strong ground motion in normal-faulting earthquakes - geophysical

Geophysical Journal (1989) 96, 529-559

Strong ground motion in normal-faulting earthquakes

Rob Westaway*,$ and Robert B. Smith? * Department of Earth Sciences, University of Liverpool, Liverpool L69 3BX, UK and -f Department of Geology and Geophysics, University of Utah, Salt Lake City, UT 84112, USA

Accepted 1988 August 19. Received 1988 August 19; in original form 1988 February 15

SUMMARY We investigate the character of strong ground motion in normal-faulting earthquakes from the western USA, Italy, Greece, Turkey and New Zealand, with magnitudes from 4 to 7.5.

In all cases where seismic phases can be identified, peak horizontal ground acceleration occurs in the direct S-phase. Crustal anelasticity for S-waves, which varies locally, is shown for events above magnitude 5 at distances of tens of km to be relatively unimportant in comparison with geometrical spreading in determining the variation of peak horizontal ground acceleration with source-station distance. This permits us to treat our set of records, regardless of source region, as a single worldwide data set. For events between magnitudes 4 and 5, peak horizontal ground acceleration appears not to be controlled by geometrical spreading. At source-station distances greater than about 10 km, it decreases approximately in inverse proportion to distance squared.

Earthquakes with magnitudes greater than 5 cause ground acceleration equivalent to that in reverse-faulting and strike-slip events. This result contradicts the widely held view that normal-faulting earthquakes generate systematically smaller ground accelerations than other events. It implies that the orientation of the crustal stress-field, which will be very different in extensional regions from other regions, has little effect on the amplitude of high-frequency seismic waves generated by earthquakes.

Key words: acceleration, earthquake, normal faulting, strong ground motion

1 INTRODUCTION involves normal-faulting earthquakes with a substantial

Knowledge of the character of ground acceleration expected close to the sources of moderate and large earthquakes is important in the design of earthquake-resistant structures. The response of any structure depends on the duration of earthquake-induced ground motion, and the relationship between its frequency content and natural resonant frequencies of the structure, as well as on the strength of the ground acceleration observed or predicted at the site in the absence of the structure. Our analysis is restricted to the strength of ground shaking, expressed as peak horizontal ground acceleration (PHGA). Although this provides an incomplete description of the character of strong ground motion, it has been widely used in many previous studies. Normal-faulting earthquakes occur in many actively- extending continental regions, including parts of the Basin and Range province of the western USA (e.g. Doser 1985), Italy (e.g. Westaway & Jackson 1987), the Aegean Sea and surrounding regions of Greece and western Turkey (e.g. Jackson et al. 1982a, b; Eyidogan & Jackson 1985), China (e.g. Deng et al. 1984) and New Zealand (e.g. Walcott 1984), and in some other much less active intraplate regions also. In Great Britian, the low level of seismic activity

component of strike-slip faulting (e.g. Ansell e i al. 1986; Marrow & Walker 1988). Much of the work that has been camed out in the past aimed at quantifying PHGA has used information from reverse-faulting and strike-slip earthquakes that predominate in California. It is not clear a priori to what extent results established for this region need to be modified to be appropriate for other regions, where differences in focal mechanism orientations and/or in crustal structure may affect observed PHGA.

Several lines of evidence have suggested that, after taking into account source-station distance and earthquake magnitude, PHGA may be significantly smaller for normal-faulting earthquakes than for reverse-faulting or strike-slip events. First, Campbell (1981), in a study of strong ground motion in a worldwide set of earthquakes that included two normal-faulting events, suggested that PHGA was 28 per cent larger for reverse-faulting earthquakes than for other events. Second, McGarr (1984), in a similar study, defined a scaled parameter proportional to PHGA, which he showed was only about 33 per cent as large for his set of normal-faulting earthquakes as for other events. McGarr (1984) drew attention to the limited damage resulting from the large (M, 7.3) normal-faulting earthquake of 1983

$Present address: Department of Geological Sciences, University , of Durham, Durham DH1 3LE, UK.

October 28 at Borah suggesting that this may have been the result of anomalously

Idaho, in the

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low ground acceleration in the epicentral region. Finally, the pattern of crustal deformation in normal-faulting earthquakes, in which the principal effect is subsidence of the hanging wall of the normal fault, may also affect observed PHGA. Some models of lithosphere rheology (e.g. Kusznir & Park 1986) suggest that the distribution of stress at mid-crustal depths, where large earthquakes usually nucleate (e.g. Sibson 1982; Smith & Bruhn 1984), can be very different in an extensional region from that expected in compression. If the coefficient of friction across a fault is about 0.5, a plausible value, the deviatoric stress required to initiate brittle failure is only about one third as great for normal faulting as for reverse faulting (Turcotte & Schubert 1982; p. 355). This is because in normal faulting the principal stress is assisted by gravity, whereas gravity must be overcome before reverse-faulting slip can occur. If this is a correct description of the physics of faulting, then it suggests that normal-faulting earthquakes may have significantly smaller stress drops than other events. Some dynamic theories of fault rupture (e.g. Boatwright 1984) suggest that ground acceleration is proportional to stress drop. Consequently, smaller PHGA may be expected for normal-faulting earthquakes than for other events.

The first two arguments are based on analyses of limited amounts of observational data for large normal-faulting earthquakes, and the results obtained by McGarr (1984), in particular, have been reviewed by Campbell (1987). The third argument depends on knowledge of stress drop, a source parameter that is difficult to measure reliably. Given these limitations, we have collected as many strong motion records for normal-faulting earthquakes as possible, and have compared the observed ground accelerations with those predicted for other events using empirical laws. In making this comparison, we have defined as a normal- faulting earthquake any event for which the focal mechanism is a double couple with a rake angle between -50" and -130", using the coordinate system of Aki & Richards (1980; p. 115). To anticipate our conclusions, we find that PHGA for normal-faulting earthquakes is not significantly different from that predicted using empirical laws for reverse-faulting and strike-slip events.

In Section 2, we summarize our collection of strong ground motion records and earthquake source parameters. This collection comprises 93 sets of ground acceleration records for normal-faulting earthquakes with magnitude 5 or greater, and 150 sets for events between magnitudes 4 and 5. This is much more information than has been used in previous studies of strong ground motion in normal-faulting earthquakes, and is comparable to the amounts used in the derivation of some established empirical laws for prediction of ground acceleration. In Section 3, we discuss the timing of PHGA in our records. We show that for records from sufficiently close to the earthquake sources for seismic phases to be reliably identifiable, PHGA occurs during the direct S-phase. Taking plausible estimates of crustal anelasticity for S-waves, it appears that geometrical spreading is likely to be more important than crustal anelasticity, particularly for the largest events, in determining the variation of PHGA with distance when up to tens of km from earthquake sources. Having established that over this distance range PHGA does not depend critically on anelasticity, which is likely to vary with source region, our

R. Westaway and R . B. Smith

records may be merged into a worldwide data set. In Section 4, we compare these observed ground accelerations with those predicted using two established empirical laws. This comparison incorporates estimates of the uncertainty with which PHGA and earthquake source parameters can be measured.

2 SOURCES OF STRONG GROUND MOTION RECORDS A N D OTHER INFORMATION

In investigating the dependence of PHGA on earthquake source parameters, it is important to include records from earthquakes with a wide range of magnitudes, recorded over a wide range of source-station distances, to be able to separate distance-dependence and magnitude-dependence of PHGA. Smaller earthquakes are much more numerous, and can contribute large amounts of information. However, smaller events are much less important as far as earthquake hazard is concerned. When collecting strong ground motion records, we therefore established a cutoff magnitude below which records were disregarded.

Several past studies of strong ground motion, including those by Campbell (1981) and Joyner & Boore (1981), who devised the empirical laws that we will test in Section 4, were concerned only with earthquakes above magnitude 5 . We chose a lower cutoff magnitude (either M, or ML) of 4 instead (Table 1). This is because, first, earthquakes with magnitudes between 4 and 5, including the Denizli, Turkey, event of 1976 (Ates 1985), and some events from the Ancona, Italy, swarm of 1972 (Lander 1973), have caused substantial damage. Second, in some relatively inactive regions, such as Great Britain, whatever small earthquake hazard exists is predominantly due to events about or below magnitude 5 (e.g. Neihon & Burton 1985). Third, this lower magnitude cutoff enables investigation of whether the variation of ground acceleration with source-station distance for these smaller events corresponds with what occurs for larger events. No earthquake below magnitude 4 appears to have caused significant damage and many below magnitude 4 are located in routine studies with great uncertainty. An extreme example is the event at 19:21 on 1972 February 14 (mb 3.8), from the Ancona, Italy, swarm of crustal earthquakes, from which we obtained a set of strong ground motion records. This event was located by the US National Earthquake Information Service (NEIS) at an implausible depth of 183 km. Consequently, we excluded all events below magnitude 4.

PHGA decreases rapidly as source-station distance increases. Consequently, it is important to use estimates of source-station distance that are as reliable as possible. We have therefore compiled both source and station coordinates, and used these to calculate this distance. This contrasts with the some earlier studies (e.g. Joyner & Boore 1981; Campbell 1981; Sabetta & Pugliese 1987), where source- station distances have been used without specifying the earthquake location methodology or listing the hypocentral or station coordinates. Documenting only distances and not coordinates does not imply that these earlier studies were not camed out carefully. Nonetheless, sometimes (e.g. for the Oroville, California, mainshock of 1975 August l), distances used in earlier studies appear to be based on

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Ground motion in earthquakes 531

Table 1. Earthquakes with magnitude 4 or greater included in our study. We list the data and time of each event; the number, N, of sets of records available; magnitudes M,, M, and ML; and a reference code confirming that the event involved normal faulting.

Date Time N M, M w ML

1935 Oct 31 1935 Nov 28 1935 Nov 28 1949 Apr 13 1959 Aug 18 1962 Aug 30 1972 Feb 6 1972 Feb 8 1972 Jun 14 1972 Jun 14 1972 Jun 21 1974 Jan 29 1975 Apr 4 1975 May 13 1975 Oct 12 1975 Aug 1 1975 Aug 2 1975 Aug 2 1975 Aug 3 1975 Aug 3 1975 Aug 6 1975 Aug 8 1975 Aug 11 1975 Aug 16 1975 Sep 26 1975 Sep 27 1976 Aug 19 1977 Dec 9 1977 Dec 16 1978 Jun 20 1979 Jul 18 1979 Sep 19 1980 May 25 1980 May 25 1980 May 25 1980 May 27 1980 May 27 1980 May 28 1980 May 28 1980 May 31 1980 May 31 1980 May 31 1980 May 31 1980 Jun 5 1980 Nov 23 1980 Nov 23 1980 Nov 24 1980 Dec 1 1981 Jan 16 1981 Feb 24 1981 Feb 25 1983 Jul5 1983 Oct 28 1983 Oct 29 1983 Oct 29 1983 Oct 30 1983 Oct 30 1983 Nov 2 1983 Nov 6 1984 Apr 29 1984 May 7 1984 May 11 1984 May 11 1984 May 11 1984 May 11 1984 May 11 1984 May 11 1984 May 11 1986 Sep 13

18:37 14:41 14:42 19:55 06:37 13:35 21:44 12:19 185.5 21:Ol 15:06 15:12 05:16 OO:22 08:23 20:20 20:22 20'59 01:03 02:47 0350 07:OO 06:ll 0548 02:31 22:34 01:12 1553 07:37 20:03 13:12 21:35 16:33 16:49 19:44 14:51 19:Ol M:03 0516 0058 1 O : l l 15:16 1520 19:41 18:34 18:35 OO:23 19:04 OO:37 20:53 02:35 12:Ol 1496 23 : 29 23:39 01:24 0159 23:43 21:04 05:m 17:49 10:41 10:50 11:26 13:14 13:39 16:39 23:35 17%

1 1 1 1 2 1 1 2 2 2 3 1 1 1 1 5 2 3 7 8

10 9 9

11 10 10 1 1 1 1 1 5 1 1 1 3 1 4 4 5 5 3 4 2

21 12 1 4 8 1 1 5 6 3 3 1 1 2 3 5

15 10 2 6 6 2 4 3 1

(6.0) (5.8) (5.8) 7.1 7.5 5.7

(3.5) (3.9)

(3.3) (2.7) (3.5)

(3.9) (4.5)

4.6

4.6

5.7 4.5 4.7

(4.5) (3.7)

(4.5) (4.3) (3.3) (2.9) (5.0)

(4.3)

4.0

4.9

4.9 6.4 4.9 5.5 6.1

6.0 6.0 3.4 2.6 3.7 2.7 3.0 3.7 2.9 2.4 6.8

4.7 4.6 4.7 6.7 6.4 5.8 7.3 4.9 5.0

(5.6)

(6.3)

(3.5) (3.1) (3.5) (3.3) 5.2 5.8 5.2

5.9

6.72 7.31

4.95 4.32 4.79 4.34 4.72 4.65 4.44 4.13 4.19 4.60

6.19:

5.89: 5.85* 4.58 3.98 4.62 4.35 4.18 4.69 4.01 4.05 6.92: 6.28

6.67* 6.36: 6.10: 6.% 5.47: 4.69 4.34 4.16 4.10 4.15 5.65 5.89 5.49

5.90

(6.0) (5.8) (5.8)

5.7 (4.4) (4.6) 4.7 4.7 4.0 4.4 5.1

4.6 5.7 5.1 5.2 4.6 4.1 4.7 4.9 4.3 4.0 4.0 4.6 4.7 4.9 5.3

5.2 5.9 6.1 6.0 6.1 6.2 4.8 3.9 4.9 4.5 4.2 4.9 4.0 4.3

(4.6)

