This study presents an optimized gravity-sparse inversion method. The proposed method minimizes the global objective function using interior-point method for boundary constraints and a general weighting function comprising the depth, compactness, and kernel weighting functions of the density models. For the compactness weighting function, practical experiments demonstrate that the recovered model becomes more compact with an increasing value for the relative exponential factor β. However, if no appropriate boundary-constraint method is applied, the inversion results cannot be controlled within the designated constraint bounds when β needs to be set to a large value to obtain compact inversion results. The interior-point method allows the use of a larger β to obtain more compact inversion results without violating the boundary constraints. Additionally, models in close proximity can more clearly be recognized using this method. To improve the computational efficiency and obtain a more accurate regularization parameter, the preconditioned conjugate gradient and L-curve, or line search methods, were also applied. The proposed method was applied for three synthetic examples: two positive bodies adjacent to each other at different depths inverted using noise-free gravity anomaly data, three bodies (positive or negative) at different depths inverted using noise-free or contaminated gravity anomaly data, and three bodies (positive or negative) characterized by a certain dip angle inverted using contaminated gravity anomaly data. This method was also applied for the inversion of a Woodlawn sulfide body, Missouri iron ore body, and granitoid rock body in the Rio Maria region in the state of Para, Brazil. In all six test cases, larger β values were used and the density models were recovered with sharper boundaries within the designated bounds.

这项研究提出了一种优化的重力稀疏反演方法。所提出的方法使用内部点方法对边界约束和包含密度模型的深度，紧实度和核加权函数的一般加权函数，将全局目标函数最小化。对于紧凑性加权函数，实践实验表明，随着相对指数因子β值的增加，恢复的模型变得更加紧凑。但是，如果未应用适当的边界约束方法，则当需要将β设置为较大值以获得紧凑的反演结果时，无法将反演结果控制在指定的约束范围内。内点法允许使用较大的β来获得更紧凑的反演结果，而不会违反边界约束。此外，使用此方法可以更清楚地识别出附近的模型。为了提高计算效率并获得更准确的正则化参数，还应用了预处理的共轭梯度和L曲线或线搜索方法。所提出的方法适用于三个合成示例：使用无噪声重力异常数据将两个不同深度的正体彼此颠倒；使用无噪声或污染重力异常数据将两个不同深度的正体（正负）颠倒；和三个物体（正负），其特征是使用受污染的重力异常数据反转一定的倾角。这种方法也适用于伍德劳恩硫化物体，密苏里州铁矿体，巴西帕拉州里约玛丽亚地区的花岗岩和花岗岩岩石体。在所有六个测试案例中，都使用了较大的β值，并且在指定范围内以更清晰的边界恢复了密度模型。