Highland Boundary Fault Zone: Tectonic implications of the Aberfoyle earthquake sequence of 2003

Tectonophysics 430 (2007) 83 – 95 www.elsevier.com/locate/tecto

Highland Boundary Fault Zone: Tectonic implications of the Aberfoyle earthquake sequence of 2003 L. Ottemöller ⁎, C.W. Thomas British Geological Survey, Murchison House, West Mains Road, EH9 3LA, Edinburgh, United Kingdom Received 30 January 2006; received in revised form 6 November 2006; accepted 15 November 2006 Available online 3 January 2007

Abstract The Highland Boundary Fault Zone (HBFZ) is one of the major faulted tectonic boundaries in Great Britain. Historically, seismicity has occurred in this zone around the town of Comrie. But an earthquake sequence that occurred in 2003 near the village of Aberfoyle (ML 1.3–3.2) was the first significant activity to be recorded in the HBFZ since the installation of modern seismograph networks in the 1970s. This study describes detailed analysis of these data. The waveform signals of the events were almost identical and by applying a cross-correlation technique combined with multiple event location, the alignment of the events was found to be WSW–ENE. This alignment matches one of the nodal planes determined by joint focal mechanism analysis. The fault plane dips to the northwest, and shows oblique sinistral strike–slip with normal movement. The orientation of the event alignment matches the direction and orientation of observed features in the HBFZ. Hence, it is concluded that the WSW–ENE striking nodal plane was the causative fault that is associated with the HBFZ. The orientation of maximum compressional stress is rotated from the regional average expected due to the Mid-Atlantic ridge-push force. This rotation is possibly explained by stresses due to postglacial rebound. Smaller events in the sequence were used as empirical Green's functions and deconvolved from the larger events to determine source time functions. The corresponding corner frequencies matched results from spectral fitting, showing that the events were of relatively low stress drop. © 2006 Elsevier B.V. All rights reserved. PACS: 91.30.Bi; 91.30.Dk; 91.30.Vc Keywords: Highland Boundary Fault; Waveform correlation; Empirical Green's function; Multiple event location

1. Introduction The Aberfoyle earthquake sequence that occurred between June and September 2003 was located about 3.5 km WSW of the village of Aberfoyle, where the larger events were felt (Figs. 1 and 2). The epicentres lie adjacent to the surface trace of the Highland Boundary Fault Zone (HBFZ), one of the fundamental structural

⁎ Corresponding author. Tel.: +44 131 6500224. E-mail address: [email protected] (L. Ottemöller). 0040-1951/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.tecto.2006.11.002

boundaries in Scotland, defining the southeastern limit of the Grampian Highlands (Fig. 1). On land, the HBFZ trace extends from Stonehaven on the east coast to the Isle of Arran in the west, and it forms a major basement structure northeastwards into the North Sea, where it is interpreted to have influenced late Palaeozoic and Mesozoic (24–65 Ma) rifting patterns and to coincide with changes in thickness of Permian and Triassic strata (Zanella et al., 2003). To the west, it continues southeast of the Kintyre Peninsula (Pharoah et al., 1996) into Northern Ireland, where it appears to be represented by the Antrim–Galway Line, a prominent lineament

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Fig. 1. Tectonic overview showing the Highland Boundary Fault Zone extending from the Isle of Arran to Stonehaven, the locations of Aberfoyle, Dunoon and Comrie seismic events, and tectonic lineations. Circles show earthquake locations (ML ≥ 2.5). Historic seismicity (before 1970) is light grey, and instrumental seismicity (since 1970) is dark grey. The inset map shows the location in Great Britain. The box including the Aberfoyle earthquakes indicates the area shown in Fig. 2.

defined on geological and geophysical grounds (Ryan et al., 1995). The HBFZ separates rocks in the Scottish Midland Valley from Neoproterozoie to Cambrian rocks of the Dalradian Supergroup underlying the Highlands (Fig. 2). Included within the fault zone are slivers of Cambro–Ordovician rocks of oceanic origin assigned to the Highland Border Complex. It is a complex structure with a long history. Its significance as a major tectonic boundary is unquestioned, although its origins and significance as an early structure remain unclear (Dentith et al., 1992). Other major faults converge in the Aberfoyle area. The principal ones include the Loch Tay Fault Zone and the related Duke's Pass and Loch Ard faults (Fig. 2). These faults are essentially strike– slip structures that were active in mid-Palaeozoic times (Treagus, 1991) and upon which there has been strike– slip of the order of kilometres and dip slips of the order of hundreds of metres. It is likely that the Loch Tay to Loch Ard fault system represents a strike–slip transfer system that accommodated SSW to SW directed sinistral movement within the Grampian Highlands.

