# Simulation of Wave Propagation Using Finite Differences in Oil Exploration
## 3 Results
### Algorithm  
The sources were placed at a particular separation distance called (offset). The sources were assumed to be separated at the same distance to determine the number of shots fired. The integer division between the length of the profile from the location of the initial source (\(x_{source}\)) and the distance between the sources defined the total shots. This is expressed in the following equation:  
\[nshots=\left[\frac{Nx-x_{source}}{offset}\right] \tag{16}\]  
Once the number of shots was known, they were distributed equally among the number of processors. Thus, the number of shots per processor were obtained from the integer division of the number of shots by the number of processes. The remainder of this division meant one more shot in the first process. In this way, each process generated the locations of its sources and executed the sequential code for each of them.  
The authors used a simple geologic model to demonstrate the validity of the code application. The model (Figure 1) comprised three layers. The velocity for the first layer was set at 610 m/s (due to the limitations of the machine used), the second layer at 700 m/s velocity, and the last layer at 830 m/s velocity. Additionally, the authors set a constant density of 2.0 g/cm\({}^{3}\) for all three layers.  
Figure 5 shows the additional parameters used in the simulation. For this model, it took 98.10 s to place a source on the horizontal reference axis position. Using the data presented in Figure 5, the authors generated 87 horizontally placed sources, resulting in a sequential run time of 98.10 \(\times\) 87 = 8534.7 s. As the complexity of the model increased and longer recording times were needed, the computational cost also increased.  
This paper demonstrated the validity of the code using a simple geologic model. The model (Figure 5) consisted of three layers. The authors set the velocity of the first layer at 610 m/s (due to limitations in the cluster used), the second layer at 700 m/s, and the last layer at 830 m/s. Additionally, they set a constant density of 2.0 g/cm\({}^{3}\) for all three layers. The additional parameters are provided in Table 2.  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Time & 5 s \\ \hline Maximum frequency & 14 Hz \\ \hline Number of receptors & 1000 \\ \hline Distance between receptors & 40 m \\ \hline Length in \(x\) & 100,000 m \\ \hline Depth & 17,400 m \\ \hline Distance between sources & 50 m \\ \hline \end{tabular}
\end{table}
Table 2: Parameters considered in the simulation.  
Figure 5: The geological model was used in the simulation [31]. The depth is displayed, P(m), as a function of distance (m).  
For this model, it took 98.10 s to place a source in a horizontal position. Based on the data presented in Figure 2, 87 sources were located horizontally in total. Consequently, firing each source sequentially would result in an execution time of 98.10 \(\times\) 87 = 8534.7 s, equivalent to over two hours of execution. The computational cost increased if the model was more complex and required a longer recording time.  
The code was implemented using a finite difference scheme on a cluster of 16 processors.  
Distance (m) 0 2e + 04 4e + 04 6e + 04 8e + 04 10e + 04 P(m) 2.0  
Table 2 shows the parameters used in the simulation, including aspects of the receivers' position and sources.  
Figure 6 shows the seismogram generated by propagating the acoustic wave equation on the model of Figure 4 and the parameters presented in Table 2.