Monitoring of fracture propagation by quartz tiltmeters
-
Upload
bassam-saleh -
Category
Documents
-
view
214 -
download
0
Transcript of Monitoring of fracture propagation by quartz tiltmeters
www.elsevier.com/locate/enggeo
Engineering Geology 7
Monitoring of fracture propagation by quartz tiltmeters
Bassam Saleha,T, Pierre Antoine Blumb
aDept. of Surveying and Geomatics Engineering, Faculty of Engineering, Al-Balqa’ Applied University, Al-Salt 19117, JordanbEarth’s Physics, Institut de Physique du Globe de Paris, 4 Place Jussieu, 75252 Paris Cedex 5, France
Received 24 June 2003; received in revised form 28 April 2004; accepted 1 October 2004
Available online 20 April 2005
Abstract
The growth of a hydrofracture can be monitored by observation of the ensuing deformation of the earth’s surface. The field
data are processed and analyzed to yield a characterization of the deformation source. Several methods are used for measuring
the surface deformation. Geodetic techniques are used for monitoring slow deformation over large areas, where tiltmeters may
be used to complement geodetic networks by providing continuous records. In this paper, two different case studies are
presented in which tiltmeters are used for measuring surface deformation. The first case deals with measurements of surface tilts
obtained during an induced hydraulic fracture experiment. The fracture characteristics are obtained by comparing the measured
deformation with those provided by a mathematical model. Nonlinear inversion of surface tilts gave estimates of the fracture
geometry: depth, length, and thickness. The second case deals with tilts measured during a naturally induced hydraulic fracture
in a volcanic area. The analysis of field data enabled good understanding of the volcano behavior.
D 2005 Elsevier B.V. All rights reserved.
Keywords: Tiltmeter; Hydrofracture; Volcano; Deformation; Vertical displacement; Tilt; Inflation; Deflation
1. Introduction
Recently a considerable research effort has been
directed toward the formulation of practical guidelines
for predicting the geometrical characteristics of
hydraulic fractures. Substantial advances have been
made through theoretical and laboratory studies of the
various mechanisms thought to play a role in
determining fracture geometry (Davis, 1983, 1986;
Okada, 1985, 1992; McTigue, 1987; Zeller and Pol-
0013-7952/$ - see front matter D 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.enggeo.2004.10.009
T Corresponding author.
E-mail address: [email protected] (B. Saleh).
lard, 1992; Rani and Singh, 1992; Cayol and Cornet,
1997; Bonaccorso and Davis, 1999). Different tech-
niques are used in fracture mapping. The seismic
method is used to locate the path of fluid penetration
into the medium from the hypocentral distribution of
microseismic emissions stimulated as a result of
increased pore pressure (Cornet and Yin, 1992). A
variety of borehole logging techniques have been
developed that are potentially sensitive to fracture
geometry in the immediate vicinity of the wellbore.
These include seisviewer imagery (Dudley, 1993),
temperature logs, gamma ray logs (Blanks, 1976), and
the use of impression packers. Although these
9 (2005) 33–42
Fig. 1. (a) Photography of the compact quartz tiltmeter. (b) Main
parts of the compact tiltmeter.
B. Saleh, P. Antoine Blum / Engineering Geology 79 (2005) 33–4234
technologies provide a means of deducing aspects of
fracture geometry, they are not sensitive to fracture
aperture. Downhole television is used to obtain directly
the width of the fracture (Lau and Auger, 1987).
Geodetic techniques are used in volcanic areas to
obtain the vertical and horizontal displacements due to
an inflation or deflation induced by a magmatic source
(Bonaccorso et al., 2003; Jousset et al., 2000;
Matsushima and Takagi, 2000; Miura et al., 2000;
Nishi et al., 1999; Beauducel, 1998; Dvorac and
Dzurisin, 1997). GPS and total stations are used for
measuring these displacements. Fracturing pressure
records can be used to determine some aspects of
fracture behavior (Lili, 1997; Nolte and Smith, 1981).
