Fast modeling of gravity gradients from topographic surface data using GPU parallel algorithm

Abstract

The gravity gradient is a secondary derivative of gravity potential, containing more high-frequency information of Earth's gravity field. Gravity gradient observation data require deducting its prior and intrinsic parts to obtain more variational information. A model generated from a topographic surface database is more appropriate to represent gradiometric effects derived from near-surface mass, as other kinds of data can hardly reach the spatial resolution requirement. The rectangle prism method, namely an analytic integration of Newtonian potential integrals, is a reliable and commonly used approach to modeling gravity gradient, whereas its computing efficiency is extremely low. A modified rectangle prism method and a graphical processing unit (GPU) parallel algorithm were proposed to speed up the modeling process. The modified method avoided massive redundant computations by deforming formulas according to the symmetries of prisms' integral regions, and the proposed algorithm parallelized this method's computing process. The parallel algorithm was compared with a conventional serial algorithm using 1″ elevation data in two topographic areas (rough and moderate terrain). Modeling differences between the two algorithms were less than 0.1 E, which is attributed to precision differences between single-precision and double-precision float numbers. The parallel algorithm showed computational efficiency approximately 200 times higher than the serial algorithm in experiments, demonstrating its effective speeding up in the modeling process. Further analysis indicates that both the modified method and computational parallelism through GPU contributed to the proposed algorithm's performances in experiments.