Gravitational attraction of a vertical pyramid model of flat top-and-bottom with depth-wise parabolic density variation

In 3D gravity modelling, right rectangular vertical prism model with linear and nonlinear density and polyhedral bodies with linear density variation exist in geophysical literature. Here, we propose a vertical pyramid model with depth-wise parabolic density contrast variation. Initially, we validate our analytic expression against the gravity effect of a right rectangular parallelepiped of constant density contrast. We provide two synthetic examples and a case study for illustrating the effectiveness of our pyramid model in gravity modelling. The included case study of Los Angeles basin, California demonstrates the comparative advantages of our pyramid model over a conventional right rectangular vertical prism model. Our pyramid model could be quite effective as a building block for evaluating the gravity effect of an arbitrarily-shaped 3D or 2.5-D source(s).