In historic times, the area around Comrie has been fairly active with 33 events between 1608 and 1921; the largest event was an ML4.8 event in 1839. The magnitudes of historic events are determined from macroseismic observations and are calibrated against the instrumental local magnitude scale (Musson, 1996). Since the installation of seismic stations in the 1970s, few earthquakes have been observed in the HBFZ. Of note is an earthquake that occurred on 16 September 1985 near Dunoon in the HBFZ at a depth of about 6.5 km with ML3.3. Redmayne and Musson (1987) suggested that leftlateral strike–slip movement with a small normal component had occurred on a fault striking WSW–ENE and dipping south. A composite focal mechanism for an earthquake swarm in the Kintail area of NW Scotland in 1974 similarly showed left-lateral movement on the SW– NE striking Strathconon fault (Assumpção, 1981). The Arran earthquake of 1999 also showed the same style of faulting (Bott et al., 1999). Earthquake swarms are relatively common in Great Britain, examples include Comrie (1788–1801, 1839–46), Glenalmond (1970–72),

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Fig. 2. Simplified and schematic geological map of the Aberfoyle district, showing the principal fault systems. Fault planes within the HBFZ are not seen in outcrop. Evidence from the zone elsewhere along its length indicates that it is a steeply NW-dipping structure. Other faults are near-vertical where seen in surface outcrop. From geological surveys in the district and from other regional data, the Loch Tay – Duke's Pass – Loch Ard fault system is known to have a significant strike–slip displacement of the order of kilometres, in common with other similarly orientated faults in the Scottish Grampian Highlands (Treagus, 1991).

Doune (1997), Blackford (1997–98, 2000–01), Constantine (1981, 1986, 1992–4), John Stonbridge (mid 1980s), Dumfries (1991, 1999), Manchester (2002) and Eskdalemuir (2003). The regional stress pattern in Great Britain shows predominantly horizontal compression in the NNW– SSE direction (Gölke and Coblentz, 1996; Main et al., 1999; Baptie, 2002) due to ridge-push forces from the Mid-Atlantic ridge. Stresses arising from postglacial rebound, with present maximum uplift rates of 2 mm/ year in the Scottish Highlands (Shennan, 1989) are also considered to cause earthquakes in Scotland (Main et al., 1999; Stewart et al., 2000; Firth and Stewart, 2000; Muir-Wood, 2000). It is disputed whether the ridge-push or glacial rebound is the dominant force causing earthquakes in NW-Europe (Stein et al., 1989; Gregersen, 1992; Stewart et al., 2000; Fejerskov and Lindholm, 2000; Fjeldskaar et al., 2000; Hicks et al., 2000b). Following a review of the tectonic history of the HBFZ, we describe our analysis of the seismic recordings of the 2003 earthquake sequence. We determine precise relative locations using multiple event location

techniques, a joint focal mechanism and spectral source parameters. Based on these results we give a tectonic interpretation. 2. Tectonics of the Highland Boundary Fault Zone The origin and earliest history of the HBFZ are obscure, but available geological evidence indicates that the Midland Valley and Highlands terrains were juxtaposed across the HBFZ by late Silurian times (443–417 Ma) (Haughton et al., 1990) within a sinistral–transpressional, strike–slip regime. Subsequently, periodic movements from the late Silurian to Early Carboniferous (354–290 Ma) focussed on the HBFZ and related fracture systems considerably influenced the tectonic development of, and sedimentation within, the Midland Valley. Although the geometry and history of fault movement within the HBFZ are complex, in general the gross sense of movement was reverse across apparently high angle, north-west dipping fault planes. Surface exposures along the length of the fault zone indicate steeply dipping faults, but the nature of the HBFZ at depth is

