**1. Introduction**

Gravity data interpretation has been widely used to appraise the different types of subsurface structures and their locations [1–8]. Gravity methods have been widely applied to ore and mineral exploration [9–13], hydrocarbon exploration [14–16], cave detection [17, 18], hydrogeology [19, 20], geothermal and volcanic activity [21–23], locating of unexploded military ordnance [24], environmental and engineering application [25, 26] and archaeological investigations [27, 28].

The quantitative interpretation of gravity data using simple models (spheres and cylinders) is common in exploratory geophysics and continues to be of interest [29–33]. In geologic contexts with a single gravity anomaly, it can be quite appropriate [34]. A single isolated causal body can invert this recorded gravity anomaly to establish its distinctive inverted parameters and fit the recorded data.

The simple geometric models can be matched with the subsurface structures encountered during application of several approaches for inversion [35–39]. These methods include graphical and numerical characteristic points approaches [40–42], ratio technique [43], Fourier transform method [44], the neural network algorithms [45], Mellin transform technique [36], and Werner deconvolution technique [46]. However, the drawbacks of these methods based on tending to generate high number of invalid solution due to few numbers of points and data used, noise or window size incompatibility. As a result, these approaches are subjective, which can

lead to significant inaccuracies in calculating the buried anomalous body's characteristic inverse parameters [41, 47], which is to be expected. Gupta [48] and Essa [49] developed techniques depending on successive minimization approaches, which utilize the whole measured data to assess the depth parameter and then used some of characteristic points to continue in estimating the rest parameters such as amplitude coefficient. Shaw and Agarwal [37] used the Walsh transform scheme to determine the depth of buried bodies. Mehanee [47] used the regularized conjugate gradient method to construct an effective iterative method based on the use of logarithms of the model parameters for gravity inversion. The method inverts the residual gravity data acquired along profile for evaluating a depth and amplitude coefficient of buried bodies and suitable for subsurface imaging and mineral exploration.

Here, the study proposed an application of the robust R-parameter imaging method to interpret residual gravity data along a profile over idealized geometric bodies such as semi-infinite vertical cylinder, infinitely long horizontal cylinder, and sphere models. The goal is to establish the underlying approximative model by determining the body parameters, which include its origin, depth, amplitude coefficient, and shape. The R-parameter imaging method depends on the correlation coefficient amongst the analytic signal of the collected and calculated gravity data. The optimum solution occurs at the maximum R-parameter value.

The benefit behind the use of this method is fall in estimating the depth and body location with an acceptable value compared to the true ones and used the whole gravity data points of the profile, instead of just a few characteristic points. In addition to the method does not require priori information of the subsurface and directly interpret the anomaly from the given observed data. This chapter begins with a layout of the forward modeling, which contains a theoretical gravity formula, an R-parameter imaging approach description, numerical models test without and including noise, and a field data for slat dome investigation.
