**4.2 Model 2: neighboring effect**

The performance of the proposed inversion method with complicated field anomalies and the effect of interfering subsurface structures was investigated. To achieve this, we once again generate a synthetic model data from multiple source bodies as a horizontal cylinder model with *A*<sup>1</sup> = 100 mGal m, *z*<sup>1</sup> = 3 m, *x*<sup>1</sup> = 30 m, and *q*<sup>1</sup> = 1) and a sphere model with *A*<sup>2</sup> = 400 mGal m2 , *z*<sup>2</sup> = 4 m, *x*<sup>2</sup> = 80 m, and *q*<sup>2</sup> = 1.5) (**Figure 7a**).

**Figure 7b** and **c** illustrate the horizontal and vertical gradients of the composite gravity anomaly, as well as the amplitude of the analytic signal. The R-parameter values were determined using Eq. (5) for each source location and a 2-D mosaic surface S of 101 11 m in the X- and Z-directions constructed and discretized into 1-m intervals in both directions. The 2-D mosaic (**Figure 7d**) indicates that the R-max value for each source is 0.8 and 0.62 at *q* equal 1 and 1.5, respectively.

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

### **Figure 6.**

*Model 1: Noisy data. (a) Analytic signal anomaly (Figure 5c) 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 4.**

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

The obtained model parameters for horizontal cylinder and sphere are *A*<sup>1</sup> = 120.1 mGal m, *z*<sup>1</sup> = 3.6 m, and *x*<sup>1</sup> = 30 m and *A*<sup>2</sup> = 443.1 mGal m<sup>2</sup> , *z*<sup>2</sup> = 4.2 m, and *x*<sup>2</sup> = 80 m, respectively, which the results shows that the method is stable and robust.

**Figure 7.**

*Model 2: Interference/neighboring effect. (a) Gravity anomaly generated by two different adjacent bodies, (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 values.*

To better understand the procedure, we tainted the composite anomaly (**Figure 7a**) with a 20% noise level (**Figure 8a**). The horizontal and vertical derivatives, as well as the corresponding amplitude of the analytic signal, are shown in **Figure 8b** and **c**. The retrieved R-parameter image is shown in **Figure 8d**, with R-max values of 0.79 and 0.61 for a horizontal cylinder and a sphere, respectively. The drop in maximum parameter values compared to (**Figure 7d**) is attributable to the noise introduced into the data as well as the effect of the nearby objects. The model parameters for the first and second bodies revealed by imaging are: *A*<sup>1</sup> = 126.9 mGal m, *z*<sup>1</sup> = 3.8 m, and *x*<sup>1</sup> = 30 m and *A*<sup>2</sup> = 556.3 mGal m2 , *z*<sup>2</sup> = 4.7 m, and *x*<sup>2</sup> = 80 m, respectively, which are quite adjacent to the real values.

**Figure 9** depicts the results of the study of the noisy analytic signal data seen in **Figure 8c**. The amplitude coefficients and burial depths recovered from the elucidation are exaggerated (**Figure 9a–d**), as shown in **Table 5**, which coincides with and confirms the aforementioned results.

On the basis of the theoretical models presented above, it can be inferred that the technique described here is stable and robust.

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

**Figure 8.**

*Model 2: Interference/neighboring effect with noise. (a) Noisy gravity anomaly of Figure 7a 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 values.*