The latter approach to fracture mapping has become
known as the surface tiltmeter technique, it is found
that the most practical way of obtaining a satisfactory
description of the elastic field is through the deploy-
ment of an array of continuously recording tiltmeters
(Fujita et al., 2002; Ukawa et al., 2000; Yamashina and
Shimizu, 1999; McTigue and Segall, 1988; Evans et
al., 1982). The surface tiltmeter technique is sensitive
to the broad-scale geometry of fractures and not limited
to near-wellbore fracture detection. It is particularly
well-suited to the study of shallow fracture growth and
shut-in consolidation characteristics (Evans et al.,
1982). Mean width of the fracture also can be estimated
from the amplitude of the surface deformation. This
technique is limited by the depth of hydraulic fracture.
The depth should not exceed 450 m (Evans, 1983).
Different analytic models are used for the inter-
pretation of tilt data. Mogi model (1958) is widely
used in the literature for volcanic areas and represents
the magma chamber as a spherical source of dilatation.
Sun (1969) considered the case of a horizontal coin-
shaped crack in which the fluid pressure is uniform.
Pollard and Holzhausen (1979) represented the frac-
ture as a uniformly pressured fluid-filled crack of a
dipping plain-strain. Savage (1980) among others is an
important reference in the area of dislocation theory.
Davis (1983) represented the fracture by an opening
mode slit of arbitrary dip that is rectangular in both
cross-sectional and plane views. Okada (1985, 1992)
investigated 3D problems of surface deformation and
internal deformation due to shear and tensile faults in a
half-space. Cayol and Cornet (1997) developed a 3D
boundary element method combining the direct and
displacement continuity methods.
B. Saleh, P. Antoine Blum / Engineering Geology 79 (2005) 33–42 35
In this paper we present two case studies, in which
the surface tiltmeter technique is used for fracture
mapping. Sun’smodel is used to calculate the geometric
characteristics of the fracture in the first experiment
because the induced hydraulic fracture is horizontal.
2. Description of the quartz tiltmeter
Many types of tiltmeters were developed for
deformation measurements during the last three
decades (D’Oreye, 1998; Wyatt and Berger, 1980;
Goulty, 1976). Due to the importance of measuring
tilts using accurate devices of low drift and low cost,
two tiltmeters of high resolution, in the range of 10�8
rad were developed by Blum and Saleh between 1981
and 1986 (Saleh and Blum, 1990; Saleh et al., 1991).
The quartz tiltmeter with a mirror (Saleh and Blum,
1990) was used for the first experiment and the
compact quartz tiltmeter (Saleh et al., 1991) was used
for the second experiment (Fig. 1). It is a horizontal
pendulum made of melted silica which can operate in
Fig. 2. Site location map of the indu
vacuum, the rotation of the pendulum mass is trans-
formable into voltage variation using a photoelectric
detector. Both the range and the resolution depend on
the pre-chosen natural period of the pendulum. The
advantages of this instrument are: the low instrumen-
tal drift, which is estimated at 3�10�7 rad/year
(Saleh and Blum, 1990); the low cost of manufactur-
ing; and it can be installed on a horizontal or vertical
surface. However, this instrument is not robust and the
relative orientation is given with low precision
compared with the modern bi-axial instruments. In
our case study, the period of the instrument is fixed at
8 s, which gives a resolution of 10�7 rad.
3. Application to induced hydrofracture
This experiment is carried out in the east of France
(see Fig. 2) in order to connect two wells by an induced
hydraulic fracture at 200 m depth. This technique is
usually applied to increase the permeability of a
petroleum reservoir or to make use of rocks at large
ced hydrofracture experiment.
Fig. 4. Surface deformation associated with a horizontal fracture.
B. Saleh, P. Antoine Blum / Engineering Geology 79 (2005) 33–4236
depths for geothermal energy and other purposes.
Sixteen tiltmeter stations were installed around the
injection well to measure the surface deformation
during the experiment. Each station is equipped by two
quartz tiltmeters, one to measure the radial tilt and one
to measure the tangential tilt. The resultant of the two
components gives the tilt at each station.
