Appendix A. Calculation of gravitational quantities

The Earth's gravitational potential G is a scalar quantity, its shape can be constrained by its slope in the x, y and z directions, called the gravitational attraction G_x, G_y and G_z (gravity vector field). In this work, we have investigated how to parallelize the analytical calculation of the components of the gravity field vector and the gravity gradients represented by a nine component tensor, because of the symmetrical or irrotational attribute, the gravity gradient tensor is reduced to only six independent components: G_xx, (the vertical gravity gradient), and For the right rectangular prism model, the analytical formulae for the three components vectors and the six gravity gradient components, corresponding to the Eq. (2) are given by: