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

Highland Boundary 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, 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 boundaries in , defining the southeastern limit of the Grampian Highlands (Fig. 1). On land, the HBFZ The Aberfoyle earthquake sequence that occurred trace extends from Stonehaven on the east coast to the between June and September 2003 was located about in the west, and it forms a major basement 3.5 km WSW of the village of Aberfoyle, where the structure northeastwards into the North Sea, where it is larger events were felt (Figs. 1 and 2). The epicentres lie interpreted to have influenced late Palaeozoic and adjacent to the surface trace of the Highland Boundary Mesozoic (24–65 Ma) rifting patterns and to coincide Fault Zone (HBFZ), one of the fundamental structural 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 ⁎ Corresponding author. Tel.: +44 131 6500224. Northern , where it appears to be represented E-mail address: [email protected] (L. Ottemöller). by the Antrim–Galway Line, a prominent lineament

0040-1951/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.tecto.2006.11.002 84 L. Ottemöller, C.W. Thomas / Tectonophysics 430 (2007) 83–95

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 In historic times, the area around Comrie has been et al., 1995). The HBFZ separates rocks in the Scottish fairly active with 33 events between 1608 and 1921; the Midland Valley from Neoproterozoie to Cambrian rocks largest event was an ML4.8 event in 1839. The mag- of the Supergroup underlying the Highlands nitudes of historic events are determined from macro- (Fig. 2). Included within the fault zone are slivers of seismic observations and are calibrated against the Cambro– rocks of oceanic origin assigned to instrumental local magnitude scale (Musson, 1996). the Highland Border Complex. It is a complex structure Since the installation of seismic stations in the 1970s, with a long history. Its significance as a major tectonic few earthquakes have been observed in the HBFZ. Of boundary is unquestioned, although its origins and sig- note is an earthquake that occurred on 16 September 1985 nificance as an early structure remain unclear (Dentith near Dunoon in the HBFZ at a depth of about 6.5 km with et al., 1992). Other major faults converge in the ML3.3. Redmayne and Musson (1987) suggested that left- Aberfoyle area. The principal ones include the Loch lateral strike–slip movement with a small normal Tay Fault Zone and the related Duke's Pass and Loch component had occurred on a fault striking WSW–ENE Ard faults (Fig. 2). These faults are essentially strike– and dipping south. A composite focal mechanism for an slip structures that were active in mid-Palaeozoic times earthquake swarm in the Kintail area of NW Scotland in (Treagus, 1991) and upon which there has been strike– 1974 similarly showed left-lateral movement on the SW– slip of the order of kilometres and dip slips of the order NE striking Strathconon fault (Assumpção, 1981). The of hundreds of metres. It is likely that the Loch Tay to Arran earthquake of 1999 also showed the same style of Loch Ard fault system represents a strike–slip transfer faulting (Bott et al., 1999). Earthquake swarms are system that accommodated SSW to SW directed relatively common in Great Britain, examples include sinistral movement within the Grampian Highlands. Comrie (1788–1801, 1839–46), Glenalmond (1970–72), L. Ottemöller, C.W. Thomas / Tectonophysics 430 (2007) 83–95 85

