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2014-011research-articleResearch ArticleXXX10.1144/qjegh2014-011R. Westaway & P. L. Younger‘Fracking’-Induced Microseismicity In The Uk
2014
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Quantification of potential macroseismic effects of the 
induced seismicity that might result from hydraulic 
fracturing for shale gas exploitation in the UK
Rob Westaway1,2* & Paul L. Younger1
1School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK
2Newcastle Institute for Research on Sustainability, Devonshire Building, Newcastle University,  
Newcastle upon Tyne NE1 7RU, UK
*Corresponding author (e-mail: xxxxxx.xxxxxxxx@xxxxxxx.xx.xx)
Abstract:  The furore that has arisen in the UK over induced microseismicity from ‘fracking’ for shale 
gas development, which has resulted in ground vibrations strong enough to be felt, requires the urgent 
development of an appropriate regulatory framework. We suggest that the existing regulatory limits 
applicable to quarry blasting (i.e. peak ground velocities (PGV) in the seismic wavefield incident on any 
residential property of 10 mm s−1 during the working day, 2 mm s−1 at night, and 4.5 mm s−1 at other times) 
can be readily applied to cover such induced seismicity. Levels of vibration of this order do not constitute 
a hazard: they are similar in magnitude to the ‘nuisance’ vibrations that may be caused by activities such 
as walking on wooden floors, or by large vehicles passing on a road outside a building. Using a simple 
technique based on analysis of the spectra of seismic S-waves, we show that this proposed daytime 
regulatory limit for PGV is likely to be satisfied directly above the source of a magnitude 3 induced 
earthquake at a depth of 2.5 km, and illustrate how the proposed limits scale in terms of magnitudes of 
induced earthquakes at other distances. Previous experience indicates that the length of the fracture 
networks that are produced by ‘fracking’ cannot exceed 600 m; the development of a fracture network 
of this size in one single rupture would correspond to an induced earthquake c. magnitude 3.6. Events 
of that magnitude would result in PGV above our proposed regulatory limit and might be sufficient to 
cause minor damage to property, such as cracked plaster; we propose that any such rare occurrences 
could readily be covered by a system of compensation similar to that used over many decades for dam-
age caused by coal mining. However, it is highly unlikely that future ‘fracking’ in the UK would cause 
even this minor damage, because the amount of ‘force’ applied in ‘fracking’ tends to be strictly limited 
by operators: this is because there is an inherent disincentive to fracture sterile overburden, especially 
where this may contain groundwater that could flood-out the underlying gas-producing zones just devel-
oped. For the same reason, seismic monitoring of ‘fracking’ is routine; the data that it generates could 
be used directly to police compliance with any regulatory framework. Although inspired by UK conditions 
and debates, our proposals might also be useful for other regulatory jurisdictions.

 
Gold Open Access: this article is published under the terms of the CC-BY 3.0 license.
The mechanisms whereby human activities can affect seismicity 
regulating this issue under other jurisdictions, as an alternative to 
have been widely discussed in recent years (e.g. Seeber 2002; West-
the rather laissez-faire approach to regulation that has hitherto 
away 2002, 2006; Klose 2007, 2013; Ellsworth 2013). Following 
applied in the country where this technology was first developed.
Klose (2013), an ‘anthropogenic earthquake’ can be defined as any 
The history of ‘fracking’ as a technology for production of shale 
seismic event for which a human activity can reasonably be shown 
gas has been well documented (e.g. Martineau 2007); the much more 
to be the cause, or at least a major influence on event timing. Anthro-
limited extent of use of ‘fracking’ in the UK has been summarized by 
pogenic earthquakes can in turn be subdivided into ‘triggered’ and 
Mair  et al. (2012) and Younger (2014). ‘Fracking’ can indeed be 
‘induced’ events; a triggered event is one that would have occurred 
regarded as an artificial analogue of natural geological processes 
anyway, because the state of stress in the area was tending towards 
involving over-pressured fluids, such as the injection of sills (e.g. 
the condition for shear failure, so that the human activity merely 
Goulty 2005) or clastic dykes (e.g. Van Der Meer et al. 2009). The 
brought the earthquake forward in time or ‘advanced the clock’. An 
first ‘fracking’ tests on a shale gas well in the UK took place in early 
earthquake is ‘induced’ if there is no reason to consider that, in the 
2011, at Preese Hall near Blackpool, in NW England. This test gave 
absence of human activity, the state of stress in the area was heading 
rise to about 50 microearthquakes, concentrated around the c. 2.5 km 
towards the condition for shear failure: in other words, without the 
depth of the ‘fracking’. Remarkably, given that tens of thousands of 
human activity the earthquake would never have occurred. This 
boreholes have been used for ‘fracking’ in the USA without similar 
paper will consider the strength of ground vibrations caused by 
outcomes (e.g. Hitzman et al. 2013), two of these seismic events 
earthquakes that may be induced by hydraulic fracturing, or ‘frack-
were of elevated magnitude: one of local magnitude (M ) 2.3 on 1 
L
ing’, for shale gas development. Although tailored towards UK-
April 2011 and another of M  1.5 on 27 May 2011 (BGS 2011a,b). 
L
based issues, it may also be of interest to those responsible for 
As would be expected, neither of these events caused any surface 
Quarterly Journal of Engineering Geology and Hydrogeology, Vol. 47, 2014, pp. 333 –350
© 2014 The Authors
http://dx.doi.org/10.1144/qjegh2014-011
Published Online First on November 11, 2014

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334
R. WESTAWAY & P. L. YoUNGER  
damage; they were also not felt by scientific staff at the drilling site 
blasting, have a long history of regulation in the UK. On the other 
(P. Turner, pers. comm.). Only one person claimed to have felt the 
hand, other forms of ‘nuisance’ ground vibration, such as those 
subsequent M  1.5 event. In the ensuing furore, the ‘fracking’ opera-
resulting from people jumping onto hard surfaces or slamming 
L
tions were suspended pending a government investigation. 
doors, are subject to no legal regulatory framework at all, owing to 
Subsequent studies (De Pater & Baisch 2011; Green et al. 2012) 
their essentially trivial character (Table 1). The aims of the present 
established that previously unmapped faults in the vicinity, which 
paper are to establish where the observed ‘fracking’-induced 
must have already been close to the condition for rupture, were 
microseismicity should be placed within this spectrum (ranging 
brought to this condition by the increase in fluid pressure resulting 
from hazard to significant nuisance to trivial nuisance) and to sug-
from the ‘fracking’; the timing and location of the induced seismicity 
gest a strategy for the development of the regulatory framework for 
leave no doubt that the ‘fracking’ activities were the cause (Mair 
microseismicity induced by future ‘fracking’ operations in the UK.
et al. 2012). The scale of the related media and political fallout can-
not be overstated, and has been described as ‘hysterical’ (Younger 
2014). Subsequently, several attempts have been made to propose or 
Conceptual background
recommend guidelines for the magnitude of the ground vibrations 
induced by ‘fracking’ that can be deemed acceptable in the UK (e.g. 
In general, ‘fracking’ may induce seismicity via two general 
De Pater & Baisch 2011; Green et al. 2012; Mair et al. 2012; 
methods (e.g. Šílený et al. 2009; Song & Toksöz 2011; Eaton 
UKOOG 2013), to permit the resumption of development of what 
et al. 2014; Song et al. 2014). First, the ‘fracking’ fluid may leak 
may prove to be an important energy resource (see Andrews 2013). 
into pre-existing faults or fractures in the surrounding rock mass; 
However, there has been no consensus between these proposals, 
by increasing the local fluid pressure it may bring such a fault to 
which differ markedly from corresponding recommendations for the 
the condition for shear failure, thus inducing a conventional shear 
USA (e.g. Bull 2013), where there is much greater experience of 
earthquake. Second, the ‘fracking’ process may directly result in 
‘fracking’ (e.g. Hitzman et al. 2013). The recent proposals also fail to 
the creation of tensile fractures, associated with the occurrence of 
take account of the mainstream literature on engineering seismology 
earthquakes with tensile mechanisms. ‘Mixed-mode’ earthquakes, 
and earthquake hazards. Although one of the principal conclusions of 
involving both tensile and shear components in variable propor-
the Hitzman et al. (2013) report by the US Academy of Sciences was 
tions, are also possible (e.g. Ramsey & Chester 2004; Fojtíková 
indeed that ‘The process of hydraulic fracturing a well as presently 
et al. 2010). Theory for amplitudes of the resulting seismic 
implemented for shale gas recovery does not pose a high risk for 
waves, based on the established literature on fracture mechanics 
inducing felt seismic events’, one looks in vain within this lengthy 
(e.g. Griffith 1924; Sneddon 1951; Eshelby 1957), which is itself 
document for any quantitative recommendation.
ultimately derived from pioneering studies of the fracturing pro-
The broader context of these debates lies in the energy markets. 
cess such as those by Rankine (1843, 1858), is presented in the 
Heat energy, primarily for heating buildings, has been estimated as 
Appendix. For conventional shear earthquakes the S-wave usu-
42% of total energy demand for the UK as a whole and, owing to the 
ally has larger amplitude than the P-wave; the same is shown to 
harsher climate, >50% of the total for Scotland (e.g. IMechE 2011). 
be usually true for tensile fracture earthquakes, at least in rocks 
Some 70% of domestic energy consumption in the UK is from natu-
of low Poisson’s ratio such as Carboniferous mudstones. The 
ral gas, most of which is used for heating (e.g. DECC 2013a), a 
ability to form tensile and shear fractures in previously intact 
pattern that is predicted to continue for the foreseeable future, and 
rock is determined by the tensile strength  and cohesion  of 
T
C
will require supply on a large scale. Furthermore, the combined 
the rock, respectively (e.g. Eaves & Jones 1971; Bourne & 
cycle gas turbine (CCGT), in which the hot exhaust from a gas tur-
Willemse 2001); it is likewise also arguable that reactivation of 
bine is used to generate steam to power a steam turbine, and both the 
pre-existing faults or fractures is also governed by their cohesion, 
gas turbine and associated steam turbine drive an alternator, is the 
rather than being a purely frictional process, as fractures may 
most thermally efficient technology for using fossil fuel for electric-
‘heal’ following single ruptures (e.g. Reches 1999; Muhuri et al. 
ity generation, overall thermal efficiencies of >60% being achieva-
2003). The stress drop Δσ that occurs as a result of any earth-
ble (e.g. Bartos 2011). Management of the British national electricity 
quake, and that relates to the displacement-to-length ratio c of the 
grid includes balancing generation by wind turbines and CCGT 
associated fault slip or tensile fracture opening, thus depends on 
plant, the latter providing backup for the former on days with little 
 or . In the analysis presented in the Appendix, therefore, 
C
T
wind (e.g. Gridwatch 2014). CCGT capacity is thus an essential ele-
these rock mechanical properties are factored in explicitly.
ment of any ‘low-carbon’ energy strategy for the foreseeable future; 
Earthquake magnitude scales, such as the aforementioned M , 
L
hence the production of shale gas offers the potential for significant 
provide an empirical basis for quantifying the ‘size’ of earthquakes, 
environmental as well as economic benefits, provided any social 
each being based on the logarithm of the amplitude of seismic 
and environmental disbenefits can be quantified and managed. In 
waves recorded on a particular type of seismograph located at a 
this regard, shale gas does not differ from any other energy conver-
standard distance from the seismic source (e.g. Richter 1958). The 
sion technology, be it fossil or renewable. For a broader discussion 
fundamental physical quantity defining the size of an earthquake is 
on the pros and cons of shale gas development, the interested reader 
its seismic moment M , where
o
is referred to the House of Lords (2014).
How do the concerns over ‘fracking’-induced seismicity relate 
M
µ   d
(1)
to the wider field of earthquake hazard mitigation? Most work in 
o ≡ ∫S
u s  
engineering seismology concerns quantification of hazard from 
relatively large earthquakes, to mitigate the loss of life and damage 
u being the coseismic displacement and μ the shear modulus of the 
to property that can result. In comparison, the extent of past inves-
adjoining rock at each point on the seismogenic fault plane of area 
tigations of macroseismic effects of microearthquakes, such as 
s (e.g. Keilis-Borok 1959). If, for simplicity, μ and u are assumed 
those induced by ‘fracking’, has been relatively limited, presuma-
to remain constant across the fault rupture, then M  can be equated 
o
bly owing to a lack of severe consequences. It should nonetheless 
to μ u s. To facilitate comparison with existing magnitude scales, a 
be apparent that there is a gradation of effects, as the size of earth-
‘moment-magnitude’ scale, M , has been defined, thus:
w
quakes and the amplitude of the resulting seismic vibrations 
decreases, from ‘hazard’ to ‘nuisance’. In turn, some aspects of 
‘nuisance’ ground vibrations, notably those arising from quarry 
log (M / Nm) = 9 0
. 5 +1.5M
10
o
w  
(2)

