Development of the gradient ratio method for depth estimation of the subsurface bodies using Bouguer gravity map data

Summary The semi-automatic techniques play an important role in interpretation of potential field data. There are many semi-automatic interpretation techniques available for interpretation of gravity data, such as Werner deconvolution (Hartman et al., 1971) and Euler deconvolution (Thompson, 1982; Reid et al., 1990). Some methods (Hsu et al., 1998; Keating and Pilkington, 2004; Salem, 2005) use the analytic signal amplitude. Other methods involve use of the gradient ratio of the potential field data and often give the edges of the bodies. In this paper, the gradient ratio method has been applied on gridded gravity map data for simultaneous estimation of the location and depth of the subsurface bodies. This method has been applied on synthetic gravity data as well on high resolution real gravity data acquired from Shavaz Iron Ore in southwest of Yazd province.
Introduction Circular structures in gravity data may correspond to kimberlite pipes or to meteorite impact structures. They can be modelled in different ways such as inversion. The horizontal gradient of a potential field dataset in a given direction enhances linear features which trend at 90° to that direction, while diminishing those that lie parallel to that direction. Such directional derivatives are commonly applied to potential field data to enhance or diminish features such as dykes, faults, and trends. These derivatives are easily computed in the space or frequency domains. One of the filters, in which gradient ratio factor is used, is tilt angle (Miller and Singh 1994). Tilt angle is an attribute of potential field data and is becoming increasingly popular among geoscientists for interpreting potential field, especially, the magnetic data. Salem et al. (2007) obtained tilt angle by substituting the analytic expressions for horizontal and vertical derivatives of the magnetic field over a vertical contact. This paper generalizes this idea and applies it to gravity data related to vertical cylinder and buried sphere models.
Methodology and Approaches The interpretation methods existed for circular features are restricted to edge detection only. This paper generalizes tilt-depth method for the magnetic vertical contact model to gravity data of vertical cylinder and buried sphere models. For simultaneous depth and edge estimation of such structures, we can use from gradient ratio method. The meaning of the gradient ratio is the ratio between vertical and horizontal derivatives. The method computes the ratio of the vertical derivative to the total horizontal derivative of data, and then, identifies circular contours within it. Having the radius of the contour and the contour value itself, we can determine the depth to the source. In this regard, a second order analytical equation is developed in which solving it leads to estimation of the depths of circular features. This method can be classified into model-dependent methods. In this paper, vertical cylinder and sphere have been used as synthetic models.
Results and Conclusions The following results and conclusions can briefly be drawn from the study made in this paper: 1. The ratio between vertical and horizontal gradients of the gravity anomaly related to cylinders can be used to estimate depth and location of the subsurface bodies. 2. The problem of noise enhancement in the computation of the gradients can be solved via the following two approaches: - acquiring the vertical and horizontal gradients in the field by gravity gradiometer or - calculating the vertical derivatives (more capable in noise amplifying) by means of Hilbert transform. The Hilbert transform is more stable than fast Fourier transform (FFT) and the results are more consistent. 3. The method has been tested on synthetic gravity data and on real gravity data from Shavaz Iron ore in southwest of Yazd province.