
Click on the poster to reach text, photos and figures. Return to AGU98 Abstract 
From deformation field analysis, we solve the boundary conditions common to the solid mechanics and the magma flux problems: internal structures geometry (“plumbing system”), pressure, stress and volume variations. The study also allows a better appraisal of monitoring measurements, thus helps hazard mitigation.
Objectives We focus our study on Mt. Merapi, Java, Indonesia, a Decade Volcano with a quasi continuous activity: dome growth, explosions and pyroclastic flows. Deformation field measurement come from GPS network and multicomponent continuous stations (tiltmeters and extensometers). Data are always validated by compensation to determine uncertainties. For modeling, we use threedimensional elastostatic boundary elements [Cayol & Cornet, 1997] including topography, fractures and complex geometry sources. Inversion processes are used to estimate parameter evolution and model probability from observations.
Methodology
Some conclusions
 Combination of highprecision tilt, displacements and topography constrains the modeling
 Evidence for a deep magma chamber at Merapi
 Evidence for fracture existence and their implications on the summit deformation field
 Compatibility of displacement observations and multiphase seismic events: summit deformation field is controlled by magma flux
 Apparent elastic behaviour, but Young’s modulus less than 1 GPa (possibly linear viscoelastic reality)
 Mass balance must include rock avalanches
 Identify potential rock slope problems
Cayol, V., and F.H. Cornet, 3D mixed boundary elements for elastostatic deformation field analysis, Int. J. Rock Mech. Min. Sci., 34, 275–287, 1997.
References
See also Beauducel [1998], Beauducel and Cornet [1999], Beauducel et al. [1999].
Photos. Merapi presents an activity of quasi continuous extrusion of lava which forms a dome in a horseshoe shaped crater. The dome is continuously and partially destroyed by avalanches and pyroclastic flows. 
1. View of Merapi from the North that reveals the strong asymetry of the edifice, and the high slopes of the volcano, reaching 57° near the summit. 
2. The January 30 1992 lava dome (Cliché J. Tondeur). 
3. November 22, 1994 pyroclastic flow that killed 69 people (Cliché M. Mongin). 
Figure 1. Location and geodynamical context of Mt. Merapi (2964 m). Merapi is a young stratovolcano located in Central Java, Indonesia, in a frontal subduction zone. Population of Yogyakarta (25 km from the summit) and arround is about 3 millions people, up to 500,000 are living directly on the flank of the volcano, above 500 m of elevation. Merapi is one of the « Decade Volcano » declared by the United Nations IDNDR program. 
Figure 2. Geological setting and deformation network at Merapi. In red, benchmarks and stations installed for this study (GPS, tilts and extensometers). In blue, other collaborations with VSI (USA, Germany, Japan). 
Figure 3. The Deles tilt station is located on the SouthEst flank of Merapi (3 km from summit), on a compact and massive rock identified as a 5,000 years old pyroxene andesitic lava flow. The thickness reaches 200 m at some places and a few meters of young pyroclastic deposits cap it, constituting a thermal isolator, as compared with the massive rock below. (a) Scheme of the horizontal pendulum Compact Blum made from welded silica. (b) Sensor location (horizontal view) : 5 tiltmeters, 1 thermometer and 1 rainmeter. (c) Vertical section of site 3 tilt installation. 
Sensor  Unit  Range  Resolution  2Minute Noise  1Day Noise 
Tilt tan. CH379 (site 1)  µrad  155  1.15 10^{–5}  0.0121  0.4106 
Tilt rad. CH380 (site 1)  µrad  195  5.40 10^{–5}  0.0099  0.3888 
Tilt rad. CH376 (site 2)  µrad  248  2.14 10^{–5}  0.0136  0.3163 
Tilt tan. CH427 (site 3)  µrad  218  2.00 10^{–5}  0.0117  0.7835 
Tilt rad. CH429 (site 3)  µrad  578  1.00 10^{–5}  0.0302  0.2693 
Temp. LIP (site 1)  °C  100  1.75 10^{–4}  0.0050  0.0837 
Rainmeter (station)  mm  100 000  1  —  — 
Resistor bridge (site 3)  mV  10 000  1.09 ^{10–3}  0.0968  0.4471 
Figure 4. GPS baselines measured in March 1997, with 2 singlefrequency receivers SERCEL NR101. The network was measured in 1993, 1994, 1995, 1996 and 1997. 