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unclear. Gravity anomaly data from the vicinity of the HBFZ were interpreted by Dentith et al. (1992) to show that the fundamental bounding structure may be a lowangle, northerly-dipping thrust fault, supporting the suggestion by Bluck (1984) that the present-day line of the fault is due to later thrusting in the Late Devonian (417–354 Ma) and Early Carboniferous. However, strike–slip movement is recorded locally by horizontal slickensides (Anderson, 1951). This, coupled with the evidence for the faults being high-angle, northwesterly dipping structures, at least near surface, indicates major strike–slip movement within the transpressive regime that juxtaposed the different Highlands and Midland Valley terrains during the late Silurian and early Devonian (Haughton et al., 1990). The present distribution of the Lintrathen Pophyry (Crawton Volcanic Formation), exposed in Glen Isla and farther to the east and southeast of the HBFZ (Trench and Haughton, 1990) implies a sinistral offset of about 40 km, which occurred in Mid-Devonian (Acadian) times. During Lower Devonian times, the Midland Valley to the south of the HBFZ was a major, NE-trending, subsiding basin that was flanked to north and south by upland areas, with rejuvenation of the northern uplands resulting from intermittent uplift on the HBFZ. In the Middle Devonian, Acadian compressive earth movements briefly brought about marked changes in the palaeogeography of Central Scotland. The deposition of the ca. 1750 m thick Strathfinella Conglomerate in the late Emsian implies that the Highland area was also uplifted significantly relative to the Midland Valley, coeval with the earliest phase of these movements. Lower Devonian rocks were folded into NE-trending structures, most notably the Strathmore Syncline, the steep northern limb of which lies adjacent to the HBF. Continued uplift and thrust movements on elements of the HBFZ resulted in the erosion of any Lower Devonian rocks deposited to the north of the fault system, whilst within the Midland Valley basin, Lower Devonian rocks were deeply eroded, particularly along anticlinal axes. Detritus in Upper Devonian strata in the Aberfoyle district were probably derived from a Highland source area, maintained as an area of positive relief by continued uplift along the HBFZ. Southwest of Loch Lomond, Late Devonian and Early Carboniferous rocks are preserved on the northwest side of the HBFZ, down-thrown by Carboniferous or later normal fault movement. The deposition of the Early Carboniferous Inverclyde Group was preceded by uplift, erosion and renewed subsidence, again focused along the HBFZ and there is evidence for further reactivation during the Early Carboniferous

(Paterson et al., 1990). However, most faults and fractures affecting Lower Carboniferous and older strata in this area have the NE and NW trends that are developed widely in the Midland Valley. Such structures are common in the vicinity of the HBF, particularly in the Aberfoyle district; these fractures are probably of Variscan age or younger. Most are major joints with little displacement across them, but some are faults with minor oblique slip displacements. Normal, dip–slip faults in this set displace rocks belonging to the Early Devonian Arbuthnott and Garvock groups in the Aberfoyle district. Fault movements thus continued at least into late Palaeozoic times. The lack of rock units younger than the Carboniferous along the HBFZ in Scotland preclude elucidation of post-Carboniferous movements. However, given the influence of the HBFZ on rift structures and interpretation of late Palaeozoic and Mesozoic strata in the North Sea, some activity on the fault since the Carboniferous is considered likely. 3. Multiple event location 3.1. Method and data processing The clustering of events combined with good station coverage (Fig. 3) suggested that the relative locations of the events could be improved using multiple event location techniques. Furthermore, visual inspection of the seismograms recorded from the earthquakes in the sequence indicated a high degree of similarity between the individual events; seismograms from station Carrot (PCA) are given in Fig. 4 as an example. The waveform similarity suggested that the events were located within a small source volume and associated with a single source mechanism. Waveform similarity had previously been reported for earthquake sequences in Scotland at Kintail (Assumpção, 1981) and Carlisle (Marrow and Roberts, 1985). We used two different techniques for multiple event location (MEL) to evaluate the stability of the results. First, we applied the double difference method (DD) of Waldhauser and Ellsworth (2000) which has provided significantly improved relative locations in a number of cases (e.g., Waldhauser and Ellsworth, 2002; Hauksson and Shearer, 2005). The DD minimises the difference between the travel time residuals of earthquake pairs and since the velocities along a path for neighbouring earthquakes recorded on one station are nearly identical, no station- or source-specific corrections are required. The method allows combination of catalogue readings with precise relative travel time differences obtained through

