In 3D gravity inversion, a regularization technique must be introduced in order to deal with the non-uniqueness and stability of the inversion process. For this purpose, stabilizing functionals based on minimum norm and maximum smoothness have been utilized as the regularization item in the objective function of gravity inversion, but yield a smoothed distribution of subsurface density which does not give a clear delineation of the boundaries of blocky geological units. Although some functionals such as minimum support and minimum gradient support functionals have been applied to focusing inversion of potential field data, these functionals need to be provided with a suitable focusing parameter for successful inversion. In this paper, we have developed a focusing 3D inversion of gravity data based on an arctangent stabilizing functional. To deal with the numerical solution to the gravity inversion problem, the arctangent-function-based stabilizing functional is first reformulated in pseudo-quadratic form as a weighting matrix. The Gauss Newton (GN) minimization scheme is then employed to perform an optimization process. For the stabilizing functional introduced in this study, there is no need to determine in advance two optimum parameters involved in the stabilizing functional. A test on synthetic examples demonstrates that the boundaries of the anomalous bodies recovered are sharper and the density values are also closer to the true model. We also apply this approach to field gravity data collected from the San Nicolas deposit in Mexico, illustrating that the inversion result shows good consistency with the a priori information available.

在3D重力反演中，必须引入正则化技术以处理反演过程的非唯一性和稳定性。为此，基于最小范数和最大平滑度的稳定功能已被用作重力反演目标函数中的正则项，但产生了地下密度的平滑分布，无法清晰地描述块状地质单元的边界。尽管已将某些功能（例如最小支持和最小梯度支持功能）应用于潜在场数据的聚焦反演，但需要为这些功能提供合适的聚焦参数才能成功进行反演。在本文中，我们基于反正切稳定函数开发了重力数据的聚焦3D反演。为了解决重力反演问题的数值解决方案，首先将基于反正切函数的稳定函数重新拟定为伪二次形式作为加权矩阵。然后采用高斯牛顿（GN）最小化方案来执行优化过程。对于本研究中引入的稳定功能，无需预先确定涉及稳定功能的两个最佳参数。通过对合成示例的测试表明，恢复的异常体的边界更清晰，密度值也更接近真实模型。我们还将这种方法应用于从墨西哥圣尼古拉斯矿床收集的现场重力数据，这表明反演结果与现有的先验信息显示出良好的一致性。