Monitoring of fracture propagation by quartz tiltmeters

$Page 1: Monitoring of fracture propagation by quartz tiltmeters$
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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.


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.


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

� �:


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.


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.


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.


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.


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.

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Monitoring of fracture propagation by quartz tiltmeters