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‘FRACKING’-INDUCED MICRoSEISMICITY IN THE UK
335
Table 1. Amplitudes of ground vibrations that might cause hazard or nuisance
Item
Amplitude  (mm s−1)
Reference
Threshold for major damage
60
1
Threshold for plaster cracking
50
2
600 m × 600 m vertical fracture initiated at 2.5 km depth in Carboniferous mudstone (M  3.6)
c. 50
3
W
Threshold for minor damage at Modified Mercalli Intensity V
34
4
Threshold for cosmetic damage
15
1
‘Safe’ limit
12.7
5
Slamming door
12.7
6
Upper limit for quarry blasting during the working day (allowable if unavoidable)
10
7
Jumping onto a wooden floor
8
6
Upper limit for quarry blasting during the working day (desirable)
6
7
Upper limit for quarry blasting during daytime outside the working day
4.5
7
Upper limit for quarry blasting at night
2
7
Lorry at a distance of c.  8 m
2
8
Threshold for felt effect at Modified Mercalli Intensity II
1
4
Walking on a wooden floor
0.8
6
DECC (2013b) limit for suspension of fracking (M  = 0.5 tensile earthquake) at 2.5 km depth
c. 0.4
3
W
Minimum threshold of perception for ground vibrations caused by blasting
0.25
9
Minimum threshold of perception for ground vibrations caused by road traffic
0.15
10
Reference codes: 1, BS7385-2 (BSI 1993); 2, Calder (1977); 3, predictions from this study, which include radiation pattern effects, but for reasons dis-
cussed in the text are probably overestimates; 4, Wald et al. (1999); 5, Siskind et al. (1980); 6, Stagg et al. (1980); 7, BS6472-2 (BSI 2008); 8, NCHRP 
(1999); 9, Oriard (1972, 2002); 10, Whiffen & Leonard (1971).
(Hanks & Kanamori 1979), equivalent to
predicted radius of c. 14 m. However, such analysis does not 
make any deterministic prediction of the amplitude of the 
2
ground vibrations expected for induced earthquakes of any 
M = log

0 (M / Nm) − 9 0
. 5
w
1
o
.
3
 
(3)
size; more elaborate investigation is evidently needed.
Looking at the mechanics in more detail, we assume once again 
Without explicitly stating so, the analyses by De Pater & Baisch 
that microearthquakes rupture circular patches of fault with radius 
(2011) and Green et al. (2012) have assumed that the reported M  
a, such that
L
values for the ‘fracking’-induced microearthquakes in the UK 
equate to M , and so can be converted into M . To facilitate com-
(5)
w
o
M
parison with their work, we will make the same assumption; this 
o = πµa U
2
 
allows the reported magnitudes to be related to a substantial body 
of theory and empirical evidence, although it should be noted that 
where U is the spatial average coseismic slip. For a circular fault, 
many earthquakes induced by ‘fracking’ have tensile fracture focal 
the static stress drop Δσ can be determined (e.g. Lay & Wallace 
mechanisms and thus differ from the double-couple mechanisms 
1995) as
characteristic of ‘conventional’ earthquakes that occur as a result of 
π U
π
7
(6)
shearing across faults (e.g. Walter & Brune 1993; Shi & Ben-Zion 
∆σ = 7 µ =
µc
16
a
16
 
2009; Eaton et al. 2014); some of the consequences of such differ-
ences become apparent during the course of our analysis.
where c = U/a is the ratio of average displacement to radius of the 
Theory relating to elastic stresses and associated seismic radiation 
fault. Combining equations (5) and (6) thus gives, for a circular 
from a circular fracture of radius a, which opens in rock of Poisson’s 
fault, the standard expression
ratio ν as a result of a uniform excess internal pressure P, is presented in 
the Appendix. Combining one of these equations (equation (A11)) with 
equation (2) gives a simple scaling relation linking M , a, ν, and P:
Mo
(7)
w
∆σ = 7
.
16 3
a
 
log (a) = 9 0
. 5 − log

(8 / 3) / 3
10
10

(4)
However, the standard derivation of this formula (like many others 
+ 0.5 M − log (P) / 3 − log 1
(
w
10
10
−ν ) / 3  
in this field) has included the assumption that the faulting is in rock 
with a Poisson’s ratio ν = 0.25; for the general case it adjusts (see 
with a in metres and P in pascals. Eaton et al. (2014) derived a 
the Appendix, equation (A20)) to
similar equation but their analysis utilized a different relation 
between M  and M  and also incorporated the unstated assump-
3 (2 − ν)M
w
o
∆σ =
o
tion that ν = 0.25. Equation (4) demonstrates that there is a clear 
.
(8)
16  1
( − ν 3
)a
link between the ‘fracking’ procedure in operation, represented 
 
by P, the dimensions of the fractures produced (represented by 
a), the magnitudes of the resulting earthquakes (represented by 
Equation (6) likewise adjusts to
M ), and the physical properties of the rock mass that is being 
w
‘fracked’ (represented by ν). Thus, for example, with P = 1 MPa 
3 (2 − ν)π
and ν = 0.2, if an M  = 0.5 earthquake occurs as a result of 
∆σ =
µ .
c
(9)
w
the creation of a new circular fracture, this fracture will have a 
16  1
( − ν)
 

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336
R. WESTAWAY & P. L. YoUNGER  
The energy radiated by an earthquake source in the form of seismic 
even so, the Appendix shows that the S-wave radiated by a tensile 
waves, , can also be estimated, after Kanamori (1977), as
fracture earthquake will usually be stronger than the P-wave, espe-
s
cially in rocks with a low Poisson’s ratio.
∆σ M
One long-standing approach to the quantification of macroseis-
E
o
s =
.
(10)
mic effects has been via empirical prediction equations for either 
µ
2
 
peak ground acceleration or peak ground velocity. Historically, in 
engineering seismology, felt effects and damage were generally 
Many studies (e.g. Ide & Beroza 2001; Allmann & Shearer 2009) 
related to peak ground acceleration; however, in recent years, peak 
have shown that across many orders of magnitude of M , earth-
ground velocity (PGV) has been perceived as an appropriate proxy 
o
quakes maintain constant stress drops Δσ in the range c.  1–10 MPa 
in many circumstances (e.g. Wald et al. 1999; Wu et al. 2004; 
(typically c. 3 MPa) and, although exceptions have been noted (e.g. 
Bommer & Alarcón 2006; Akkar & Bommer 2007). Such empiri-
Archuleta et al. 2012), constancy of stress drop (or constancy of the 
cal predictions are nonetheless subject to considerable variability, 
ratio of coseismic slip to the dimensions of the seismogenic fault) 
in part owing to different approaches to quantifying earthquake 
is generally regarded as the key basis for the scaling behaviour of 
sources, such as specifying the limits of any fault plane (e.g. 
earthquakes (e.g. Shaw 2009).
Westaway & Smith 1989). Prediction of PGV or peak ground 
Furthermore, theory (e.g. Aki 1967; Brune 1970) indicates that 
acceleration for microearthquakes, for which the dimensions of the 
the spectral amplitude of the particle displacement for seismic 
fault plane will be small compared with source–station distances, is 
S-waves (which usually produce the strongest ground vibrations 
likewise subject to considerable variability, not least because rela-
near any earthquake source) radiated by an earthquake is flat at 
tively few prediction equations have been calibrated for these small 
frequencies  f below the corner frequency  (at a low-frequency 
events, so what constitutes a ‘reasonable prediction’ has not previ-
c
asymptote Ωs given by
ously been straightforward to ascertain (e.g. Bommer et al. 2007). 
Figure 1 illustrates the predictions for peak horizontal and vertical 
M
ground velocity at zero epicentral distance d, corresponding to a 
Ωs
θφ
o
=
(11)
point on the Earth’s surface directly above an earthquake source, 
3
4πρ s
v R  
for one prediction equation, from Bragato & Slejko (2005), which 
has been calibrated down to magnitude 2.5. For example, for M  4, 
L
where  R
the resulting predictions of PGV are 21 mm s−1 (vertical) and 
θϕ is the directional coefficient for the S-wave radiation 
pattern, r and  are the density and S-wave velocity of the rock 
7 mm s−1 (horizontal). However, this prediction equation does not 
S
adjoining the fault, and R is distance from the source), but decreases 
explicitly incorporate the depth h of any seismic source; its predic-
rapidly (as c. f −2) for f >> . This theory was originally developed 
tions depend on a distance parameter x = √(d2 + k2) where k is an 
c
for conventional double-couple seismic sources, representing shear 
empirical constant (specified as 7.3 km and 9.1 km, respectively, 
fractures; however, as is discussed in the Appendix, similar formu-
for the vertical and horizontal components) that effectively limits 
lae are applicable for both P- and S-waves radiated either by shear 
the magnitude of the prediction as d → 0. Because the depth of the 
fractures or by tensile fractures. It follows that the spectral velocity 
observed induced seismicity (c. 2.5 km) is rather less than this, 
amplitude increases in proportion to f for f <  but decreases as c. 
these predictions can be expected to underestimate the ground 
c
−1 for f >> . The strongest velocities of ground motion produced 
velocities that are actually anticipated. To overcome this effect, one 
c
by an earthquake will thus be at frequencies around . Theoretical 
might ‘doctor’ the prediction equations by setting x = 2.5 km;  the 
c
models predict that for a circular earthquake source of radius a
(much higher) predictions that result (e.g. PGV c.  200 mm s−1 for 
magnitude 4) are also indicated in Figure 1.
Another long-standing method for prediction of macroseismic 
Λ v
f
s s
(12)
effects has been through stochastic modelling, in which earthquake-
c = 2 a
π  
induced ground vibrations are simulated by treating the seismic 
source as a combination of oscillators of random phase, distributed 
where Λ  is a dimensionless factor; for example, for the Brune 
with appropriate amplitude ranges across an appropriate frequency 
S
(1970) source model, Λ  ≈ 2.34. However, as is discussed in the 
range, with effects of geometrical spreading and anelastic attenua-
S
Appendix, for a given seismic event  may be higher for P-waves 
tion also factored in (e.g. Boore 2003; Boore & Thompson 2012). 
c
than for S-waves. Furthermore, the root mean square angular aver-
Boore (2003) illustrated such a simulation for a magnitude 4 event 
age of R
at a distance of 10 km, in which the PGV was calculated as 
θϕ for tensile fracture events is higher for the P-wave than 
for the S-wave (from Walter & Brune 1993, it is √(47/15) for the 
6.1 mm s−1, the strongest spectral velocity components being c. 
P-wave, in rock with a Poisson’s ratio of 0.25, and √(8/15) for the 
f = 8 Hz. Scaling for geometrical spreading would increase this pre-
S-wave), whereas for shear fracture events the reverse is true 
diction  to  24.4 mm s−1 at 2.5 km distance. Correction for anelastic 
(√(4/15) and √(6/15), respectively; e.g. Aki & Richards 1980,  
attenuation can also be made using the standard equation
p. 120). In addition, the S-wave radiation pattern for a tensile frac-
ture earthquake has nodal directions, along which the amplitude of 
A
− Rf
oexp  π
/ (Qv )

the radiated wave is zero, whereas P-waves are radiated in all direc-
 
(13)
tions (e.g. Shi & Ben-Zion 2009). Each of these factors will result 
in stronger P-waves than S-waves, although this effect is offset by 
(e.g. Toksöz & Johnston 1981), where  and A are the amplitudes 
o
presence of 3 rather than 3 in the denominator of the P-wave 
of a seismic wave of frequency f before and after correction for 
P
s
version of equation (11). Overall, the amplitudes of P-waves rela-
propagation for a distance R through a medium with S-wave velocity 
tive to S-waves are thus expected to be higher for tensile fracture 
 and anelastic quality factor Q. Taking Q = 500  for  f = 8 Hz,  and 
s
earthquakes than for shear earthquakes, thereby providing a stand-
 = 3500 m s−1 (Boore 2003), one arrives at a PGV prediction at 2.5 km 
s
ard method for identifying the former (or for determining the rela-
distance from a magnitude 4 event of c.  27 mm s−1. This prediction is 
tive contributions of tensile and shear deformations for ‘hybrid’ 
thus somewhat higher than those obtained by direct use of the Bragato 
events) (e.g. Walter & Brune 1993; Ramsey & Chester 2004; 
& Slejko (2005) empirical prediction equations but much 
 