3.1. Results and discussion
The tilt signals were recorded continuously by XY
recorders to follow the growth of the fracture in real
time. Recording was started 1 h before the beginning
of injection and continued 3 h after its end. Five
stations did not work properly during the experiment
due to problems with the acquisition system. The
signals were digitized by taking one point each 2 min.
Fig. 3 shows a typical example of tilt signals recorded
by 5 stations during the experiment. Tilt variations
were observed during the first 2 h of the experiment
Fig. 3. Typical tilt signals recorded by different tiltmeter stations on Sep. 6th, 1982.
due to injection interruptions. Then the rate of tilt
became constant during 8 h of injection. The observed
tilt at most stations is large in the radial direction and
very small in the tangential direction. This indicates
that the deformation takes the form of a dome and the
fracture is horizontal (Davis, 1983; Evans, 1983) (see
Figs. 4 and 5). The vectors shown in Fig. 5 represent
the tilt resultants of the radial and tangential tilts
observed at 11 stations. The tilt values are estimated
6
5
27
8
4x10-6 rad
9
15 0
10
4 11 16
50 100 m
Tranqueville
Forest path
Injection wellReception wellTiltmeter stationTilt: downwarddirection
Fig. 5. Tilt vectors observed at different tiltmeter stations on Sep. 6th, 1982.
B. Saleh, P. Antoine Blum / Engineering Geology 79 (2005) 33–42 37
with a relative error less than 5%. This error is due to
uncertainties on the calibration factors of the instrument
and on the drift estimation. The drift is approximately
calculated at the injection interruptions. The effect of
topography on tilt measurements is negligible because the
ground surface is flat (Cayol and Cornet, 1998a).
Ground Surface
z
a a
r
h
B
Fig. 6. Elliptical cross-section of the Sun (1969) penny shaped crack
model.
The horizontal coin-shaped crack model (Sun,
1969) was used in the analysis of the experimental
results. This model gives the vertical displacement of
the surface at a distance r from the injection well in
terms of the fracture depth h, radius a, volume V,
maximum separation B, and the distance r as follows
(Fig. 6):
W ¼ Bffiffiffik
psin
h2
� �� h
affiffiffik
p cosh2
� �� �ð1Þ
where
B ¼ 3V
pa2
ffiffiffik
p¼ r2
a2þ h2
a2� 1
� �2
þ 2h
a
� �2" #1=4
h ¼ cot�1 r 2 þ h2 � a2
2ah
� �:
B. Saleh, P. Antoine Blum / Engineering Geology 79 (2005) 33–4238
The tilt at a distance r from the injection well is
given by the first derivative with respect to r.
An inversion method based on the least squares
criteria was used to determine the geometric charac-
teristics of the fracture. The error function E in terms
of fracture depth h and radius a was defined as
follows:
E h; að Þ ¼Xi¼n
i¼1
tiltmeasured � tiltcalculatedð Þ2 ð2Þ
where n is the number of tiltmeter stations (n =11 in
our case study).
E was computed for different values of h and a.
The minimum value of E gave the best values of h
and a. It is found that a =77 mF11 m, h =225 mF9
m, and B =0.016 mF0.004 m for an injection volume
of 100 m3.
4. Application to naturally induced hydrofracture
This experiment is carried out at Piton de la
Fournaise volcano on the Reunion Island in the
Indian Ocean. This volcano occupies the southeast
Eruptio
Radial Tilt
Tangential Tilt
d
e
cba
de
200
160
120
8040
0
4 8 12
Time
Tilt
( µ
rad)
Jan. 18th 1990
Fig. 7. Tilt curves observed by the first tiltmeter station during Jan. 18th, 19
of magmatic intrusion. (c) Beginning of tremor. (d) Lava arrival on Dolu
corner of the island. It is considered as one of the
biggest and most active volcanoes in the world,
Piton de la Fournaise erupts with surprising regu-
larity (more than 100 times since the start of the last
century, the last two eruptions both being in January
2002). The eruptions of Piton de la Fournaise, like
Mauna Loa in Hawaii, are the result of the extrusion
of a small magma pocket located near to the
volcano’s summit (Lenat and Bachelery, 1990;
Bureau et al., 1998a,b; Cayol and Cornet, 1998b).
