Three-Dimensional Gravity Forward Modeling of Prismatic Models Using Gauss–Kronrod Numerical Integration

Abstract

Three-dimensional gravity-anomaly forward modeling is a critical component in geophysical exploration for delineating subsurface geological structures and mineral resources. Conventional numerical-integration methods, however, often suffer from insufficient accuracy and low computational efficiency, particularly when dealing with complex density distributions and irregular geometries. To overcome these limitations, we introduce the Gauss–Kronrod numerical integration scheme, which combines high-order Gaussian quadrature with embedded error estimation. We derive the integral formulations for gravitational potential, gravity field, and gravity gradients under both constant-density and variable-density assumptions. A numerical algorithm is developed by applying the Gauss–Kronrod rule in three dimensions. Extensive synthetic model tests are conducted to evaluate the performance of the proposed method. The results show that our approach achieves substantial improvements in accuracy, with errors converging to the order of 10−12 for constant-density models, and significantly reduces computation time compared with the MATLAB R2024a built-in function integral3. The method effectively handles variable-density models and provides stable solutions for complex geological scenarios. This work offers a practical and efficient tool for high-precision gravity forward modeling, with potential applications in mineral exploration and geodynamic studies.