Šílený et al. 2009; Song & Toksöz 2011; Vavryčuk 2011; Kwiatek 
lower than those obtained for x = 2.5 km using the ‘doctored’ ver-
& Ben-Zion 2013; Eaton et al. 2014; Song et al. 2014). However, 
sions of their equations. For comparison, in a discussion of 
 


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‘FRACKING’-INDUCED MICRoSEISMICITY IN THE UK
337

 1.4; 
 in the 
 =
B
 1980) 
developed 
(so 
 al.
et

 4 
 =
method 
m
spectral 
for the 
, then equation (A54) to determine 
H
 0.7; prediction S2) or 
 =
B
 from 
 from a slamming door (Stagg 
o
predictions 
−1
(so 
 s
All 
 2 
 mm

 =
m
only
Those for small circular shear fractures (prediction S1; 
.  o and 
purposes 
 from M
 2 MPa 
 may reach 12.7
L
 =
fects, proposed magnitude thresholds for regulating ‘fracking’
 M
 T
 =
 =
W
P
felt ef
illustrative 
able 1), PGV
 from Bragato & Slejko (2005) and from the spectral method developed in this study
magnitudes for 
 1.4); they utilize equation (A34) to determine M
 =
B
lower 
(so 
 km; the two sets of predictions after Bragato & Slejko (2005) correspond to the original (lower) and 
to 
 4 
 =
 2.5
 =
m
R
 and 
 2, and use equation (3) to determine M
 =
−1  m
 km, so 
Φ
 Pa
and extrapolated 
and 
 15500
 ≥ 2.5 
 0.5, 
 =
L
η =
K
for M
 at a depth of 2.5
 1.6, 
b =
, −1 s
 vibrations correspond to those depicted; thus, for example (T
calibrated 
 km
 0.7); those for small circular tensile fractures (equation (A49)) assume 
 =
being 
 2.15
B
 =
s

(so 
−3
 2 
 1999).
 m
 =
m
 kg
and 
both versions 
), vertical tensile fractures assume 
 2550
 H
 =
 m (NCHRP
s surface directly above ‘fracking’
ρ =
L
 4 MPa 
 =
c. 8
equations, 
 0.18, 
 C
ν =
S =
of their 
 GPa, 
ge, square (i.e. 
 12.7
 from various other forms of environmental nuisance, and predictions of vertical and horizontal PGV
μ =
versions 
Those for lar
assume 
 (higher) 
 from a lorry at a distance of −1 s
 Comparison of regulations for peak ground velocity at residential property from quarry blasting, applicable in the UK, with 
study 
 (prediction S4). Other estimates of the magnitudes of ‘nuisance’
this 
2 mm
Fig. 1.
UK, estimates of PGV
All predictions are for points on the Earth’
‘doctored’
in 
based on equation (A45)) assume 
prediction S3). 
PGV
or 

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338
R. WESTAWAY & P. L. YoUNGER  
regulatory limits for ‘fracking’, Bull (2013) estimated that an 
being due in part to the dependence of the predictions on different 
induced earthquake of M  4.5 would have a PGV of c.  34 mm s−1.
rock properties and in part to their different angular variations in 
L
This stochastic modelling approach has not previously been 
seismic radiation. The predictions scale in relation to the parameter 
applied to quantification of the hazard (or nuisance) caused by the 
S, the initial shear stress in the adjoining rock mass, for shear earth-
microseismicity induced by ‘fracking’ in the UK. Pending a formal 
quakes, and P, the excess fluid pressure, for tensile earthquakes. 
analysis of this type, a simpler approach will be provided here. 
Our calculations incorporate the assumptions that for fracturing to 
Thus, if it is assumed that all frequency components radiated by the 
occur S will be equivalent to the cohesion () of the rock mass, 
C
earthquake source oscillate in phase (rather than having random 
and P to its tensile strength (). Part of the basis for our prediction 
T
phase relations) with spectral displacement amplitudes as described 
of larger PGV for shear earthquakes is that  > ; even if these 
C
T
above (i.e. constant at Ω (equation (11)) for f ≤  and proportional 
quantities were set equal to one another, however, the differences 
c
to −2 for f > , up to some limiting frequency mf ) and anelastic 
between the seismic radiation patterns would still result, for a given 
c
c
attenuation is neglected, the peak ground velocity v
 can be eval-
value of m, in the prediction of larger PGV for shear earthquakes. 
max
uated as described in the Appendix as
Furthermore, strictly speaking, the independent variable used in 
our predictions in Figure 1 is, in effect, M , not M ; in the analysis 
o
L
to produce these predictions, M  has been converted to M  using 
v
= π Φ Ω 2
   
(1 + 2B
o
W
max
c
)  (14)
equation (3), and the resulting values of M  are assumed (as 
W
already stated) equivalent to M . However, the realization that 
L
where B = ln(m), Ω might be ΩSP, ΩSS, ΩTP, or ΩTS (see Appendix), 
shear earthquakes and tensile earthquakes of a given seismic 
depending on whether one is considering P- or S-waves radiated by 
moment will produce systematically different PGV values suggests 
a shear or tensile earthquake source, and Φ is the free-surface 
that, in reality, these two types of earthquake will have different 
amplification factor for this type of seismic wave (see also the 
M –M  relations. This is one reason why it is undesirable to base 
o
L
Appendix). As already noted, the Appendix also demonstrates that 
regulation of ‘fracking’ on any threshold for M , and why it is 
L
the familiar property of shear earthquakes, that the S-wave is typi-
therefore preferable to use felt effects, expressed as PGV, instead.
cally stronger than the P-wave, is also usually the case for tensile 
earthquakes as well, especially in rocks of low Poisson’s ratio. 
Hence, our analysis of PGV from ‘fracking’ concentrates on the 
Application to the induced seismicity 
amplitudes of S-waves; the resulting equations are stated in full in 
from ‘fracking’ in the UK
the Appendix (equations (A46) and (A50), respectively, for 
S-waves from shear and tensile earthquakes).
An initial requirement before any of the theory discussed above 
Figure 1 shows predictions on this basis, with Rθϕ taken as its 
can be applied to assess the potential nuisance caused by ‘frack-
maximum value of unity and with Φ = 2 (see Appendix), for shear 
ing’ in the UK is to constrain the relevant physical properties for 
earthquakes for m = 2,  such  that  B ≈ 0.7, and for tensile earthquakes 
the lithologies present. However, there is relatively little quanti-
for m = 2,  such  that  B ≈ 0.7,  and  for  m = 4,  such  that  B ≈ 1.4,  in  each 
tative information on such properties for lithologies that might 
case at a distance of 2.5 km. The first of these predictions indicates 
be subjected to ‘fracking’ in Britain. Waltham (2009, p. 48) 
v
 = 52 mm s−1 for M  4, somewhat in excess of the stochastic pre-
max
L
listed as 10 GPa and 2300 kg m−3 the typical Young’s modulus 
diction derived from Boore (2003). This difference is partly a 
and density of ‘Carboniferous mudstone’ that might represent 
reflection of differences in method (e.g. Boore (2003) factored in 
the Bowland Shale. With a Poisson’s ratio ν of 0.2, the former 
anelastic attenuation and assumed an angular average of the radia-
value would indicate μ c. 4.2 GPa (equation (A3)), so equation 
tion pattern, whereas for this calculation we have not considered 
(A1) would indicate  c.  1.35 km s−1  and,  with  Δσ = 3 MPa,  equa-
s
any effect of anelastic attenuation and have assumed the maximum 
tion (9) would give c c.  5 × 10−4. Carter & Mills (1976) had pre-
of the radiation pattern in every direction; there are also differences 
viously determined 2–14 GPa for the Young’s modulus, 1–8 MPa 
in the approaches regarding calculation of the corner frequency and 
for the tensile strength S  and 2–12 MPa for the cohesion S , for 
T
C
different choices of rock properties). Furthermore, generations of 
no more than 24 samples of Middle Carboniferous (Namurian) 
seismological studies (e.g. Aki 1969; Aki & Chouet 1975; Frankel 
age mudstone from sites in NE England, which might represent 
& Clayton 1986; Frankel & Wennerberg 1987; Sato & Fehler 1998; 
analogues for the Bowland Shale. We thus adopt 4 MPa and 
Gao et al. 2013) have established that scattering of seismic waves 
2 MPa as representative values of  and  for this lithology. 
C
T
by heterogeneities transfers energy from direct seismic phases into 
Significant variability in properties is nonetheless indicated; with 
other phases that arrive later, reducing the amplitude of the direct 
such limited sampling it is apparent that these choices are sub-
phases. By neglecting any effect of scattering our analysis will thus 
ject to considerable uncertainty.
overestimate the amplitude of the expected seismic ground vibra-
To avoid any risk of systematic errors arising in our work as a 
tions. In addition, any prediction using equation (14) is also likely 
result of using such a limited set of data values, we base our analy-
to overestimate the true PGV because in reality the different fre-
sis instead on the physical properties of the Barnett Shale. This is a 
quency components of any earthquake source will not be in phase 
mudstone of Mississippian (i.e. Carboniferous) age that is wide-
(and so will partly cancel one another) and because anelastic atten-
spread in the Fort Worth area of Texas and was the first deposit to 
uation (cf. equation (13)) will be significant, especially at high fre-
be developed as a shale gas resource (e.g. Martineau 2007). An 
quencies. Conversely, to match the much higher PGV predictions 
abundance of data is therefore available for it, including the follow-
derived from the ‘doctored’ use of the Bragato & Slejko (2005) 
ing representative properties, which we have taken from Varga 
prediction equation (h set to zero and x = 2.5 km),  much  higher  val-
et al. (2012) and which are all mutually consistent given equations 
ues of B would be necessary. Alternative predictions on this basis, 
(A1), (A3), (A4), and (A5): E c. 30 GPa; ρ c.  2550 kg m−3;    c
p
not illustrated in Figure 1, would require very high values of m, c
31000 g cm−3 × ft s−1 or c
9.45 × 106 kg m−2 s−1; 
 
c
S
1013, which would require significant contributions to v
 from 
max
19400 g cm−3 × ft s−1 or c.  5.91 × 106 kg m−2 s−1; ν c. 0.18; μ c
very high frequencies of ground motion that would be physically 
12.7 GPa;   c.  3.44 km s−1;  c.  2.15 km s−1. Others have reported 
P
s
implausible were anelastic attenuation to be taken into considera-
somewhat different values; for example, Agarwal et al. (2012) 
tion. Figure 1 also indicates that for a given M , tensile earth-
L
quoted  E = 45 GPa  and  ν = 0.2,  whereas  Song  et al. (2014) gave 
quakes are predicted to cause significantly smaller PGV than 
 = 4.11 km s−1,   = 2.44 km s−1,  and  ρ = 2500 kg m−3. With 
P
S
for shear earthquakes. As is discussed in the Appendix, this distinc-
 = 4 MPa (see above) and ν c. 0.18, E = 30 GPa would imply, from 
C
tion arises from differences in the underlying source mechanics, 
equation (9), c c.  2.4 × 10−4, whereas E = 45 GPa  would  give  c c

