Gravitational Attraction of a Vertical Pyramid Model of Flat Top and Bottom with Depth-Wise Linear Density Variation

In 3D gravity modelling, a right rectangular parallelepiped with either constant density or variable density functions in spatial and spectral domains enjoys wide popularity. However, better unit models are needed to meet the large variety of geological scenarios. Here, we present an analytical expression for the gravity effect of a vertical pyramid model with depthwise linear density variation. Initially, we validate our analytic expression against the gravity effect of a right rectangular parallelepiped and 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, USA, demonstrates the comparative advantages of our pyramid model over the conventional right rectangular vertical prism model. Thus, our pyramid model could be quiet effective as a building block for evaluating the gravity effect of an arbitrarily-shaped 3D or 2.5D source(s).