**3. Synthetic example**

To test the ability of each suggested approach in assessing the buried model parameters for the simple geometric shapes such as spheres, cylinders, and sheets. Two synthetic examples are suggested for these interpretation. First one is belonging to use the gravity data and second is applying the self-potential data.

### **3.1 Gravity anomaly model**

A gravity anomaly of a horizontal cylinder model is generated using the following parameters *K* = 200 mGal�m, *z* = 5 m, *xo* = 0, *q* = 1.0, and profile length = 100 m *Combined Gravity or Self-Potential Anomaly Formula for Mineral Exploration DOI: http://dx.doi.org/10.5772/intechopen.92139*

### **Figure 2.**

*A gravity model due to horizontal cylinder without and with a 10% of random noise (*K *= 200 mGalm,* z *= 5 m,* xo *= 0,* q *= 1, and profile length = 100 m).*

(**Figure 2**). The procedures of interpreting the forward model are done using three steps as follows:

First step: using the least-squares approach to interpret the gravity anomaly yielding from the above mentioned parameters for different s-values for the three suggested shape bodies, i.e., *q* = 0.5, *q* = 1.0, and *q* = 1.5, after that the RMS is


### **Table 1.**

*Numerical results using the least-squares approach for a gravity model due to horizontal cylinder without and with a 10% of random noise (*K *= 200 mGalm,* z *= 5 m,* xo *= 0,* q *= 1, and profile length = 100 m).*


### **Table 2.**

*Numerical results using the particle swarm approach for a gravity model due to horizontal cylinder without and with a 10% of random noise (*K *= 200 mGalm,* z *= 5 m,* xo *= 0,* q *= 1, and profile length = 100 m).*

calculated to execute the best-fit parameters (happens at the lowest RMS) (**Table 1**). Second step: Werner deconvolution approach is utilized to infer the same gravity data. An 11 clustered solutions to determine in the average evaluated depth (4.9 m) (**Figure 2**). Third step: the particle swarm method is applied to obtain the parameters (**Table 2**).

Moreover, a 10% random noise added to the synthetic gravity data mentioned above (**Figure 2**) to test the efficiency of the suggested approaches in interpreting the gravity data. Also, the three approaches are used for this data as mentioned in

**Figure 3.**

*Werner deconvolution solutions for a gravity model due to horizontal cylinder without and with a 10% of random noise (*K *= 200 mGalm,* z *= 5 m,* xo *= 0,* q *= 1, and profile length = 100 m).*

**Table 1** (the least-squares approach results), **Figure 3** (Werner deconvolution results), and **Table 2** (the particle swarm results). Finally, the estimated parameters are in all case are in good agreement with the true parameters.

**Figure 4.**

*A self-potential model due to horizontal cylinder without and with a 10% of random noise (*K *= 200 mVm,* z *= 5 m,* θ *= 45°,* xo *= 0,* q *= 1, and profile length = 100 m).*


### **Table 3.**

*Numerical results using the least-squares approach for a self-potential model due to horizontal cylinder without and with a 10% of random noise (*K *= 200 mVm,* z *= 5 m,* θ *= 45°,* xo *= 0,* q *= 1, and profile length = 100 m).*