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‘FRACKING’-INDUCED MICRoSEISMICITY IN THE UK
339
1.6 × 10−4. Our analysis also requires ; however, this quantity 
observational data indicating that fractures created by ‘fracking’ may 
T
exhibits considerable variability and is thus subject to some uncer-
grow to lengths of c. 600 m. Davies et al. (2012) likewise proposed 
tainty. For example, Gale & Holder (2008) reported values ranging 
that the maximum vertical extent of a fracture that can develop as a 
from 12 to 44 MPa, whereas Tran et al. (2010) reported values 
result of ‘fracking’ is c. 600 m, although natural fracture systems are 
between c. 1.4 MPa (i.e. 200 p.s.i.) and c. 21 MPa (i.e. 3000 p.s.i.). 
known with lengths of up to c. 1000 m (e.g. Geiser et al. 2012; Davies 
It would indeed appear from these and other studies that 
et al. 2013; Lacazette & Geiser 2013). As Fisher & Warpinski (2012) 
Carboniferous mudstones typically consist of relatively weak zones 
explained, fractures induced by ‘fracking’ will tend to develop 
with    c. 2 MPa, which are most likely to fracture, interspersed 
upwards because the ‘fracking’ fluid is less dense than the surround-
T
with zones where  is an order of magnitude larger.
ing rock, so if the conditions at the point of initiation favour the crea-
T
Taking the above theory into account, assuming Δσ =  = 4 MPa, 
tion of a fracture then the conditions at a slightly shallower depth will 
C
μ = 12.7 GPa,  and  ν = 0.18,  so  c ≈ 2.4 × 10−4, the induced Preese Hall 
exceed the failure criterion for the initial development of the fracture 
earthquake with M  = 2.3 is predicted to have had M  c. 3 × 1012 N m 
to a greater extent, so the fracture can propagate. However, such 
L
o
(equation (3)) and to have involved c. 17 mm of slip on a fault plane 
propagation is ultimately limited by the excess pressure in the ‘frack-
of radius c. 70 m and area c.  14000 m2 (equation (8)). It released c
ing’ fluid and by the volume of this fluid that is available; the reported 
500 MJ of energy in the form of seismic waves (equation (10)), 
c. 600 m size limit is thus a reflection of operating practices at the US 
with the strongest ground velocities at estimated frequencies (c. f 
‘fracking’ sites that provided the data for Fisher & Warpinski (2012). 
c
of c. 11 Hz (equation (12), assuming  = 2.15 km s−1). The subse-
Assuming the same set of rock properties as before, including 
s
quent M  1.5 event had M  c.  2 × 1011 N m  and  involved  c. 7 mm of 
μ = 12.7  GPa,  ν = 0.18,  and  ρ = 2550 kg m−3, if the vertical stress is 
L
o
slip on a fault plane of radius c. 30 m and area c. 2000 m2, releasing 
lithostatic (such that the parameter K in equation (A30) is c
c. 30 MJ of energy as seismic waves with the strongest ground 
15500 Pa m−1), then the minimum excess pressure in the ‘fracking’ 
velocities around c. 27 Hz. For comparison, detonation of a stand-
fluid, required to create such a large fracture, would be c.  2.3 MPa 
ard c. 200 g stick of dynamite would release c. 1 MJ of energy; it is 
(equation (A30)) and the minimum volume of ‘fracking’ fluid, 
common practice to use c. 100 kg of explosive in single quarry 
required to keep the fracture open and allow it to reach this size, 
blasts in the UK, thus releasing c. 500 MJ of energy. According to 
would be c.  25000 m3 (equation (A32)). If such a large fracture 
BGS (2011a) the M  = 2.3 event caused no damage but was felt at 
formed in a single rupture, the resulting earthquake would have M  c
L
o
23 locations and was assigned an epicentral intensity of IV on the 
3 × 1014 N m (equation (A34)), corresponding to M  c. 3.6 (equation 
w
European Macroseismic Scale (EMS). From Figure 1, the PGV in 
(3)). With this set of parameter values, and again assuming Rθϕ = 1, 
its epicentral area, predicted by our method, was unlikely to have 
our prediction method (equation (A54)) would suggest a PGV of c
exceeded  7 mm s−1. BGS (2011b) reported that the M  = 1.5  event 
65 mm s−1 at the Earth’s surface directly above the fracture, at a dis-
L
also caused no damage but was felt by at least one person (it 
tance of 2.5 km (Fig. 1). However, the S-wave radiation pattern for a 
occurred in the middle of the night when ambient levels of ground 
vertical tensile fracture would have Rθϕ = 0 in the vertical direction 
vibration would have been low) and was assigned an EMS epicen-
(see Appendix), so the actual amplitude of the direct S-wave that 
tral intensity of III. From Figure 1, our method predicts that the 
travels in this direction will in fact be zero. The maximum amplitude 
PGV in its epicentral area may have reached 3 mm s−1. Nonetheless, 
of this direct S-wave will instead be expected at points for which the 
this instance, of two earthquakes large enough to be felt being 
ray inclination is c. 35° to the vertical (see the Appendix; equation 
induced by the ‘fracking’ of a single well, contrasts markedly with 
(A58)); in this direction Rθϕ ≈ 0.94 and the path length for a 2.5 km 
US experience. Thus, as Hitzman et al. (2013) noted, up to 2011 
deep source will be c. 3.1 km, so the prediction of PGV decreases to 
some 35000 wells in the USA had been ‘fracked’ but only one 
c.  50 mm s-1 (equation (A54)). Even this prediction will exceed the 
induced earthquake large enough to be felt had been reported; this 
likely true PGV that would result from the (very unlikely) event of a 
was of M  2.8, and occurred on 18 January 2011 as a result of 
fracture of this size forming in a single rupture, because the method 
L
‘fracking’ at c. 3 km depth to stimulate oil production at Eola, 
assumes all frequency components in the seismic S-wave will be in 
Oklahoma (Holland 2011). Scaling Figure 1 for the different 
phase (as was noted above, others have estimated that the PGV for 
source depth, our method predicts that this event might have pro-
induced earthquakes of roughly this size would be c. 30 mm s−1 rather 
duced a PGV of c.  11 mm s−1. This discrepancy may have some-
than c.  50 mm s−1). This eventuality is anyway amenable to regula-
thing to do with the fact that US landowners own the mineral 
tion; imposing a tighter regulatory limit on the pressure and/or vol-
rights beneath their property whereas those in the UK do not. On 
ume of the ‘fracking’ fluid would force a lower limit for this ‘worst 
the other hand, according to Mair et al. (2012), some 200 onshore 
case scenario’ prediction.
wells in the UK have been ‘fracked’ for purposes other than shale 
We note in passing that gas contamination of drinking water wells 
gas production (such as improving oil recovery), with no record 
has been reported near shale gas extraction sites in the USA (e.g. 
of any induced microearthquake having been felt. The largest 
Osborn et al. 2011; Jackson et al. 2013) and that such evidence has 
ever earthquake that is generally accepted as having been induced 
been cited by environmental groups and in the media (e.g. Fox 2010) 
by ‘fracking’ occurred on 19 May 2011 in the Horn River Basin, 
as evidence that the fracture networks produced by ‘fracking’ may be 
near the town of Fort Nelson in NE British Columbia, Canada. It 
much more extensive than the evidence in the previous paragraph 
had M  3.8 and was felt but caused no damage (BCOGC 2012); it 
would suggest. However, subsequent work indicates that this con-
L
was considered equivalent to M  3.6 by Ellsworth (2013). 
tamination has nothing directly to do with ‘fracking’ but is caused 
W
Nonetheless, other activities in the USA have been associated 
instead by defects such as leaking well casing or faulty cementation in 
with much larger earthquakes that have arguably been induced 
the annulus outside the well casing (Darrah et al. 2014).
(e.g. Ellsworth 2013; Kerr 2013; Van Der Elst et al. 2013); for 
De Pater & Baisch (2011) proposed that future ‘fracking’ opera-
example, wastewater injection into a borehole at Prague, 
tions should be permitted in the UK subject to real-time seismic 
Oklahoma, was associated with significant seismicity, including 
monitoring, with work being allowed to proceed with caution 
an event of M  5.7 on 6 November 2011 (Keranen et al. 2013).
should any event above M  0.0 occur, but that it should be sus-
w
L
De Pater & Baisch (2011) estimated the maximum size of any 
pended if any event as large as M  1.7 were to occur. However, 
L
‘fracking’-induced microearthquake in the UK as M  c. 3, based on 
Green et al. (2012) regarded the latter limit as insufficiently cau-
L
long-standing experience of mining-induced seismicity (see Kusznir 
tious and recommended a lower threshold of M  0.5 for the suspen-
L
et al. 1980; Bishop et al. 1993; Donnelly 2006), although Mair et al. 
sion of ‘fracking’. Mair et al. (2012) noted that one of these 
(2012) suggested a limit of M  4 without clear explanation. 
recommendations was much more conservative than the other but 
L
Subsequently, Fisher & Warpinski (2012) reported an abundance of 
declined to adjudicate. Guidelines for future ‘fracking’ operations, 