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Fig. 3. Locations of stations used for waveform cross-correlation. The black square in the centre represents the epicentral area. The inset map shows the location in Great Britain.

waveform correlation. The absolute locations are determined by the catalogue data, while the relative locations are determined by precise travel time differences. The hypoDD software (Waldhauser, 2001) was used for computation. Second, we used Joint Hypocenter Determination (JHD), which jointly inverts for hypocentre locations and station residuals (e.g., Pujol, 1988; Kissling et al., 1994). With event clustering, as in this case, inversion for station corrections leads to improved relative event locations. The JHD was performed using the VELEST software (Kissling, 1995) by damping velocity in the inversion. In both methods, the velocity model derived from the LISPB profile for Central Scotland was used (Assumpção and Bamford, 1978; Bamford et al., 1978). The similarity in the seismograms was used to obtain accurate and consistent phase arrivals by computing waveform cross-correlation (Schaff and Richards,

2004). The correlation rxy function between two signals x and y is given by X

xj yiþj

j

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : rxy ðiÞ ¼ rffiffiffiffiffiffiffiffiffiffiffiffi X rX x2j y2iþj j

ð1Þ

j

The maximum amplitude in the cross-correlation function was used in two ways: 1) Relative travel time differences were measured between all events at individual stations. Both P and S wave data were extracted based on computed arrival times. This data was then used in the DD calculations. 2) Seismograms from the first event in the sequence were used as master signals. Based on manual phase picks, signals from subsequent events were extracted, and correlated with the master signals to determine consistent and precise absolute

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Fig. 4. Band-pass filtered (3–8 Hz) displacement (in nm) seismograms for events of the Aberfoyle earthquake sequence as recorded on the shortperiod station at Carrot (PCA) at an epicentral distance of 54 km. The time scale (in UT hh:mm:ss) is identical for all traces while the amplitude scale is set for each trace individually. The traces are aligned on the P-wave arrival indicated by the first vertical line. The second vertical line is aligned with the approximate S-wave arrival.

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arrival times to be used as input for the JHD calculations. In both cases, data were filtered with a pass-band of 3 to 8 Hz. Window lengths for P and S waves were 2 and 4 s, respectively. A minimum correlation of 0.7 was required for a reading to be made. A number of stations were selected to achieve good azimuthal coverage (Fig. 3). The cross-correlation provided robust results. For smaller events in particular, where the signal to noise ratio was worse, more consistent phase arrivals were obtained compared to those obtained by manual analysis. For smaller events (ML ≤ 1.5) at larger distances (N150 km) the initial Ponset, as seen for the larger events, disappeared in the noise, while later larger arrivals appeared to be first arrivals. The cross-correlation technique identified the

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correct arrival time based on correlation of the latter part of the signal. 3.2. Results Fig. 5 shows the comparison of results from DD and JHD with single event locations (SEL) based on manual phase readings. The results from both DD and JHD are rather similar with a clear alignment of hypocentres in the WSW–ENE direction at a depth of about 4 km. The cluster size of the DD locations is slightly less than for the JHD locations. Therefore we consider the DD locations to be superior and use them in the following analysis (Table 1). However, both methods provide a significant improvement in location compared to the

Fig. 5. Top: comparison of SEL epicentre locations (squares) with locations obtained through a) DD and b) JHD, based on arrival times measured with cross-correlation technique (circles). Bottom: depth section in EW direction, comparison as in top plot, c) DD and d) JHD.

