**4.1 Model 1**

## *4.1.1 Noise-free data*

The R-parameter imaging method is applied to noise-free numerical gravity anomaly due to simple model consisting of a a horizontal cylinder model (*q* = 1) with *zo* = 5 m, A = 100 mGal m, and *xo* = 51 m along a 101-m profile length (**Figure 2a**). This anomaly is the observable (measured) data that needs to be interpreted. The suggested methodology was initiated with estimating the horizontal and vertical derivative anomalies of the residual anomaly in **Figure 2a** (**Figure 2b**), and then calculate the amplitude of the analytic signal (**Figure 2c**). The 2-D mosaic surface S is constructed with depending on calculating the R-parameter values and discretized into 1-m intervals in X- and Z-directions and covers an area of 101 � 11 m in the Xand Z directions. Based on a priori information, the range of the model parameters was selected. The R-parameter values were obtained from (Eq. (5)) by setting the shape to its true value (i.e., *q* = 1) and utilizing the abovementioned ranges of the model location parameters *xo* and *zo*. The R-max value is represented by a black dot and equal 1 (**Figure 2d**). This is demonstrating that the methodology fruitfully recovered the real values of the location of the inferred gravity profile's origin point (*xo* = 51 m) and the depth of the target (*zo* = 5 m).

*Gravity Anomaly Interpretation Using the R-Parameter Imaging Technique over a Salt Dome DOI: http://dx.doi.org/10.5772/intechopen.105092*

#### **Figure 2.**

*Model 1: Noise-free data. (a) Horizontal cylinder gravity anomaly, (b) Horizontal and vertical gradients of (a), (c) Analytic signal anomaly using the data of (b), and (d) 2-D mosaic of the R-parameter and the R-max value.*

**Table 2** shows a different shape values that employed in the interpretation process. The results (**Figure 3** and **Table 2**) reveal that at *q* = 1, the R-max = 1 and indicating that the method is stable and capable of capturing thel exact values of the model parameters.

We applied the same procedures (by utilizing Eq. (4) as the forward modelling formula in this case) to the analytic signal data presented in **Figure 2c** to explore the recital of the current scheme when used to the analytic signal data themselves instead of the residual gravity data. **Figure 4** shows the outcomes, which are match with those derived from the above-mentioned elucidation of gravity data (**Table 3**).

## *4.1.2 Noisy data*

Given the lack of totally noise-free gravity field data, a 20% random noise (**Figure 5a**) has been introduced to the data in **Figure 2a**. The horizontal and vertical


## **Table 2.**

*Model 1: Noise-free data. The R-parameter computed for the different shape factors.*

**Figure 3.** *Model 1: Noise-free data. The R-parameter, depth and shape factor relationship.*

derivatives, besides the magnitude of the analytic signal of the measured gravity anomaly, are depicted in **Figure 5b** and **c**. The R-parameter values were evaluated utilizing Eq. (5) and created a 2-D mosaic surface (**Figure 5d**). The maximum R-parameter value is 0.94. The imaging-derived model parameters (*zo* =6m and *xo* = 51 m) are quite near to the real values, indicating that the established technique is stable.

The amplitude coefficient (*A*) is substantially overstated (**Figure 6a–d**) when the analytic signal data (**Figure 5c**) is interpreted. This is unsurprising given that the technique tries to fit the real data, and the anomalous body's inferred depth (*z*) is likewise overstated (**Figure 6a**). **Table 4** shows a comparison of model parameters derived by the established technique from the elucidation of each analytic signal and

*Gravity Anomaly Interpretation Using the R-Parameter Imaging Technique over a Salt Dome DOI: http://dx.doi.org/10.5772/intechopen.105092*

#### **Figure 4.**

*Model 1: Noise-free data. (a) Analytic signal anomaly (Figure 2c) subjected to the same interpretation, (b) Horizontal and vertical gradients of (a), (c) Analytic signal anomaly using the data of (b), and (d) 2-D mosaic of the R-parameter and the R-max value.*


#### **Table 3.**

*Model 1: Noise-free data. Comparison between the model parameters estimated from the interpretation of using residual anomaly and analytic signal anomaly.*

residual anomaly data. This investigation shows that using the given technique to analyses gravity data produces more precise findings than using analytic signal data.

**Figure 5.**

*Model 1: noisy data. (a) Noisy gravity anomaly of Figure 2a after adding 20% noise level, (b) Horizontal and vertical gradients of (a), (c) Analytic signal anomaly using the data of (b), and (d) 2-D mosaic of the R-parameter and the R-max value.*