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340
R. WESTAWAY & P. L. YoUNGER  
issued subsequently by industry practitioners (UKOOG 2013), rec-
c.  0.4 mm s−1 if the radiation pattern for vertical tensile fractures 
ognized that other industrial processes that generate vibration, such 
were taken into account; see the Appendix). This seems exces-
as quarry blasting, are regulated within the UK on the basis of 
sively cautious and, thus, inappropriate as a regulatory limit; ground 
thresholds of ground velocity or acceleration (rather than M ), and 
vibration at this level would have a chance of being felt only under 
L
‘fracking’ should be analogously regulated with corresponding 
low ambient noise conditions and would be exceeded by the effects 
thresholds.
of many domestic activities. Likewise, the suggestion by Bull 
Guidelines for the allowable amplitudes of ground vibrations 
(2013) that ‘fracking’ should be suspended following the occur-
induced by quarry blasting are indeed currently provided for the 
rence of any induced earthquake of M  ≥ 4.5 is based on the notion 
L
UK by British Standards (BS) 6472 part 2 (BSI 2008) and 7385 
that this threshold corresponds to PGV c.  34 mm s−1 and epicentral 
part 2 (BSI 1993). BS6472-2 is primarily concerned with quantify-
intensity V (see Wald et al. 1999). However, it is much too high as 
ing the peak ground velocity v
 that can be anticipated at a given 
a threshold for regulating ground vibrations on the basis that they 
max
distance d from the detonation of a mass m of explosive; it predicts 
result in environmental nuisance comparable with other potential 
that, with a 10% probability of exceedence,
causes; it is a threshold for the prediction of damage to buildings. 
On the other hand, the statement by Mair et al. (2012, p. 16) that 
‘vibrations from a seismic event of magnitude 2.5 M  are broadly 
v
ambd b
L
max =
−2  (15)
equivalent to the general traffic, industrial and other noise experi-
enced daily’ is not entirely correct. From Figure 1, an M  2.5 tensile 
L
where b = 1.227  and  a = 168700  to  give  v
 in mm s−1 with m in kg 
fracture earthquake with B = 1.4 at 2.5 km depth would be expected 
max
and d in metres. For m = 100 kg (see above), equation (15) thus pre-
to produce a PGV of c. 6 mm s−1, albeit reducing to c. 4 mm s−1 if the 
dicts, for example, v
  c.  100 mm s−1 at d = 100 m  and  v
  c
radiation pattern were taken into account. This is rather greater than 
max
max
2 mm s−1 at d = 1000 m. Conversely, BS7385-2 is primarily con-
might be expected for traffic (for example, at a distance of c.  8 m 
cerned with specifying allowable levels of ground vibration to 
from a moving lorry the PGV would be c.  2 mm s−1 according to 
avoid damage to buildings. It recommends frequency-dependent 
NCHRP (1999)) although it would be within the 10 mm s−1 regula-
allowable limits for components of peak ground velocity ranging 
tory limit for quarry blasting during the working day.
linearly from 15 mm s−1 at 4 Hz to 20 mm s−1 at 15 Hz and 50 mm s−1 
We thus suggest that the existing UK regulatory thresholds for 
at 40 Hz to avoid cosmetic damage. As an alternative, BS6472-2 
ground vibrations induced by quarry blasting can form the basis of 
recommended that PGV in the seismic wavefield incident on any 
regulatory limits for ‘fracking’: a PGV of 10 mm s−1 during the 
residential building should not exceed 10 mm s−1 during the work-
working day, 2 mm s−1 at night, and 4.5 mm s−1 at other times. These 
ing day (8 a.m. to 6 p.m. on Mondays to Fridays or 8 a.m. to 1 p.m. 
thresholds might be considered reasonable limits on the levels of 
on Saturdays), 2 mm s−1 at night (11 p.m. to 7 a.m.), or 4.5 mm s−1 at 
ground vibration that can be anticipated in any area when ‘frack-
other times, these guidelines being for avoidance of disturbance to 
ing’ is under way, and might also be used as criteria for the suspen-
occupants rather than considerations of damage. An alternative 
sion of fracking to avoid the possibility of a larger event occurring 
lower limit of 6 mm s−1 during the working day was also recom-
that might exceed these PGV values. As noted above, for tensile 
mended, with PGV between 6 and 10 mm s−1 allowable if justifiable 
fracture earthquakes caused by ‘fracking’ at a depth of 2.5 km these 
on a case-by-case basis. For comparison, in the USA Siskind et al. 
‘working day’ and ‘night time’ thresholds correspond roughly to 
(1980) recommended that PGV ≤12.7 mm s−1 (i.e. ≤0.5 inches s−1) is 
magnitudes of 3.0 and 1.7. Figure 2 illustrates how the associated 
‘safe’ (i.e. will not cause even cosmetic damage), but occupants of 
magnitude thresholds scale for ‘fracking’ at different depths, to 
buildings might nevertheless experience nuisance from less strong 
maintain the same limits for PGV at the Earth’s surface in the epi-
ground vibrations. The BS6472-2 guideline would prevent, for 
central area, subject to the adoption of the scaling behaviour for the 
example, a quarry operator from blasting during the working day 
induced seismicity that is discussed above, for both tensile fracture 
using 100 kg explosive charges if there is a residential property 
and shear fracture earthquakes. Furthermore, it is apparent that, 
within c. 530 m and would limit blasting outside the working day to 
although such events will be very rare (see Fisher & Warpinski 
charges of <53 kg and at night to charges of <27 kg if the nearest 
2012), the largest possible tensile fracture earthquakes that might 
residential property were at this distance threshold.
occur are capable of producing PGV well in excess of the 10 mm s−1 
Figure 1 compares the UK regulatory guidelines for PGV from 
regulatory limit that we have suggested, if consistency with exist-
quarry blasting and other thresholds of PGV estimated to cause 
ing regulations for quarrying is to be achieved. The possibility of 
hazards (i.e. damage) or various forms of environmental nuisance 
such large PGV values arising from ‘fracking’ cannot be excluded, 
with the predictions of PGV as a function of magnitude that have 
but the probability of such long fractures developing in a single 
been discussed above. It is thus apparent, notwithstanding the ten-
rupture is evidently very low (see Davies et al. 2013), so any result-
dency of our spectral technique to over-predict PGV, that for 
ing nuisance could be covered by a system of compensation. The 
‘fracking’ at 2.5 km depth, resulting in tensile fracture earthquakes 
long-standing systems that operate in the UK, whereby, for exam-
with B = 1.4, the suggestion by De Pater & Baisch (2011) of a limit 
ple, the Coal Authority compensates owners of property for dam-
to induced microseismicity of M  1.7 is roughly equivalent to the 
age caused by mining subsidence (e.g. Coal Authority 2004) or the 
L
BS6472-2 guideline that exposure to PGV from quarry blasting at 
Royal Air Force provides compensation for damage caused by 
night should not exceed 2 mm s−1. This threshold also roughly 
sonic booms from military aircraft, provide robust precedents.
matches the limit to PGV expected from movement of heavy vehi-
It is apparent that the development of any ‘fracking’ site should 
cles past residential property (from NCHRP 1999), as might be 
be preceded by site surveys (e.g. using 3D seismic reflection profil-
expected, for example, to deliver supplies to any shale gas project. 
ing) to exclude the presence of any pre-existing faults large enough 
Likewise, the BS6472-2 upper limit to exposure to PGV from 
that, if they were to slip in an induced earthquake, would result in 
quarry blasting during the working day of 10 mm s−1 roughly 
ground motions on a scale that could cause damage. Modern seismic 
matches the upper bound to PGV expected for a microearthquake 
survey techniques can readily resolve faults with dimensions of tens 
of M  3 at 2.5 km depth. Conversely, and again notwithstanding the 
of metres and vertical offsets of c. 10 m (e.g. Arthur et al. 2013), 
L
tendency of our spectral technique to over-predict PGV, the thresh-
provided the interpretation is carried out with appropriate expertise 
old of M  0.5 suggested by Green et al. (2012) and adopted by 
(see Bond et al. 2012). Thought also needs to be given to the perme-
L
DECC (2013b) for suspension of ‘fracking’ would correspond to 
ability of such faults, as this influences the potential for ‘fracking’ 
very small values of PGV (e.g. c.  0.5 mm s−1 for tensile fracture 
fluid to escape into them and potentially lubricate larger patches of 
earthquakes with B = 1.4; Figure 1; which would reduce to 
 
fault (see Lunn et al. 2008; Solum et al. 2010). A trade-off evidently 


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‘FRACKING’-INDUCED MICRoSEISMICITY IN THE UK
341
mic radiation in relation to human perceptions of 
 
nuisance), the recommendations summarized in Figure 2 can thus 
provide a basis for regulation of induced seismicity from ‘fracking’. 
To implement them will require any site at which ‘fracking’ is under-
taken to be instrumented with seismographs for real-time monitoring 
of the activities, as specified by Mair et al. (2012) (cf. Warpinski 
2013). Such installations will require three-component broadband 
seismometers of appropriate bandwidth to allow spectral studies to 
determine seismic moment and to permit reliable identification of 
seismic phases for earthquake location. Once determined, the seis-
mic moment can be converted to M  using equation (2) and the com-
w
bination of source depth, magnitude and focal mechanism compared 
with the recommendations in Figure 2 to determine the chance of any 
‘nuisance’-level ground vibrations occurring anywhere at the Earth’s 
surface and, thus, whether any action need be taken, such as to mod-
ify the ‘fracking’ process or compensate anyone affected. The 
requirement for such monitoring measures should not impose any 
onerous burden on the developer of any proposed shale gas site. 
Moreover, the ability to seismically monitor the manner in which 
induced microearthquakes propagate over time away from sites of 
fluid injection will provide useful information to developer; for 
example, it allows the permeability of the rock mass to be determined 
using standard techniques (e.g. Li 1984), and provides a means of 
maintaining the propagation of fractures at a safe distance from any 
rock unit that should not be fractured, say because it forms an aquifer 
(cf. Davies et al. 2012; Fisher & Warpinski 2012; Geiser et al. 2012). 
Propagation of fractures into an aquifer is unlikely to result in aquifer 
pollution, given the lack of any sustained hydraulic gradient towards 
the Earth’s surface from a naturally under-pressured shale gas zone 
(Younger 2014). Rather, avoidance of ‘fracking’ connections into 
aquifers is first and foremost a concern for the developer, as intercep-
tion of permeable, water-bearing zones in sterile overburden is 
highly likely to flood-out the underlying gas-producing zones just 
developed at great expense. For this reason, microseismic monitor-
ing of ‘fracking’ processes is routine (e.g. Warpinski 2013): the 
amount of ‘force’ applied in fracking indeed tends to be strictly con-
trolled, so it is limited to that required to increase the permeability of 
the target gas-rich zones, avoiding sterile overburden, especially 
where this may be water-bearing. The same microseismic data could 
also be readily used to assess compliance with any framework for 
regulating induced seismicity. Furthermore, the eventual recording 
of large quantities of data of this type should be beneficial to future 
refinements of any regulatory framework for the induced ground 
vibrations and may contribute to refining theory for the triggering 
and scaling behaviour of microearthquakes.
Nonetheless, as discussed, for example, by Mair et al. (2012), a 
proportion of the fluid injected to ‘frack’ a borehole returns to the 
surface when the well is subsequently depressurized; although this 
‘flowback fluid’ can be recycled, ultimately, any shale gas produc-
tion development must be accompanied by a wastewater disposal 
system. In the USA it is common practice to dispose of wastewater 
Fig. 2. Predictions of magnitude thresholds for a given PGV at a given 
epicentral distance from an earthquake source of a given magnitude, cal-
from this and other industrial processes in boreholes. This action 
culated, using the same procedures and parameter values as for Figure 1, 
(rather than ‘fracking’ per se) appears to be the main cause of the 
for the limits for PGV at different times of day that are recommended by 
significant increase in seismicity observed in the USA over the past 
BS6472-2. (a) Shear fracture earthquakes with B = 0.7;  (b) tensile fracture 
decade (e.g. Ellsworth 2013; Hitzman et al. 2013; Van Der Elst 
earthquakes with B = 0.7;  (c) tensile fracture earthquakes with B = 1.4.
et al. 2013). Furthermore, as already noted, much larger induced 
earthquakes are attributed to this mechanism than to the ‘fracking’ 
directly, such as the aforementioned Prague, Oklahoma, event. The 
exists between the level of detail to which such surveys are under-
case study of the Denver, Colorado, sequence of induced earth-
taken and the consequences of induced nuisance shear earthquakes 
quakes in 1967–1968 (including the M  4.8 event of 9 August 
w
on faults that are overlooked. The graphs in Figures 1 and 2 can thus 
1967), following disposal in a deep borehole of hazardous waste-
help guide such decision-making, as well as informing consideration 
water from the manufacture of nuclear weapons, is indeed well 
of pressure and volume of ‘fracking’ fluid to limit the size of ‘worst 
known (e.g. Healy et al. 1968; Herrmann et al. 1981; Hsieh & 
case scenario’ induced tensile earthquakes, rare though the latter 
Bredehoeft 1981; Ellsworth 2013). Mair et al. (2012) described the 
might be. Pending further refinements (such as consideration of ran-
extant regulatory framework for wastewater disposal in the UK; 
dom phase variations between different frequency components of the 
DECC (2014) has subsequently established a regulatory frame-
seismic waves and consideration of the spectral content of the seis-
work specifically for the disposal of ‘flowback fluid’. This latter 