5.9

5.8 5.4 4.8 4.7 4.2 4.6 5.0 5.7 5.4 4.2 4.2 4.3 4.1 4.3 4.1 6.0

FA76

BL87 DD85 ss74

GA85

LB76 FA84 FA84 FA84 FA84 FA84 FA84 FA84 FA84 FA84 FA84

JB82 SS81

DS84 ED85

ED85 ED85

AA82 PA85

AA82 BA81 WJ87

JA82 JA82 DA84 ED85 ED85 RA87 RA87

RA87 RA87 DA85 DA85 DA85

LA87

Helena, MT Helena, MT Helena, MT Puget Sound, WA Hebgen Lake, MT Cache Valley, UT Ancona, Italy Ancona, Italy Ancona, Italy Ancona, Italy Ancona, Italy Patras, Greece Patras, Greece Xylokastron, Greece Corinth, Greece Oroville, CA Oroville, CA, aftershock Oroville, CA, aftershock Oroville, CA, aftershock Oroville, CA, aftershock Oroville, CA, aftershock Oroville, CA, aftershock Oroville, CA, aftershock Oroville, CA, aftershock Oroville, CA, aftershock Oroville, CA, aftershock Denizli, Turkey Izmir, Turkey Izmir, Turkey Thessaloniki, Greece Dursunbey, Turkey Norcia, Italy Mammoth Lakes, CA Mammoth Lakes, CA Mammoth Lakes, CA Mammoth Lakes, CA Mammoth Lakes, CA, aftershock Mammoth Lakes, CA, aftershock Mammoth Lakes, CA, aftershock Mammoth Lakes, CA, aftershock Mammoth Lakes, CA, aftershock Mammoth Lakes, CA, aftershock Mammoth Lakes, CA, aftershock Mammoth Lakes, CA, aftershock Campania, Italy Campania, Italy Campania, Italy, aftershock Campania, Italy, aftershock Campania, Italy, aftershock Corinth, Greece Corinth, Greece Biga, Turkey Borah Peak, ID Borah Peak, ID, aftershock Borah Peak, ID, aftershock Borah Peak, ID, aftershock Borah Peak, ID, aftershock Borah Peak, ID, aftershock Borah Peak, ID, aftershock Gubbio, Italy Abruzzo, Italy Abruzzo, Italy Abruzzo, Italy, aftershock Abruzzo, Italy, aftershock Abruzzo, Italy, aftershock Abruzzo, Italy, aftershock Abruzzo, Italy, aftershock Abruzzo, Italy, aftershock Kalamata, Greece

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Table 1. (Continued)

Date Time N M, M w ML

1986 Sep 15 11:41 2 4.9 Kalamata, Greece, aftershock 1987 Mar 2 01:35 1 5.2 Edgecumbe, New Zealand 1987 Mar 2 01:42 3 6.6 6.63 6.3 WS88 Edgecumbe, New Zealand 1987 Mar 2 0151 1 5.6 Edgecumbe, New Zealand

A value for Ms in brackets indicates an approximate surface-wave magnitude derived from mb using the relation of Marshall (1970). For the Helena earthquakes, Ms was obtained from felt area, as reported by Coffman & von Hake (1973). We estimated moment magnitude M, of the Edgecumbe event from the dimensions of the fault plane (Beanland & Blick 1987). Other M, values were calculated using the relation of Hanks & Kanamori (1979) from estimates of seismic moment. Most estimates of seismic moment were derived from spectral studies of body-wave phases recorded in the near-field (sometimes as the average of two or more independent results). M, values marked with an asterisk have been obtained from long-period teleseismic waveforms using the CMT inversion technique of Dziewonski et al. (1981). These moments have been taken from either Boschi et al. (1981), Dzeiwonski & Woodhouse (1983), Dziewonski, Franzen & Woodhouse (1984) or Ekstrom & Dziewonski (1985). Codes for focal mechanisms denote: AA82, Archuleta er al. (1982); BA81, Boschi et al. (1981); BL87, Baker & Langston (1987); DA 84, Dziewonski et al. (1984); DA85, Dziewonski, Franzen et al. Woodhouse (1985); DD85 Doser (1985); DS84, Deschamps, Iannacone & Scarpa (1984); ED85; Ekstrom & Dziewonski (1985); FA76, Friedline, Smith & Blackwell (1976); FA84, Fletcher et al. (1984); GA85, Gasparini et al. (1985); JA82, Jackson et al. (1982a); JB82, Jackson et al. (1982b); LA87, Lyon-Caen et al. (1987); LB76, Langston & Butler (1976); PA85, Priestley et al. (1985); RA87, Richins et al. (1987); SS74, Smith & Sbar (1974); SS81, Soufleris & Stewart (1981); WJ87, Westaway & Jackson (1987); WS88, Westaway & Smith (1988; this study).

preliminary estimates of coordinates, and may be several km from later estimates obtained after more detailed investigation and likely to be more reliable. If the source and station coordinates used were both available, these cases would be much more straightforward to identify. With one exception, we have included only events that we consider, given the uncertainties in their locations, to have occurred in the uppermost 20 km of the crust. The exception is the Puget Sound, Washington, event of 1949 Arpil 13 (depth 54 km; Baker & Langston 1987), included on account of the great interest at present in earthquake hazard caused by the possible Benioff zone beneath the northwestern USA (e.g. Heaton & Kanamori 1984).

The strong motion records available can be grouped into four categories, according to their quality. First, in the highest-quality category, are records from digital recording systems such as GEOS (Borcherdt et al. 1985). Second, are analogue records digitized using scanners; third, analogue records digitized by hand; and finally, reproductions or tracings of analogue records, not in machine-readable form. In some cases we have included peak acceleration values, tabulated by other people, for significant earthquakes for which strong motion records were not available in any form (Table 2).

2.1 Accelerograph station coordinates and instrumental response

Most station coordinates, instrumental frequency responses and orientations of the three components of ground motion were available from the same sources as the records, either as machine-readable documentation, or listed in notes or other publications. However, in a few cases, mentioned below and in Table 2, this additional information was obtained elsewhere. In some cases, station coordinates were not tabulated, but only marked on local large-scale maps. If a station site was named, and neither tabulated coordinates nor a local map was available, we used the coordinates of the named locality measured either from US Geological

Survey (USGS) 1 : 250 OOO scale maps covering the western USA or US Defense Mapping Agency 1:5OOOOO scale Tactical Pilotage Charts covering the eastern Mediter- ranean. We also checked the coordinates of stations in the western USA against lists prepared by US Geological Survey (1977). Most records included the instrumental response but in a few cases this had been removed to give true ground acceleration. On the basis of tectonic and geographical setting, the data collected can be grouped into eight regional categories: Borah Peak, Idaho; Mammoth Lakes, California; Oroville, California; earlier western USA events; and Italian, Greek, Turkish and New Zealand earthquakes.

The Borah Peak, Idaho, mainshock of 1983 October 28 (Ms7.3; Mo 31 X 1018Nm) was recorded by accelerographs at the Idaho National Engineering Laboratory, about 80 km SE of its epicentre (Jackson & Boatwright 1987). We have used tabulated values of ground acceleration, after removal of the instrumental response, for six of these stations. Several of its larger aftershocks were recorded by temporary accelerographs deployed by the USGS in the epicentral area following the mainshock. We obtained, by courtesy of J. Boatwright, 38 sets of records of aftershocks with ML > 3.5, recorded using GEOS digital instruments operated by the USGS, Menlo Park, California. We also obtained, by courtesy of A. Espinosa, four sets of records for two of the largest aftershocks with ML about 5 , recorded using analog SMA-1 instruments installed by the USGS, Boulder, Colorado.

The Mammoth Lakes, California, earthquake sequence of 1980 May-June provided the largest number of records available to us. The four large events that began the sequence, at 16:33 (M, 6.1; Mo 2.2 x lOl'Nm), 16:49 (Ms approximately 5.6) and 19:44 (M, 6.0; Mo 0.77 x 10l8 Nm) on May 25, and at 14:51 on May 27 (M, 6.0; Mo 0.67 x 10l8 Nm), were recorded by the permanent analog accelerograph station at Long Valley Dam (LVD) (see, e.g. Porcella 1983), and at several more distant stations. We note that the coordinates of the station LVD were

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Caltech, and supplied to us from the archive at the Department of Civil Engineering, Imperial College London (ICL). In this archive the station site is incorrectly listed as Carroll College, Helena. Tracings of the records of the two events of November 28 were published by Ulrich (1936) and by Neumann (1937). Both Ulrich (1936), who was in charge of the installation of the instrument, and Neumann (1937) indicate the polarity of each record, while Neumann (1937) also lists the instrumental response. The instrument comprised three overdamped accelerometers, each with natural frequency about 10 Hz. These records are thus better documented than many from more recent earthquakes.

Our Italian strong records are from the Campania- Basilicata sequence of 1980, the central Italy sequence of 1979-1984, and the Ancona sequence of 1972. The Campania-Basilicata mainshock, which occurred at 18 : 34 on 1980 November 23 (M, 6.8; Mo 26 x 1018Nm), was the largest normal-faulting earthquake in Italy for many years. It was recorded by 21 SMA-1 analogue accelerograph stations of the national network (Basili 1987) operated by the Italian nuclear energy authority, and situated between about 20 and about 150 km from its nucleation point. Records from the closest stations were digitized using a scanner, and the remainder by hand (Beradi, Berenzi & Capozza 1981; Fels, Pugliese & Muzzi 1981). They were supplied to us by courtesy of M. Peronaci and D. Rinaldis of the Italian nuclear energy authority. Station coordinates, listed by Berardi et al. (1981), were checked by Westaway (1985) who found that the positions of several stations were inaccurately listed and corrected them using large-scale maps. Bernard & Zollo (1987) have suggested that Berardi et al. (1981) incorrectly reported the coordinates of one further station, Calitri (CL3), and that its true position was approximately 2km south of the published position. This 2km offset is smaller than the uncertainties in the locations of the Campania-Basilicata events, and will have negligible effect on our results. We have used the published coordinates of this station. This earthquake involved a complex pattern of fault ruptures lasting for more than 40 s (see, e.g. Westaway & Jackson 1987). One fault rupture sub-event, about 38s after the origin time of the earthquake, is sufficiently distinct from the earlier ruptures that we treat it as a separate event. Aftershocks were recorded by some of these permanent stations and by additional temporary accelerograph stations deployed in the epicentral area. One of the larger aftershocks, at 00:23 on November 23 (M, 4.7), was recorded at Calitri; records were available from the archive at ICL. Twelve further sets of records, from aftershocks at 19:W on 1980 December 1 (ML 4.6) and at 00:37 on 1981 January 16 (ML 4.7) have been documented by Sabetta & Pugliese (1987). The archive at ICL also supplied 14 sets of records from four stations, three SMA-1 (Palombina or PB1, Rocca or RC1 and Torre d'Ago or TA1) and one AR-240 (Vigil del Fuoco or VF1) for nine earthquakes of the Ancona, northern Italy, swarm of 1972 February-June, with magnitudes (ML) up to 4.7. No information was available concerning the coordinates of station Rocca, and we have used those of the centre of the village of Rocca, several km west of Ancona. Several of these small events generated PHGA of approximately 3 m s-', and caused considerable damage. Nineteen further sets of records, from

incorrectly listed by US Geological Survey (1977), but have subsequently been corrected by Switzer (1981). The May 27 event and many smaller aftershocks were also recorded by a temporary network of DR-100 digital instruments operated by the USGS (Mueller et al. 1981). Due to the large number of records available from this network, we restricted our investigation to those available for events that have already been studied in detail by Archuleta et al. (1982). We obtained 122 sets of records for these events from the USGS, Menlo Park, including two for the event at 14:51 on May 27.

The Oroville, California, earthquake (ML 5.7) of 1975 August 1 was recorded by five analogue accelerograph stations, of which three were SMA-1 instruments. Tracings of records from two stations, Oroville Dam Station (ODs), an AR-240 instrument, and Oroville Dam Crest (ODC), a USGS standard instrument, were published by Maley et al. (1976). Also, 14 aftershocks with ML up to 5.2 were recorded by a temporary network of similar analog instruments, installed by the USGS and the California Division of Mines and Geology. The 111 hand-digitized sets of records available (also from USGS, Menlo Park) from this temporary network have already been investigated in detail by Fletcher et al. (1984).

We have also obtained information from four earlier significant earthquakes or earthquake sequences in the western USA: the Cache Valley, Utah, event of 1962 August 30; the Hebgen Lake, Montana, event of 1959 August 18; the Puget Sound, Washington, event of 1949 April 13; and the Helena, Montana, events of 1935 October and November. The Cache Valley event (ML 5.7) was recorded by an analogue accelerograph station at Utah State University in Logan, Utah. Records from this instrument were digitized using a scanner at California Institute of Technology (Caltech) (Smith & Lehman 1979), and the instrumental response was removed using the procedure of Trifunac & Lee (1973). The Hebgen Lake earthquake was the largest (M, 7.5; M, 100 X 10"Nm) normal-faulting event in the western USA this century (Doser 1985). Tracings of analog records from Butte, Montana, and Bozeman, Montana, were published by Eppley & Cloud (1961). Although these records are from epicentral distances greater than 100 km, PHGA of about 1 m s-' was observed. Similarly high PHGA values have also been reported in the distance range 60-150km by Burger et al. (1987), for earthquakes in eastern North America. In Sections 3 and 4 we consider further their suggestion that these high accelerations are a consequence of S-waves being guided within the crust. The Puget Sound event was recorded by accelerographs at Olympia Highway Test Center (OHT) and Seattle. The records from OHT were published by Baker & Langston (1987). The earthquake swarm around Helena that began on 1935 October 4 involved significant events at 07:51 on October 12 (magnitude about 5.7), at 04:48 on October 19 (6.3) and at 18:37 on October 31 (6.0), and at 14:41 and 14:42 (magnitude about 5.8) on November 28 (Coffman & von Hake 1973). Following the largest event on October 19, a three-component accelerograph was brought from California and installed in the Federal Building in Helena, where it recorded the events of October 31 and November 28. The records of the October 31 event were digitized by hand at

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534 R. Westaway and R . B. Smith

moderate-sued earthquakes in central Italy between 1979 and 1984, have been documented by Sabetta & Pugliese (1987). These include five from the Norica event at 21:35 on 1979 September 19 (M, 5 . 9 , five from the Gubbio event at 05 : 02 on 1984 April 29 (Ms 5.2), and seven and five from the Abruzzo events at 17:49 on 1984 May 7 (M, 5.8) and at 1 U : l l on 1984 May 11 (M,5.2). Additional scanner- digitized records from the Abruzzo events and six smaller aftershocks were obtained from ICL.

