In this study, a new approach to improve the 3D Cauchy-type integral is presented for faster and more accurate forward modeling of gravity data produced by a sediment-basement interface. The conventional method for calculating the gravity effect of a sedimentary basin is to discretize that into right-rectangular prisms. Its associated volumetric integral over the prisms has computational complexity which makes volumetric integral time-demanding for 3D modeling. A 3D Cauchy-type integral only discretizes the density contrast surface. In fact, it is a surface integral without transcendental functions, which enables fast computation of potential fields. The purpose of the technique is to increase the accuracy of the customary Cauchy-type integral in order to calculate the gravity field over a sedimentary structure which is more likely in real geological structures. To achieve this, the vertical planes located between basement edges and the horizontal reference plane are considered. The accuracy and computational cost is assessed by synthetic gravity data modeling. Three forward functions, namely improved Cauchy-type integral, customary Cauchy-type integral, and volumetric integral, are applied to calculate the gravity field over synthetic sedimentary basins with different geometries. The volumetric integral is set as a benchmark to validate the efficiency of the presented method. Results are analyzed by comparing the dissimilarities of gravity anomalies calculated using the volumetric integral and each of the customary and improved Cauchy-type integrals. The resulting anomaly differences indicate that, compared with the customary Cauchy-type integral, the improved Cauchy-type integral increases the accuracy in calculated gravity anomalies considerably. Furthermore, forward calculations using the improved Cauchy-type integral require approximately the same time as the customary Cauchy-type integral, and are about 50 times faster than the volumetric integral. In addition, the improved Cauchy-type integral gives better results if the edges of the basement are not at an equal level, which is very likely in real geological structures. The new approach is tested on the basement of the Yucca Flat basin to assess the viability of the proposed model in real cases.

中文翻译：

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改进的 3D Cauchy 型积分，可更快、更准确地对由地下室浮雕引起的重力数据进行正向建模

在这项研究中，提出了一种改进 3D 柯西型积分的新方法，以更快、更准确地对沉积物-基底界面产生的重力数据进行正演建模。计算沉积盆地重力效应的传统方法是将其离散为直角棱柱。其在棱镜上的相关体积积分具有计算复杂性，这使得体积积分对于 3D 建模非常耗时。3D Cauchy 型积分仅离散密度对比表面。事实上，它是一个没有超越函数的表面积分，可以快速计算势场。该技术的目的是提高惯用柯西型积分的精度，以便计算更可能出现在真实地质结构中的沉积结构上的重力场。为了实现这一点，需要考虑位于地下室边缘和水平参考平面之间的垂直平面。精度和计算成本是通过合成重力数据建模来评估的。应用改进的柯西型积分、惯用的柯西型积分和体积积分三个正向函数计算不同几何形状的合成沉积盆地上的重力场。体积积分被设置为基准来验证所提出方法的效率。通过比较使用体积积分计算的重力异常的不同与每个惯用的和改进的柯西型积分来分析结果。由此产生的异常差异表明，与通常的柯西型积分相比，改进的柯西型积分显着提高了计算重力异常的精度。此外，使用改进的柯西型积分进行前向计算所需的时间与通常的柯西型积分大致相同，并且比体积积分快约 50 倍。此外，如果基底边缘不在同一水平面上，改进的柯西型积分会得到更好的结果，这在真实的地质结构中很可能发生。