On the Optimization of Spherical Convolution Integral: Efficiency Analysis

We test the performance of an optimized algorithm that reduces the total run time (TRT) of the numerical evaluation of the spherical convolution integrals for geoid computation. For practical considerations, the performance of the algorithm is tested based on the Stokes's convolution which is used for the determination of regional geoid modeling from the terrestrial gravity measurements. The optimization algorithm is presented in Matlab Software to accelerate the computation's run time using vectorization techniques and relational operators. The presented algorithm is validated over different gravity grid resolutions and spherical capsize values σ
₀
over the selected area. The optimized algorithm shows merits in all testing parameters in both kernel performance and TRT. The TRT of the geoid determination yields 7 times improvements over the largest σ
₀
and most dense resolution grid (1 × 1 arc-min) where large data are truncated. A numerical investigation is conducted thoroughly over all suggested scenarios and shows high efficiency. The Matlab vectorization techniques and the relational operators are found to be very efficient to improve the code performance.