Our Greek records are from two Kalamata earthquakes of 1986 September, the two large Gulf of Corinth events of 1981 February, the Thessaloniki mainshock of 1978 June, and four earlier Gulf of Corinth events during 1974-1975. The Kalamata mainshock at 17:24 on 1986 September 13 (Ms5.9), in southern Greece, was recorded by one SMA-1 instrument in Kalamata. The largest aftershock, at 11 : 41 on September 15 ( M L 4.9), was recorded by the same instrument and by another installed nearby. Tracings of all three sets of records have been published by Papastamatiou, Elnashai & Pilakoutas (1987a), and other documentation has been published by Papastamatiou et al. (1987b), and, in summary form, by Person (1987). The Gulf of Corinth earthquakes, which occurred in central Greece at 20:53 on 1981 February 24 (Ms6.7; M, 11.4 X 101"Nm), and at 02:35 on 1981 February 25 (M, 6.4; M, 3.9 X 101"Nm), were recorded by SMA-1 accelerographs at Corinth and Xylokastron. Tracings of the sets of records from Corinth station have been published by Carydis et al. (1982). The Thessaloniki, northern Greece, earthquake at 20 : 03 on 1978 June 20 (M, 6.4; M, 5.2 x 101'Nm) was recorded by a SMA-1 accelerograph at Thessaloniki, for which hand- digitized records were available from ICL. These were incorrectly documented as being from the aftershock of July 4. However, Soufleris (1980) showed tracings of records from both the June 20 and July 4 events, enabling our set of hand-digitized records to be correctly identified. Hand- digitized records of four smaller earthquakes from the eastern Gulf of Corinth have been published by Brady et al. (1978). We regenerated the digitized time series from these tabulated values. The four earthquakes occurred near Patras at 15: 12 on 1974 Jaunary 29 (ML 4.4) and at 05: 16 on 1975 April 4 (ML 5.1), near Xylokastron at 00: 22 on 1975 May 13 (ML 4.6), and near Corinth at 08:23 on 1975 October 12 (ML 4.6). Each of these events was recorded at a single accelerograph station.

Our data set for western Turkish earthquakes comprises five events, recorded at eight stations operated by the Turkish Ministry of Public Works Earthquake Research Institute (ERI) in Ankara. Tracings of records from SMA-1 or similar instruments have been published either by Ate8 & Bayulke (1981) or by Ate8 (1985). These events occurred near Denizli at 01: 12 on 1976 August 19 (ML 4.7), near Izmir at 15:53 on 1977 December 9 (ML 4.9) and at 07:37 on 1977 December 16 (ML 5.3), near Dursunbey at 13: 12 on 1979 July 18 (ML 5.2), and near Biga at 12:Ol on 1983 July 5 (ML 5.9; M, 5.8; M, 1.6 x 10'" Nm). Ate9 (1985) mistook the records of the Biga event for those of a much smaller aftershock 3 h later. Station coordinates for the first three events were measured from large-scale maps published by Ate8 (1985). For the other stations triggered, at Balikesir, Dursunbey, Edincik, Edremit, Gonen and Tekirdag, which we have designated BSR, DSB, EDK, EDR, GON and

TRD, we used the coordinates of the centres of these villages.

Our data set from New Zealand consists of records of the Edgecumbe events (Beanland 8c Blick 1987; New Zealand Department of Scientific and Industrial Research 1987) that occurred in the North Island of New Zealand on 1987 March 2. A foreshock ( M L 5.2) at 01:35 was followed by a mainshock at 01:42 (M, 6.6; M, approximately 10 X 1018Nm), which was in turn followed by a sequence of moderate-sized aftershocks, the first of which occurred at 01:51 ( M L 5.6). The mainshock was recorded at Matahina Dam, about 20km south of its epicentre, by five three-component New Zealand MO analogue accelerographs installed in different parts of the dam. We have obtained, by courtesy of G. McVerry, tracings of records from station D at the base of the dam, which we have designated MDD. This instrument is likely to have been the least affected by the presence of the dam. This same instrument also recorded the foreshock and aftershock. The mainshock was also recorded by two similar stations at Maraenui Primary School (MPS) and at Wairoa Telephone Exchange ( W E ) . The records have been digitized and band-pass filtered to eliminate signal below 0.1 Hz and above 25.5 Hz.

We excluded many other records, either because they were reproduced too badly to be legible, or because, due to the absence of absolute timing, they could not be unambiguously associated with any earthquake, because the station coordinates could not be determined, or, for some smaller events, because we were not confident that their sources involved normal faulting.

The records represent many types of instrument, plus a few from which the instrumental response has been removed. The majority of the analog records are from SMA-1 or similar instruments, with natural frequency about 25Hz and damping about 0.6 of critical. The DR-100 and GEOS data sets were digitally recorded using sensors with damping also about 0.6 of critical, and with anti-aliasing filters that removed signal above 50 Hz. A damping value of 0.6 leads to a roughly uniform amplitude response up to the natural frequency, and a roughly constant phase relationship between the ground acceleration and the record. Published body-wave spectra of events between magnitudes 5 and 6 (e.g. Archuleta et al. 1982) from instruments with 50Hz natural frequency show relatively little signal content above about 20Hz. Also, for events above magnitude 5 the pulse that contains the peak acceleration usually has a duration much longer than 0.1 s, so that substantial signal content at frequencies of the order of tens of Hz is not expected. Furthermore, when some Borah Peak aftershocks were recorded by both 25 Hz and 50 Hz sensors at adjacent sites, both types of instrument gave comparable PHGA (Table 2). These observations suggest strongly that, as long as the natural frequency of the sensor is 25Hz or greater, the observed PHGA is not sensitive to the precise value of the natural frequency. Consequently, we have not attempted to substitute the response of an instrument with 25 Hz natural frequency onto records with broader instrumental bandwidth. Some European countries, including Romania, operate accelerograph stations using the Japanese SMAC recorder (e.g. Brady et af. 1978; Campbell 1981). These instruments have natural frequency about 10 Hz, within the

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range at which substantial ground accelerations are expected, leading to a loss of signal at higher frequencies and possibly to a smaller PHGA than would be observed on an instrument with broader bandwidth. Records are also skewed by the arcuate pen traverse of the SMAC recorder, which is difficult to correct for after digitization. Consequently, measurements of PHGA on SMAC records are difficult to compare with measurements from other instruments. However, none of the records that we obtained was from this type of recorder.

2.2 Earthquake magnitudes Some earthquakes for which we have obtained records, including the Borah Peak and Campania-Basilicata events, have been studied in detail by many people, while others, including some in Greece and western Turkey in the 1970s, appear to have only been investigated by agencies carrying out routine locations for their bulletins. We have compiled information on earthquake source parameters that is as uniform in quality as possible, given this variation in the extent to which earthquakes have been studied. Our primary source of information has been the Bulletin of the International Seismological Centre (ISC), which provides hypocentral coordinates, local magnitudes, ML (determined using procedures that vary between source regions), and body-wave magnitudes, mb. For events above magnitude 5, surface-wave magnitude, M,, is also listed. For most events that have occurred since the mid 1970s with M,>5.5, seismic moment (Ma) has been determined by the centroid-moment tensor (CMT) inversion technique of Dziewonski, Chou & Woodhouse (1981), using long-period waveforms recorded at teleseismic distances. Moment tensors for two of our events, the Corinth and Borah Peak mainshocks, were also determined using the procedure of Sipkin (1986b). For some other events, seismic moment has been estimated from long-period teleseismic waveforms using other inversion or forward modelling procedures. Estimates of Ma have also been made, using the long-period asymptote of displacement spectra (e.g. Brune 1970), for some smaller western USA events recorded by dense networks of temporary stations. Where an estimate of Ma was available, we calculated moment magnitude, M,, from it using the definition of Hanks & Kanamori (1979): log,,(M,/Nm) = lSM, + 9.05.

Where multiple estimates of Ma were available, we used, in order of preference, moment from CMT inversion, then moment from other long-period teleseismic studies, then moment from near-field spectral studies. We also compiled ML. As has already been pointed out by Joyner & Boore (1981), use of ML in the quantification of strong ground motion may present a difficulty due to the different procedures for determining it in different source regions. For events below magnitude 5, we also estimate M, from mb using the empirical relation of Marshall (1970)

M, = 2.08mb - 5.65. (2.2) Surface-wave magnitudes estimated in this way are compared with ML and Mw estimates in Table 1. Excluding the Borah Peak aftershocks, for events between magnitudes 4 and 5 Mw and ML usually agree to within 0.2 of a unit or better. Around Mammoth Lakes, an anomalous pattern of

seismic wave attenuation has led to ML estimates made at different permanent stations being strongly scattered (Hutton & Boore 1987), and the overall ML value obtained by averaging these estimates depends on which stations are included in the averaging. However, the Mammoth Lakes aftershocks give agreement between ML and Mw that is roughly as good as for the Oroville aftershocks, where no such scatter has been reported. Local magnitudes in California were determined using Richter’s (1935) method, based on body-wave amplitudes, corrected for distance, on a standard (or simulated) Wood-Anderson seismograph. In contrast, local magnitudes for the Borah Peak aftershocks were calculated using a formula based on signal duration (Richins et al. 1987). The systematic difference between ML and Mw for Borah Peak aftershocks, were Mw is up to 0.7 smaller than ML, may be a consequence of this different method used for ML. The good agreement between ML and M,, when ML is determined in the standard way using amplitudes, suggests that this ML is a reasonable measure of earthquake size and can be substituted for Mw when Mw estimates are unavailable. However, M, becomes systematically much smaller than both Mw and ML as magnitude decreases below 5.5. We think that for such small events that are only weak sources of surface-waves, M, is not a good measure of earthquake size and, in addition, is frequently very unreliably determined. We show in Section 3 that PHGA for these smaller events and for many larger ones occurs during the direct S-phase and, consequently, measures of earthquake size based on body-wave amplitudes or spectra are more appropriate than a measure based on surface-wave amplitudes. Many determinations of seismic moment quote uncertainties of the order of 20 per cent, implying uncertainty of about 0.05 in M,. Although the second decimal digit in M, is thus not significant, we quote M, to two decimal places to avoid rounding errors and so that seismic moment can be recovered from it using equation (2.1) without loss of precision.

2.3 Earthquake locations Our starting point for hypocentral coordinates was also the ISC bulletin. However, ISC hypocentres for Mediterranean earthquakes are often systematically mislocated by up to 20 km due to the uneven distribution of seismograph stations around this region (e.g. Soufleris & Stewart 1981; Jackson et al. 1982a; Westaway & Jackson 1987). Frequently, this results in a location up to 20 km north of the true location, an apparent origin time several seconds later than the true origin time, and a focal depth that may be of the order of 50 km deeper than the true depth (e.g. Jackson & Fitch 1979). This effect occurs because most ray-paths take off downwards to stations that lie at regional or teleseismic distances in the northern quadrant of the focal sphere. The hypocentral solution thus exhibits strong trade-off between origin time and position along the direction of these ray paths. We could not find any equivalent systematic mislocation effect for ISC locations of western USA earthquakes. Presumably this is because, even though the distribution of teleseismic stations about a focal sphere situated in the western USA is uneven, sufficient regional stations now exist to constrain most hypocentral solutions. Because of the much smaller number of stations operating in 1959, substantial uncertainty, greater than

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10 km, exists in the location of the Hebgen Lake event (e.g. Doser 1985). However, because the accelerograph stations that recorded this event are 100 km or more distant, this uncertainty does not have a critical effect on our conclusions.

Due to these potential problems with ISC locations, we have preferred to use hypocentres, where available, from other non-routine studies. In cases where more than one detailed study has been carried out on any earthquake, we have judged the reliability of the different solutions for the hypocentral coordinates in determining our preferred location. We have sometimes adopted hypocentres from particular studies, and sometimes calculated hypocentral coordinates as the average of two or more independent solutions, determining a standard error in the solution to include the error bounds of all the independent solutions used to derive it (Table 2). The need to correctly measure source-station distances for large earthquakes, where the size of the fault plane is comparable to the source-station distance, is discussed in Section 4.

2.4 Earthquake focal mechanisms

To confirm that the events that we have studied involved normal faulting, we searched the literature for focal mechanisms both from first motion polarities and from waveform modelling. Most of the larger events unequiv- ocably involved normal faulting (Table l ) , although in many cases the ambiguity as to which nodal plane was the fault plane has not been resolved. We highlight here uncertainties concerning some earthquakes from Mammoth Lakes, Italy and western Turkey.

Interpretation of the Mammoth Lakes earthquakes of 1980 May and June has been the subject of controversy (e.g. Mueller et al. 1981; Archuleta ef al. 1982; Given, Wallace & Kanomori 1982; Barker & Langston 1983; Ekstrom 1983; Julian 1983; Ghavez & Priestley 1985; Ekstrom & Dziewosnki 1985; Priestley, Brune & Anderson 1985; Lide & Ryall 1985; Wallace 1985; Chouet & Julian 1985; Julian & Sipkin 1985; Sipkin 1986a). These earthquakes occurred near the Long Valley caldera, a Quarternary volcanic field in NE California near the boundary between the Basin and Range province and the Sierra Nevada mountains. Julian (1983) suggested that first-motion polarities for several of the larger events, in particular that at 14:51 on May 27, could not be resolved into quadrants of opposite polarity separated by orthogonal nodal planes, implying that these sources did not involve shearing motion on faults. He described the mechanisms of these earthquakes as compensated linear vector dipoles, a type of source that can be produced by rapid widening of a fissure, and suggested that the events occurred because magma was being forced into a fissure at high speed. Earthquakes with non-double- couple focal mechanisms have been reported in Quatenary volcanic regions elsewhere. For example, Foulger & Long (1984) identified in Iceland anomalous magnitude 1 (Mo approximately 0.000001 X 10l8 Nm) events, six orders of magnitude smaller than the Mammoth Lakes earthquakes. These Icelandic events have been interpreted as a consequence of thermal contraction of cooling magma. In contrast, only the largest Mammoth Lakes events have shown any sign of anomalous sources. Aftershocks with

magnitude 5 or less have double-couple focal mechanisms (Archuleta et al. 1982; Priestley et al. 1985), indicating normal or oblique normal faulting in many cases. However, further investigation has shown that the timing of the first motion polarity picks was not consistent in some studies of the largest events that suggested anomalous focal mechanisms. The event at 16: 33 on May 25 has been modelled as a multiple event, with a normal-faulting rupture followed 7 s later by a strike-slip rupture (Ekstrom & Dziewonski 1985). Priestley et al. (1985) have shown that the S-wave spectra of the Mammoth Lakes earthquakes are typical of events caused by shearing on faults and not what would be expected from rapid opening of a fissure.

