Optimization algorithm for analytical downward continuation based on improved radial derivative

doi:10.11947/j.AGCS.2023.20220625

Abstract

Abstract: Analytical continuation algorithm is an important continuation method for the potential field, which has important application value in the construction of the (quasi-) geoid or vertical deflection models based on the second or third geodetic boundary-value theory. Compared with Poisson continuation, the analytical continuation algorithm is simpler and faster. The calculation of the radial derivative is crucial for the analytical continuation algorithm. However, the traditional method for the radial derivative of the analytical continuation introduces a certain approximation error. An improved method for radial derivative is proposed in this paper. The optimization of the analytical continuation algorithm is then realized. In this research, it is proved by spherical harmonic method that the improved radial derivative is closer to the theoretically true radial derivative than the traditional one. The conclusion is displayed by the longitude and latitude profiles. The test of a large mountainous area conducted in central China shows that the accuracy of the improved radial derivative is 32.45% higher than that of the traditional radial derivative. When the errors contained in the gravity data are 1, 2, 3 and 4 mGal, the downward continuation accuracies of analytical continuation based on the improved radial derivative is 29.04%, 19.48%, 10.12% and 2.65% higher than that of the traditional analytical continuation, respectively. Theoretical analysis and test proves the effectiveness of the analytical downward continuation based on the improved radial derivative, which is useful in the geodetic boundary-value problem.

Key words: analytical continuation algorithm, traditional radial derivative, improved radial derivative, downward continuation, spherical harmonic method

CLC Number:

P223

MA Jian, ZHAI Zhenhe, FENG Changqiang, GUAN Bin, WANG Yunpeng, LI Duan. Optimization algorithm for analytical downward continuation based on improved radial derivative[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(10): 1650-1660.

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