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342
R. WESTAWAY & P. L. YoUNGER  
document lists the procedures that will be allowable; however, dis-
Appendix: Seismic radiation from 
posal down boreholes is not given as an option, because it is forbid-
den under the terms of the European Water Framework Directive 
tensile fractures; comparison with 
and its daughter Groundwater Directives. Reinjection of spent 
shear fractures
‘fracking’ fluids will therefore not be permitted in the UK: hence, 
the issue of induced seismicity caused by borehole disposal of 
Other workers have previously derived from first principles or 
‘flowback fluid’ will simply never arise in this jurisdiction.
utilized the seismic radiation patterns for P- and S-waves radi-
ated by tensile fractures (e.g. Rice 1980; Walter & Brune 1993; 
Shi & Ben-Zion 2009; Eaton et al. 2014). These analyses are 
Conclusions
based on the more general literature in fracture mechanics (e.g. 
Griffith 1924; Sneddon 1951; Eshelby 1957), which itself builds 
In December 2013 the UK authorities issued a formal set of 
on earlier analyses (e.g. Rankine 1843, 1858). However, the 
regulations governing ‘fracking’, which include the threshold of 
practical implications of such results for regulating ‘fracking’ 
M  0.5 for the suspension of operations (DECC 2013b). 
have not previously been assessed. Furthermore, most previous 
L
Fortunately, this document also states that this set of regula-
treatments have expressed the theoretical results in terms of an 
tions will be ‘subject to review’; it is our hope that the contents 
idealized rock rheology with a Poisson’s ratio of 0.25, rather 
of the present paper may be of value in guiding these authori-
than stating them in general terms that are applicable to any lin-
ties towards an improved regulatory process, to avoid unfairly 
ear elastic rheology.
disadvantaging the new shale gas industry relative to existing 
The relevant theory for tensile fracture earthquakes is based on 
industries (many of which are far more carbon-intensive: for 
considerations of energy storage by elastic deformation during the 
instance, opencast coal mining, which is subject to the quarry-
opening of a tensile crack, from Sneddon (1951). This theory thus 
ing regulations discussed above). We indeed propose a frame-
concerns mechanical properties of rocks, which include shear mod-
work for regulating induced microseismicity from ‘fracking’ in 
ulus (μ), Young’s modulus (E), density (ρ), P-wave and S-wave 
the UK based on the existing regulatory limits applicable to 
velocities ( and ) and acoustic impedances ( and ), Poisson’s 
P
S
p
s
quarry blasting (from BS6472-2); namely, that peak ground 
ratio (ν), and the first Lamé parameter (λ), which are interrelated 
velocities in the seismic wavefield incident on any residential 
using standard formulae such as
property should not exceed 10 mm s−1 during the working day, 
2 mm s−1 at night, or 4.5 mm s−1 at other times. Levels of vibra-
µ
tion of this order do not constitute a hazard, but are similar in 
vs ≡
(A1)
ρ
magnitude to the ‘nuisance’ vibrations that result from activities 
 
such as slamming doors, walking on a wooden floor or driving 
a heavy goods vehicle down a residential road (Fig. 1). Using a 
λ + 2µ
2µ 1
( − ν)
2 1
( − ν)
simple technique based on analysis of the spectra of seismic 


v
bv
P
s
s
ρ
ρ 1
( − 2ν) ≡
1
( − 2ν) ≡
(A2)
S-waves, we have shown that this proposed daytime regulatory 
 
limit for PGV is likely to be satisfied directly above the source 
of a magnitude 3 induced earthquake at a depth of 2.5 km (Fig. 
≡ 2(1+ ν)µ
(A3)
1), and illustrate how the proposed regulatory limits scale in 
 
terms of magnitudes of induced earthquakes at other distances 
(Fig. 2). Previous experience (cf. Davies et al. 2012, 2013; 
(2
P
s ) − 2
Fisher & Warpinski 2012) indicates that the length of the frac-
ν ≡
(A4)
2(2
P
s )
ture networks that are produced by ‘fracking’ cannot exceed c
− 2  
600 m, this limit being determined by the available volume and 
pressure of the ‘fracking’ fluid. The development of a fracture 
≡ ρ v
s
s
network of this size in one single tensile rupture would corre-
 
(A5)
spond to an induced earthquake c. magnitude 3.6, although the 
probability of this happening is very low. Events of this size 
and
would result in PGV above our proposed maximum regulatory 
limit (Figs 1 and 2) and might be sufficient to cause minor 
µν
λ ≡ 2
.
(A6)
damage to property, such as cracked plaster; however, such 
1 − 2ν  
occurrences, if they ever occur, will be infrequent. If any such 
incidents do occur, they could be readily handled under a sys-
Much of the relevant analysis for the properties of seismic radia-
tem of compensation similar to that operated by the Coal 
tion from tensile fractures was worked out by Walter & Brune 
Authority for mining subsidence, or that operated by the Royal 
(1993); however, their analysis was subject to the simplifying 
Air Force to compensate for the effects of sonic booms. The 
assumption that ν = 0.25, which, for example, constrains λ = μ and 
data to operate such a system will be available, as seismic mon-
 = √3 . Because we are now concerned with tensile fractures in 
P
s
itoring of ‘fracking’ is essential both to follow the progression 
lithologies for which ν ≠ 0.25, we shall derive some of the rele-
of the process in the interests of the developer, and also to 
vant equations over again, without building in this simplifying 
demonstrate compliance with any regulatory framework. There 
assumption.
is thus no scientific reason why seismicity induced by shale gas 
Sneddon (1951; equation 128 on p. 490) showed that a circular 
‘fracking’ should not be regulated in a manner analogous to the 
crack of radius a, which opens in rock as a result of a uniform 
way in which quarry blasting has been successfully and uncon-
excess internal pressure P, has an elliptical profile with each face 
troversially regulated in the UK for decades.
displaced by a distance w where
Acknowledgements. P.L.Y. gratefully acknowledges funding from 
4 (1 2
− ν )
NERC (grant NER/A/S/2000/00249). We also thank the anony-
P
( ) =
√( 2 − 2)
(A7)
mous reviewers for their thoughtful and constructive comments.
w r
a
r
E
π
 


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‘FRACKING’-INDUCED MICRoSEISMICITY IN THE UK
343
r being the distance from the centre of the crack. Sneddon (1951; 
equation 131 on p. 491) also showed by integration that the elastic 
strain energy W required to open this crack is
8P2a3 (1 2
− ν ) 4P2a3(1− ν)
=
=
.
(A8)
3E

 
Walter & Brune (1993) stated this expression as
2 3
λ = P a
(A9)
µ  
which is consistent for ν = 0.25.
Equating u = 2w and using equation (1), the seismic moment of 
the tensile fracture earthquake that occurs if the crack described in 
equation (A7) forms in a single rupture can be determined as
ð a 8 P
µ (1 2
− ν )
Mo =
√(a2 − r2)×2 r
 d
π r
(A10)
0
E
π
 
or, given the interrelationships noted above between E, μ and ν,
8
M
1 − ν a3
o =
(
) .
(A11)
3
 
For ν = 0.25, equation (A11) simplifies to the form  = 2Pa3 stated 
o
by Eaton et al. (2014), although this limit to validity was not noted 
by those researchers.
Theory for the spectral amplitudes of the displacement in seis-
Fig. A1. (a) Graphs illustrating the variations with ν of P-wave and S-wave 
mic waves from conventional earthquakes (e.g. Aki 1967; Brune 
corner frequencies for tensile earthquakes, plotted as TP × 2πa/ and 
c
s
1970) was extended by Walter & Brune (1993) to tensile fracture 
TS × 2πa/, for different values of ζ , calculated as explained in the text. (b
c
s
T
earthquakes, with some aspects generalized for λ ≠ μ or ν ≠ 0.25 by 
Equivalent graphs illustrating the variations in P-wave and S-wave corner 
SP
SS
Shi & Ben-Zion (2009). Spectra of tensile fracture earthquakes are 
frequencies for shear earthquakes, plotted as  × 2πa/ and  × 2πa/
c
s
c
s
for different values of ζ . The graphs for ζ  or ζ  = b and ζ  or ζ  = 1.4  con-
thus flat at frequencies f below the corner frequency T, at low-
S
T
S
T
S
c
verge as ν → 0 because b → 1.4  as  ν → 0,  b being √2 or c. 1.41 when ν = 0.
frequency asymptotes ΩTP and ΩTS given by
(A13) this term was determined as 8/15 by Walter & Brune (1993); 
TP
2
R
M
λ / µ + 2cos (θ)M
that for equation (A12) requires evaluation, for λ ≠ μ, as k/15, where
o
ΩTP
θϕ
o
=
= 

(A12)
3
3
4πρ P
v R
4πρ P
v R
 
15 π
2
=
c +
(θ) sin(θ)dθ =1 c
5 2
cos2
+ 2 c
0
12
(A14)
2


+
∫0
 
and
with c = λ/μ.  Thus,  k = 47  when  c = 1, consistent with the Walter & 
TS
R
M
θϕ
sin (2θ)M
ΩTS
o
o
=
=
Brune (1993) analysis.
3
3
(A13)
4πρ
Putting all this together gives
S
v R
4πρ S
v R  
1/3
where TP and TS are the directional coefficients for the P- and 

5

θϕ
θϕ
TS

45 b
π η

v
S-wave radiation patterns from a tensile source, R is distance from 
f
S
(A15)
c
= 
3
5
( −

ν
ζ
π

( +
a
)
the source, and the angle θ is measured from zero in the direction 
1
k
b
T
8
2

perpendicular to the fracture plane. The angular variations in TP 
 
θϕ
and TS have been depicted graphically in multiple publications 
θϕ
which, for b = √3, ν = 0.25, and k = 47, is consistent with equation (17) 
(e.g. as fig. 2 of Walter & Brune (1993), fig. 2b of Shi & Ben-Zion 
of Walter & Brune (1993). Equation (A15) can also be written as
(2009), fig. 2 of Vavryčuk (2011), and fig. 2 of Eaton et al. (2014)).
The analysis by Walter & Brune (1993) to determine the corner 
TS
vS
frequencies for the P- and S-waves radiated by tensile fracture earth-
fc = ΛT
(A16)
a
π
quakes, TP and TS (where ζ  = TP/TS), also requires generalization 
 
c
c
T
c
c
for λ ≠ μ. This analysis equates the integrals of the energy radiated as 
where
P- and S-waves at all frequencies up to TP and TS, averaged over all 
c
c
directions around the seismic source, to a fraction η of the elastic 
1/3


strain energy available, from equation (A8). This in turn requires the 
5
πη
Λ

45
=

(A17)
angular averages of the squares of the trigonometric functions that 
T

.
3
5 
1
( − ν) kζ
b

( +8 )
appear in the numerators of equations (A12) and (A13). For equation 
T

 




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344
R. WESTAWAY & P. L. YoUNGER  
Fig. A3. Graphs of SS as a function of ν and ζ for the case where 
TS
P/S = 0.5  (a) Comparison of tensile and shear earthquakes with the same 
source radius, based on equation (A64). (b) Comparison of tensile and 
shear earthquakes with the same seismic moment, based on equation 
(A65).
The parameter Λ  thus factors in both the direct dependence of 
T
corner frequencies on ν and the indirect dependence owing to b 
and  k also depending on ν (equations (A2), (A6) and (A14)). 
The resulting variations of Λ  with ν, illustrated for η = 0.5  
T
(Fig. A1a), are consistent with values determined previously  
for ν 