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Table 1 Results from DD location of phase arrivals obtained with crosscorrelation technique #

Date Time ML Lat (ddmmyyyy) (hhmm) (° N)

Lon (° W)

Depth rms (km) (s)

1 2 3 4 5 6 7 8 9 10 11

20062003 20062003 20062003 23062003 25062003 26062003 27062003 27062003 27062003 23082003 15092003

4.4333 4.4342 4.4351 4.4375 4.4321 4.4373 4.4407 4.4380 4.4389 4.4373 4.4345

4.286 4.232 4.376 4.391 4.182 4.375 4.365 4.233 4.415 4.219 4.212

0644 0653 0903 1005 1153 0957 0209 0211 0312 0335 0800

3.2 2.8 2.5 1.3 1.4 1.5 2.8 1.3 1.3 1.5 2.2

56.1714 56.1705 56.1710 56.1701 56.1712 56.1699 56.1690 56.1690 56.1696 56.1692 56.1699

0.028 0.024 0.026 0.024 0.021 0.025 0.031 0.029 0.023 0.023 0.026

rather diffuse hypocentre distribution determined by SEL. The formal errors for the largest event in the sequence determined using SEL (Lienert and Havskov, 1995) were 3.1 km in longitude and in 1.3 km in latitude (90% confidence), which is representative of the error in absolute location of the sequence as a whole. The width of the alignment in the NNW–SSE direction is of the order of 100 m, the length is about 600 m in the WSW– ENE direction and the vertical extent is about 150 m. Synthetic tests were carried out to test the reliability of the results and to estimate uncertainties. We computed synthetic arrival times for the same stations and phases as used to obtain the SEL locations. The synthetic event epicentre locations were arranged in a cross shaped configuration of epicentres covering an area of the same size as the SEL locations. The hypocentral depths were set to the values computed from the real observations. The synthetic data-set was inverted with hypoDD, using the centre of the cluster as the starting location for all events. Fig. 6 shows that the synthetic locations were well resolved, which implies that the results of the real data are to be trusted. Based on the dimension of the source zone, the maximum error in relative locations of the sequence in all three dimensions was assumed to be less than 100 m. The synthetic tests showed that the error in relative location is even less, about 50 m. This represents a reduction in relative hypocentral error by a factor of more than 20 compared to SEL.

mechanism for the sequence based on first motion polarities was determined through a grid-search (Snoke et al., 1984) using polarity readings from 13 stations (Fig. 7). The solution was well constrained and out of several solutions we selected an average given by a strike of 243.8, dip of 65.6 and rake of − 32.7. The first nodal plane strikes in a WSW–ENE direction and dips to the northwest with oblique lateral strike–slip and normal movement. The second nodal plane strikes in a NNW–SSE direction and dips eastward with oblique right-lateral strike–slip and normal movement. The solution for the focal mechanism was verified by synthetic forward modelling (Fig. 7). The programs of Herrmann were used to compute full waveforms based on wavenumber integration (Herrmann, 1979; Wang and Herrmann, 1980). The good match between observed and computed seismograms for a number of stations further supports the results for both the hypocentre depth and source mechanism. The amplitude ratio between P and S waves is well modelled, as is the difference between nodal (e.g. ELO) and antinodal stations (e.g. PMS). Even at the shortest recording distance, station EAB (6 km) observed and computed seismograms were well matched. 5. Source parameters The source time functions of the larger events in the sequence (ML ≥ 2.5) were determined by using the smaller events (ML ≤ 1.5) as empirical Green's function

4. Focal mechanism The similarities in the observed waveforms between the events indicated that they followed the same rupture mechanism, and, as expected, there was a match in first motion polarities between the events. A joint focal

Fig. 6. Results from synthetic test: synthetic arrival times were computed for fixed locations forming a cross (stars) using the same station configuration as given for SEL locations (squares); the resulting locations (circles) when applying the DD method to the synthetic data-set were computed using the centre of the cluster as starting location for all events.

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Fig. 7. Top: observed (black) and synthetic (grey) displacement seismograms at selected stations for the event on 20 June at 09:03. The seismograms are filtered in the frequency band 0.5–2.0 Hz. The seismograms for station EAB are for a smaller event on 27 June at 03:12, and are filtered 3–8 Hz. Note the time scale for EAB is twice that of the other traces. Bottom: focal mechanism plot (lower hemisphere projection) of the Aberfoyle earthquake sequence. This mechanism (strike = 243.8, dip = 65.6 and rake = − 32.7) was used to compute the synthetic seismograms (top).