This reservoir is probably located between 500 and
1300 m below the summit craters of the volcano.
Eruptions since 1977 are interpreted to be fed by a
larger crystallizing reservoir located below sea level
(Lenat et al., 1989; Sapin et al., 1996; Albarede,
1993). The nature of the connection between the
deeper reservoir and the shallow reservoir is
unknown. The magma migrates towards the flanks
of the volcano where fissures appear. The hollow
magma chamber left behind once the eruption has
finished causes subsidence, creating a pit, which
may be several hundreds of meters wide. This
process eventually creates a large caldera. Such a
caldera has formed in la Reunion. It is known as
l’Enclos Fouque. In the center of the caldera, or
enclosure (also known as Le Grand Brule) lies a
n Phase
16
(hours)
20 00
90 eruption. (a) Seismic swarm under dolomieu crater. (b) Beginning
mieu surface. (e) Beginning of the eruptive fissure extension.
Tilt
50
µrad
Time (Julian Days)200 240 280 320 360 400 440
Tangential Tilt
Radial Tilt
EruptionJan. 18th 1990
Fig. 8. Tilt curves observed before and after Jan. 18th, 1990 eruption.
B. Saleh, P. Antoine Blum / Engineering Geology 79 (2005) 33–42 39
large volcanic cone of 400m height. The summit of
this structure is flat and comprises two large craters:
Bory, to the west, which is very old, and Dolomieu
to the east, which appears in 1766. Four tiltmeter
stations were installed around the craters to study the
behavior of the volcano before, during and after
eruption.
PITON DE LA FOURNAISE
Dolomieu Cra
Lava FlowFissure
Projection
Bory Crater Jan. 18th 1990
2
4
3
2600
2550
2450
2400
2350
2300
2250
2200
2150
2
0 500m
Tilt: DownwardDirection
Lava Flow
Projection
Fissure 100 µrad
Fig. 9. Tilt vectors for the perio
4.1. Results and discussion
Fig. 7 shows the tilt curves recorded by the first
tiltmeter station during the eruptive episode of Jan.
18th, 1990. The surface deformation follows three
phases:
(i) The inflation phase, which is observed before
eruption (Fig. 8), the total measured tilt by the
first station over 8 months is 68�10�6 rad,
which is due to the migration of magma toward
a small magma pocket located near to the
volcano’s summit.
(ii) The eruption phase, which is associated with a
variable deformation (Fig. 7). The follwing
episodes are observed: (a) A seismic swarm
under Dolomieu crater; (b) The beginning of
the magamatic intrusion; (c) A tremor which is
due to the magmatic dike propagation; (d) The
arrival of lava on the surface of Dolomieu
crater; and (e) The beginning of the eruptive
fissure extension in the northwest and south-
east directions.
(iii) The deflation phase, which is observed during
and after eruption (Figs. 7 and 8).
ter
MallardCrater
1
100
2050
1950
1900
2000
Jan. 1
8th 19
90
Lava F
low
LangloisCrater
d 23/11/1989–28/2/1990.
B. Saleh, P. Antoine Blum / Engineering Geology 79 (2005) 33–4240
Tilt vectors are calculated for the period 23/11/
1989–28/2/1990 and represented in Fig. 9. These
vectors indicate a rotation movement of the part of the
volcanic cone situated to the west of the eruptive
fissure in their direction. The amplitude, as well as the
direction of each tilt is given in Table 1. The tilts are
estimated with an error less than 5% as mentioned in
paragraph 3. The effect of topography on tilt measure-
ments is not negligible. McTigue and Segall (1988)
showed that a slope of 208 implies ground surface
displacements that are at some points 40% smaller
than those associated with a flat ground surface. For
an average slope of the volcano of 308, the tilt valuesin Table 1 are 50% smaller than those measured on a
flat terrain (Cayol and Cornet, 1998a).
