To take the sphericity of the Earth into account, tesseroids are often utilized as grid elements in large-scale gravitational forward modeling. However, such elements in a latitude–longitude mesh suffer from degenerating into poorly shaped triangles near poles. Moreover, tesseroids have limited flexibility in describing laterally variable density distributions with irregular boundaries and also face difficulties in achieving completely equivalent division over a spherical surface that may be desired in a gravity inversion. We develop a new method based on triangular spherical prisms (TSPs) for 3D gravitational modeling in spherical coordinates. A TSP is defined by two spherical surfaces of triangular shape, with one of which being the radial projection of the other. Due to the spherical triangular shapes of the upper and lower surfaces, TSPs enjoy more advantages over tesseroids in describing mass density with different lateral resolutions. In addition, such an element also allows subdivisions with nearly equal weights in spherical coordinates. To calculate the gravitational effects of a TSP, we assume the density in each element to be polynomial along radial direction so as to accommodate a complex density environment. Then, we solve the Newton’s volume integral using a mixed Gaussian quadrature method, in which the surface integral over the spherical triangle is calculated using a triangle-based Gaussian quadrature rule via a radial projection that transforms the spherical triangles into linear ones. A 2D adaptive discretization strategy and an extension technique are also combined to improve the accuracy at observation points near the mass sources. The numerical experiments based on spherical shell models show that the proposed method achieves good accuracy from near surface to a satellite height in the case of TSPs with various dimensions and density variations. In comparison with the classical tesseroid-based method, the proposed algorithm enjoys better accuracy and much higher flexibility for density models with laterally irregular shapes. It shows that to achieve the same accuracy, the number of elements required by the proposed method is much less than that of the tesseroid-based method, which substantially speeds up the calculation by more than 2 orders. The application to the tessellated LITHO1.0 model further demonstrates its capability and practicability in realistic situations. The new method offers an attractive tool for gravity forward and inverse problems where the irregular grids are involved.

为了考虑地球的球形度，在大规模重力正演建模中通常使用宇宙地球作为网格元素。然而，经纬度网格中的此类元素会退化为极点附近形状不佳的三角形。此外，网格体在描述具有不规则边界的横向可变密度分布方面的灵活性有限，并且在实现重力反演中可能需要的球形表面上的完全等效划分方面也面临困难。我们开发了一种基于三角球面棱镜 (TSP) 的新方法，用于球坐标中的 3D 重力建模。 TSP 由两个三角形球面定义，其中一个是另一个的径向投影。由于上表面和下表面的球面三角形形状，TSP在描述不同横向分辨率的质量密度方面比方矩体更具优势。此外，这样的单元还允许在球坐标中以几乎相等的权重进行细分。为了计算 TSP 的引力效应，我们假设每个单元的密度都是沿径向的多项式，以适应复杂的密度环境。然后，我们使用混合高斯求积法求解牛顿体积积分，其中使用基于三角形的高斯求积规则通过将球面三角形转换为线性三角形的径向投影来计算球面三角形上的表面积分。二维自适应离散化策略和扩展技术也相结合，以提高质量源附近观测点的精度。 基于球壳模型的数值实验表明，在不同尺寸和密度变化的TSP的情况下，该方法从近地表到卫星高度都具有良好的精度。与经典的基于网格的方法相比，该算法对于具有横向不规则形状的密度模型具有更好的精度和更高的灵活性。结果表明，在达到相同精度的情况下，该方法所需的单元数量远少于基于Tesseroid的方法，从而将计算速度大幅提高了2个数量级以上。镶嵌LITHO1.0模型的应用进一步证明了其在现实情况下的能力和实用性。新方法为涉及不规则网格的重力正向和反演问题提供了一个有吸引力的工具。