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), Constan- techniques, a joint focal mechanism and spectral source tine (1981, 1986, 1992–4), John Stonbridge (mid 1980s), parameters. Based on these results we give a tectonic Dumfries (1991, 1999), Manchester (2002) and Eskdale- interpretation. muir (2003). The regional stress pattern in Great Britain shows 2. Tectonics of the Highland Boundary Fault Zone predominantly horizontal compression in the NNW– SSE direction (Gölke and Coblentz, 1996; Main et al., The origin and earliest history of the HBFZ are 1999; Baptie, 2002) due to ridge-push forces from the obscure, but available geological evidence indicates Mid-Atlantic ridge. Stresses arising from postglacial that the Midland Valley and Highlands terrains were rebound, with present maximum uplift rates of 2 mm/ juxtaposed across the HBFZ by late times year in the (Shennan, 1989) are also (443–417 Ma) (Haughton et al., 1990)withina considered to cause earthquakes in Scotland (Main sinistral–transpressional, strike–slip regime. Subse- et al., 1999; Stewart et al., 2000; Firth and Stewart, quently, periodic movements from the late Silurian to 2000; Muir-Wood, 2000). It is disputed whether the Early Carboniferous (354–290 Ma) focussed on the ridge-push or glacial rebound is the dominant force HBFZ and related fracture systems considerably causing earthquakes in NW-Europe (Stein et al., 1989; influenced the tectonic development of, and sedimen- Gregersen, 1992; Stewart et al., 2000; Fejerskov and tation within, the Midland Valley. Although the Lindholm, 2000; Fjeldskaar et al., 2000; Hicks et al., geometry and history of fault movement within the 2000b). HBFZ are complex, in general the gross sense of Following a review of the tectonic history of the movement was reverse across apparently high angle, HBFZ, we describe our analysis of the seismic record- north-west dipping fault planes. Surface exposures ings of the 2003 earthquake sequence. We determine along the length of the fault zone indicate steeply precise relative locations using multiple event location dipping faults, but the nature of the HBFZ at depth is 86 L. Ottemöller, C.W. Thomas / Tectonophysics 430 (2007) 83–95 unclear. Gravity anomaly data from the vicinity of the (Paterson et al., 1990). However, most faults and frac- HBFZ were interpreted by Dentith et al. (1992) to show tures affecting Lower Carboniferous and older strata in that the fundamental bounding structure may be a low- this area have the NE and NW trends that are developed angle, northerly-dipping thrust fault, supporting the widely in the Midland Valley. Such structures are com- suggestion by Bluck (1984) that the present-day line of mon in the vicinity of the HBF, particularly in the the fault is due to later thrusting in the Late Aberfoyle district; these fractures are probably of (417–354 Ma) and Early Carboniferous. However, Variscan age or younger. Most are major joints with strike–slip movement is recorded locally by horizontal little displacement across them, but some are faults with slickensides (Anderson, 1951). This, coupled with the minor oblique slip displacements. Normal, dip–slip evidence for the faults being high-angle, northwesterly faults in this set displace rocks belonging to the Early dipping structures, at least near surface, indicates major Devonian Arbuthnott and Garvock groups in the strike–slip movement within the transpressive regime Aberfoyle district. Fault movements thus continued at that juxtaposed the different Highlands and Midland least into late Palaeozoic times. Valley terrains during the late Silurian and early Devo- The lack of rock units younger than the Carboniferous nian (Haughton et al., 1990). The present distribution of along the HBFZ in Scotland preclude elucidation of the Lintrathen Pophyry (Crawton Volcanic Formation), post-Carboniferous movements. However, given the exposed in Glen Isla and farther to the east and influence of the HBFZ on rift structures and interpreta- southeast of the HBFZ (Trench and Haughton, 1990) tion of late Palaeozoic and Mesozoic strata in the North implies a sinistral offset of about 40 km, which occurred Sea, some activity on the fault since the Carboniferous is in Mid-Devonian (Acadian) times. considered likely. During Lower Devonian times, the Midland Valley to the south of the HBFZ was a major, NE-trending, 3. Multiple event location subsiding basin that was flanked to north and south by upland areas, with rejuvenation of the northern uplands 3.1. Method and data processing resulting from intermittent uplift on the HBFZ. In the Middle Devonian, Acadian compressive earth move- The clustering of events combined with good station ments briefly brought about marked changes in the coverage (Fig. 3) suggested that the relative locations of palaeogeography of Central Scotland. The deposition of the events could be improved using multiple event the ca. 1750 m thick Strathfinella Conglomerate in the location techniques. Furthermore, visual inspection of late Emsian implies that the Highland area was also the seismograms recorded from the earthquakes in the uplifted significantly relative to the Midland Valley, sequence indicated a high degree of similarity between coeval with the earliest phase of these movements. the individual events; seismograms from station Carrot Lower Devonian rocks were folded into NE-trending (PCA) are given in Fig. 4 as an example. The waveform structures, most notably the Strathmore , the similarity suggested that the events were located with- steep northern limb of which lies adjacent to the HBF. in a small source volume and associated with a single Continued uplift and thrust movements on elements source mechanism. Waveform similarity had previously of the HBFZ resulted in the erosion of any Lower been reported for earthquake sequences in Scotland at Devonian rocks deposited to the north of the fault sys- Kintail (Assumpção, 1981) and Carlisle (Marrow and tem, whilst within the Midland Valley basin, Lower Roberts, 1985). Devonian rocks were deeply eroded, particularly along We used two different techniques for multiple event anticlinal axes. location (MEL) to evaluate the stability of the results. Detritus in Upper Devonian strata in the Aberfoyle First, we applied the double difference method (DD) of district were probably derived from a Highland source Waldhauser and Ellsworth (2000) which has provided area, maintained as an area of positive relief by continued significantly improved relative locations in a number of uplift along the HBFZ. Southwest of , Late cases (e.g., Waldhauser and Ellsworth, 2002; Hauksson Devonian and Early Carboniferous rocks are preserved and Shearer, 2005). The DD minimises the difference on the northwest side of the HBFZ, down-thrown by between the travel time residuals of earthquake pairs and Carboniferous or later normal fault movement. The since the velocities along a path for neighbouring earth- deposition of the Early Carboniferous Inverclyde Group quakes recorded on one station are nearly identical, no was preceded by uplift, erosion and renewed subsidence, station- or source-specific corrections are required. The again focused along the HBFZ and there is evidence method allows combination of catalogue readings with for further reactivation during the Early Carboniferous precise relative travel time differences obtained through L. Ottemöller, C.W. Thomas / Tectonophysics 430 (2007) 83–95 87