According to seismic data (Lenat et al., 1989; Sapin
et al., 1996), the main magma reservoir is situated
below see level at 5 km depth from the summit, so the
estimated tilt by Mogi Model is less than 10�8 rad for
pressure variations. This tilt is very small and less than
the resolution of the tiltmeter. We conclude that the
observed deformation is related with volume varia-
tions of the small magma pocket located near the
volcano’s summit and intrusion of a magamatic dike
during the eruptive episode. Approximately 2 h before
each eruptive episode, seismic swarms were recorded
to the southwest of Dolomieu crater (Lenat et al.,
1989). Then seismicity decreased before starting again
at the eruption onset. Cayol and Cornet (1998b)
assumed that these seismic swarms correspond to the
initiation (first episode) and the reopening (second
episode) of a macroscopic dike and that the subsequent
decrease of seismicity corresponds to the quasi-static
propagation of this dike toward the ground surface.
They also assumed that the dike starts from the top of
the seismic swarm at a depth of approximately 1000 m
above see level, directly below the southwestern rim of
Dolomieu crater. According to this hypothesis, the
Table 1
Amplitude and azimuth of resultant tilts for the period 23/11/1989–
28/2/1990
Station
number
Amplitude of resultant
tilt (10� 6 rad)
Azimuth of resultant
tilt (deg)
1 157 313
2 22 329
3 59 252
4 100 220
dike propagated upward for an hour at an average
speed of 0.3 m/s. The initial length of the dike is 400
m. The length of the dike near the ground surface is
1000 m over which eruptive fissures span. The dip of
this dike is approximately 458. The strike of the deep
dike is N1658E. The displacements induced by this
dike for 1983–1984 eruption were modeled by Cayol
and Cornet (1998b) using a 3D mixed boundary
element method. The results were compatible with
the above assumptions. The effect of topography is
taken into account in this method. The measured tilts
can be combined with geodetic measurements to
constrain the previous modeling and to enable good
understanding of the volcano behavior.
5. Conclusion
Through the previous experiments, it was able to
monitor the propagation of a hydraulic fracture with
the quartz tiltmeters. The tilt vectors observed during
the first experiment showed that the fracture was
horizontal. The inversion of the tiltmeter data in the
first experiment enabled the determination of the
radius, depth and width of the induced hydraulic
fracture using Sun’s model (1969). The surface tilt
associated with Piton de la Fournaise volcano eruption
on Jan. 18th, 1990 was successfully followed by the
quartz tiltmeters. The tilts provided by four stations
are partial and should be combined with geodetic data
to get the geometric characteristics of the deformation
source. Finally, we conclude that the surface tiltmeter
method of studying the development of shallow
hydraulic fractures has the following merits compared
with the borehole installations:
1. The measurement is entirely passive and neither
interrupts nor is interrupted by the injection
operation.
2. The technique is sensitive to broad-scale features of
the fracture geometry rather than having a field of
view restricted to the immediate vicinity of the
wellbore.
3. The technique is sensitive to fracture width, and,
hence, the closure behavior of the fracture follow-
ing shut-in can be inferred.
4. The occurrence of changes in the plane of fracture
growth during any phase can be detected.
B. Saleh, P. Antoine Blum / Engineering Geology 79 (2005) 33–42 41
References
Albarede F., 1993. Residence time analysis of geochemical
fluctuations in volcanic series. Geochim. Cosmochim. Acta
57, 615–621.
Beauducel, F., 1998. Structure et comportement mecanique du
volcan Merapi (Java): une approche methodologique du champ
de deformation, PhD thesis, Paris 7 University, France.
Blanks G.L., 1976. Incorporation of temperature with gamma ray
logging techniques in analyzing fracture placement. Proc.
Stimulation of Low Permeability Reservoirs Symposium,
Golden, Colo., pp. 105–134.
Bonaccorso A., Davis P.M., 1999. Models of ground deformation
from vertical conduits with application to eruptions of Mount St.
Helens and Mount Etna. J. Geophys. Res. 104, 531–541.
Bonaccorso A., Mattia M., Puglisi G., Rossi M., 2003. GPS
monitoring on Stromboli volcano 1997 U 2003: results and
inversion of main data related to 2002 U 2003 eruption.
Geophys. Res. Abstr. 5, 03496.
