78 Proceedings of CITEE, August 4, 2009 ISSN: 2085-6350 Conference on Information Technology and Electrical Engineering (CITEE) Adaptive Polynomial Approximation for Gravimetric Geoid: A case study using EGM96 and EIGEN-GL04C Geopotential Development Tarsisius Aris Sunantyo Geodetic Department, Faculty of Engineering, Gadjah Mada University. 55000, Indonesia sunantyo@yahoo.com Muhamad Iradat Achmad Electrical Department, Faculty of Engineering, Gadjah Mada University 55000, Indonesia iradat@ymail.com Abstract— In this paper, adaptive polynomial approximation method to model the gravimetric geoid is presented. The polynomial approximation model to arrange training of input is for adaptive system. Training data pairs (input and output) were compiled from latitude and longitude data sequences as input training, and an associated geopotential developments datum on each spatial position as output training. By preceded centering of latitude and longitude data, input training formed with following appropriate formula is the polynomial terms. Adaptation process used LMS (least mean square) algorithm in weight updating, and after training session, approximation of desired target was computed by reloading weights into the polynomial model. Model of assessment test used was to validate adaptive model by comparing residual distance of consecutive point from both geopotential developments data and respective adaptive model in geocentric coordinates system. Using geopotential developments data around of Merapi and Merbabu as a case study, the results show that the residual distance between geopotential developments data and respective adaptive model are about 0.0014417 m (in total absolute value with standard deviation is about 4.6906x10 -5 m) using EGM96 geoid and about 0.0014468 m (in total absolute value with standard deviation is about 4.702x10 -5 m) using EIGEN-GL04C geoid. Better result could be achieved by adding more training session with smaller gain factor. Keywords— Adaptive polynomial approxima- tion,gravimetric geoid, geopotential developments, and model assesment. I. INTRODUCTION One of the fundamental problems in geodesy is to define the shape and size of the earth and its gravity field taking into account its temporal variation. Representation of the shape of the earth can be carried out by several methods; one of them is by geoid. Geoid is an equipotential surface of the earth at mean sea level (Heiskanen and Moritz, 1967). The use of precise geoid related data, in particular its undulation, is widespread in all branches of geodesy and it is often analyzed in other Earth sciences for example in geophysics, oceanography, as well as in civil engineering (Zhicai and Yong-qi, 2002). Figure 1. Distribution of the Indonesian active volcanoes as the Ring of Fire (Red color is active volcano) (Sunantyo, 2008) Indonesia, as an archipelago, located partly on the Eurasian plate, which is subducted by the three major plates: the Indo-Australian plate in the south and in the west; the Pacific plate in the East and the Philippine Sea plate in the north. These subduction zones around Indonesia create a ring of volcanoes, which is called “the Ring of Fire” (see Figure 1). A total of 129 active volcanoes exist, and one of them is Merapi as a result of the subductions. Purbawinata et al.,(1997) state that the subduction zone is marked by a chain of active and dormant volcanoes which spreads along Sumatra, Java, Bali, Lombok, Sulawesi to the eastern part of Indonesian. North of Merapi volcano is Merbabu volcano which has not had activities more than 200 years. These two volcanoes are located in Yogyakarta city and Central Java (Purbawinata et al., (1997)). These two volcanoes are very often to be used as a research area too many scientists (i.e. geophysicist, geologist, geodesist etc) to have a comprehensive understanding about them. Merapi volcano has been labeled as one of 15 high risk volcanoes by the International Decade of Natural Disaster Reduction program (IDNDR) of UNESCO (Sunantyo, 2008). The integration a multidisciplinary approach (geodesy, geology, geophysics, seismology etc) concerning to understand the structure and volcanic activities of Merapi in more detail is very important and urgent (Zschau et al., 1998). In physical geodesy aspect, gravimetric geoid determination in these two volcanoes using geopotential developments is discussed in this research.