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 2004). The correlation rxy function between two signals determined by the catalogue data, while the relative x and y is given by locations are determined by precise travel time differ- X ences. The hypoDD software (Waldhauser, 2001) was xjyiþj used for computation. Second, we used Joint Hypocen- j rxyðiÞ¼rXffiffiffiffiffiffiffiffiffiffiffiffirX ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : ð1Þ ter Determination (JHD), which jointly inverts for 2 2 xj yiþj hypocentre locations and station residuals (e.g., Pujol, j j 1988; Kissling et al., 1994). With event clustering, as in this case, inversion for station corrections leads to The maximum amplitude in the cross-correlation improved relative event locations. The JHD was function was used in two ways: 1) Relative travel time performed using the VELEST software (Kissling, differences were measured between all events at indi- 1995) by damping velocity in the inversion. In both vidual stations. Both P and S wave data were extracted methods, the velocity model derived from the LISPB based on computed arrival times. This data was then profile for Central Scotland was used (Assumpção and used in the DD calculations. 2) Seismograms from the Bamford, 1978; Bamford et al., 1978). first event in the sequence were used as master signals. The similarity in the seismograms was used to obtain Based on manual phase picks, signals from subsequent accurate and consistent phase arrivals by computing events were extracted, and correlated with the master waveform cross-correlation (Schaff and Richards, signals to determine consistent and precise absolute 88 L. Ottemöller, C.W. Thomas / Tectonophysics 430 (2007) 83–95

Fig. 4. Band-pass filtered (3–8 Hz) displacement (in nm) seismograms for events of the Aberfoyle earthquake sequence as recorded on the short- period 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. L. Ottemöller, C.W. Thomas / Tectonophysics 430 (2007) 83–95 89 arrival times to be used as input for the JHD calcula- correct arrival time based on correlation of the latter part tions. In both cases, data were filtered with a pass-band of the signal. 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 3.2. Results required for a reading to be made. A number of stations were selected to achieve good Fig. 5 shows the comparison of results from DD and azimuthal coverage (Fig. 3). The cross-correlation pro- JHD with single event locations (SEL) based on manual vided robust results. For smaller events in particular, phase readings. The results from both DD and JHD are where the signal to noise ratio was worse, more con- rather similar with a clear alignment of hypocentres in sistent phase arrivals were obtained compared to those the WSW–ENE direction at a depth of about 4 km. The obtained by manual analysis. For smaller events cluster size of the DD locations is slightly less than for (ML ≤1.5) at larger distances (N150 km) the initial P- the JHD locations. Therefore we consider the DD loca- onset, as seen for the larger events, disappeared in the tions to be superior and use them in the following noise, while later larger arrivals appeared to be first analysis (Table 1). However, both methods provide a arrivals. The cross-correlation technique identified the 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. 90 L. Ottemöller, C.W. Thomas / Tectonophysics 430 (2007) 83–95

