ارايه روشي براي محاسبه صفر ارتفاعي در شبكه ارتفاعي بر مبناي مدل‌سازي محلي ميدان گراني با استفاده از تابع‌هاي پايه شعاعي، بررسي موردي: تعيين صفر ارتفاعي شبكه ترازيابي درجه يك ايران

An approach to height datum unification based on local gravity field modeling using radial base function, case study: height datum unification of leveling network of class 1 in Iran

مبناي سامانه‌‌‌هاي ارتفاعي محلي و منطقه‌اي، سطح متوسط دريا در كشندنماهاي مرجع است. با توجه به انطباق نداشتن سطح متوسط دريا و ژيوييد، و همچنين لزوم يكسان‌سازي شبكه‌هاي ارتفاعي، در اين مقاله روشي براي محاسبه صفر ارتفاعي، براساس مدل‌سازي ميدان گراني با استفاده از مشاهدات گرانش و ارتفاع‌سنجي ماهواره‌اي عرضه شده است. در اين روش براي مدل‌سازي محلي ميدان گراني زمين ازتابع‌هاي پايه شعاعي استفاده و ارتفاع شبه‌ژيوييد در پيمانه كشندي (تايدگيج) مبنا محاسبه مي‌شود. اين پيمانه كشندي در بندر عباس واقع شده است كه در واقع با معلوم بودن ارتفاع شبه‌ژيوييد در آن، صفر ارتفاعي شبكه ترازيابي ايران قابل محاسبه خواهد بود. از جمله مزيت‌هاي روش پيشنهادي مي‌توان به استفاده از داده‌هاي ارتفاع‌سنجي ماهواره‌اي، حذف اثر جهاني ميدان گراني با استفاده از مدل ژيوپتانسيلEGM2008 تا درجه و مرتبه 360 و استفاده از تابع‌هاي پايه شعاعي براي مدل‌سازي محلي نام برد. روش پيشنهادي براي تعيين موقعيت صفر ارتفاعي شبكه ترازيابي درجه 1 ايران نسبت به ژيوييد به كار رفته است، براساس نتايج حاصل، صفر ارتفاعي شبكه ترازيابي درجه يك ايران 216/0 متر زير ژيوييد قرار دارد.

One of the most important problems in geodesy is the unification of height datum. Generally in geodesy; there are two types of height systems, the geometrical height based on ellipsoid and the physical height based on gravity-defined surface (Zhang et al, 2009). Local height datum is determined according to Mean Sea Level (MSL). In regarding to mismatch of mean sea level and geoid, on the one hand, and height datum unification requirement on the other hand, this paper defines an approach to height datum determination of Iran based on local gravity field modeling. Although there are so many algorithms to local gravity field modeling, the radial base functions (RBF) is one of the well known methods to precise local gravity field modeling using variety of data sets. Two groups of data sets, gravity acceleration observation and satellite altimetry data, are used in this paper, to determine the quasi geoid height at reference tide gauge; then the height reference of leveling network can be calculated. According to Runge-Kutla algorithm, potential anomaly on the earth can be defined as following: Where the expansion coefficients are (scale coefficients) and Bjerhammar sphere is a sphere with radius R, which is entirely inside the topographic masses of the earth, ?_i are the set of radial basis functions with following representation: Where are points inside and outside of the Bjerhammar respectively, is the Legendre polynomial function of degree and are the Legendre coefficients, the point y is called the centre of the RBF. As we can see Radial Base Functions (RBF) have some unknown parameters that should be determined precisely: the location of RBF center, shape (depth parameter) and scale coefficient. If these parameters are selected correctly we could have good representation of potential anomaly field. Examples of linear functionals used in local gravity field modeling are gravity anomalies and gravity disturbances . After linearization and spherical approximation, these functionals are related to the potential anomaly as We used Poisson-wavelet as RBF kernel, which is defined as follows: Where n is the order of Poisson wavelet kernel, | | is the operator norm. Significant points in this paper are: precise positioning of the reference bench mark point by GPS system, calculation of geoid height of reference bench mark using both geodetic and orthometric heights by leveling method, quasi geoid height determination using potential anomaly value at bench mark and convert it to geoid height and finally height datum unification using comparison of the leveling height and the height from local gravity field modeling.