Improved 3D Cauchy-type Integral for Faster and More Accurate Forward Modeling of Gravity Data Caused by Basement Relief

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.