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APPLICATION OF THE HARTLEY TRANSFORM IN THE COMPUTATION OF THE GEOID IN CHINA

NING Jinsheng, Jiancheng Li, CHAO Dingbo

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Abstract

This paper presents a method for the computation of the Stokes formula using the Fast Hartley Transform CFHT) techniques. The algorithm is most suitable for the computation of real sequence transform, while the Fast Fourier Transform (FFT) techniques are more suitable for the computa ton of complex sequence transform. A method of spherical coordinate transformation is presented in this paper. By this method the errors, which are due to the approximate term in the convolution of Stokes formula, can be effectively eliminated. Some numerical tests are given. By a comparison with both FFT techniques and numerical integration method, the results show that the resulting values of geoidal undulations by FHT techniques are almost the same as by FFT techniques, and the computational speed of FHT techniques is about two times faster than that of FFT techniques.

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What this paper is about

This paper presents a method for the computation of the Stokes formula using the Fast Hartley Transform CFHT) techniques. The algorithm is most suitable for the computation of real sequence transform, while the Fast Fourier Transform (FFT) techniques are more suitable for the computa ton of complex sequence transform. A method of spherical coordinate transformation is presented in this paper. By this method the errors, which are due to the approximate term in the convolution of Stokes formula, can be effectively eliminated. Some numerical tests are given. By a comparison with both FFT techniques and numerical integration method, the results show that the resulting values of geoidal undulations by FHT techniques are almost the same as by FFT techniques, and the computational speed of FHT techniques is about two times faster than that of FFT techniques.

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Available abstract

This paper presents a method for the computation of the Stokes formula using the Fast Hartley Transform CFHT) techniques. The algorithm is most suitable for the computation of real sequence transform, while the Fast Fourier Transform (FFT) techniques are more suitable for the computa ton of complex sequence transform. A method of spherical coordinate transformation is presented in this paper. By this method the errors, which are due to the approximate term in the convolution of Stokes formula, can be effectively eliminated. Some numerical tests are given. By a comparison with both FFT techniques and numerical integration method, the results show that the resulting values of geoidal undulations by FHT techniques are almost the same as by FFT techniques, and the computational speed of FHT techniques is about two times faster than that of FFT techniques.

Key concepts: Fast Fourier transform, Hartley transform, Discrete Hartley transform, Computation, Prime-factor FFT algorithm, Split-radix FFT algorithm, Algorithm, Convolution (computer science)

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