Ekstrom & Dziewonski (1985) suggested that the source time-function duration of the event at 14:51 on May 27 was 8s , much longer than typical for a M, 6 earthquake, but consistent with the duration of the strong part of the seismograms in Fig. 1. The best double-couple component of their centroid-moment tensor indicated normal faulting. The centroid-moment tensor of the mainshock at 16:33 on May 25 was similar. In contrast, the 16:49 event had a pure strike-slip best double-couple. However, the overall moment tensors of these three events are all similar, comprising a NW-trending dilatational quadrant within which the downward vertical is situated. Instead of decomposing these overall moment tensors into best double-couple components, we can decompose them into orthogonal double-couples representing normal and strike- slip faulting. The non-zero eigenvalues of these component tensors indicate the seimsic moment that was released on each type of fault, had faulting occurred in this manner. These were 1.5: 1.4 X 10*8Nm or 52:48 per cent for the 16: 33 event (as suggested by Ekstrom & Dziewonski 1985); 0.2 : 2.3 x 10l8 Nm or 7 : 93 per cent for the 16 : 49 event; and 0.5:0.6 x 10"Nm or 45:55 per cent for the 14:51 event. Thus, normal faulting predominated for the 16:33 event, and strike-slip faulting predominated for the 16: 49 event. Interestingly, the 14: 51 event moment tensor can be decomposed such that strike-slip faulting predominated, even though the best double-couple involved normal faulting.

We regard the Mammoth Lakes earthquakes as having occurred on complex systems of faults with various orientations and senses of slip, including a substantial component of normal-faulting motion. We consider that they are most likely to be tectonic earthquakes, not directly related to the volcanic process, that are occurring near the epicentral region. However, the large proportions of seismic moment that appear to have been released on strike-slip faults during the 16:49 and 14:51 events warrant their exclusion from our quantitative comparison in Section 4. We note in passing that strong ground motion records of the 14:51 event are unusual. On both horizontal and vertical components the duration of ground acceleration is much longer, and PHGA is much larger, than expected for an event with magnitude around 6 (see Fig. 1 and Table 2), both at station LVD that is at a site that would be expected to resonate strongly, and at FIS that is not.

The Ancona, northern Italy, earthquakes of 1972 have been the subject of some interest due to the relatively large ground accelerations that occurred. However, no detailed study of their focal mechanisms has been carried out that

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ground acceleration and its duration, measured on each component record. Each row of Table 2(b), (d) and (e) corresponds to one three component set of records. Each block of rows in Table 2(a) corresponds to one earthquake. The top row comprises our preferred values, and subsequent rows indicate results of individual studies. Comparison of the top row with rows underneath it reveals the study that contributed each of our preferred values.

conclusively identifies them as normal-faulting events. Earthquakes occur throughout the length of Italy beneath the Appennine mountains. Most events in the southern and central Appenines have normal-faulting focal mechanisms (e.g. Anderson 1987). However, in the northernmost Appenines (e.g. Cisternas et al. 1987) and the Alps of NE Italy (e.g. Cipar 1981), reverse-faulting earthquakes occur. Ancona is situated less than 100 km east of the epicentre of the Gubbio normal-faulting earthquake (M, 5.2) of 1984 April 29 (e.g. Cisternas et al. 1987). In contrast, the closest Italian reverse-faulting earthquake, the Parma event of 1983 November 9 (Ms 5.0), was almost 300 km NW (e.g. Cisternas et al. 1987), though reverse faults indicating Quaternary compressional tectonics have been imaged by seismic reflection profiling in the Po valley, 200 km NW of Ancona (Pieri & Groppi 1981). Gasparini, Iannacone & Scarpa (1985) determined an oblique normal-faulting focal mechanism, with a large component of strike-slip, for the Ancona event at 18:55 on 1972 June 14. They also determined normal-faulting mechanisms or mechanisms with a near-vertical nodal plane for five other events from this swarm. All these mechanisms relied on first-motion polarities read by station operators that were not checked by the authors, and they include a relatively large number of inconsistent polarities. Despite this, in all cases dilational first-motion polarities were reported by relatively distant stations at a wide range of azimuths, suggesting that these events involved a component of normal faulting. We conclude that the balance of evidence implies that these were normal- or oblique normal-faulting earthquakes, and are therefore appropriate to be included in this study. Sabetta & Pugliese (1987) documented four sets of strong ground motion records for the Gulf of Patti, northeastern Sicily, event at 23:33 on 1978 April 15 (Ms 5.8), which they suggested involved normal faulting. Although some earthquakes in NE Sicily have involved normal faulting, including the destructive Messina event of 1908 December 28 (e.g. Schick 1979), published focal mechanisms of the Gulf of Patti event indicate reverse faulting (e.g. Anderson 1987). Consequently, we exclude this earthquake.

Focal mechanisms have been determined for two of our five western Turkish earthquakes: the Izmir event of 1977 December 16 and the Biga event of 1983 July 5 (Table 1). The event of 1977 December 9 is likely to have also involved normal faulting due to its proximity in time and space to the other kmir event. The Denizli event of 1976 August 19 occurred at the eastern end of the Buyuk Menderes valley, a major east-west trending extensional structure bounded by normal faults that have been active in the historical past (e.g. Jackson & McKenzie 1984). The Dursunbey event of 1979 July 18 occurred near the epicentre of the Gediz earthquake of 1970 March 28 (M, 7.2; Mo 88 X 101'Nm) (Eyidogan & Jackson 1985), another major normal-faulting event. We are confident, therefore, that all five of our western Turkish earthquakes involved normal faulting.

The data that we have collected is summarized in Table 2, on microfiche. Table 2(a) lists earthquake source parameters, and Table 2(b) accelerograph station parameters. Table 2(c) lists all accelerograph station names, three letter codes, and agencies responsible for operating them or providing information. Table 2(d) and (e) list peak

3 SEISMIC PHASES RESPONSIBLE FOR PEAK HORIZONTAL GROUND ACCELERATION

Records of strong ground motion for earthquakes with magnitude 6 or larger are usually extremely complicated (Fig. 1). In many cases arrival times of seismic phases cannot be identified. However, records of smaller events (Figure 2) are frequently much simpler, and in many cases it is possible to identify the arrival time of both P- and S-waves. The P-phase is observed on many records from digital instruments that have pre-triggering buffer memory, and on some analogue records, usually when the instrument was already recording having been triggered by an earlier event. A large number of records show a later arrival, which can be identified as the direct S-phase, first, because it is frequently of much larger amplitude than the P-phase. Second, at stations close to the source, within the 'S-wave window' (e.g., Booth & Crampin 1985) where the ray-path is steeply upward, this phase is strongest on the horizontal components, indicating that it is transversely polarized. At stations that are outside the S-wave window, where the angle between the S-wave ray path and the vertical is greater than about 40°, the interaction between the S-wave and the earth's surface is much more complicated than at closer distances. S-wave energy can be strongly converted to P-wave energy, reducing the amplitude of the S- relative to the P-phase and resulting in complicated waveforms with polarization that is not straightforwardly related to that of the S-wave leaving the source. At greater distances, the S-waves become simpler again (Booth & Crampin 1985). In the distance range beyond about 10 km from the epicentre, where S-waves are relatively complicated, we could still pick some S-wave arrival times though with less confidence than at closer stations.

At stations with absolute timing, the second seismic arrival can be shown to be the direct S-phase by comparing its observed arrival time with predicted S-wave arrival times. We calculated the predicted S-wave arrival time as:

R T, = To + -,

B where T, is the origin time of the earthquake, R the distance from its hypocentre to the station, and /3 the S-wave velocity. We also calculated the uncertainty in predicted arrival time, AT,, where

assuming that the uncertainties in To, R and /3 (AT,, AR and

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LON0 VALLEY DAM - 5/27/00. 1450 riTc:M~:6.2

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3

F I S 2 14:51 81.BBB

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I I I I I 1 I I I 0 1 2 3 4 5 6 7 8 9

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Mammoth Lakes : 27 May 1980 14:51

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F@ore 1. Strong ground motion records of a large earthquake: the Mammoth Lakes event at 14:51 on 1980 May 27 (ML6.2), recorded at USGS temporary station FIS, north of the epicentre, and at permanent station LVD, to the NE. Both stations are about 15 km from the epicentre, and both sets of seismograms have similar character even though they were recorded at stations with different frequency response, with one of the stations in a dam. At FIS, the three components of ground acceleration shown are up (l), north (2) and east (3). Note that the character of both sets of records is similar. Due to the pre-triggering buffer memory in the digital recorder, the record starts about 0.6s before the P-wave arrival time. The very strong phase, about 5.5 s after the record starts, which causes the PHGA, is about 3 s too late to be the S-wave arrival from the nucleation point. This strong phase is most likely to be from a rupture that initiated several seconds after the event nucleated. The LVD seismograms are from fig. 1 of Porcella (1983).

A g ) are uncorrelated. We used AT, and AR from our location study (Section 2), or assumed values of 1 s and 3 km if none were available, and assumed values of 3.5 f 0.5 km s-’ for /3 f AS.

Many empirical definitions, for engineering purposes, of the duration of peak ground acceleration in earthquakes have been suggested (see, e.g. Trifunac & Brady 1975; Sabetta, 1983). Seed & Idriss (1982), in particular, have

proposed that the peak should be considered to begin when the ground acceleration first exceeds 65 per cent of its eventual maximum value (Ti), and to end when it drops below 65 per cent of this maximum for the last time (T3). We determine maximum accelerations, their times (T2), and the start and end times of peaks by numerically searching through%he acceleration time series. We determined the peak acceleration values for the horizontal two-component

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3

F I S 2 10:11 33.000

1

1 1 2 3 4 5 6 7 8 9

I I I I I I I I I 3 1 2 3 4 5 6 7 8 9 10

T i m e / s

0

M a m m o t h Lakes : 31 M o y 1980 1 @ : 1 1 Ei%pre 2. An example of a strong ground motion record of a smaller earthquake; the Mammoth Lakes event at 1O:ll on 1980 May 31 (ML 4.2), also recorded at USGS temporary station FIS. This event occurred at a depth of about 4 km, about 3 km south of this station (Mueller et al. 1981, Priestley et al. 1985) so the source-station distance is about 6 km. The strong phase about 1 s after the P-wave arrival time is most likely to be the direct S-phase: a P-to4 interval of 1 s is reasonable at a distance of 6 km.

vector sum, for the three-component vector sum, and in the positive and negative directions for each component of ground motion (Table 2d and e).

Hanks & McGuire (1981) showed that PHGA decreased as the reciprocal of source-station distance for stations within 150 km of the San Fernando, California, earthquake of 1971 February 9 (ML 6.4), and its timing agreed well with the direct S-wave arrival time, implying that it Gas controlled by geometrical spreading of the direct S-phase. The maxima of the S-wave radiation patterns of many normal-faulting earthquakes lie at a steep angle to the horizontal, so sometimes at stations at distances of the order of tens of km the direct S-wave signals will be much less strong than the maxima generated by the earthtquake. Consequently, we considered it worthwhile to investigate whether PHGA lies in the direct S-phase for our set of normal-faulting earthquakes also. In Fig. 3 the timing of the observed S-wave arrival is compared with predicted direct S-wave arrival time, and in Fig. 4 the timing and duration of PHGA, calculated using the Seed & Idriss (1982) definition, are compared with the observed S-wave arrival time. Three important features can be seen in these figures. First, at stations with absolute timing, our observed S-wave arrival times agree with predicted direct S-wave arrival times

within a margin of the order of I s , comparable to the uncertainty in the predicted arrival times. This suggests that the simple techniques described above for picking S-wave arrival times are reliable, and their timing is consistent with their being direct S-waves and not S-waves that have propagated along more complicated, slower, paths. Second, the durations of peak accelerations, calculated using the method of Seed & Idriss (1982), are substantially skewed about the time of the peak. In most cases, the rise time of the peak, T, - TI, is a small fraction of 1 s, much smaller than the decay time, T3 - T,. The most likely explanation of this is that the peaks are due to the arrival of an impulsive seismic phase. If the peaks were mostly due to site resonance it is unlikely that they would be skewed in this way. Third, the times TI and T2 are usually within about 1 s of the observed and predicted S-wave arrival times. If the peaks were caused by S-waves that are guided by, and reverberate within, some layer of velocity structure such as the crust, or caused by surface waves, they would be delayed relative to the .direct S-wave arrival time by a time that increases with source-station distance. All this evidence is consistent with the suggestion that at close distances the PHGA is in the direct S-phase. In contrast, the timing of peak vertical ground acceleration is much less readily

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540

predictable. This sometimes occurs during the P-phase, sometimes between P- and S-wave arrival times, sometimes during the direct S-phase and sometimes several seconds later than PHGA in what may be a surface-wave phase or a guided S-phase.

It is of course not possible to prove that the PHGA values observed at close stations are in the direct S-phase; to do that would require modelling every seismogram using some technique that can synthesise high-frequency waveforms (see, e.g. Spudich & Archuleta 1987). This would be an immense task, far beyond the scope of this article. Nonetheless, the consistency of timing between PHGA and direct S-wave arrival times at close stations is striking and, we believe, indicates that this inference of the nature of the phase containing PHGA is reasonable.