Bureau H., Metrich N., Pineau F., Semet M.P., 1998a. Magma-
conduit Interaction at Piton de la Fournaise Volcano (Reunion
Island): a melt and fluid inclusion study. J. Volcanol. Geotherm.
Res. 84, 39–60.
Bureau H., Pineau F., Metrich N., Semet M., Javoy M., 1998b.
A melt and fluid inclusion study of the gas phase at Piton
de la Fournaise volcano (Reunion Island). Chem. Geol. 147,
1115–1130.
Cayol V., Cornet F.H., 1997. 3D mixed boundary elements for
elastostatic deformation fields analysis. Int. J. Rock Mech. Min.
Sci. Geomech. Abstr. 34, 275–287.
Cayol V., Cornet F.H., 1998a. Effects of topography on the
interpretation of the deformation field of prominent
volcanoes—application to Etna. Geophys. Res. Lett. 25,
1979–1982.
Cayol V., Cornet F.H., 1998b. Three-dimensional modeling of the
1983–1984 eruption at Piton de la Fournaise volcano, Reunion
Island. J. Geophys. Res. 103, 18025–18037.
Cornet F.H., Yin J.M., 1992. Induced seismicity and flow paths
associated with forced fluid flow. Trans. -Geotherm. Resour.
Counc. 16, 287–297.
Davis P.M., 1983. Surface deformation associated with a dipping
hydrofracture. J. Geophys. Res. 88 (B7), 5826–5834.
Davis P.M., 1986. Surface deformation due to inflation of an
arbitrarily oriented triaxial ellipsoidal cavity in an elastic half-
space, with reference to Kilauea volcano, Hawaii. J. Geophys.
Res. 91, 7429–7438.
D’Oreye N., 1998. Qualification test of a dual-axis bubble type
resistive tiltmeter (AGI-700 series): earth tides recorded and
analyzed in the underground laboratory of Walferdange. Marees
Terr. Bull. Inf. 129, 9953–9961.
Dudley J.W., 1993. Quantitative fracture identification with the
borehole televiewer. Society of Professional Well Log Analysts
Annual Logging Symposium, 34th Calgary, Alberta, Canada,
Transactions. , pp. CC1–CC4.
Dvorac J.J., Dzurisin D., 1997. Volcano geodesy: the search for
magma reservoirs and the formation of eruptive vents. Rev.
Geophys. 35, 343–384.
Evans K.F., 1983. On the development of shallow hydraulic
fractures as viewed through the surface deformation field: Part
2. Case histories. J. Pet. Technol., 411–420.
Evans K.F., Holzhausen G.R., Wood M.D., 1982. The geometry of a
large-scale nitrogen gaz hydraulic fracture formed in Devonian
shales: an example of fracture mapping using tiltmeters. Soc.
Pet. Eng. J., 755–763.
Fujita E., Ukawa M., Yamamoto E., Okada Y., 2002. Scenarios of
dike intrusions at the beginning of the Miyakejima volcano
activities. Bull. Earthq. Res. Inst. 77, 67–75.
Goulty N.R., 1976. Strainmeters and tiltmeters in geophysics.
Tectonophysics 34, 245–256.
Jousset Ph., Mori H., Okada H., 2000. Possible magma intrusion
revealed by temporal gravity, ground deformation and ground
temperature observations at Mount Komagatake (Hokkaido)
during the 1996–1998 crisis. Geophys. J. Int. 143, 557–574.
Lau J.S.O., Auger L.F., 1987. Subsurface fracture surveys using a
borehole television camera and acoustic televiewer. Can. Geo-
tech. J. 24, 499–508.
Lenat J.F., Bachelery P., 1990. Structure and dynamics of the central
zone of Piton de la Fournaise volcano. Le volcanisme de la
Reunion-Monographie. CRV, Clermont-Ferrand, pp. 257–296.
Lenat J.F., Bachelery P., Bonneville P., Hirn A., 1989. The beginning
of the 1985–1987 eruptive cycle at Piton de la Fournaise (LA
Reunion); new insights in the magmatic and volcano-tectonic
systems. J. Volcanol. Geotherm. Res. 36, 209–232.