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(EGF) (Mueller, 1985). The deconvolution of the EGF from the larger events was performed in the frequency domain applying water-level stabilisation (Clayton and Wiggins, 1976). The smaller events used as the EGF were small enough to be considered point sources and of the same mechanism as the larger events. P-wave source time functions were computed for three stations by stacking results obtained from a total of 6 smaller events as EGF. Source time durations determined from either P or S waves were nearly identical. Examples of stacked source time functions at station PCA are shown in Fig. 8. The displacement pulse for the three events on 20 June was of rather simple shape. In contrast, a double pulse was obtained for the event on 27 June. Comparing the seismograms of this event to the others (Fig. 4) a more complicated P-wave onset was observed supporting the model of a double rupture for the 27 June event.

Table 2 Source parameters, seismic moment and corner frequency ( fc-spec) automatically determined from displacement source at stations EDI, ELO, KAR, KPL, MCD, MDO, PCA, PCO and PMS #

Date/time

M0 (Nm)

σ fc-spec fc-egf R MW ML (bars) (Hz) (Hz) (km)

1 2 3 4 5 6 7 8 9 10 11

20062003 0644 20062003 0653 20062003 0903 23062003 1005 25062003 1153 26062003 0957 27062003 0209 27062003 0211 27062003 0312 23082003 0335 15092003 0800

2.5E13 1.3E13 1.0E13 4.0E11 4.0E11 5.0E11 7.9E12 2.5E11 2.5E11 4.0E11 3.2E12

3.1 3.8 3.6 0.6 0.2 0.5 1.5 0.5 1.0 1.5 0.6

3.5 4.8 5.2 7.6 5.9 7.2 4.1 7.8 9.8 11.1 4.9

4.1 5.4 5.7

4.4

0.44 0.32 0.29 0.21 0.25 0.21 0.37 0.24 0.18 0.15 0.32

2.9 2.7 2.6 1.7 1.7 1.7 2.6 1.6 1.6 1.7 2.3

3.2 2.8 2.5 1.3 1.4 1.5 2.8 1.3 1.3 1.5 2.2

For comparison the table also gives fc-egf determined using EGF at stations PCA, PCO and PMS. The event numbering is as in Table 1.

In addition, both the seismic moment and corner frequency were determined for each event individually by an automated grid-search method (Ottemöller and Havskov, 2003). In this method, corner frequency ( fc) and seismic moment (M0) are found by minimising the difference between the observed displacement spectrum and the S-wave spectrum assuming a simple ω2 model (Aki, 1967; Brune, 1970). The computation was undertaken using S-wave spectra, where S-wave attenuation is described by the diminution function D( f )   −kTf Dð f Þ ¼ exp expð−kjf Þ ð2Þ Qð f Þ where T is travel time, f is frequency, κ describes nearsurface attenuation (Singh et al., 1982) and Q( f ) is the frequency dependant quality factor given by Sargeant and Ottemöller (submitted for publication)  0:45 f Qð f Þ ¼ 337 : ð3Þ 1:6

Fig. 8. Stacked source time functions obtained for events at station PCA. The source time functions were obtained by deconvolution of the smaller events, used as empirical Green's function, from the larger earthquakes.

The determination of fc is sensitive to the choice of κ. Our results (Table 2) are obtained without correction for κ as Q( f ) was derived without accounting for it. Tests confirmed that the correction for near-surface attenuation leads to higher corner frequencies and higher stress drop. The spectral analysis of the smaller events in the sequence (ML b 2.2) for κ = 0.0 resulted in rather low stress drop values. These may be unrealistic suggesting that correction for κ is required. The resulting corner frequencies are compared to the values obtained from the duration of the displacement pulse (Table 2). There is a good match between the results from the two methods showing the expected