Figure 4(b) deserves some comment. The points shown are from the Thessaloniki and Campania-Basilicata earthquakes, which were multiple events with long time-functions: about 9s in the case of the Thessaloniki event (Soufleris & Stewart 1981); and about 15 s in the case of the initial ruptures of the Campania-Basilicata event (Westaway & Jackson 1987). However, the durations of the peaks shown are typically much shorter than the far-field source time-functions obtained in these teleseismic waveform-modelling studies. The time of PHGA is 4 s or more after the S-wave arrival time, for both the Campania-Basilicata events, at CL3, BC3 and RV3. At BI3, ST3 and MS3, in contrast, this delay is never more than about 2s. Stations BC3, CL3 and RV3 are situated on several km of relatively unconsolidated sediments (clays, sandstones and volcanic ash); whereas BI3, with a short delay, is on crystalline Mesozoic limestone. However, MS3 and ST3, also with short de s, are on relatively soft

R. Westaway and R. B. Smith

sediments, suggesting that the CP elay to the peak is not only a

Tlming OF peak h o r acc and S-wave

10. D i s t c l n c e 1 k m

Figure 3. Comparison of observed and predicted direct S-wave amval time versus hypocentral distance for events with magnitude less than 6, recorded on instruments with absolute timing. Predicted S-wave arrival time is indicated by a small circle, and its standard error, calculated in the manner described in the text, is indicated by an error bar. In all cases the observed S-wave arrival time is within about 1 s of the predicted direct S-wave arrival time.

Timing OF peak h o r . acc. and S-wave

v1

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10. Distance / km

(a1 L

10. Distance ’ km

Cbl Figure 4. Comparison of observed S-wave arrival times and the peak acceleration duration measure of Seed & Idriss (1982), against hypocentral distance. Horizontal bars indicate the uncertainty in hypocentral distance, and pass through the time T,. Vertical bars extend from T, to &. See text for notation. (a) Events with magnitude 6 or less. In virtually all cases the PHGA occurs within 1 s of the observed S-wave arrival time. The one clear exception is the point at distance about 18km and time about 2.5s, which is from the records shown in Fig. 1, from a complex earthquake: the Mammoth Lakes event at 14:51 on 1980 May 27, for which Ekstriim & Dziewonski (1985) have suggested a source time- function of 8 s duration. (b) Events with magnitude greater than 6. All these points are from either the Campania-Basilicata or Thessaloniki earthquakes. Points A, C, E, G, I and K are from the Campania-Basilicata initial ruptures: A from CL3; C from BC3; E from B13; G from ST3; I from RV3; and K from MS3. Points B, D, F, H and J are from the Campania-Basilicata 4 0 s sub-event: B from CL3; D from BC3; F from B13; H from ST3; and J from RV3. Point L is from the Thessaloniki event, recorded at THE.

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in some places than the value 250 considered reasonable in the previous paragraph. For example, MacBeth & Burton (1987) have suggested that it may lie in the range 10-50 in the upper crust beneath parts of Scotland. With a value of Q this low, PHGA would be controlled by anelasticity within only a few km of any earthquake source. However, in Section 4 we show that there is good agreement between observed PHGA values and those predicted using an empirical law that implicitly assumes Q is of the order of several hundred, for distances up to a few tens of km from earthquake sources. In contrast, in a region with Q, = 10 seismic waves would be attenuated very rapidly. From equation (3.4) they would lose about 60 per cent of their energy per cycle. Thus, it would be very difficult to record strong ground motion at all, given that recording station can never be within 5-10 km of the earthquake source, even if it is sited directly above the hypocentre. This effect may potentially bias observations to reflect areas of high Q, where strong ground motion can be successfully recorded. However, to anticipate the results of Section 4, we find no systematic bias in PHGA between source regions that would imply a substantial difference in Q between those regions. We find good agreement between observed PHGA and values predicted assuming that Q is large. Conse- quently, we are confident that Q is sufficiently and uniformly large to enable our sets of data from different source regions to be merged into a single global data set. We find no evidence that Q is as low as 10-50 anywhere in the regions that we have investigated.

Because of their smaller (-R-'") geometrical spreading factor, guided S-wave and surface-wave phases such as L, may become stronger than the direct S-phase at distances greater than a few tens of km. The relative strength of L, at distances of the order of 100 km has been recognised before, and L, has been studied extensively because of its potential importance in the discrimination between earthquakes and underground nuclear explosions (e.g. Nuttli 1986). The possible importance of a guided phase such as L, becoming the strongest seismic phase at distances of the order of 100 km is illustrated schematically in Fig. 5. This shows an hypothetical variation of PHGA with distance for an earthquake with magnitude about 7, neglecting the effect of the source radiation pattern that introduces an azimuthal variation in PHGA in addition to the suggested radial variation. It also neglects 'near-field' phases that have been shown to contribute to PHGA in numerical studies of normal faulting at distances no greater than several times the source dimension (Benz & Smith 1987). In this suggestion, PHGA is not a continuous function of distance, but it varies with distance in three separate regions. In the first, at epicentral distances closer than about 10 km, PHGA is in the direct S-phase. At this distance range, the station will be in the S-wave window, and the direct S-phase is consequently relatively strong. In the second region, at distances between approximately 10 and 50-100 km, PHGA is still in the direct S-phase. Just beyond 10 km distance, the direct S-phase may be abruptly weakened due to the effect of the free surface. At greater distances still, PHGA decreases as R-' due to geometrical spreading, plus a relatively small additional effect due to anelasticity. Beyond 60-100km, PHGA may be in a guided phase, and is assumed to decrease as R-l" plus the additional effect of

function of the site conditions. N. Ambraseys (pers. comm.) has suggested the following explanation for the peak being delayed only at relatively close stations situated in relatively unconsolidated rock. At these stations, the first S-wave arrival may be sufficiently strong to cause the soft sediments to behave in a non-linear manner, in which their strength decreases as acceleration increases. Under these circumstances, the velocity of propagation of subsequent S-wave pulses that contain the PHGA is reduced, thus increasing the delay between the first S-wave arrival and the peak. Testing this suggestion further would require modelling the waveforms, which, as we have already indicated, is beyond the scope of this article.

We now consider the relative importance of anelasticity and geometrical spreading in determining the PHGA at different distances from the source. An S-wave Fourier component at frequency f has amplitude A at distance R from a point source, where

(3.3)

/3 is the S-wave velocity and Q,(f) is the frequency- dependent quality factor for S-waves:

(3.4)

and k is a constant, proportional to the seismic moment of the earthquake, that determines the amplitude of the seismic signal close to the point source. AEIE is the proportion of the energy lost per cycle from the S-wave. In many regions, Qs(f) is of the order of several hundred for frequencies between approximately 2 and 20 Hz for S-waves propagating through the crust (e.g. Aki 1980). Evaluation of the exponential term in equation (3.3) for f = 10 Hz and f i = 3.5 km s-l indicates that with Q, = 250 the term remains close to 1 with R up to 20 km. Even with R as great as 40 km, the exponential term has only decreased to 0.25. Fourier components at frequencies lower than 10 Hz will be attenuated by smaller proportions. For earthquakes with magnitude 6 or greater the source time-function usually has a duration of several seconds or more, and the comer frequency, f, (e.g. Brune 1970), will be of the order of several tenths of 1 Hz or less. Near-source spectral accelerations will be greatest at frequencies both close to, and somewhat above, f,. The dominant frequencies contributing to PHGA will be of the order of 1 Hz, and will thus be unaffected by anelasticity at distances of the order of tens of km. For smaller events, fc is larger, and spectral acceleration is concentrated at higher frequencies, where it will be more strongly affected by anelasticity. This discussion suggests that for larger events at distances up to tens of km, crustal anelasticity is likely to be much less important than geometrical spreading in determining the strength of ground acceleration, in agreement with the conclusions of earlier investigations (e.g. Joyner & Boore 1981; Archuleta et al. 1982). However, for smaller events, anelasticity has, potentially, a more important effect. In Section 4 we show that threshold below which anelasticity is important at distances of the order of tens of km is likely to be about magnitude 5.

Some people have suggested that Q, may be much lower

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10.0r 4.1 Definitions of empirical laws for predicting PHGA

Joyner & Boore (1981) derived an empirical law of form equivalent to:

A = 0.937 exp (0.573 M ) exp (-0.00587 R)R-' , (4.1)

where A is median predicted PHGA in m s - ~ , defined as the greatest acceleration observed on either horizontal component of ground motion, M is M,, determined from seismic moment M, using equation (2.1). R is defined as:

R = (D2 + k2)0.5, (4.2)

where D is the distance in km between the recording station and the closest point on the surface projection of the fault and k is an empirical constant equal to 7.3 km. Joyner & Boore (1981) chose this form of their law because it implies that A varies with distance due to geometrical spreading of body-waves and crustal anelasticity with constant Q, independent of earthquake magnitude. Using equation (3.3), their exponential coefficient corresponds to Qs 350 at frequency 2 Hz. Likewise, M was chosen as Mw because this is related directly to seismic moment, a source parameter with a physically well-defined meaning. In the absence of M,, ML was used.

Joyner & Boore (1981) determined the empirical constants in their law by regression analysis, using 180 PHGA vaues from 23 shallow western USA earthquakes with magnitude 5 or greater, recorded at distances up to 370 km. Only one of these events involved normal faulting, the Oroville mainshock of 1975 August 1, from which Joyner & Boore (1981) used four PHGA values. The Joyner & Boore (1981) law can thus be regarded as a prediction of PHGA for reverse-faulting and strike-slip earthquakes in the western USA.

Campbell (1981) proposed an empirical law of the form:

A = 0.156 exp (0.868 M ) [ R + h exp (0.7 M)]-'.09, (4.3)

where A is median predicted PHGA in m s - ~ , defined as the mean of the peak accelerations observed on the two horizontal components. Because M , was not uniformly available for any earthquake sue range, M was Ms for earthquakes with M > 6, and ML for smaller events. R is distance in km between the recording station and the closest point on the fault rupture, and h is an empirically- determined constant equal to 0.0606km. This law was established using 116 PHGA values from within 60 km of 27 shallow earthquakes with magnitude 5 or greater. The set of earthquakes was described as 'worldwide', although all except five are western USA or Alaskan events. Two of these 27 earthquakes involved normal faulting: the Helena event of 1935 October 31 and the Oroville mainshock, providing five PHGA values in total. Thus, most of the data used by Campbell (1981) are also typical of reverse-faulting and strike-slip earthquakes.

Both Joyner & Boore (1981) and Campbell (1981) use different definitions of PHGA, of source-station distance (the two definitions are only equivalent for a vertical fault plane that breaks the surface), and of earthquake magnitude. For any comparison with either of these laws to be fair, the parameters being compared must be calculated in each case using valid definitions.

1 I

1 10 100 Source - Station distance (/km)

0.1 ' Figure 5. A suggested composite relationship between PHGA, a?", and source-station distance, R, for a hypothetical earthquake with magnitude about 7. PHGA in the direct S-phase will lie along branches (1) and (2). PHGA in guided S-phases or surface-wave phases will lie along branch (3). The discontinuity between branches (1) and (2) is due to the strong effect of S-waves on the free surface when the S-wave is incident on it at about 40" to the vertical. This relationship is discussed further in the text.

anelasticity, and will lie on the upper branch in Fig. 5. At some azimuths, at stations at distances greater than about 60 km, the guided phase may be far away from any of the maxima of its radiation pattern, but the direct S-wave from the source may be radiated at close to one of the maxima in its radiation pattern. In these circum&ances, such a station may lie on the lower branch in Fig. 5.

Records of events with magnitude about 6.5 or greater at distances up to about 60 km usually contain a strong arrival that can be identified as the direct S-phase (Fig. 6). In contrast, some records from more distant stations contain no such clear arrival (Fig. 7), either because the instruments triggered after the direct S-phase arrived, implying that some slower phase was stronger than S, or because the direct S-phase was too weak to be clearly identified. We suggest, without attempting a rigorous proof, that the strongest signals observed on these records may be guided S-phases or surface waves.

4 COMPARISON OF OBSERVED AND PREDICTED PEAK HORIZONTAL GROUND ACCELERATION

Several investigators have suggested empirical laws for predicting ground acceleration in earthquakes (see Campbell 1985, for a review of this subject). Laws differ partly as a result of different choices of ground acceleration data used in their derivation, and partly as a result of different choices of the algebraic form of the desired relation between ground acceleration and earthquake source parameters. We have restricted our comparison of observed PHGA for normal-faulting earthquakes to two widely-used empirical laws, by Joyner & Boore (1981) and by Campbell (1981).

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Lake, Thessaloniki, Campania-Basilicata, the 1981 Corinth events, Borah Peak and Edgecumbe, produced surface faulting, enabling the dimensions of their sources to be estimated. The Hebgen Lake and Borah Peak events were only recorded at distances much greater than the dimensions of their fault planes, so we approximate them as point sources. For the Thessaloniki and Campania-Basilicata events, the observed surface faulting was much shorter than that predicted from seismic moments or from the distributions of aftershocks (Soufleris & Stewart 1981; Westaway & Jackson 1987), indicating that additional faulting occurred elsewhere.