Lili, 1997. Etude experimental du comportement hydromecanique
d’une fracture, PhD thesis, Paris 7 University. France.
Matsushima T., Takagi A., 2000. GPS and EDMmonitoring of Unzen
volcano ground deformation. Planets Space 52, 1015–1018.
McTigue D.F., 1987. Elastic stress and deformation near a finite
spherical magma body: resolution of the point source paradox.
J. Geophys. Res. 92 (12), 931–940.
McTigue D.F., Segall P., 1988. Displacements and tilts from dip-slip
faults and magma chambers beneath irregular surface top-
ography. Geophys. Res. Lett. 15, 601–604.
Miura S., Ueki S., Sato T., Tachibana K., Hamaguchi H., 2000.
Crustal deformation associated with the 1998 seismo-volcanic
crisis of Iwate volcano, Northeastern Japan, as observed by a
dense GPS network. Earth Planets Space 52, 1003–1008.
Mogi K., 1958. Relations between the eruptions of various
volcanoes and the deformation of the ground surfaces around
them. Bull. Earthq. Res. Inst. Univ. Tokyo 36, 99–134.
Nishi K., Ono H., Mori H., 1999. Global positioning system
measurements of ground deformation caused by magma
intrusion and lava discharge: the 1990–1995 eruption at
Unzendake volcano, Kyushu, Japan. J. Volcanol. Geotherm.
Res. 89, 23–34.
Nolte K.G., Smith M.B., 1981. Interpretation of fracturing
Pressures. J. Pet. Technol., 1767–1773.
Okada Y., 1985. Surface deformation due to a shear and tensile
faults in a half-space. Bull. Seismol. Soc. Am. 75, 1135–1154.
Okada Y., 1992. Internal deformation due to shear and tensile faults
in a half-space. Bull. Seismol. Soc. Am. 82, 1018–1040.
Pollard D.D., Holzhausen G., 1979. On the mechanical interaction
between a fluid-filled fracture and the earth’s surface. Tectono-
physics 53, 27–57.
B. Saleh, P. Antoine Blum / Engineering Geology 79 (2005) 33–4242
Rani S., Singh S.J., 1992. Static deformation of a uniform
half-space due to a long dip-slip fault. Geophys. J. Int. 109,
469–476.
Saleh B., Blum P.A., 1990. Study of temperature effect on behavior
of structures. J. Surv. Eng., ASCE 116 (1), 1–12.
Saleh B., Blum P.A., Delorme H., 1991. New silica compact
tiltmeter for deformations measurement. J. Surv. Eng., ASCE
117 (1), 27–35.
Sapin M., Hirn A., Lepine J.C., Nercessian A., 1996. Stress, Failure
and fluid flow deduced from earthquakes accompanying
eruptions at Piton de la Fournaise volcano. J. Volcanol.
Geotherm. Res. 70, 145–167.
Savage J.C., 1980. Dislocation in seismology. In: Nabarro, F.R.N.
(Ed.), Dislocation in Solids, vol. 3. North Holland Publishing
Co., Amsterdam, The Netherlands, pp. 251–339.
Sun R.J., 1969. Theoretical size of hydraulically induced horizontal
fracture and corresponding surface uplift in an idealized
medium. J. Geophys. Res. 74 (25), 5995–6009.
Ukawa M., Fujita E., Yamamoto E., Okada Y., Kikuchi M., 2000.
The 2000 Miyakejima eruption: crustal deformation and earth-
quakes observed by the NIED Miyakejima observation network.
Earth Planets Space 52, xix–xxvi.
Wyatt F., Berger J., 1980. Investigation of tilt measurements
using shallow borehole tiltmeters. J. Geophys. Res. 85 (B8),
4351–4362.
Yamashina K., Shimizu H., 1999. Crustal deformation in the mid-
May 1991 crisis preceding the extrusion of a dacite lava dome at
Unzen volcano, Japan. J. Volcanol. Geotherm. Res. 89, 43–55.
Zeller S.O., Pollard D.D., 1992. Boundary conditions for rock
fracture analysis using boundary element method. J. Geophys.
Res. 97, 1991–1997.