Table 1 mechanism for the sequence based on first motion Results from DD location of phase arrivals obtained with cross- polarities was determined through a grid-search (Snoke correlation technique et al., 1984) using polarity readings from 13 stations # Date Time ML Lat Lon Depth rms (Fig. 7). The solution was well constrained and out of (ddmmyyyy) (hhmm) (° N) (° W) (km) (s) several solutions we selected an average given by a 1 20062003 0644 3.2 56.1714 4.4333 4.286 0.028 strike of 243.8, dip of 65.6 and rake of −32.7. The first 2 20062003 0653 2.8 56.1705 4.4342 4.232 0.024 nodal plane strikes in a WSW–ENE direction and dips 3 20062003 0903 2.5 56.1710 4.4351 4.376 0.026 – 4 23062003 1005 1.3 56.1701 4.4375 4.391 0.024 to the northwest with oblique lateral strike slip and 5 25062003 1153 1.4 56.1712 4.4321 4.182 0.021 normal movement. The second nodal plane strikes in a 6 26062003 0957 1.5 56.1699 4.4373 4.375 0.025 NNW–SSE direction and dips eastward with oblique 7 27062003 0209 2.8 56.1690 4.4407 4.365 0.031 right-lateral strike–slip and normal movement. 8 27062003 0211 1.3 56.1690 4.4380 4.233 0.029 The solution for the focal mechanism was verified by 9 27062003 0312 1.3 56.1696 4.4389 4.415 0.023 10 23082003 0335 1.5 56.1692 4.4373 4.219 0.023 synthetic forward modelling (Fig. 7). The programs of 11 15092003 0800 2.2 56.1699 4.4345 4.212 0.026 Herrmann were used to compute full waveforms based on wavenumber integration (Herrmann, 1979; Wang and Herrmann, 1980). The good match between ob- rather diffuse hypocentre distribution determined by served and computed seismograms for a number of SEL. The formal errors for the largest event in the stations further supports the results for both the hypo- sequence determined using SEL (Lienert and Havskov, centre depth and source mechanism. The amplitude ratio 1995) were 3.1 km in longitude and in 1.3 km in latitude between P and S waves is well modelled, as is the (90% confidence), which is representative of the error in difference between nodal (e.g. ELO) and antinodal sta- absolute location of the sequence as a whole. The width tions (e.g. PMS). Even at the shortest recording dis- of the alignment in the NNW–SSE direction is of the tance, station EAB (6 km) observed and computed order of 100 m, the length is about 600 m in the WSW– seismograms were well matched. ENE direction and the vertical extent is about 150 m. Synthetic tests were carried out to test the reliability 5. Source parameters of the results and to estimate uncertainties. We com- puted synthetic arrival times for the same stations and The source time functions of the larger events in the phases as used to obtain the SEL locations. The syn- sequence (ML ≥2.5) were determined by using the thetic event epicentre locations were arranged in a cross smaller events (ML ≤1.5) as empirical Green's function 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.