The Gulf of Corinth earthquakes of 1981 February and March have been studied in detail (e.g. Jackson et al. 1982a; Carydis et al. 1982; Kim, Kulhanek & Meyer 1984; Vita-Finzi & King 1985). After the first two large events (Table l ) , about 15 km of fresh surface faulting was visible, dipping north along the northern shore of the Perachora peninsula at the eastern end of the Gulf (Jackson et al. 1982a). A third large event about 8 days later produced more surface faulting on an antithetic fault dipping south. Focal mechanisms for the first two events are similar (Jackson et al. 1982a; Carydis et al. 1982; Kim et al. 1984), with nodal plane dipping north or NNE with an orientation similar to that of the surface faulting. However, because both earthquakes occurred during the same night, no-one noticed which produced this faulting. Jackson et al. (1982a) suggested that it was all produced by the second earthquake, and that the first event occurred offshore to the west. This suggestion was based on their location of the first event, which was 10km west of the western end of the surface faulting. They reported geomorphological evidence of an uplifting shoreline at this western end of the Perachora peninsula, and suggested that this uplift is occumng because the area is in the footwall of their inferred offshore normal fault. However, Vita-Finzi & King (1985) tried to measure elevation changes in the same area by noting uplift or subsidence of landmarks whose positions before the earthquakes were known to local people. They concluded, in contrast, that the western end of the Perachora peninsula subsided as a result of the earthquakes. Carydis et al. (1982) located the first earthquake several km east of the Jackson et al. (1982a) location, and suggested that the surface faulting on the Perachora peninsula was produced by both the first and the second earthquakes. The field moment (5.4x IOl8 Nm) calculated from this surface faulting (Jackson et al. 1982a) is larger than the seismic moment of the second event (3.9 x 10l8 Nm; Dziewonski & Woodhouse 1983) but is smaller than the moment of the first (11.4 x 10I8Nm; Dziewonski & Woodhouse 1983). This suggests that some of the surface faulting on the Perachora peninsula may have been produced by the first earthquake. Jackson et al. (1982) suggested that the February 24 event occurred on a normal fault about 10 km long mainly striking at 300", offshore of Kiaton, about 15 km NW of Corinth town, where the closest accelerograph that recorded it was situated. At its SE end, the change in trend of the bathymetric slope suggests a change in trend of the fault to about 045", for about 5 km close to the western end of the Perachora peninsula. The corresponding nodal plane of the first-motion focal mechanism of Jackson et al. (1982) strikes at 300", so we use the segment of fault with this trend as our extended source

4.2 Definition of magnitudes

Use of magnitudes in any comparison requires careful thought, because of the larger number of measures of magnitude with different definitions. Both Joyner & Boore (1981) and Campbell (1981) stressed the suitability of moment magnitude, M,, due to its direct relationship (equation 2.1) to seismic moment. However, because M, values were not available for all events they were obliged in some cases to use other types of magnitude, as already described. Joyner & Boore (1981) and Campbell (1981) used data mostly from California, and were able to make use of the uniform definition of ML for this region (although revisions to improve this definition have recently been suggested-see Hutton & Boore 1987). Many studies (e.g. Hanks & Kanamori 1979) have established that, for events between magnitudes 5 and 7.5, M, and M, are very similar (Table 1). Excluding the Borah Peak aftershocks discussed in Section 2, for events between magnitudes 4 and 6 where M, is available, ML and M, are also very similar (Table 1). Consequently, throughout the magnitude range 4-7.5, we have used Mw where available in comparisons with both empirical laws. If no M, value was available, then M, was used, unless M, < 4.5 (see Section 2), and, if no Ms value was available then ML was used.

All the comparisons, for both empirical laws, presented in the rest of this section were made under the above definition of magnitude. We carried out two further tests to investigate whether our conclusions are sensitive to the precise definition of magnitude used. First, we used the different definitions suggested by Joyner & Boore (1981) and Campbell (1981), excluding all events for which the required measure of magnitude was unavailable. Second, for events below magnitude 6 where M, was unavailable, we calculated M, from mb using equation (2.2). Both alternative definitions complicate the presentation of our results, because they result in some earthquakes being assigned different magnitudes for comparison with the different laws. An earthquake that lies close to an integer magnitude unit may be included in one comparison but excluded from the other. However, we found that none of our conclusions is sensitive to the definition of magnitude used.

4.3 Definition of source-station distance; use of finite

Both empirical laws measure source-station distance to the closest point on either the fault plane or its surface projection, not to the epicentre or hypocentre. However, for earthquakes below about magnitude 6, the dimensions of the source are likely to be smaller than the uncertainties in hypocentral coordinates. If these smaller events are approximated as point sources, the Joyner & Boore (1981) definition of source-station distance becomes equivalent to epicentral distance, and the Campbell (1981) definition to hypocentral distance. For the larger events, dimensions of fault planes become substantially larger than uncertainties in h p n t r a l coordinates, and, particularly when recorded at close stations, it is important to measure source-station distance in a manner that is consistent with these laws. This requires knowledge of the position of the fault plane.

All seven crustal earthquakes with M,>6.3: Hebgen

SOUrceS

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in Table 3. Notwithstanding the observations above that the seismic moment of the February 25 event is insufficient to account for the field moment of surface faulting on the Perachora peninsula, in the absence of more detailed information we use the full extent of faulting on the Perachora peninsula as the extended source of the February 25 event (Table 3).

The earthquakes that occurred in 1978 close to the city of Thessaloniki in northern Greece have also been studied in detail (e.g. Carver & Bollinger 1981; Soufleris & Stewart 1981). Four large events occurred, of which the mainshock (M, 6.4; M, 5.2x 1018Nm) was at 20:03 on June 20. Activity was concentrated about 25 km NE of Thessaloniki along the Mygdonian graben, an east-west trending structure up to 10 km wide bounded on its north and south sides by normal faults, the floor of which comprises a lake, Lake Langadas. Focal mechanisms for the largest earthquakes (Soufleris & Stewart 1981) indicate normal faulting with nodal planes striking west and east. The largest events have been reliably located north of this graben (Soufleris & Stewart 1981), where many smaller aftershocks also occurred. Approximately 12 km of surface faulting was identified, with average slip 0.12 m. 8 km of this was on the south side of the graben, dipping north. All this evidence suggests that the mainshock occurred on this north-dipping fault. However, the length of surface faulting, the depth of nucleation (6-8 km) and the average slip are insufficient to explain the seismic moment. Consequently, either faulting continued further along strike at depth than at the surface or the slip was greater at depth than at the surface. We have assumed (Table 3) a fault plane with the dip and strike determined by Soufleris & Stewart (1981), extending west from the eastern end of the surface break, near (40" 39.5' N, 23"15'E), along the south shore of Lake Langadas for 16km, ending at the western end of the zone of densest aftershock activity (Soufleris & Stewart 1981). The dapth limit of this fault plane, 8 km, is constrained using teleseismic waveform-modelling by Soufleris & Stewart (1981).

Although the Edgecumbe earthquake only occurred a few months ago, it has already been studied thoroughly (e.g. Beanland & Blick 1987; New Zealand Department of Scientific and Industrial Research 1987). About 15 km of surface faulting has been mapped, striking approximately SW from near (37" 58.5' S, 176" 51' E) to near (38" 03'S, 176"46'E), with a maximum downthrow to the NW of about 2m. No focal mechanism has yet been published.

However, we have obtained, by courtesy of H. Anderson, numerous World-Wide Standard Seismograph Network records of the mainshock, for which the first motion polarities are consistent with a focal mechanism having strike 225", dip 45" and rake -127". This focal mechanism must be regarded as preliminary, particularly since the Antarctic stations, which will help constrain one of the nodal planes, have not yet reported. However, the position of the hypocentre (near 37" 55' S, 176" 48' E) and the surface faulting, and the orientation of the NW dipping nodal plane of our preliminary focal mechanism are all consistent. The hypocentre, at a depth of 12 km, lies on a downdip projection of the N E end of the surface faulting, and the NW dipping nodal plane has a very similar orientation to the surface faulting. These observations indicate, first, that the seismogenic fault was approximately planar, with a dip of about 45" from the depth of nucleation to the surface, as is generally observed elsewhere (e.g. Jackson 1987), and, second, that the normal fault rupture propagated to the SW from its nucleation point towards Matahina dam station (38" 06.92' S, 176" 45.60' E), with a substantial component of right-lateral strike slip (Table 3). This example illustrates the importance of choice of definition of source-station distance. The station is more than 20km south of the mainshock epicentre, but only about 10 km from the closest point on the seismogenic fault.

For the Campania-Basilicata earthquake we have assumed that the fault plane comprises the areas of fault that Westaway & Jackson (1987) inferred moved in the first three sub-events (Table 3), giving an area of fault plane much larger than would be inferred solely on the basis of the observed surface faulting (Westaway & Jackson 1984). Because of this large area of fault, the definition of source- station distance is also critical (Westaway & Jackson 1987). Westaway & Jackson (1987) drew attention to the difference in character of the records from two stations, Auletta (AU3) and Brienza (BZ4), in comparison with all other relatively close stations, and suggested that PHGA at these two stations, SE of the mainshock eipcentre, was due to an additional relatively small fault rupture close to them, though they were unable to constrain the position of this additional fault rupture well. Because of this complication, we have excluded these two sets of records. For the Puget Sound eatthquake, if the results of Baker & Langston (1987) are accepted, station OTC was situated directly above the fault plane in the upper mantle. The Joyner & Boore (1981) definition of source-station distance thus gives

Table 3. Coordinates that we have used for the fault planes for the five earthquakes for which accelerograph stations are sufficiently close and the fault plane is sufficiently large for it to be inappropriate to treat the earthquake as a point source. I$ and 6 are the strike and dip of the fault plane, using the convention of Aki & Richards (1980; p. 106). Lat, and Lon, ( i = 1-4) are the latitudes and longitudes of the four corners, and H, and H, the depths of the upper ,and lower edges, of the fault plane. Fault plane corners are listed in order as follows. Corner 1 is at depth Hl at the end of the fault in the direction of strike. Comer 2 is at depth H, at the same end, and corners 3 and 4 are at depths H2 and H,, respectively, at the other end of the fault.

Date Lat, Lon, Lat, Lon, Lat, Lon, Lat, Lon, Hl H, 6 I$ ~~

1978 Jun 20 40.68 23.07 40.75 23.10 40.72 23.29 40.65 23.26 0.0 8.0 46 278 1980Nov 23 40.86 15.15 40.90 15.21 40.74 15.42 40.70 15.37 0.0 10.0 60 317 1981 Feb 24 38.08 22.66 38.14 22.72 38.07 22.88 38.01 22.82 0.0 10.0 42 300 1981 Feb 25 38.02 22.95 38.12 22.92 38.16 23.10 38.06 23.13 0.0 10.0 42 248 1987 Mar 2 -38.06 176.75 -38.01 176.67 -37.93 176.77 -37.98 176.85 0.0 12.0 45 225

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approaches the station at a steep angle to the horizontal. The free-surface boundary condition near the station, which, when not in the 'S-wave window', affects the radial SV- and SH-components very differently, may accentuate this effect (e.g. Booth & Crampin, 1985). In these circumstances, averaging observed peak acceleration over the two horizontal components may substantially underestimate the PHVSGA.

Combining equations (4.9) and (4.10) indicates that, from our set of data:

a; = (0.85 f 0.16)~',, (4.11)

which is very similar to the result obtained by Campbell (1981):

a; = 0.87 uL. (4.12)

a value of zero, even though no part of the fault plane was within 50 km of this station. To overcome this anomaly, this event has been approximated as a point source. Both because this earthquake was not crustal, and because its rake angle was outside our specified range, we will not include it in any quantitative comparison, so no bias will result from this point source approximation.

4.4 Delioitions of PHGA

We now consider the two different definitions of PHGA already described. An alternative important parameter is the peak horizontal vector-sum ground acceleration (PHVSGA), aFax, which we define as:

a r m = max [[a:(n) + u3(n)ln], n = I, N] (4.4) at any of the N samples in the record, where az(n) and a3(n) are samples of acceleration recorded on the two orthogonal horizontal components. PHVSGA is thus the largest ground acceleration in any horizontal direction during the record. To investigate the suitability of the two definitions of PHGA as an approximation to our definition of PHVSGA, we searched sets of horizontal-component records to find a y , to find the Campbell (1981) PHGA, a;:

a; = {max [la,(n)l, n = 1, N ] + max [la,(n)l, n = I, N ] } , (4.5)

and to find the Joyner & Boore (1981) PHGA, a;:

a; = max {max [la,(n)l, n = 1, N], max [la3(n)l, n = 1, N]}. (4.6)

Figures 8 and 9 shows the results of this comparison. For our complete set of digital and digitized records, for earthquakes above magnitude 4 (182 data):

a:, = (0.930 f 0.075)ar"

a; = (0.770 f 0.102)ay. (4.7)

(4.8) For earthquakes with magnitude 5 or greater and ground accelerations 0.1 m s-' or greater (50 data):

ah = (0.896 f 0.086)aF" (4.9) a; = (0.757 f 0.122)ay. (4.10)

The scattering in these relationships does not depend on the ground accelerations observed (Fig. 8a) nor on source-station distance (Fig. 8b). We conclude that the Joyner & Boore (1981) definition of PHGA, as the greater of the peak accelerations on the two horizontal components, gives the better approximation to PHVSGA and is subject to less scatter. This seems surprising, as one might expect that averaging peak acceleration over two horizontal components to determine a; should reduce, not increase, the scatter in the result. However, given that for most events PHVSGA is within the direct S-phase (Section 3), some stations will be positioned such that the radial direction from the source to the station is approximately perpendicular to one of the horizontal components of ground motion recorded. The SH-component of particle motion on this component may be much larger than the radial SVcomponent on the other, unless the S-wave

4.5. Comparison of observed and predicted PHGA

In Fig. 10, PHGA observed in our set of normal-faulting earthquakes is compared with PHGA predicted by the Joyner & Boore (1981) and Campbell (1981) laws. In each case, appropriate definitions of PHGA and source-station distance have been used. Several points are apparent. First, for magnitudes greater than 5 and source-station distances upto about 60 km, most data points lie close to the values predicted by both laws, Second, at distances above about 60 km, the Joyner & Boore (1981) law underestimates many observed PHGA values (Fig. 10f, g and h). As mentioned in Section 3, this may be because at these relatively large distances PHGA is not in the direct S-phase. Figure 11 compares observed PHGA values with a composite law (Fig. 5) that allows for PHGA to be in a guided phase at distances of the order of 100 km. This law has been fitted crudely by eye to illustrate schematically its match to the observations. Third, some points have clearly either much higher or much lower PHGA than is predicted. All points for the 38s late rupture of the Campania-Basilicata mainshock and for the Helena events have systematically low PHGA. On the other hand, records of the Mammoth Lakes events from station LVD show much greater PHGA than is predicted. Fourth, at source-station distances greater than 10 km, PHGA from earthquakes with magnitude below 5 decreases abruptly with distance. This decrease with distance is much more rapid than that expected by extrapolating the laws of both Joyner & Boore (1981) and Campbell (1981) to magnitudes below 5. It suggests that, for these small events, geometrical spreading is not responsible for the variation of PHGA with distance. Fitting a line crudely by eye through the points in Fig. lO(a) and (b) suggests that,

ah Q R-', (4.13)

with R < 10 km. We suggest that these small events, which are likely to have source dimensions of the order of hundreds of metres and corner frequencies above lOHz, may radiate sufficient signal at high frequencies that anelasticity may control the attenuation of PHGA with distance, in contrast with larger events. The lack of data in the magnitude range 5.0-5.5 (Fig. 1Oc) prevents us addressing the question as to how the behaviour at magnitudes above 5.5, where PHGA appears to be

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546 R. Westaway and R . B. Smith

- - -

-

Peak h o r . a c c . 1 peak h o r . v e c t o r sum

Joyner and Boore ( 1981 ) parameters

- -

- -

1 .