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increase in corner frequency with decreasing event size for the three events on 20 June. However, the corner frequency for the event on 27 June at 02:09, derived using both methods. was smaller than for the event of the same magnitude on 20 June at 06:53, resulting from the double pulse as mentioned above. The EGF method is independent of correction for attenuation and, therefore, provides a means of evaluating the correction for attenuation in the spectral analysis. Our results show that the average Q( f ) for Great Britain is appropriate for the Aberfoyle area. Source parameters including seismic moment, moment magnitude, local magnitude, corner frequency and stress drop were derived for 11 events (Table 2). The moment magnitude for the larger events is below ML. However, in general there is reasonable agreement. Based on the source radius R assuming a circular fault (R = 0.35νs/fc) the stress drop was estimated (σ = 0.44 M0/ R3). Source radii were in the range 150 to 440 m. The stress drop values are in the range of about 0.2 to 3.8 bars, which means that within the errors there is no significant difference between the events. Fault slip computed for the largest event from the seismic moment using M0 = μ × A × d for μ = 2 × 1010 N/m2 is of the order of 0.4 cm. 6. Tectonic interpretation The match of epicentre alignment with the WSW– ENE striking nodal plane suggests that this was the causative fault plane. All events in the sequence occurred on a single rupturing fault segment. The source dimensions indicate that parts of the fault moved more than once, with maximum source size covering twothirds of the sequence length. Most of the events were contained within the source volume of the largest events (Fig. 9). However, the double rupture event on 20 June at 02:09 lies to the southwest of the main cluster. This location is possibly due to the larger uncertainties in phase times due to the more complicated source time function that resulted in waveform differences compared to the other events. The strike and northwesterly dip of the resolved fault compare well with the general orientation of faulting observed in the HBFZ at surface. At a depth of about 4 km, the earthquake hypocentres lie on a fault plane with a dip of about 65°. As a first-order estimate, simple trigonometry shows that this fault plane would project up to the southeast, intersecting the surface about 1.8 km from the epicentres. This is very close to the measured horizontal distance of the HBFZ from the epicentres. Although the absolute epicentre locations errors are

93

Fig. 9. Source size as given in Table 2 projected along the epicentre alignment in WSW–ENE direction.

larger than l km, the simplest interpretation is that the earthquakes result from movement on a fault plane that, at depth, lies within the HBFZ. The orientation of maximum compressional stress (σH) determined from the focal mechanism solution, is NNE–SSW (Fig. 7). For comparison, σH derived for other earthquakes in Scotland is directed predominantly N–S: Kintail, 1974 (Assumpção, 1981), Carlisle 1979 (Marrow and Roberts, 1985) Dunoon 1985 (Redmayne and Musson, 1987) and Arran 1999 (Bott et al., 1999). While these are the only earthquakes in Scotland for which a reliable focal mechanism has been determined, there are many more events of unknown mechanism that could be different from this trend. The orientation derived for the Aberfoyle earthquake sequence is rotated by about 90° from the expected σH due to the midAtlantic ridge-push that is observed in Great Britain south of Carlisle (Baptie, 2002). Rotation of σH is significantly less for the other Scottish earthquakes, and considering that the P and T axes derived from focal mechanisms may vary significantly from the principal stresses (McKenzie, 1969) are arguably in line with the regional stress pattern. The normal component of the oblique mechanism observed for Aberfoyle suggests that the vertical stress is larger than the minimum horizontal stress component leading to extensional tectonics. The estimated stress drop for the Aberfoyle events was less than the averages observed elsewhere (Kanamori, 1975). Considering the low stress drop, and rotation of σH from the regional average it is unlikely that the Aberfoyle earthquake sequence was caused by ridge-push stresses only. The

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earthquakes could be the result of localised stress sources such as lateral density contrasts and topography (Fejerskov and Lindholm, 2000). Considering a degree of consistency between the earthquakes in Scotland it is possible that they are the result of a less localised source such as flexural stresses due to postglacial unloading. Hicks et al. (2000a) found a similar rotation of σH for earthquakes in the Rana region on the Norwegian west coast, and observing similarities to the Meloy and Steigen earthquake swarms (see references in Hicks et al. (2000a)) argue that postglacial flexure is providing a consistent stress source over distances of several hundred kilometres along the Norwegian coast where uplift gradients are the highest. However, Hicks et al. (2000b) stress that the rotation of maximum compression is easily achieved if the ratio of maximum and minimum horizontal stress is near unity. The Aberfoyle earthquake sequence is similar to the Kintail earthquake swarm in 1974 (Assumpção, 1981) in various ways, and thus not uncommon. As mentioned above, fault orientation and direction of slip and thus stress orientation are similar. In addition, the earthquakes showed a high degree of waveform similarity within the respective sequences consistent with repetitive slip on the same fault. However, the earthquakes were slightly deeper at about 10 km. Earthquake sequences like these may be characteristic under the present tectonic setup in Scotland. 7. Conclusion The remarkable similarity amongst the events of the Aberfoyle earthquake sequence of 2003 was used to resolve relative hypocentre locations and to determine a joint focal mechanism. The data can be explained by a fault plane striking WSW–ENE with a dip to the northwest, matching the orientation of features in the HBFZ. Waveform modelling confirmed both the hypocentral depth of about 4 km and the fault plane solution. Horizontal dimensions of the sequence were 600 m by 100 m. With source radii of up to 440 m significant overlap of fault segments is indicated, and some of the segments probably moved more than once. Using smaller events in the sequence as empirical Green's function (EGF), source time functions were obtained for the larger events by deconvolution of the EGF. Interestingly, a ML2.8 event was shown to have been a double rupture. Results for corner frequencies determined from spectral fitting and EGF deconvolution were similar, suggesting that the average correction for attenuation was appropriate for the Aberfoyle area. However, an additional correction for near-surface attenuation may be required. The data and analysis indi-

