MODELS AT MERAPI VOLCANO DERIVED FROM GPS AND GRAVITY DATA A SUMMARY

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1 Tiede et al. 117 MODELS AT MERAPI VOLCANO DERIVED FROM GPS AND GRAVITY DATA A SUMMARY C. Tiede 1, K.F. Tiampo 2, J. Fernández 3 1 Max-Planck Institut für Astronomie, Heidelberg, Germany 2 Department of Earth Sciences, University of Western Ontario, London, ON, Canada. 3 Instituto de Astronomía y Geodesia (CSIC-UCM), Facultad de Ciencias Matemáticas,Ciudad Universitaria, Madrid, Spain Abstract Merapi, located at Central Java, Indonesia is one of the most active volcanoes in the entire world. Within the joint Indonesian-German research project several models have been generated to understand the volcano, its structure and behavior. We describe here a model based on the joint interpretation of the GPS and gravimetry measurements as well as a sensitivity analysis approach for network configuration purposes. 1. Introduction Merapi volcano (φ = ; λ = ; h = 2969 m (ellipsoidal, based on WGS84, measured in 2000)) located on Central Java, Indonesia, is one of the approximately 129 active volcanoes in the Indonesian islands. It is one of the most active and hazardous volcanoes worldwide as a result of the approximately 2 million people living in the nearby surroundings of this high-risk volcano who are permanently threatened by its activity. The high rate of volcanic and seismic activity along the entire Sunda arc between Sumatra and Flores is caused by the subduction zone which forms the 6000 to 7000 m deep Java trench approximately 250 km south of the coastline of Indonesia. An interdisciplinary research cooperation called MERAPI (Mechanism Evaluation, Risk Assessment, Prediction Improvement) between the Geoforschungszentrum Potsdam and the Volcanological Survey of Indonesia as coordinating parties studied the region from 1997 through An overview of all 13 projects of MERAPI is given by Zschau et al. (1998) whereby the project parts can be distinguished via their different targets into History: Geological work on magma evolution and eruption history Monitoring: Continuous measurements of seismology, gas analysis and deformation for monitoring purposes Structure analysis: Geophysical measurements of DC geoelectrics, gravity, Long Offset Transient Electromagnetics (LOTEM), magnetotellurics and seismics for exploration of the structure of the volcano. The group under the lead of Prof. C. Gerstenecker (Darmstadt University of Technology) was responsible for the project Untersuchungen säkularer Schwereänderungen am Merapi, Java: Ursachen und Wirkungen, Ge 381/ in the time period between 1997 and Results of the measurements, carried out within this subproject are shown in this article. For a detailed

2 118 Tiede et al. overview about the measurements, the circumstances and the details behind the observations, see Läufer et al. (2007), this issue. 2. Gravity and deformation network In 1997 a gravity and deformation network at Merapi volcano consisting of 23 stations was established, see Figure 1, to measure deformation and gravity changes related to the volcanic activity. Gravity changes dgi and three-dimensional deformations in east, north and height uxi, uyi, uzi with i=1, 2,..., 23, have been observed between 1997 and 2002 during 6 field campaigns, using 4 relative spring gravimeters (LaCoste & Romberg) and up to 11 Trimble GPS receivers. Figure 1: Gravity and three-dimensional deformation network organized in a loop configuration around Merapi volcano, Java, Indonesia. The numbers of the measured points correspond to the points given in Figure 2 Prior to the modelling of the gravity and deformation measurements a data preprocessing and analysis was carried out which required a detailed digital elevation model. This had been generated by the fusion of SAR-data and photogrammetric images, Läufer (2003) and validated by comparison with further satellite based digital elevation models Gerstenecker et al. (2005). Figure 2 shows the actual changes between observations in 2000 and Observed dg, ux, uy and uz are given as a straight, bold line including 1-σ error bars for each of the 20 observation points for which data was available in both epochs (2000 and 2002).