4. Focal mechanism Fig. 6. Results from synthetic test: synthetic arrival times were The similarities in the observed waveforms between computed for fixed locations forming a cross (stars) using the same station configuration as given for SEL locations (squares); the the events indicated that they followed the same rupture resulting locations (circles) when applying the DD method to the mechanism, and, as expected, there was a match in first synthetic data-set were computed using the centre of the cluster as motion polarities between the events. A joint focal starting location for all events. L. Ottemöller, C.W. Thomas / Tectonophysics 430 (2007) 83–95 91

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). 92 L. Ottemöller, C.W. Thomas / Tectonophysics 430 (2007) 83–95

(EGF) (Mueller, 1985). The deconvolution of the EGF Table 2 from the larger events was performed in the frequency Source parameters, seismic moment and corner frequency ( fc-spec) automatically determined from displacement source at stations EDI, domain applying water-level stabilisation (Clayton and ELO, KAR, KPL, MCD, MDO, PCA, PCO and PMS Wiggins, 1976). The smaller events used as the EGF σ were small enough to be considered point sources and of # Date/time M0 fc-spec fc-egf R MW ML (Nm) (bars) (Hz) (Hz) (km) the same mechanism as the larger events. P-wave source time functions were computed for three stations by 1 20062003 0644 2.5E13 3.1 3.5 4.1 0.44 2.9 3.2 2 20062003 0653 1.3E13 3.8 4.8 5.4 0.32 2.7 2.8 stacking results obtained from a total of 6 smaller events 3 20062003 0903 1.0E13 3.6 5.2 5.7 0.29 2.6 2.5 as EGF. Source time durations determined from either P 4 23062003 1005 4.0E11 0.6 7.6 0.21 1.7 1.3 or S waves were nearly identical. Examples of stacked 5 25062003 1153 4.0E11 0.2 5.9 0.25 1.7 1.4 source time functions at station PCA are shown in 6 26062003 0957 5.0E11 0.5 7.2 0.21 1.7 1.5 Fig. 8. The displacement pulse for the three events on 20 7 27062003 0209 7.9E12 1.5 4.1 4.4 0.37 2.6 2.8 8 27062003 0211 2.5E11 0.5 7.8 0.24 1.6 1.3 June was of rather simple shape. In contrast, a double 9 27062003 0312 2.5E11 1.0 9.8 0.18 1.6 1.3 pulse was obtained for the event on 27 June. Comparing 10 23082003 0335 4.0E11 1.5 11.1 0.15 1.7 1.5 the seismograms of this event to the others (Fig. 4)a 11 15092003 0800 3.2E12 0.6 4.9 0.32 2.3 2.2 more complicated P-wave onset was observed sup- For comparison the table also gives fc-egf determined using EGF at porting the model of a double rupture for the 27 June stations PCA, PCO and PMS. The event numbering is as in Table 1. event. 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 under- taken using S-wave spectra, where S-wave attenuation is described by the diminution function D( f )  −kTf Dð f Þ¼exp expð−kjf Þð2Þ Qð f Þ where T is travel time, f is frequency, κ describes near- surface attenuation (Singh et al., 1982) and Q( f ) is the frequency dependant quality factor given by Sargeant and Ottemöller (submitted for publication)

