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

Tilt-Depth and the improved methods are receiving increasing attention from geophysicists. However, 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 numerical 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.