3 Tiede et al. 119 Figure 2: Gravity changes (dg) and three-dimensional deformation (ux, uy, uz) measured between 2000 and 2002 at Merapi volcano. The measured data are shown as thick solid line including 1-σ error bars. Points are sorted with respect to the distance to the top of the volcano (distance given in the right legend). The dashed line shows the effects of the combined fault, the thin solid line shows the superposed effects of the combined fault and the elasticgravitational model, Tiede et al. (2007) Only very small gravity changes and deformations at stations of distances larger than 2 km from the crater rim were measured (Figure 2, stations point number 8-20), and the near field stations show significant gravity changes and three-dimensional deformations. These local effects at the crater are modelled and explained by the superposition of the effects produced by a) a local, extensional, reverse fault in the summit region, b) a spherical magma intrusion, modeled as a point source in an elastic-gravitational medium. To model deformation and gravity changes produced by both of the sources, we consider the theoretical model developed by Manshina et al. (1971) for the source (a), and by Rundle (1982), Fernández et al. (1997; 2006) for source (b). The unknown model parameters have been determined by using global optimization techniques. For details see Tiede (2005a) and Tiede et al. (2007). The results of the model computation are given in Figure 2. The dotted line shows the effect of the reverse fault zone, the straight line shows the superposition of effects produced by both sources. Here it can be seen that the model explains those observations which are near the summit (Figure 2, point number 1-5) as well as those located at larger distances. A visualization of the superimposed models is shown in Figure 3. Both plots show the structural map after Beauducel et al. (2000) in which fracture zones are displayed as black straight lines. Again, the derived fault model fits very well to the existing and displayed faults from Beauducel et al. (2000).

4 120 Tiede et al. Figure 3: Plan view and three-dimensional view of Merapi. The plan view shows the superimposed model given by an elastic-gravitational source (black sphere) in the east as well as a normal fault (black area). The structural map of Beauducel et al. (2000) including fracture zones as solid lines is merged on the digital elevation model derived by Läufer (2003). In the three-dimensional view the dip angle of the fault is shown, Tiede et al. (2007).

5 Tiede et al. 121 The fault is explained by a normal fault with a horizontal opening of the fracture to the north. The elastic-gravitational source is located near the fumarole fields Woro and Gendol. Due to the very small mass of the source it is unlikely that this model represents a magmatic chamber, but is instead related to the fumarole fields. It is only necessary to consider both types of source, a fault and magma intrusion, in the modeling for the area closest to the crater, therefore the question can be raised which of the observation points are of interest for deriving this specific physical model. Or equivalent to that: If one can assume an a-priori physical model (e.g. the elastic-gravitational source model) for the region of interest, where should the sensors be placed in order to best determine the unknown model parameters and which sensor placements which can be neglected for the correct determination of the physical model of interest. In order to follow up this idea a global sensitivity analysis (Tiede et al., 2005a, 2005b) was applied to a synthetic generated sensor grid in the area of interest. The analysis has been computed for the different measurements (dg, ux, uy, uz) and for the unknown parameters given by the elastic-gravitational model on each of the grid points. 3. Sensitivity analysis Before the determination of the elastic-gravitational source parameters within the optimization approach a global sensitivity analysis has been applied, Tiede et al. (2005b) with the purpose of computing how and to what extent each unknown model parameter contributes to the variance in the observed values (dg, ux, uy, uz). Sensitivity analysis are used for answering questions like how much does each input parameter contribute to the variance in the output values are there any interactions between the input parameters is there a region of input parameter range for which the model variation is the largest are there insignificant model input parameters Sensitivity analysis can be divided into local and global approaches with respect to how they treat the input factors, Saltelli et al. (2004). Local sensitivity analyses are based on computing partial derivatives of the output function. It is practicable if the variation around the midpoint of the input factors is small. Generally the relation between input and output variables is assumed to be linear. Global sensitivity analyses explain the uncertainty in the output variables by the uncertainty of each input factor. The input factors are given with a probability density distribution. They are varied simultaneously and the sensitivity is measured over the whole range of each input factor. One example of a global sensitivity analysis method is given by the variance-based techniques which are based on Monte Carlo sampling, Saltelli et al. (2000). The basic idea of such types of sensitivity analyses is given by the expression of the sensitivity of the variance sigma. It is determined how much the variance of the input parameters contributes to the variance of each output value. When the model is non-linear and various input variables are affected by uncertainties of different orders of magnitude, a global sensitivity analysis should be used. Therefore, in this computation the Sobol variance-based global sensitivity analysis is used, Sobol (1993).