-

0 . 5

=k ++%+ *++

++?A + 4 +++Q%+ ++

-

I I I I I I l l I 1 l l l I 1 l

' - t + +

+

+ + %+

I I I l l l l ' I I I 1 1 1 1 1

I

I

Campbell ( 1981 ) parameters

-s U U 4

0 . 5

10. 100 * D i s t a n c e / k m

Campbell ( 1981 ) parometers

1 .0 + t

+ +

Figure 8. Comparison of ab and aF, with a:", using the notation explained in the text, for all events with magnitude 5 or greater. (a) ab/aY against a/, and a:/af" against a:. (b) ab/a;P" and aF,/arax against source-station distance.

controlled by geometrical spreading, merges with the behaviour below magnitude 5, when it is not. However, the behaviour of PHGA with distance for events below magnitude 5 needs to be explained if, for example, these events are to be fully incorporated into studies of the scaling of PHGA at larger magnitudes, or are to be used as empirical Green's functions for modelling larger events. We will investigate this question further in a future article. Finally, points A and B in Fig. 10(f and g), from the Corinth mainshock recorded at COR and from the Campania-

Basilicata mainshock recorded at ST3, are from stations where the ray-path azimuth is closely in line with the fault plane strike, in the direction towards which the fault rupture principally propagated. The anomalously high PHGA observed at these stations may be a consequence of the fault rupture propagating towards them, in agreement with some theoretical models of rupture propagation (e.g. Madariaga 1983). Comparison of Fig. 1O(f) and (g) indicates that the PHGA is most anomalously high when the point source approximation is used, but this effect remains when

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1 I l l l l

Peak h o r . a c c . / peak h o r . v e c t o r sum Joyner and Boore ( 1 9 8 1 ) parameters

I I I l l l l l I

1 r

-I-

-I c

I I I I l l 1

0 .5

1 . 10.

Peak h o r i z acc. /( m/s/s )

I

0

3 d L

U U a

A

(a)

Campbell C 1981 ) parameters

Peak h o r . acc. / peak h o r . d e c t o r SUQ)

Joyner and Boore ( 1 9 8 1 ) parameters

1 t

Campbell ( 1981 ) parameters

1 t

1.0 1 n I ----+==+ I

Flgare 9. Comparison of ai and a; with a;P”, using the notation explained in the text, for all events with magnitude 4 or greater. (a) ai /oru against ak and a;/&‘” against a;. (b) ah/aFPx and aK/ar’ against source-station distance.

the extended sources are used. These points are included in our quantitative comparison.

4.6 Qnantitative estimptiOn of mismpteb between observed pad predicted PHGA

In order to compare observed ground accelerations with those predicted from empirical laws, we measured PHGA, ah, from the records of ground acceleration, using the

definition appropriate to the law under comparison. We calculate predicted PHGA, a:, for each empirical law, given the earthquake magnitude and source-station distance. We have defined an uncertainty in observed PHGA, u(ah), as: (J(ah) = o . h h , (4.14) or

la: - lGll+ 1.3’ - 1.3’11 (4.15)

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5.18 R. Westaway and R . B. Smith

A

111 \ 111 \ E

W

\

U U d

L 0 L A d a, a

Joyner and Boore ( 1981 > law

1 .01

I l l , . I

I , 1

Distance ’ km

Campbell (1981 ) law

A

ul \ 111 \ E v

\

U U a

L 0 L

A 6 a, a

10.0

1.0

Joyner and Boore ( 1981 ) law

Distance / k m

Campbell (1981) law

1 4 t

I 4 4 . 5 I 1 . 100.

Distance I k& Distance / km (a) (b)

Figure 10. Comparison of observed PHGA with PHGA predicted by Joyner & Boore (1981) and by Campbell (1981). Horizontal error bars indicate our estimates of standard deviation in source-station distance. Vertical error bars indicate our measure of uncertainty in PHGA. To improve clarity, the uncertainty displayed is half that calculated using equations (4.14) and (4.15). Points with PHGA much smaller or larger than expected are annotated and discussed in the text. (a) Records for events with 4.0CM <4S. Note the rapid decay of PHGA with source-station distance. Points A and B with anomalously high PHGA are from the Ancona, Italy, event at 15:06 on 1972 June 21, recorded at PBl; and the Abruzzo, Italy, aftershock at 13: 14 on 1984 May 11, recorded at MAN. (b) Records for events with 4.5 c M < 5.0. Note the rapid decay of PHGA with source-station distance. Point C with anomalously low PHGA is from the Oroville, California, aftershock at 20:22 on 1975 August 2, recorded at CD1. (c) Records for events with 5 . 0 5 M <5.5. Point D with anomalously high PHGA is from the Abruzzo, Italy, event at 10:41 on 1984 May 11, recorded at MAN. Points E and F with anomalously low PHGA are from the same event, recorded at PES and ATI. The three points with anomalously low PHGA at >60 km distance are also from the same event, recorded at RIP, POG and BAR. (d) Records for events with 5.5 I M < 6.0. Points G and H with anomalously low PHGA are from the Helena events of 28 November 1935; points K and L with anomalously high PHGA are from the Mammoth Lakes event at 14:51 on 1980 May 27, recorded at LVD and FIS; point J is from the event at 19:44 on 1980 May 25, recorded at LVD; and points M and N are from the Abruzzo, Italy, event at 17:49 on 1984 May 7, recorded at CAS and MAN. (e) Records for events with 6.0 5 M < 6.5. Point N with anomalously high PHGA is from the Mammoth Lakes event at 16:33 on 1980 May 25, recorded at LVD. Point P with anomalously low PHGA is from the Helena event of 1935 October 31, and the other points at greater distances with anomalously low PHGA are from the Campania-Basilicata 38 s event. ( f ) Records for events

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A

m \ m \ E v

\

U U 6

L 0 L A d (L, cl

10.0

1 .0

Joyner and Boore (1981 ) law

Campbell ( 1 9 8 1 ) law

1 .0

n

m \ m \ E

W

\

U U d

L 0 L A d al a

Joyner and Boore ( 1981 ) law

10.0 I I I 1 I I I l l I I I I I I l l

K

1 .0

1 . 10. 100. Distance / km

Campbell ( 1981 ) laN

1 . 10. Distance / k m

(C)

lqgmre l@. (Continued.)

1.0

1 . 10. 100. Distance / km

with 6.5 I M < 7.0, approximating all events as point sources. Point S is from the Corinth event at 20:53 on 1981 February 24, recorded at COR. Point R is from the Campania-Basilicata event at 18:34 on 1980 November 23, recorded at ST3. Point U is from the Puget Sound, Washington, event at 19: 55 on 1949 April 13, recorded at OHT. Point T is from the Edgecumbe event at 01 : 42 on 1987 March 2, recorded at MDD. (g) Records for events with 6.5 I M < 7.0, approximating all events as extended sources, using fault plane coordinates listed in Table 3. Points R, S and T and U are documented in the caption for (f). (h) Records for events with 7 . 0 5 M I 7.5.

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A

m \ 111 \ E

W

\

u U d

L 0 L

1' d a, a

Joyner and Boore ( 1981 ) law Joyner and Boore ( 1981 1 law

t

1 .0

10.0

1.0

Distance / k m

Campbell (1981) law

Figure 10. (Continued.)

whichever is greater. In the second definition, superscripts + and - denote peaks in the positive and negative directions of the record on the two orthogonal horizontal components, denoted by subscripts 2 and 3 in Table 2; thus, a; means the peak acceleration in the negative direction on component 2 of horizontal ground acceleration. The second definition is an attempt to take into account the differences in peak acceleration in opposite directions on an individual horizontal component, as well as variations in peak acceleration between horizontal components. The first definition sets a minimum level for the uncertainty of a particular peak horizontal acceleration, to allow for

* 10.0 ln \ m \ E

W

\

u U d 1.0

L o r A d aJ Q

Distance / k m

Campbell (1981 ) law

10.0

1.0

0- 10. 100.

Distance k m

uncertainty in instrumental calibration, digitization, and in the fitting of a baseline through the records. The margin of 20 per cent is consistent with the scatter identified in different processing procedures through tests carried out by Boore & Joyner (1982). We have also defined a scaled predicted PHGA, A:

(4.16) A =Fa;,

where F is a dimensionless scale factor of the order of 1. Thus, if, for a particular set of records, A and ah are on average equal, with F = 1, then the empirical law predicts the observed PHGA well. If A and ah are on average equal,

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Joyner avld Boore ( 1981 ) law Joyner aod Boore C 1981 ) law

10.0 m \ 111 \ E

W

\

U : 1 . 0

d a, a

Distav lce ’ km

Campbel l (1981 ) law

10-0-

1 . 0

Figure 10. (Conrinued.) with F < 1, then the law overestimates observed PHGA. To investigate the ability of empirical laws to predict observed PHGA, we have looked for the value of F that minimizes, overall, the mismatch, ah - A, between the observed and predicted PHGA. We have weighted the mismatch of each of N data points by a factor W using a Gaussian weighting scheme:

(4.17)

and have defined a correlation coefficient C as the mean of

A

111 \ m \ E

W

\

U cl

L 0 8

d aJ a

10.0

1 .0

10. 100 * D i s t a n c e ’ km

Campbell C 1981 ) law

10. 100. D i s t a n c e / km

the N weighted mismatches:

(4.18)

The value of F that maximizes C indicates the condition under which, overall, the scaled predicted PHGA most closely matches the observed PHGA.

We compiled information on site conditions of accelerograph stations in Table 2. However, neither Joyner & Boore (1981) nor Campbell (1981) predicted that PHGA depends on site conditions, so these are not used in our

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552 R. Westaway and R. B. Smith r\

\ ul \ E v * 10mOm ul \ E v

1 0 . 100. Distance 1 km

Rgme 11. Comparison of observed PHGA values for earthquakes of magnitude 6.5 or greater with a law of the type shown in Fig. 5. PHGA and source-station distance have been calculated using the Joyner & Boore (1981) definitions, using the extended source coordinates in Table 3.

comparison. We have not considered any possible upward bias on observed PHGA due to the absence, for some earthquakes, of records from stations where PHGA was too low to trigger recording. Our weighting scheme assigns equal a priori weight to each record, unlike, for example, the Campbell (1981) procedure that weighted all data from each earthquake within specified distance ranges equally regardless of the number of records.

Before making our quantitative cornparison, we eliminate the 'anomalous' ground acceleration records from the Mammoth Lakes, Helena, and Campania-Basilicata events. Due to the large number of records that the Campania- Basilicata mainshock contributes, an additional effect that we consider concerns the range of estimates of magnitude for it. These include M, 6.92 (Boschi et al. 1981), Ms 6.9 (NEIS) and Ms 6.8 (ISC). Also, Westaway & Jackson (1987) have suggested that the initial ruptures in this event, which we believe were responsible for the observed PHGA values, had a seismic moment of 13.2 X 10" Nm, equivalent

From Fig. 10(d) and (e), we note that all records from station LVD for the Mammoth Lakes earthquakes involve PHGA several times that predicted by the empirical laws. Station LVD is in a dam, where amplification of ground accelerations by a factor of 2 or more (e.g. Priscu, Popovici & Stematiu 1985) may occur due to the response of the structure. Consequently, we exclude these records. How- ever, we note in passing that in the case of the Edgecumbe mainshock, PHGA in the direction perpendicular to the Matahina Dam face increased by less than 50 per cent at the dam crest (3.43ms-*) compared with at the base of the dam (2.36ms-*) (Prender & Robertson 1987). As was mentioned in Section 2, all records of the Mammoth Lakes event at 14:51 on 1980 May 27 should be excluded because this event probably involved too large a component of strike slip. Consequently, no Mammoth Lakes records have been included at all, and our conclusions are therefore

to Mw 6.71.

independent of any controversy concerning the source mechanics of the Mammoth Lakes events. The Puget Sound event has also been excluded , for the reasons discussed in Section 4.3. As can be seen from Fig. lO(f), it generated a PHGA about three times larger than would be predicted from the empirical laws, for a source-station distance of 50km. We also note that PHGA for the Helena earthquakes is a factor of 2 or more below that expected from the empirical laws. The low natural frequency, only lOHz, of the accelerograph installed at Helena in 1935 (Section 2) would eliminate higher frequencies that may have otherwise contributed to the observed PHGA. Campbell (1981) included the records from the 1935 October 31 event in his analysis, and his conclusion that PHGA from normal-faulting and strike-slip earthquakes is anomalously low may be due to the use of these records from a non-typical instrument. We exclude these records also. Points due to the 38s late rupture in the Campania-Basilicata event (Fig. 10e) lie systematically below the values predicted by empirical laws. Our choice of M, 6.28 for this event is from teleseismic waveform modelling by Westaway & Jackson (1987). These authors stressed that the seismic moment that they deduced is subject to great uncertainty because of the very limited number of teleseismic stations in a suitable distance range to record this sub-event clearly. The trend of data in Fig. lO(e) suggests that Westaway 8c Jackson (1987) overestimated the seismic moment, and hence M,, for this event. Nonethe- less, to illustrate the importance of this event, we will compare observed and predicted PHGA both including and excluding it.