: f 0 45 Qð f Þ¼337 : ð3Þ 1:6

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 attenua- tion leads to higher corner frequencies and higher stress drop. The spectral analysis of the smaller events in the sequence (ML b2.2) 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 Fig. 8. Stacked source time functions obtained for events at station PCA. The source time functions were obtained by deconvolution of the values obtained from the duration of the displacement smaller events, used as empirical Green's function, from the larger pulse (Table 2). There is a good match between the earthquakes. results from the two methods showing the expected L. Ottemöller, C.W. Thomas / Tectonophysics 430 (2007) 83–95 93 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, mo- ment 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/ Fig. 9. Source size as given in Table 2 projected along the epicentre R3). Source radii were in the range 150 to 440 m. The alignment in WSW–ENE direction. stress drop values are in the range of about 0.2 to 3.8 bars, which means that within the errors there is no larger than l km, the simplest interpretation is that the significant difference between the events. Fault slip earthquakes result from movement on a fault plane that, computed for the largest event from the seismic moment at depth, lies within the HBFZ. 10 2 using M0 =μ×A×d for μ=2×10 N/m is of the order The orientation of maximum compressional stress of 0.4 cm. (σH) determined from the focal mechanism solution, is NNE–SSW (Fig. 7). For comparison, σH derived for 6. Tectonic interpretation other earthquakes in Scotland is directed predominantly N–S: Kintail, 1974 (Assumpção, 1981), Carlisle 1979 The match of epicentre alignment with the WSW– (Marrow and Roberts, 1985) Dunoon 1985 (Redmayne ENE striking nodal plane suggests that this was the and Musson, 1987) and Arran 1999 (Bott et al., 1999). causative fault plane. All events in the sequence oc- While these are the only earthquakes in Scotland for curred on a single rupturing fault segment. The source which a reliable focal mechanism has been determined, dimensions indicate that parts of the fault moved more there are many more events of unknown mechanism that than once, with maximum source size covering two- could be different from this trend. The orientation thirds of the sequence length. Most of the events were derived for the Aberfoyle earthquake sequence is rotated contained within the source volume of the largest events by about 90° from the expected σH due to the mid- (Fig. 9). However, the double rupture event on 20 June Atlantic ridge-push that is observed in Great Britain at 02:09 lies to the southwest of the main cluster. This south of Carlisle (Baptie, 2002). Rotation of σH is location is possibly due to the larger uncertainties in significantly less for the other Scottish earthquakes, and phase times due to the more complicated source time considering that the P and T axes derived from focal function that resulted in waveform differences compared mechanisms may vary significantly from the principal to the other events. stresses (McKenzie, 1969) are arguably in line with the The strike and northwesterly dip of the resolved fault regional stress pattern. compare well with the general orientation of faulting The normal component of the oblique mechanism observed in the HBFZ at surface. At a depth of about observed for Aberfoyle suggests that the vertical stress 4 km, the earthquake hypocentres lie on a fault plane is larger than the minimum horizontal stress component with a dip of about 65°. As a first-order estimate, simple leading to extensional tectonics. The estimated stress trigonometry shows that this fault plane would project drop for the Aberfoyle events was less than the averages up to the southeast, intersecting the surface about 1.8 km observed elsewhere (Kanamori, 1975). Considering the from the epicentres. This is very close to the measured low stress drop, and rotation of σH from the regional horizontal distance of the HBFZ from the epicentres. average it is unlikely that the Aberfoyle earthquake Although the absolute epicentre locations errors are sequence was caused by ridge-push stresses only. The 94 L. Ottemöller, C.W. Thomas / Tectonophysics 430 (2007) 83–95 earthquakes could be the result of localised stress cate that the earthquakes originated within the HBFZ, sources such as lateral density contrasts and topography one of Scotland's major tectonic features. The orienta- (Fejerskov and Lindholm, 2000). Considering a degree tion of σH derived from the Aberfoyle earthquake of consistency between the earthquakes in Scotland it is sequence shows a rotation by about 90° from the ex- possible that they are the result of a less localised source pected regional σH due to the mid-Atlantic ridge-push such as flexural stresses due to postglacial unloading. force. As this inferred stress orientation seems to prevail Hicks et al. (2000a) found a similar rotation of σH for across Western Scotland, the earthquakes possibly are earthquakes in the Rana region on the Norwegian west the result of flexural stresses caused by postglacial coast, and observing similarities to the Meloy and isostatic rebound. The HBFZ is a highly fractured zone Steigen earthquake swarms (see references in Hicks and similar activity is to be anticipated in the future. et al. (2000a)) argue that postglacial flexure is providing a consistent stress source over distances of several Acknowledgements hundred kilometres along the Norwegian coast where uplift gradients are the highest. However, Hicks et al. We appreciate discussions with Brian Baptie that (2000b) stress that the rotation of maximum compres- helped to improve this work. The comments by two sion is easily achieved if the ratio of maximum and anonymous reviewers have helped to strengthen the minimum horizontal stress is near unity. paper. This paper is published with the permission of The Aberfoyle earthquake sequence is similar to the the Executive Director of the British Geological Survey Kintail earthquake swarm in 1974 (Assumpção, 1981)in (NERC). various ways, and thus not uncommon. 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