cate that the earthquakes originated within the HBFZ, one of Scotland's major tectonic features. The orientation of σH derived from the Aberfoyle earthquake sequence shows a rotation by about 90° from the expected regional σH due to the mid-Atlantic ridge-push force. As this inferred stress orientation seems to prevail across Western Scotland, the earthquakes possibly are the result of flexural stresses caused by postglacial isostatic rebound. The HBFZ is a highly fractured zone and similar activity is to be anticipated in the future. Acknowledgements We appreciate discussions with Brian Baptie that helped to improve this work. The comments by two anonymous reviewers have helped to strengthen the paper. This paper is published with the permission of the Executive Director of the British Geological Survey (NERC). References Aki, K., 1967. Scaling law of seismic spectrum. J. Geophys. Res. 72, 1217–1231. Anderson, E.M. (Ed.), 1951. The Dynamics of Faulting. Oliver and Boyd, Edinburgh, UK. Assumpção, M., 1981. The NW Scotland earthquake swarm of 1974. Geophys. J. R. Astron. Soc. 67, 577–586. Assumpção, M., Bamford, D., 1978. LISPB V. Studies of crustal shear waves. Geophys. J. R. Astron. Soc. 54, 61–73. Bamford, D., Nunn, K., Prodehl, C., Jacob, B., 1978. LISPB-IV, crustal structure of Northern Britain. Geophys. J. R. Astron. Soc. 54, 43–60. Baptie, B.J., 2002. State of stress in the UK from observations of local seismicity. European Seismological Commission XXVIII General Assembly, Book of Abstracts. University of Genoa, Italy, p. 73. Bluck, B.J., 1984. Pre-Carboniferous history of the Midland Valley of Scotland. Earth Sci. 75, 275–295. Bott, J.D., Walker, A.B., Ritchie, M.E., 1999. Instrumental seismicity of Western and Central Scotland, 1969–1999. AGU Fall Meeting, Book of Abstracts. Brune, J.N., 1970. Tectonic stress and the spectra of seismic shear waves from earthquakes. J. Geophys. Res. 75, 4997–5009. Clayton, R.W., Wiggins, R.A., 1976. Source shape estimation and deconvolution of teleseismic bodywaves. Geophys. J. R. Astron. Soc. 47, 151–177. Dentith, M.C., Trench, A., Bluck, B.J., 1992. Geophysical constraints on the nature of the Highland Boundary Fault Zone in Western Scotland. Geol. Mag. 129, 411–419. Fejerskov, M., Lindholm, C., 2000. Crustal stress in and around Norway: an evaluation of stress-generating mechanisms. In: et al., A.N. (Ed.), Dynamics of the Norwegian Margin. Vol. 167 of Special Publications. Geological Society, London, pp. 451–467. Firth, C.R., Stewart, I.S., 2000. Postglacial tectonics of the Scottish glacio-isostatic uplift centre. Quat. Sci. Rev. 19, 1469–1493. Fjeldskaar, W., Lindholm, C., Dehls, J.F., Fjeldskaar, I., 2000. Postglacial uplift, neotectonies and seismicity in Fennoscandia. Quat. Sci. Rev. 19, 1413–1422.

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