Figure 5. Meteorological data measured on the field during 1997 GPS campain. They have been reduced with respect to 3000m elevation using standard vertical profiles of temperature, pressure and relative humidity, and are presented on a single day scale in local time. These data allow to determine a local meteo model of the troposphere for each time period of the GPS measurements, and are introduced in the double difference processing to compute baselines vectors. Introduction of meteo data is essential when the network covers large height differences as is the case for Merapi (1600 m). 
Figure 6. Cumulated displacements at the summit obtained by compensation of GPS baselines from 1993 to 1997. An important movement occured (about 40 cm) on the Northern part of the crater rim. Four « independent » zones separeted by fractures with different behavior are observed. (a) Horizontal view. (b) Vertical view from azimuth N145°E. 
Figure 7. (a) Relative tilt signals at Deles between the 2 GPS campains (dashed zones): 2 radial and 2 tangential components. Inset plot shows the horizontal projection of the average motion of the tip of the normal to ground surface. (b) Dome volume estimation (solid line and triangles) and number of pyroclastic flows (bars) within the period. Dotted vertical line corresponds to the time of the dome explosion (January 17th, 1997). 
Figure 8. Example of tilt signal correction from temperature effects by a nonstationary linear method and comparison with theoretical earth tide variations computed for this location. This result validates the sensor coupling with the ground and the signal processing method used, which did not affect the complex tide signal included. 
Figure 9. MonteCarlo nearneighbor sampling inversion method (least squares best solution for 3D displacements and tilt vectors): projection of the model space in a 2parameter plan (volume variation versus source depth). Dot size represents probability of each model (364 samples). Volume variation is well constrained but not the source shape and size. 
Figure 10. (a) 3D mesh of topography around Deles tilt station. (b) Relative tilt computed along the crosssections for the final elliposoidal source solution. The tilt varies within ±1 µrad at ±20 m around the station. 
Figure 11. 3D deformation field modeling at Merapi on the 19961997 period: GPS displacements (red arrows), computed tilt field at the surface of the volcano (contour lines) and location of the tilt station (DEL). Deep magma chamber is deduced from both displacements and tilt observations. Because in elasticity, dP ÷ dV ÷ displacements, we avoid the difficult task of Young’s modulus estimation, and resolve only the volume variation of the source. Superficial magma chamber has been proposed from seismic observations but is not compatible with our deformation data. The computed volume variation is 3 times larger than the observed volume at the summit (3.2 ± 0.2 10^{6} m^{3}). 
Figure 12. Types of source considered for the summit modeling of displacement field: dome weight effect on the crater floor, magma pressure in the duct and wall shear stress due to flux variation of viscous fluid. Computation of the dome weight effect for 19931994 period showed that this effect is negligeable on displacements. 
Figure 13. 3D modeling of the summit deformations with 3 free fractures in the medium (horizontal view): displacement field (light arrows) and blowup displacements on GPS points (heavy arrows). The displacement unit corresponds to 1 mm with a 1 MPa source and a Young’s modulus of 30 GPa. (a) Results with wall shear stress in the duct. (b) Results with pressure source. A linear combination of the two sources effects allows to reproduce correctly the observed displacements pattern from 1993 to 1997 for all the points except for the NorthWest one (NTR), which probably exhibits an inelastic behavior. 
Figure 14. We processed an inversion from the linear combination of the two forward problem solutions (Fig. 13), constrained by the 19931997 GPS 3D displacements. The computed wall shear stress variations are compatible with recorded « multiphase » seismic events variations. Because the two observations are independent, this gives further support that these seismic events are related with shear stress release at the duct wall. 