Modeling of local geoid using adaptive scheme :: A case study around Merapi and Merbabu volcanoes, Central Jawa, Indonesia

SUNANTYO, Tarsisius Aris, Promotor Prof. Adhi Susanto, M.Sc., Ph.D

2008 | Disertasi |

A fundamental problem in geodesy is to define the shape and size of the earth and its gravity field while taking into account its temporal variation. Representation of the shape of the earth can be expressed by several methods; one of them is the geoid surface. The geoid is an equipotential surface of the earth at mean sea level, and can be defined locally, regionally or globally. The local geoid depends on the location and is different for different location. Indonesia is an archipelago with Jawa as one of the major island, where Merapi and Merbabu volcanoes are located. These volcanoes have been of major interest for many Indonesian as well as many International geophysicists and volcanologists. A lot of research projects have been carried out at these volcanoes, one of these is the project Mechanical Evaluation, Risk Assessment, and Prediction Improvement (MERAPI) which was implemented in the years 1995 up to 2004. This project was conducted by the Volcanological Survey of Indonesia (VSI) in collaboration with a number of Indonesian and German universities, in an effort to better understand the inner and underlying structures of Merapi and Merbabu volcanoes. In this area due to the lack of topographic data (topographic maps, digital elevation model and accurate geodetic coordinates system), the use of Global Positioning System (GPS) can help to acquire the accurate geoid. However GPS determines only the ellipsoid heights (h) on the reference ellipsoid surface, while the computation of orthometric on the basis of GPS-observations requires an accurate local geoid surface. The well known Remove-Compute-Restore (RCR) technique with Stoke’s integration was used in conjunction with the Digital Elevation Model (DEM), the geopotential global models, precise terrestrial gravity, orthometric height, and geodetic positioning to determine the local geoid model. Warping with Least Mean Square (LMS) adaptive scheme is highlighted in this dissertation. The LMS adaptive scheme was first tested with 48 data points for its performance with respect to the convergence speed and the residuals Mean Square Error (MSE) level. The results were very encouraging so that the work was continued using different polynomial orders as well as the final MSE values. The progress of each adaptive modeling action was observed graphically in 1-D version along the positions of the 48 data stations, using the standard curve fitting procedure. First of all, warping with 3-D Helmert transformation was also implemented then the basic LMS algorithm was used to execute the associated iterative adaptation procedures. The results show that the optimum adaptation step size (μ) was 0.05, full adaptation was reached in about 33 iterations, and the residual MSE was about 0.001 or -30 dB. The dominant polynomial terms were in the first six lowest order or dominantly quadratic in nature. However, when it were let the iteration go further, whilst constantly fluctuating in the MSE values, the higher order polynomial terms were found to be more significant. These can be observed as the increasing details or shorter wavelength of the resulting local geoid models. Comparisons with local geoid models obtained by different methods and different data showed that the resolution of the local geoid model using 3-D Helmert transformation and LMS adaptive scheme had improved significantly. The local geoid before warping is somewhat jaggy, but after warping, the local geoid surface turned out to be very smooth and computational standard deviation was about 2 dm. The significance of the adaptive modeling scheme is the advantage that it is flexible to the demand of high resolution with merely the cost of longer computation time.

Kata Kunci : Geoid lokal, Merapi, Metode RCR, VSI, DEM, Integrasi Stokes, Warping, LMS, Transformasi Helmert 3-D