Software for generating gravity gradients using a geopotential model based on an irregular semivectorization algorithm

The spherical harmonic synthesis of second-order derivatives of geopotential is a task of major concern when the spatial resolution of synthesis is high and/or a high-resolution Earthʹs gravity model is used. Here, a computational technique is presented for such a process. The irregular semivectorization is introduced as a vectorization technique in which one loop is excluded from matrix-vector products of mathematical models in order to speed up the computation and manage the computer memory. The proposed technique has the capability of considering heights of computation points on a regular grid. MATLAB-based software is developed, which can be used for generating gravity gradients on an ordinary personal computer. The numerical results show that irregular semivectorization significantly reduces the computation time to 1 h for synthesis of these data with global coverage and resolution of 5′×5′ on an elevation model. In addition, a numerical example is presented for testing satellite gravity gradiometry data of the recent European Space Agency satellite mission, the gravity field and steady-state ocean circulation explorer (GOCE), using an Earthʹs gravity model.