6 122 Tiede et al. Sensitivity analysis computation For the sensitivity analysis computation a synthetic grid consisting of 100 points was generated covering the second and third loop of the gravity and deformation network, see Figure 4. (East m, North m). Figure 4 (following page): Location of the synthetic point grid which forms the basis for carrying out the sensitivity analysis. The probability density functions are all assumed to be unique. The unknown input parameters for the elastic-gravitational model are given by the threedimensional position of the source (ξ, ψ, ζ ), its mass (m) and its energy (e) as the product of the cubic radial component and a pressure term. A Monte Carlo sampling for these unknown input parameters with samples is investigated within the boundaries given in Table 1. For each of these samples the forward model is applied (given by the elastic-gravitational source model) and the four different output values dg, ux, uy and uz are computed. Afterwards the variation of these output values is expressed by the variation of the input parameters of the elastic-gravitational model. The resulting sensitivity indices for each of the four types of measurements are summed up and normalized. Figure 5 shows the sensitivity map whereby the sensitivities are given for all unknown parameters in common and per each point (here one point covers the measurements of dg, ux, uy, uz).

7 Tiede et al. 123 Table 1. Upper and lower limits on the unknown parameters of the elastic-gravitational model which are used for the Monte Carlo sampling parameter lower limit upper limit ξ [m] ψ [m] ζ [m] m [1012 kg] 0 2 e [1014N m] Figure 5: Sensitivity map for the synthetic grid shown in Figure 4. The color coding is done regarding the sensitivity at each point for dg, ux, uy, uz regarding the unknown parameters ξ, ψ, ζ, m, e of the elastic-gravitational source model Color coding is done with respect to the sensitivity. A bright color indicates highly sensitive regions around Merapi for the measurement of dg, ux, uy and uz and the estimation of the parameters of the elastic-gravitational source model. By comparing these results with the network which was installed at Merapi (the grey line in Figure 5 indicates the second loop around Merapi; the small square shows the region of the third loop around the crater) it can be seen that the theoretical sensitivity suggests that only the points very near to the summit are of interest for carrying out the physical model. These are the points 1-10 which are within a radius of 3000 m around the crater where a larger sensitivity occurs.

8 124 Tiede et al. 4. Summary Gravity and three-dimensional deformation data were used in order to model the summit region of Merapi volcano. Our measurements cannot be explained by a shallow or deep magma chamber as anticipated in previous modelling approaches by Beauducel and Cornet (1999), Ratdomopurbo and Poupinet (2000), Camus et al. (2000) or Setiawan (2002). Instead of the magma source model, we could explain our measurements by a normal fault with an opening of the fracture to the north in the crater region of Merapi which coincides well with the results of Beauducel et al. (2000). The attempts to model an elastic-gravitational source result in a very shallow chamber with very small mass located near the fumarole fields Gendol and Woro. A magma source cannot be the source but it may reflect changes in the fumaroles, Tiede et al. (2007). Furthermore, we showed an approach using sensitivity analysis for sensor network configuration for those cases in which the physical model is known prior to the actual measurements. The results of the approach were compared with the actual model results generated by applying the elastic-gravitational source model to the gravity residuals and three-dimensional deformations. The comparison shows that before establishing the actual measurement locations, those points which are sensitive to variation in the physical model parameters can be selected. With the use of synthetic sensitivity maps it is possible to put the sensors in these regions where they are most sensitive to the changes in the unknown parameters of the expected physical model. Results show that just the inner part of the installed network at Merapi contributes to the determination of the physical model parameters. As the computed grid is very broad, the sensitivity map does not look smooth. In future attempts the sensitivities will be carried out for a denser grid. Acknowledgements The authors want to thank C. Gerstenecker for the very fruitful collaboration in recent years. Carola Tiede would like to thank C. Gerstenecker for his patient guidance, encouragement and advice that he provided throughout the time she was a PhD student at Darmstadt University of Technology - it has been a fantastic time. Kristy Tiampo is grateful for the opportunity to have collaborated with C. Gerstenecker in a very interesting and exciting part of the world, and for his excellent judgment in evaluating both scientific opportunities and young scientists. José Fernández has been happy to cooperate with C. Gerstenecker during the last years developing new and innovative scientific ideas and research and on the training of young scientists in geodesy and volcanism, thus having the opportunity to know great colleagues, good researchers and better friends. In addition we thank B. Lühr for reviewing the article. This research has been carried out in the frame of the projects MERAPI, Untersuchungen säkularer Schwereänderungen am Merapi, Java: Ursachen und Wirkungen, Ge 381/12 1-4; Spanish MEC CGL C02/BTE and an NSERC Discovery Grant. References Beauducel, F. and F. Cornet(1999): Collection and three-dimensional modeling of GPS and tilt data at Merapi volcano, Java, J. Geophys. Res. 104,

