Rapid Construction of Marine Disturbing Gravity Gradient Reference Map by CPU and GPU Hybrid Parallel Method

Objectives High precision and high resolution marine disturbing gravity gradient reference map is one of the key technologies to put underwater disturbing gravity gradient assisted inertial navigation into practice. At present, gravity anomaly is mainly measured by satellite and calculated based on the boundary value problem theory and the removal recovery technique.

Methods The traditional serial algorithm has some problems such as low efficiency and long time consuming. In order to meet the needs of rapid construction of marine disturbing gravity gradient reference maps on a large scale and even around the world, this paper designs an efficient hybrid parallel computing scheme using central processing unit (CPU)+graph processing unit (GPU) hybrid parallel programming platform. First, the shrink and expansion method of array is proposed to solve the problem of memory conflict between read and write in Legendre recursive computation. Then Hilbert space filling curve is used to reduce the dimension of two-dimensional grid gravity anomaly data into a one-dimensional array with high clustering. The efficient calculation of Stokes integral is realized by the fast index in GPU video memory.

Results The experiments are carried out on computers with Intel Xeon (R) Gold 6130 CPU and Tesla V100 GPU. The hybrid parallel scheme is used to calculate 6°×6° range and 1' resolution full tensor marine disturbing gravity gradient reference map and only takes 15.84 seconds, while the traditional serial method takes more than 35 minutes. To calculate 2°×2° range and 30'' resolution map, the proposed method only takes 22.7 seconds, while the serial method takes 52 minutes. To calculate 2°×2° range and 10'' resolution map, the proposed method only takes 26.7 minutes, while the serial method takes more than two days.

Conclusions On the premise of ensuring that the absolute error of parallel computing is less than or equal to 1×10^-6 E, the maximum absolute value of $T_{xx}+T_{yy}+T_{zz}$ is less than 0.1 E and the root mean square error is less than 0.01 E, the rapid construction of the global total tensor marine disturbing gravity gradient reference map model is realized.