0.25 by Walter & Brune (1993): with ζ  = 1.0, 
T
TP = 2πTS ≈ 2.05/a; with ζ  = 1.4,  2πTP ≈ 2.51/a and 
c
c
S
T
c
S
TS ≈ 1.80/a; and with ζ  = √3,  2πTP ≈ 2.75/a and 
c
S
T
c
S
TS ≈ 1.59/a.
c
S
However, although it has been generalized to any value of ν, 
the above analysis incorporates the assumption of uniform P, and 
so neglects the vertical pressure gradient in the ‘fracking’ fluid 
Fig. A2. Effects of raypath inclination, θ, on predictions of peak ground 
that is causing a crack to open; it is thus valid for vertical frac-
velocity for tensile earthquakes on vertical fractures. (a) Graph of 
tures only if P >> 2 ρ ga (where ρ  is the density of the ‘fracking’ 
TP
TS
f
f
RT  ≡ v
/v
 for ν = 0.18 (for which b ≈ 1.60  and  λ/μ = 0.5625),  using 
PS
max
max
fluid and g is the acceleration due to gravity) or a << P/(2ρ g), so 
f
equations (A57) and (A58), for the specified values of ζ .  (b) Graphs of 
T
TP
TS
if  P = 1 MPa  and  ρ  = 1000 kg m−3 this analysis is valid only if 
v
 and v
 in relative units (for C/z = 1), using equations (A57) and 
f
max
max
TP
a 
(A58) again with ν = 0.18, for different values of ζ .  (c) Graphs of v
 
<< 50 m,  or  M  < c.  3 × 1011 N m (equation (A11)), or M  < c. 1.6 
o
W
T
max
and  TS, likewise in relative units and based on equations (A57) and 
(equation (3)).
max
(A58), for ζ  = b and different values of ν.
The corresponding analysis for a shear fracture, also provided 
T
by Walter & Brune (1993) only for λ = μ, can likewise be general-
ized for λ ≠ μ by a very similar procedure starting from equations 
Using equation (A11), equation (A15) can also be expressed in 
(5.3), (5.6) and (5.7) of Eshelby (1957). One thus obtains, for a 
terms of M  rather than a, as
narrow circular shear fracture of radius a with elliptical cross-sec-
o
tion, which forms as a result of a shear stress S, that the shear dis-
placement across the fracture, u, is
1/3
1/3



8 1
( − ν)P
5

TS
v

12 b
π ηP
v
8   (1− ν)
f
S

S
S
2
2
c
= 
 Λ
0
T
= 
 (A18)
( ) =

3
5
u r
a
r
 
.
 3M

(A19)

o

2

π
M
ζ

πµ (2 − ν) √(
)

(+8)
o
T

 

 by guest on November 25, 2014
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‘FRACKING’-INDUCED MICRoSEISMICITY IN THE UK
345
Thus, from equation (1),
Like Λ , Λ  thus factors in both direct and indirect dependences of 
T
S
corner frequencies on ν. The resulting variations of Λ  with ν, illus-
a
( −ν)
16
3
S
S
2
2
(1− ν)a
M
−   r
2π d
trated for η = 0.5 (Fig. A1b), are consistent with the determination 
o = ∫ 8 1
r r
 (A20)
0 π(2 − ν) √ (

=
3(2 − ν)
by Walter & Brune (1993) that with ν 

0.25 and ζ  = 1.4, 
S
SS ≈ 2.31/a.
c
S
which simplifies, for ν 

0.25, to the standard formula 
As Walter & Brune (1993) showed, ζ must lie between unity and b
M  = (16/7)a3Δσ (e.g. Lay & Wallace 1995) if the stress drop Δσ is 
The upper limit of ζ = b is for a source that ruptures instantaneously, 
o
equated to S. The work done creating this fracture is , where
whereas the lower limit of ζ = 1 is for a source for which the effective 
S
duration of rupture is long compared with the ratio of radius to seismic 
wave velocity, such that the observed corner frequency is determined 
2a3
2
( − ν) π 2
8
1
µ ε (2 − ν)
W
entirely by the rupture time. Walter & Brune (1993) also considered an 
S =
 (A21)
3µ(2 − ν) =
24 1
( − ν)
intermediate case where ζ = 1.4; Eaton et al. (2014) also adopted this 
latter value of ζ, although without noting this as the basis of their anal-
with ε denoting the maximum shear displacement (at r = 0), and the 
ysis. Many studies have noted that choice of rupture velocity (or choice 
low-frequency asymptotes of the source spectrum are
of ζ) has a substantial effect on amplitudes of seismic radiation; Figure 
A1 indicates that variations in ν can have comparable importance.
SP
R
M
The case of a rectangular vertical fracture of height H and length 
θϕ
sin (2θ)cos(φ)M
ΩSP
o
o
=
=
L, in the vertical and horizontal directions along the fracture plane, 
3
3
 (A22)
4πρ P
v R
4πρ P
v R
has been investigated by Fisher & Warpinski (2012) using theory 
by England & Green (1963) and Simonson et al. (1978). The width 
and
w of such a fracture is thus taken as varying with the vertical coor-
dinate y, measured upwards from the midpoint of the fracture (so y 
SS
R
M
 
θϕ
| cos(2θ)cos(φ)θ − cos(θ)sin(φ)φ| M
ranges between –H/2 and +H/2), as
ΩSS
o
o
=
=
(A23)
3
3
4πρ s
v R
4πρ S
v R
(1− ν)
wy) =
(2Ky)√(H2 − 4y2)
where SP and SS are analogous to TP and TS but for a shear 

 (A28)
θϕ
θϕ
θϕ
θϕ
source, ϕ is azimuth, measured relative to the slip vector, SP and SS 
c
c
are corner frequencies for the P- and S-waves radiated by shear frac-
in rock of shear modulus μ, where P is the fluid pressure at depth 
ture earthquakes (with ζ  = SP/SS), and θ and 
y = 0  and
S
c
c
φ are unit vectors in 
mutually perpendicular directions transverse to the radial direction 
from the source, in the senses indicated in figure 1 of Shi & Ben-Zion 
− g
ρ  (A29)
(2009). With ν = 0.25, these equations reduce to equations (21)–(24) 
of Walter & Brune (1993); in particular, equation (A20) reduces to 
is the difference between the vertical stress gradient C and the fluid 
the standard form given by equation (7), with the initial shear stress 
pressure gradient ρg, ρ being the density of the fluid and g the 
applied to the fracture, S in equation (A20), equivalent to the coseis-
acceleration due to gravity. Horizontal variations in w are neglected 
mic stress drop Δσ that appears in equation (7).
in this analysis, so the solution is two-dimensional. The minimum 
Similar analysis to that for the tensile fracture, utilizing the 
value of P, P , required to keep the fracture open, is
min
angular averages of the squares of SP and SS, determined as 
θϕ
θϕ
4/15 and 2/5 (e.g. Aki & Richards 1980, p. 120), gives
KH
Pmin = 4  (A30)
1/3


45
and the cross-sectional area A of the fracture is

π(2 − ν)b5
SS
η

v
f
S
c
= 
 (A24)
3

1
( − ν) ζ
π

(8  + b5
a
)
S
 12
2

(1 ) PH2
− ν π 
=
.  (A31)

which, for b = √3 and ν = 0.25, is consistent with equation (17) of 
Walter & Brune (1993). Equation (A15) can also be written as
The volume of the fracture can thus be estimated as V = AL, so with 
P set to the minimum value, from equation (A30), one obtains
SS
v
f
S
(1 ) KLH3
− ν π
c
= ΛS
 (A25)
a
π

.  (A32)
16µ
where
1/3


Fisher & Warpinski (2012) illustrated this calculation with an 
45

π(2 − ν)b
example, which we have converted into SI units, for μ = 11.5 GPa 
SS

c
= 
.  (A26)
3

1
( − ν) ζ
and ν = 0.2, in a region where K = 6 kPa m−1 owing to the effect of 

(8 + b5)
S
12

C = 16 kPa m−1,  given  that  ρ = 1000 kg m−3. A pressure P = 0.9 MPa 
could create a fracture with H = 600 m, which would have w up to c
Using equation (A20), equation (A24) can also be expressed in 
5 cm, and with L = 300 m  would  require  c.  5600 m3 of fluid. 
terms of M  rather than a, as
However, to create a fracture with H = 1200 m  would  require 
o
P = 1.8 MPa  and,  even  if  L remained only 300 m, c.  45000 m3 of 
1/3
fluid. In practice, because fluid would leak into the surrounding 
1/3



16 1
( − ν)S
5

rock mass rather than simply occupying the volume of such a large 
SS
v

Sb
π
η
v
f
S

S
c
= 
 Λ
0
S
= 
.  (A27)
fracture, the volume that would need to be injected would be larger 
3
5
 3

 (2 − ν)Mo 
2

π

 (2ζ + )
S
3
Mo 
than these limiting values.

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346
R. WESTAWAY & P. L. YoUNGER  
The seismic moment released if a fracture of height H and 
frequency  mf ) and anelastic attenuation is neglected, the peak 
c
length L forms in a single rupture can be estimated by using w from 
ground velocity v
 can be evaluated as
max
equation (A28) for u in equation (1) and is
f
mf

c
c

/2
v
= πΦΩ 
f f +
2
2
 
d
f f
max
c
d 

 (A41)
0

M
µL
wd
o ≈

 (A33)
f

c

/2
or
which evaluates, using equation (A30) as the condition for mini-
mum pressure, as
v
= πΦ 2
Ω (1+ B
max
c
2 )  (A42)
1
3
( − ν)πKLH
1
2
( − ν)πLH P
where B = ln(m). Here, Φ is the amplification coefficient of the seis-
M
min
o ≈
=
.  (A34)
16
4
mic waves, caused by the Earth’s free surface. In general, Φ varies 
with seismic wave type (P or S) and also varies in a complex man-
The work done creating this fracture, W, is
ner with the inclination of seismic raypaths relative to the free sur-
face (the full complexity of this variation is demonstrated, for 
/2
example, in the equations listed by Aki & Richards (1980, p. 190)). 
≈ L
wypyy

d  
(A35)
Nonetheless, in some situations Φ has a simple form; notably, Φ = 2 
/2
for vertically incident P-waves and SV-components of S-waves, as 
well as for SH-components of S-waves at all inclinations. The pre-
where p is the pressure at vertical position y. At the minimum pres-
sent analysis will thus proceed subject to the simplifying assump-
sure condition for initiating a fracture of height H
tion that Φ = 2 in all circumstances; however, appropriate terms for 
Φ, Φ  and Φ  will be included in equations to facilitate future deri-
/ 2)  (A36)
P
S
vation of the more general case. Typical values of Φ for general 
raypath inclinations are smaller than this limiting value of Φ = 2, so 
so W can be evaluated, after many algebraic steps, as
our simplifying assumption that Φ = 2 is consistent with our general 
objective of making conservative predictions of v
. Another con-
5 (1
K2LH4
π
ν
  

max
=
.  (A37)
sequence of this simplifying assumption is that it avoids any 
128µ
dependence of predicted values of v
 on the azimuth of seismic 
max
raypaths relative to that of fault or fracture planes activated by 
Similar analysis to that discussed above for a circular tensile crack 
‘fracking’ and thus results in the ability to make predictions of v
 
thus gives
max
as functions of distance alone.
It follows, by combining equations (A20), (A22), (A23), (A27) 
1/3

and (A42), that for shear earthquakes on circular faults
5

TS

24 b
00 η

v
 
f
S
c
= 

(A38)
1
( − ν) ζ
/

(3 + b5)
T
8

2π(LH 2 1 3

)
2/3
/
/
/ 

Φ SP
1
M
b
3 1 3S2 3
θϕ

60πη
v
SP
P
o

2
ζS (1 2B)
max
=


+
or
2
16π v
ρ R
3
5
ζ
 (
)
S
2
b
S
3

 
1/3

(A43)
5

or
TS
 150 KH
π
η 
v
 (A39)
f
S
c
= 

.
M
ζ
π

(3 + b5)
o
T
8
2

2/3
/


Φ
1/3
SPab1 3S
 (
) 
SP
P θϕ

60πη
2 1

− ν
2
ζS (1 2B)
If  L = H = 2a then equation (A38) can be written, like equation 
vmax =