In making our comparisons we need to consider the effect of uncertainty in source-station distance, both due to uncertainty in location and, in the case of larger events, due to the size of the fault-plane. Finally, we note the need to take careful account of the systematic underestimation of observed PHGA by the Joyner & Boore (1981) law at distances greater than about 60km. We achieve this by separating our data into two subsets, according to whether source-station distance is greater than or less than 60 km. This break at 60km also assists in comparison with the Campbell (1981) law, which was established using only data from distances less than 60 km.

First, restricting our comparison to distances less than Wkm, Fig. 12 shows C against F for the 40 data points from events with magnitude greater than 5 . In this comparison, we have assumed point sources for all events. Joyner & Boore (1981) overestimate observed PHGA by about 10 per cent, while Campbell (1981) underestimates it by about 20 per cent. Using the same data, but with extended sources for the events in Table 3, Joyner & Boore (1981) underestimate observed PHGA by about 12 per cent, and Campbell (1981) predicts observed PHGA well (Fig. 13). In Figs 14 and 15 we have used the same data as in Figs 12 and 13, but we have also incorporated uncertainty in source-station distance due to uncertainties in location. We achieved this by adjusting each source-station distance, within limits equal to its error bounds, in order to maximise, for each value of F, the match between observed and predicted PHGA. In the case of a point-source approximation, this results in Joyner & Boore (1981) overestimating PHGA by 15 per cent and Campbell (1981) overestimating

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0.65- .

0 .60 -

Fit to Joyner and Boore ( 1 9 8 1 ) Fit to Campbell (1981)

I I I I I I I I I 0.65 I I I I I I I I I

- 0.60 - -

C 0 . 3 0 -

r' 0.25 -

aJ 0 . 2 0 -

2 2

L : 0 . 1 5 - U

0 . 1 0 -

0 .05 -

0 .OO

it by 8 per cent (Fig. 14). Using extended sources and value of F at which this maximum value occurs. incorporating uncertainty in source-station distance (Fig, Consequently, in all subsequent figures, we have used this 15), Joyner & Boore (1981) overestimate PHGA by 20 per adjustment technique. cent and Campbell (1981) estimate PHGA well. Com- Next, we consider the distance range 60-200 km. 19 data parison of Figs 12 and 14 with Figs 13 and 15 suggests that points were available in this range: two from Edgecumbe, adjusting source-station distance within error limits im- six from Campania-Basilicata, six from Borah Peak, three proves the maximum value of C, but affects very little the from the Biga, western Turkey event of 1983 July 5 , and two

- C 0.30 - ' 4

-

- J 0.25 -

- 0 0.20 -

-

A

L -

- : 0 . 1 5 - 0

-

- 0.10 - -

- 0.05 - -

I I I I I I I I I 0 .OO I I I I I I I I I

Fit to Joyner and Boore ( 1 9 8 1 ) Fit to Campbell (1981 )

0.10 - 0.05 -

- -

0.00 J 0.5 0.6 0.7 0.8 0 .9 1 .0 1 . 1 1 .2 1 . 3 1 .4 1 .5

0 .10 -

0.05 -

0 .OO

'J

-

-

I I I I I I I I I

c' c

C L CL 0 U

0 '\

'\

0.35

Acceleration scale Factor, F Acceleration scale factor, F

Flgm W. Variation of C against F for our comparison of PHGA observed at distances 0-60 km with PHGA predicted by empirical laws. In this comparison, the larger events in Table 3 are approximated as extended sources and no allowance is made for uncertainty in hypocentral coordinates.

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6 0.35-' J 0.30 - ; 0.25 -

d

: 0 . 2 0 -

0 0.15, 0

0.10 - 0.05 - 0 .OO

F l t i o Joyner and Boore ( 1981 ) F i t t o Campbell ( 1981 )

-

-

- - - - -

I I I I I I I I I

0 0

U

6 0 . 3 5 - J 0 . 3 0 -

; 0.25 -

u 0 . 1 5 - 0.10 - 0.05 - 0 .OO

4

0 k 0 . 2 0 -

.40 4 L

- = 0.35 - - c, 0.30 - - ; 0.25 -

- u 0 . 1 5 - - - 0.10 - - - 0.05 - -

- 2 - -

- k 0.20 - -

I I I I I I I I I 0 .OO I I I I I I I I I

:;: j .25

0.00 -

u 0.15 8.10 0.05

; 0.20

0 .5 0.6 0 .7 0.8 0 . 9 1 .0 1 . 1 1 .2 1 .3 1 .4 1 .5

A c r e l e r a t i o n s c a l e Fac to r , F A c c e l e r a t i o n s c a l e Fac to r , F

Figure 14. Variation of C against F for our comparison of PHGA observed at distances 0-60 km with PHGA predicted by empirical laws. In this comparison, all events are approximated as point sources and allowance is made for uncertainty in hypocentral coordinates.

from Hebgen Lake. Using the extended source for the Campania-Basilicata event, Joyner & Boore (1981) overestimate PHGA by about 50 per cent whereas Campbell (1981) predicts observed PHGA well (Fig. 16). In Fig. 17, observed and predicted PHGA are compared over the full distance range 0-200km. In this case, Joyner & Boore (1981) overestimate observed PHGA by 17 per cent, whereas Campbell (1981) underestimates it by 8 per cent. In the case of Joyner & Boore (1981), the greater number of

data points from 0 to 60 km outweighs the number between 60 and 200 km, leading to this net overestimation.

In Fig. 18, we investigate the effect of the inclusion of 10 extra data points, in the distance range 0-60km, for the delayed 38 s rupture of the Campania-Basilicata event. With these additional data, Joyner & Boore (1981) overestimate observed PHGA by 25 per cent, and Campbell (1981) overestimates it by 10 per cent. This increase in overestimation under both laws in comparison with the data

F i t t o Joyner and Boore (1981 ) F i t t o Campbell ( 1 9 8 1 )

p*lporr 15. Variation of C against F for our comparison of PHGA observed at distances 0-60 km with PHGA predicted by empirical laws. In this comparison, the larger events in Table 3 are approximated as extended sources and allowance is made for uncertainty in hypocentral coordinates.

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? 0 . 2 0 -

0 . 1 5 -

0.10-

0.05 - 0.00

Fit to Campbell (1981) Fit to Joyner and Boore ( 1981 )

- - - -

I I I I I I I I I

I I I I I I I I I l l 0 .65

U 0.60 7 c

0.25 - 0.20 - 0.15 - 0.10 - 0.05 - 0 .OO

J ' 0.50

0.45

0 0.40

2 0.35

(L

- - - - -

I I I I I I I I ~

' z! 0 . 3 0 4

2 0.25

8.20

2, 8.15

2

u

0.05 i

L

0.00 1 0.5 0 .6 0 .7 0.8 0.9 1 .0 1 . 1 1 .2 1 . 3 1 . 4 1 .5

0.75 0.70 * .65

.60

.55

.50

.45

.40

.35

.30

2 0.25

0.20

0.15

0.10

0.05

0 .OO .--

0.5 0.6 0.7 0.8 0.9 1 .0 1 . 1 1 .2 1 .3 1 .4 1 .5

Acceleration scale Factor, F Acceleration scale Factor, F

Figure 16. Variation of C against F for our comparison of PHGA observed at distances 60-200 km with PHGA predicted by empirical laws.

presented in Fig. 15, which are otherwise equivalent, highlights the anomalously low PHGA generated by this late rupture. As already mentioned, this may be due to its magnitude having been overestimated by Westaway & Jackson (1987). Finally, we investigated the effect on our original 40 data points of substituting Mw 6.71 instead of Mw 6.92 for the main Campania-Basilicata event. This caused very little change in the profile of C against F in comparison with Fig. 15, so we omit plots of these data.

Overall, the Campbell (1981) law predicts PHGA well for normal-faulting earthquakes with magnitude greater than 5

both from 0 to 60 km, and from 60 to 200 km. We find this remarkable considering this law was derived using only data from distances below 60 km. The Joyner & Boore (1981) law slightly overestimates observed PHGA at distances closer than 60 km, but substantially underestimates it between 60 and 200 km. Campbell (1981) pointed out this overestimation over most of the range 0-60km, and showed that it is not a consequence of the different definition of PHGA used by Joyner & Boore (1981). The good match of observed PHGA for our set of normal- faulting earthquakes to the prediction by Campbell (1981) of

Fit to Joyner and Boore ( 1 9 8 1 ) Fit to Campbell (1981)

CL (L QI

U

0 L L V

Acceleration scale Factor, F Acceleration scale Factor, F

enSpre 17. Variation of C against F for our comparison of PHGA observed at distances 0-200 km with PHGA predicted by empirical laws.

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0.75 - 0.70 -

Fit to Joyner and Boore ( 1981 ) Fit to Campbell ( 1 9 8 1 )

I I I I I I I I I - -

0.40 -" 0.35 - 0.30 - 0.25 -

0.20 - 0 . 1 5 -

0.10 - 0.05 - 0 .OO

U

J c aJ

U

LL CL aJ 0 U

c 0

J 6

aJ L L 0 u

d -

- 2

- - - -

- - - -

I I I I I I I I I

0.10 - 0.05 - 0 .OO

Acceleration scale Factor, F Acceleration scale Factor, F Figure 18. Variation of C against F for our comparison of PHGA observed at distances 0-60 km with PHGA predicted by empirical laws. This figure incorporates 10 extra data points from the 38 s delayed rupture of the Campania-Basilicata earthquake in addition to the data in Fig. 15.

- -

I I I I I I I I I

PHGA for reverse-faulting and strike-slip events suggests that there are no grounds for concluding that PHGA for normal-faulting earthquakes is any different from that predicted for other events. The less satisfactory match with the Joyner & Boore (1981) law at distances greater than 60 km may, as already suggested, be an effect of their choice of algebraic form of their law, which assumes a geometrical spreading factor appropriate for direct body-waves, not guided body-waves or surface-waves.

5 CONCLUSIONS Our aim has been to investigate whether PHGA from normal-faulting earthquakes is different from PHGA due to other events. We have attempted to do this by comparison of PHGA observed in normal-faulting earthquakes with PHGA predicted for other events using empirical laws. PHGA for normal-faulting earthquakes agrees well with PHGA predicted for other events using the Campbell (1981) law. Joyner & Boore (1981) overestimate PHGA slightly at distances closer than 60 km and underestimate it at greater distances. We suggest that this underestimation is due to the Joyner & Boore (1981) law assuming that PHGA is governed at all distances by anelasticity and geometrical spreading for direct S-waves.

As part of this investigation, we have suggested several other important results. First, for smaller events at relatively small source-station distances PHGA occurs at a time that is consistent with it being in the direct S-phase. Second, for larger events at relatively small source-station distances, PHGA is frequently up to several seconds later than the direct S-wave arrival time. This may be a consequence of the duration of the source time-functions of these events. Third, for larger events, with magnitude greater than 5 , the variation of PHGA with source-station distance, at distances up to a few tens of km, is mainly controlled by geometrical spreading and not by anelasticity. Fourth, a definition of

PHGA as the maximum acceleration on either horizontal component is more robust than a definition as the means of the maximum accelerations on the two horizontal components. Fifth, PHGA for events below magnitude 5 decreases rapidly with distance at distances greater than about 10km, in a manner that approximates to being inversely proportional to distance squared. We suggest that this may be due to the effect of anelasticity on the relatively high frequency content of the signal radiated by small earthquake sources.

In Section 2 we mentioned several independent earlier results that suggested that PHGA is systematically smaller for normal-faulting earthquakes than for other events. One of these arguments was based on the idea that if normal faulting is assisted by gravity, the stress drop of normal-faulting earthquakes is likely to be smaller than for other events, and PHGA, which depends on stress drop, is also likely to be smaller. Our result that PHGA for normal-faulting earthquakes is no different from that observed for other events implies that this argument is wrong, and suggests that gravity has negligible effect on the timescale of source rupture processes that are responsible for generating high-frequency seismic waves. This suggestion could be tested independently by comparing stress drops of normal-faulting earthquakes with those of other events.

We have suggested a form for the variation of PHGA with source-station distance (Figs 5 and l l ) , which we believe is superior to the laws that we have considered. This implies that PHGA is in the direct S-phase at close distances but may be in slower guided S-phases or surface-wave phases, with different geometrical spreading, at greater distances. This form of law also incorporates the effect, at relatively close distances, of the complicated interaction between S-waves and the earth's surface. Any refined law should also incorporate correction for the radiation pattern

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of the earthquake source for the seismic phase responsible for PHGA. We will attempt the matching of observed PHGA to a law of this form in a future article.

ACKNOWLEDGMENTS Many people have assisted us, either by supplying strong ground motion records o r other information, or by discussing our results and suggesting improvements in their presentation. W e would like to thank H. Anderson, R. Ateg, H. Benz, J. Boatwright, J. Bommer, J. Brady, K. Campbell, P. Carydis, S. Crampin, J. Crowder, A. Espinosa, A. Hughes, A. McGarr, G. McVerry, J. Menu, C. Mueller, D. Papastamatiou, M. Peronaci, D. Rinaldis, J. Watson, T. Wallace, and G. Woo. W e would particularly like to thank N. Ambraseys, J. Jackson, and, especially, D. Boore, who, together with two anonymous referees, provided detailed constructive criticism of this article that improved it considerably. We are also grateful to P. Bernard, K. Campbell. and A. Cisternas for providing us with preprints of their articles. Parts of this work were carried out under contract no. 1186012542 of Science Applications International Corporation, Las Vegas, Nevada and under US Geological Survey Earthquake Hazards Reduction Program contract no. 14-08.

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