## 3 Results and Discussion
### Data Analysis
#### 3.3.3 Error Calculation  
To calculate position errors in the study area, Equation (8) is used, where the ideal spacing \(\Delta X=4\) m is assumed and the calculated spacing \(\Delta X_{cn}\) is measured from D-GPS Easting and Northing coordinates for each receiver (Table 3). Results of the position errors show that the mean and standard deviation of the errors are 0.014 and 0.041 m (0.35% and 1.025% of ideal spacing), respectively, which are negligible. Moreover, Equation (9) is used to calculate the elevation errors where a horizontal datum is chosen at the first shot elevation (i.e., datum = 9.4 m above mean sea level). Elevation errors are shown in Table 4. In comparison to position errors, elevation errors have a mean and standard deviation of 2.36 and 1.22 m (25.1% and 13% relative to the datum elevation), respectively, which are relatively considerable. Therefore, it is expected that most effects on the seismic array  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Shot Gather No.**} & \multirow{2}{*}{**Trace No**} & **Offset** & **First Arrival** & \multirow{2}{*}{**Velocity \(V_{1}\) (m/s)**} \\  & & **(m)** & **Time (s)** & \\ \hline \multirow{2}{*}{Shot Gather 1} & Trace 1 & 4 & 0.013 & 311 \\  & Trace 2 & 8 & 0.025 & 323 \\ \hline \multirow{2}{*}{Shot Gather 2} & Trace 2 & 4 & 0.013 & 299 \\  & Trace 3 & 8 & 0.026 & 320 \\ \hline \multirow{2}{*}{Shot Gather 3 (left)} & Trace 1 * & 2 & _0.004_ & _500_ \\  & Trace 2 & 6 & 0.015 & 349 \\ \hline \multirow{2}{*}{Shot Gather 3 (right)} & Trace 1 * & 2 & _0.005_ & _400_ \\  & Trace 2 & 6 & 0.016 & 344 \\ \hline \multirow{2}{*}{Shot Gather 4} & Trace 2 & 4 & 0.013 & 314 \\  & Trace 3 & 8 & 0.027 & 283 \\ \hline \multirow{2}{*}{Shot Gather 5} & Trace 1 & 4 & 0.013 & 299 \\  & Trace 2 & 8 & 0.027 & 286 \\ \hline \multicolumn{2}{l}{Average velocity \(V_{1}\) (m/s)} & \multicolumn{2}{c}{313} \\ \hline \hline \end{tabular}
\end{table}
Table 1: First arrival travel times of direct wave and corresponding offsets and velocities from all shots of the survey. The two traces from shot gather 3 (marked by *) have been excluded from averaging because they were considered outliers.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Trace Number**} & \multicolumn{2}{c}{**Shot Gather 1 (Down-dip)**} & \multicolumn{2}{c}{**Shot Gather 3 (Up-dip)**} \\  & \multicolumn{2}{c}{**Offset (m)**} & \multicolumn{2}{c}{**First Arrival**} & \multirow{2}{*}{**Offset (m)**} & **First Arrival** \\  & \multicolumn{2}{c}{**Time (s)**} & & **Time (s)** \\ \hline
13 & 48 & 0.053 & 2 & 0.004 \\
14 & 44 & 0.050 & 6 & 0.015 \\
15 & 40 & 0.047 & 10 & 0.027 \\
16 & 36 & 0.045 & 14 & 0.039 \\
17 & 32 & 0.042 & 18 & 0.043 \\
18 & 28 & 0.039 & 22 & 0.044 \\
19 & 24 & 0.036 & 26 & 0.045 \\
20 & 20 & 0.034 & 30 & 0.046 \\
21 & 16 & 0.031 & 34 & 0.047 \\
22 & 12 & 0.028 & 38 & 0.048 \\
23 & 8 & 0.026 & 42 & 0.049 \\
24 & 4 & 0.012 & 46 & 0.052 \\ \multicolumn{2}{l}{\(\alpha\) (\(deg\))} & \multicolumn{2}{c}{3.2} \\ \multicolumn{2}{l}{\(\theta_{c}\) (\(deg\))} & \multicolumn{2}{c}{9.2} \\ \multicolumn{2}{l}{Apparent velocities \(V_{u}\) and \(V_{d}\) (m/s)} & \multicolumn{2}{c}{1455} & \multicolumn{2}{c}{2967} \\ \multicolumn{2}{l}{True refraction medium velocity \(V_{2}\) (m/s)} & \multicolumn{2}{c}{1949} \\ \hline \hline \end{tabular}
\end{table}
Table 2: First arrival travel times of the head wave from shot gather 1 and 3 with the values of ground-surface dip angle (\(\alpha\)), critical angle (\(\theta_{c}\)) and refraction medium velocity (\(V_{2}\)).  
response are attributed to elevation errors in this case. The first arrival travel times of the perturbed and ideal cases are shown in Figure 6a.