+
2
8π v
ρ R

3
5 
ζ
 3(2 − ν) 
 (
)
S
2
b
3

(A15), in terms of Λ , with
S

T
 
(A44)
1/3

5

η
 (A40)
and
Λ

300b

T = 
.
3
5 
1
( − ν) kζ
b

(
)
T + 8

2/3
/
0/
/ 

Φ SS
1
M
b
3 1 3S2 3
θϕ

60πη
v
SS
S
o

(1 2B)
max
=


+
  (A45)
Comparison of equations (A17) and (A40) indicates that for a given 
2
16π v
ρ R
3
5
ζ
 (
)
S
2
b
S
3

set of values of a, b, k, ν, ζ , and η, Λ  is greater by a factor of 
T
T
[300/(45π)]1/3 or c. 1.3 for a square tensile fracture with a vertical pres-
or
sure gradient than for a circular tensile fracture at constant pressure.
Stochastic modelling has not previously been applied to quanti-
2/3
fication of the hazard (or nuisance) caused by the microseismicity 
0/


Φ
1/3
SSab1 3S
 (
) 
SS
S θϕ

60πη
2 1

− ν
induced by ‘fracking’ in the UK. A formal analysis of this type will 
v
(1 2B)
max
=


+
.
2

3
5 
π ρ
ζ
 3(2 − ν) 
 (
)
be reported elsewhere; in the mean time, a simpler approach will be 
8
v R
S
2
b
S
3


 
provided here. Thus, if it is assumed that all frequency components 
(A46)
radiated by the earthquake source in each type of seismic wave 
oscillate in phase (rather than having random phase relations) with 
In contrast, by combining equations (A11), (A12), (A13), (A18) 
spectral displacement amplitudes as described above (i.e. constant 
and (A42), for tensile earthquakes on circular fractures under con-
at Ω for f ≤  and proportional to f−2 for f > , up to some limiting 
stant pressure
c
c

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‘FRACKING’-INDUCED MICRoSEISMICITY IN THE UK
347
2/3
We now investigate the variation in predicted maximum 
/
/
/ 

Φ TP
1
M
b
3 1 3P2 3
θϕ

120πη
v
TP
P
o

2
ζ
ground velocities for the P- and S-waves radiated by vertical ten-
T (1
2B)
max
=
+
2
16π v
ρ R

3
5
ζ

sile fractures with θ, the angle between the raypath and the direc-
 (
)
S
k
+ 8b
T

tion perpendicular to the fracture. This analysis considers the 
 
effect of the radiation patterns for P- and S-waves but excludes 
(A47)
complications owing to scattering of waves or interconversions 
between wave types as a result of inhomogeneity in geological 
or
structure or the effect of the Earth’s surface. Such effects are dis-
cussed in textbooks (e.g. Aki & Richards 1980, pp. 123–167) but 
2/3
have been kept outside the scope of the present study. In the verti-
/


Φ
1/3
TPab1 3P
θϕ
120πη
 1
( − ν)
cal plane perpendicular to a fracture, θ is equivalent to the  
v
TP
P


2
ζT (1 2B)
max
=


+
2
raypath inclination (i.e. θ = 0° for horizontal raypaths and θ = 90° 
8π v
ρ R

3
5 
ζ
 3 
 (
)
S
k
+ 8b
T



 
for vertical raypaths). As already noted (equations (A12) and 
TP
TS
(A48)
(A13)) these angular variations are determined by R
 and R
 
θϕ
θϕ
where
and
2/3
TP
2
= / + 2cos ( )
/
0/
/ 

θϕ
λ µ
θ  (A55)
Φ TS
1
M
b
3 1 3P2 3
θϕ

120πη
v
TS
S
o

(1 2B)
max
=
+
2
16π v
ρ R

3
5
ζ

and
 (
)
S
k
+ 8b
T

 
(A49)
TS
θϕ
= sin(2θ) = 2sin(θ)cos(θ).  (A56)
or
If the constant C absorbs all the terms from equations (A48) and 
(A50) (or equations (A52) and (A54)) that are common for P- and 
2/3
0/


Φ
1/3
TSab1 3P
S-waves, and the distance R is written as z/sin(θ), where z is the 
θϕ
120πη
 1
( − ν)
v
TS
S


(1 2B)
depth of ‘fracking’, then, for a vertical tensile fracture,
max
=


+
.
2
8π v
ρ R

3
5 
ζ
 3 
 (
)
S
k
+ 8b
T



 
2
TP
CΦ  λ

P
2
ζT
(A50)
v

(θ)
max
=
+ 2cos
sin

(θ)
 (A57)
µ

b3
Furthermore, by combining equations (A12), (A13) (A34), (A39) 
and
and (A42), for tensile earthquakes on square vertical fractures (with 
H = L) under pressure that increases vertically,
TS

v
S
=
sin (2θ)sin(θ)
max
.  (A58)
z
2/3
/
/
/ 
Φ

TP
1
M
b
3 1 3
θϕ
(KH 2 3
)
150πη
v
TP
P
o


2
ζ
TP
TS
T (1
2B)
max
=
+
Figure A2a and b illustrate the variations in the ratio of v
/v
 
2
max
max
16π v
ρ R

3
5
ζ

TP
TS
 (
)
S
k
+ 8b
T

and in v
 and v
 with θ for λ/μ = 0.5625, corresponding to 
 
max
max
ν = 0.18,  and  Φ  = Φ  = 2, for different values of ζ . Figure A2c 
(A51)
P
S
T
shows the predictions of v
TP and v
TS for different values of ν, 
max
max
or
in each case for ζ  = b. It is thus evident that for steep or subhori-
T
zontal raypaths v
TP ≥ v
TS but for raypaths oriented at strongly 
max
max
2/3
oblique angles to the vertical, v
TP < v
TS, unless ν is relatively 
/


Φ
1/3
max
max
TPb1 3KH 2
150πη
 π 1
( − ν)
large, in which case v
TP ≥ v
TS at all values of θ.
v
TP
P θϕ


2 (
B)
max
max
max
=

 ζ
1+ 2
2
T
32π v
ρ R

3
5 
ζ

2

These patterns can be investigated in more detail by differenti-
 (
)
S
k
+ 8b
T



 
ating equations (A57) and (A58):
(A52)
v
TP
C
2
Φ ζ
 λ

2
2
and
max
=
P T
+ 2cos θ −  4 sin θ cos θ  (A59)
3

( )
( )


( )
θ
zb
µ

2/3
/
0/
/ 
Φ

TS
1
M
b
3 1 3
θϕ
(KH 2 3
)  150πη
and
v
TS
S
o

(1 2B)
max
=
+
2
16π v
ρ R

3
5
ζ

 (
)
S
k
+ 8b
T

 
v
TS
2C
max
ΦS sin θ 
2
2
θ −
θ 
(A53)
=
( ) 2cos ( ) sin ( ) .  (A60)
∂θ
z


or
Solving equation (A59) with the derivative on its left-hand side set to 
zero demonstrates that TP is at a minimum when cos(θ) = 0, at θ = 90° 
2/3
max
0/


Φ
1/3
R
b
TS 1 3KH 2
150πη
 π 1
( − ν)
(see Fig. A2b), and at a maximum when λ/μ + 2 cos2(θ) = 4 sin2(θ) or
v
TS
S θϕ


(
B)
max
=


1 + 2 .
2
32π v
ρ R

3
5 
ζ

2

 (
)
S
k
b
T
8



 
 2
λ 
cos2 (θ) =


.  (A61)
(A54)
 3
µ
6 

 by guest on November 25, 2014
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Downloaded from 
348
R. WESTAWAY & P. L. YoUNGER  
For ν = 0.18 or λ/μ ≈ 0.6, values appropriate for Carboniferous mud-
therefore, consistent with the deduction in the main text that a 
stone (see the main text), this requires cos(θ) ≈ 0.75 or θ ≈ 41°. 
tensile fracture will result in lower amplitude ground vibrations 
However, for ν = 0.26 or λ/μ ≈ 1.0 it would require cos(θ) ≈ 0.70 or 
than an equivalent shear fracture, whether the comparison is in 
θ ≈ 46°; this shift in the value of θ marking the peak in v
TP is 
terms of the radius or the seismic moment of the fracture.
max
 evident in Figure A2c. Likewise, v
TS is at a minimum (of zero) 
max
when sin(θ) = 0 or θ = 0° (see Fig. A2b), and at a maximum when  
References
2 cos2(θ) – sin2(θ) = 0,  or  cos(θ) = 1/√3,  at  θ ≈ 55°,  this  maximum 
AgArwAl, K., MAyerhofer, M.J. & wArpinski, N.R. 2012. Impact of 
value (for C/z = 1, as plotted in Fig. A2b) being sin(110°) × sin(55°) 
geomechanics on microseismicity. In:  sMith, G. & stewArt, S. 
or c. 0.770. The peak ground velocities thus occur for raypaths at 
(eds)  Proceedings of the Society of Petroleum Engineers/European 
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Association of Geoscientists and Engineers European Unconventional 
S-waves.
Resources Conference and Exhibition, 20–22 March 2012, Vienna, 
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TP exceeds  
max
Aki, K. 1967. Scaling law of seismic spectrums. Journal of Geophysical 
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ζ 2
A
T = 2 √ 2 .  (A62)
kkAr, S. & BoMMer, J.J. 2007. Empirical prediction equations for peak 
ground velocity derived from strong-motion records from Europe and the 
For the limiting case where ζ  = b, this is equivalent to
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T
AllMAnn, B.B. & sheArer, P.M. 2009. Global variations of stress drop for 
moderate to large earthquakes. Journal of Geophysical Research,  114

B01310, http://dx.doi.org/10.1029/2009JB005821.
2 −
ν =
1  (A63)
Andrews, I.J. 2013. The Carboniferous Bowland Shale gas study: geol-
2√ 2 −1
ogy and resource estimation. British Geological Survey for Department 
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or ν 
≈ 
0.227. This is consistent with Figure A2c, in which 
 
ment/uploads/system/uploads/attachment_data/file/226874/BGS_DECC_
for ν = 0.22 the peak of v
TP is slightly smaller than that for  
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ArChuletA, R.J., Cotton, F., CAusse, M. & CreMpien, J. 2012. Stress drop var-
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The above discussion establishes that unless ν is relatively 
Center for Geodynamics and Seismology Workshop 2012: Earthquake 
large, v
TS > v
TP. Similar analysis for shear earthquakes would 
source physics on various scales. Luxembourg, 3–5 October 2012
max
max
likewise establish that v
SS > v
SP. To assess the applicability 
ftp://ftp.ecgs.lu/public/publications/source2012/Presentations/Keynotes/ 
max
max
to tensile earthquakes of empirical prediction equations for 
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TS
max
max
T
S
May 2013, Abstracts Volume. Canadian Society of Petroleum Geologists, 
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θϕ
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2/3
Bgs 2011a.  Blackpool earthquake, Magnitude 2.3, 1 April 2011. British 
3

4  (2ζ + 3b5)
Geological Survey, Keyworth. http://www.bgs.ac.uk/research/earthquakes/
SS

S

P
R
1
( − ν ) /3
TS
= √
4 2
 
.  (A64)
blackpoolApril2011.html (accessed 3 January 2014).
 3  

ζ
 (3 + 8b5
S
)
T

Bgs 2011b.  Blackpool earthquake, Magnitude 1.5, 27 May 2011. British 
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2/3
3

25/3
B
 (2ζ + b5
3 )P
oMMer, J.J., stAfford, P.J., AlArCón, J.E. & AkkAr, S. 2007. The influ-
SS
S

 (A65)
TS
=


ence of magnitude range on empirical ground-motion prediction. Bulletin 
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ζ
of the Seismological Society of America97, 2152–2170.
 (3 + 8b5 )S
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
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R SS are always <0.45, and would thus not exceed 0.9, and so 
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of tensile fracturing around a small fault network at Nash Point, UK. 
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TS
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tions for the Eastern Alps in magnitude range 2.5–6.3. Bulletin of the 
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Seismological Society of America95, 252–276.

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http://dx.doi.org/10.1144/qjegh2013-063
Received 12 February 2014; accepted 13 August 2014.