# 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

Authors

1 Associate Professor, Department of Surveying and Geomatics Engineering, University College of Engineering, University of Tehran, Iran

2 Assistant Professor, Department of Surveying and Geomatics Engineering, University College of Engineering, University of Tehran, Iran

3 M.Sc. student of Geodesy, Department of Surveying and Geomatics Engineering, University College of Engineering, University of Tehran, Iran

Abstract

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,  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.

Keywords