9 Tiede et al. 125 Beauducel, F., F. Cornet, E. Suhanto, Duquesnoy and T., M. Kasser (2000): Constraints on magma flux from displacements data at Merapi volcano, Java, Indonesia, J. Geophys. Res. 105, Fernández J., J. Rundle, R. Granell and T.-T. Yu (1997): Programs to compute deformation due to a magma intrusion in elastic-gravitational layered earth models, Computer and Geosciences, 23: Camus, G., A. Gourgaud, P.-C. Mossand-Berthommier and P.-M. Vincent (2000): Merapi (Central Java, Indonesia): An outline of the structural and magmatological evolution, with a special emphasis to the major pyroclastic events, J. Volcanol. and Geotherm. Res. 100, Fernández, J., M. Charco, J.B. Rundle and K.F. Tiampo (2006): A revision of the FORTRAN codes GRAVW to compute deformation produced by a point magma intrusion in elasticgravitational layered Earth models, Computers & Geosciences, 32/2, doi: /j.cageo Gerstenecker, C., G. Läufer, D. Steineck, C. Tiede and B. Wrobel (2005), Validation of digital elevation models around Merapi Volcano, Java, Indonesia, NHESS, 5, Läufer G. (2003): Erzeugung hybrider digitaler Hoehenmodelle aktiver Vulkane am Beispiel des Merapi, Indonesien, PhD thesis, Darmstadt University of Technology, ISBN Manshina, L., D. Smylie and D. Orphal (1971): The displacement fields of inclined faults, Bulletin of the Seismological Society of America, 61: Ratdomopurbo, A. and G. Poupinet (2000): An overview of the seismicity of Merapi volcano (Java Indonesia) , J. Volcanol. Geother. Res. 100, Rundle, J. B. (1982), Deformation, gravity, and potential changes due to volcanic loading of the crust, J. Geophys. Res., 87(B12), 10,729 10,744. Saltelli, A., K. Chan, E. Scott (Eds.) (2000): Sensitivity analysis, John Wiley and Sons, LTD, Chichester, New York, Weinheim, Brisbane, Singapore, Toronto Setiawan, A. (2002): Modeling of gravity changes on Merapi volcano observed between , PhD thesis, Darmstadt University of Technology, Darmstadt, Germany Sobol, I. (1993): Sensitivity analysis for non linear mathematical models, Math. Model. Comput. Exp., 1: Tiede, C., J. Fernández, C. Gerstenecker and K. Tiampo (2007): A hybrid model for the summit region of Merapi volcano, Java, Indonesia, derived from gravity changes and deformation measured between 2000 and 2002, Pure and Applied Geophysics, 164, Tiede (2005a): Integration of optimization algorithms with sensitivity analysis, with application to volcanic regions, Ph.D. Thesis, Online publication at Universitäts- und Landesbibliothek Darmstadt:

10 126 Tiede et al. Tiede C., K. Tiampo, J. Fernández and C. Gerstenecker (2005b): Deeper understanding of nonlinear geodetic data inversion using a quantitative sensitivity analysis, Nonlinear Processes in Geophysics, 12: Zschau, J., R. Sukhyar, M. Purbawinata, B. Lühr and M. Westerhaus (1998): Projekt MERAPI Interdisciplinary research at a high-risk volcano in Decade Volcanoes under Investigation, Dt. Geophys. Gesellschaft, 3: 3-8, edited by J. Zschau and M. Westerhaus Dt. Geophys. Gesellschaft