVD for all cases that SVD, without the need to exclude any near-null vectors from we tested, indicating that the greater precision and stability of the solution, indicating that the source of the divergence was a JHD89-SVD is not required by the present problem. We used numerical instability in JHD89. Fig. A1(a) shows an example JHD89-M for all inversions in this study. of the behaviour of one aftershock during the relocation of the We recommend that authors using the method of joint aftershock sequence of earthquake 56 of Table 1. JHD89 and hypocentre determination should compare their algorithms JHD89-SVD give identical results for the first four iterations. against a high-precision alternative, preferably based on direct However, when the depths are allowed to vary in the sub- solution of eq. (A2) using SVD, for a few cases that have not sequent iterations, the solutions differ, and on the seventh converged using their algorithms. It is possible that in such iteration, division by zero occurs in JHD89. Similar behaviour cases the divergence may be due to numerical instabilities, was shown for all cases that diverged under JHD89. We also rather than being entirely due to poor data quality. # 2001 RAS, GJI 147, 272–293