重力场Tilt-Depth方法及其高阶推广

Tilt-Depth Method for Gravity Exploration and Its High Order Generation

Tilt-Depth以及其相关改进方法最初是基于磁异常基本公式推导,一直应用于磁法勘探领域。自2012年以来,不断有学者探讨重力场Tilt-Depth方法,但对重力场与磁场Tilt-Depth方法之间的关系研究较少,存在一些不同认识。梳理了重磁场之间Tilt-Depth方法的联系与区别,得出了Tilt-Depth方法在重力场中相比磁场高一阶导数的结论。验证了方法的有效性,通过对海南石碌矿区重力异常处理,提取了矿体的边界信息,突出了深部隐伏矿体产生的弱异常的边界范围,获取了矿体的位置及埋深参数,通过与已知地质剖面、反演剖面的对比,证实了重力场Tilt-Depth结论的正确性与有效性。

Tilt-Depth and the improved methods are receiving increasing attention from geophysicists. How- ever, it the Tilt-Depth method was deduced using magnetic formula, which leads to a limitation of its application to only magnetic exploration. Recently, many publications have been devoted to discussions of the Tilt-Depth method for gravity data interpretation, but little attention has been paid to the relationship of Tilt-Depth to the magnetic and gravity fields. In this paper, we review Tilt-Depth and these relationships. In order to rapidly detect boundaries and determine the depth of geological bodies, we extend Tilt-Depth and a series of associated methods from the magnetic to gravity field, and propose a specific Tilt-Depth method for processing gravity data. Based on gravity field equations in a vertical step model, we obtain an expression for the relationship between the top depth of geological body and vertical second derivative or horizontal second derivative. It shows the same results as magnetic Tilt-Depth. In addition, we deduce the V2D-depth of gravity anomies based on the third derivative for depth determination. This result is same as results from those based on the vertical second derivative of the magnetic field. Our results reveal that the Tilt-Depth method applied to gravity is a higher first-order derivative than the magnetic field. A nu- merical experiment demonstrates that the method is effective. To that end, the proposed method was used to process gravity data in a case study of the Shilu iron ore deposit. The results show that the Tilt-Depth method identified the weak gravity anomaly produced by deeply buried ore body, and also obtained convincing spatial parameters including location and depth of ore bodies.