Fast forward modeling of gravity anomalies for two-dimensional bodies of arbitrary shape and density distribution

A fast and high precision spatial domain algorithm is presented for forward modeling of two-dimensional (2D) body gravity anomalies of arbitrary shape and density distribution. The new algorithm takes advantage of the convolution properties of the expression for 2D gravity anomalies, uses a rectangular cell as a grid subdivision unit, and then 2D bodies with irregular cross-sections are approximated by a combination of 2D bodies with a rectangular cross section. The closed-form expression is used to calculate the gravitational anomalies of the combination of 2D bodies with a rectangular cross section. To improve computing efficiency, the new algorithm uses a fast algorithm for the implementation of the Toeplitz matrix and vector multiplication. The synthetic 2D models with rectangular and circular cross-sections and constant and variable densities are designed to evaluate the computational accuracy and speed of the new algorithm. The experiment results show that the computation costs less than 6 s for a grid subdivision with 10000 × 10000 elements. Compared to the traditional forward modeling methods, the proposed method significantly improved computational efficiency while guaranteeing computational accuracy