# Application of Dynamic Time Warping to Determine the Shear Wave Velocity from the Down-Hole Test
## 5 Results  
The proposed method of determining the wave speed was tested on real measurements from three SCPT tests carried out on the tailing storage facility dam. Each of the tests was carried out at a depth of about 50 m, and down-hole measurements were performed every 1 m by generating a wave from the left and right sides. This resulted in a total of almost 300 recorded signals (each using two geophones). Cross-hole tests were carried out at the same measurement points, which provide reliable information about the wave speed (later referred to as \"real\" information). These measurements were used as reference values to assess the accuracy of the estimated results of the DTW-based method. Each of the waves was also assessed in terms of signal quality according to the method of examining the similarity of signals using DTW. Figure 6 shows the results obtained for three tests (Figure 6a-c). The estimated wave speed is presented in relation to the measurement depth and compared with the actual value. In addition, the quality (Q) is marked in color, where red means a signal quality close to 0 and green means a signal quality close to 1. It can be seen that the estimated values are close to the real ones, but they do not fully coincide. There are also some large deviations that usually correlate with a poor signal quality. The worst results were obtained for measurement no. three, which is the left wave.  
The obtained wave speed estimation results were also compared using the RMSE measure, where the cross-hole test result was taken as the actual value (Table 1). The value was determined each time for all the waves and after rejecting those of a low quality (Q \(>\) 0.5 and Q \(>\) 0.7). Assuming that the quality threshold is set to be greater than 0.5, approximately 9% of the measurements are excluded on average. Raising the quality threshold to be greater than 0.7 results in the rejection of approximately 25% of signals from the analysis. However, it can be seen that the introduction of these restrictions increases the accuracy of the results. After the introduction of the first quality constraint, the RMSE was lower by an average of 37%. Increasing the constraint to Q \(>\) 0.7 no longer improves the accuracy of the result as much, so it may be unnecessary.  
Figure 6: Comparison of the estimated wave speed determined by the DTW-based method with the actual values from cross-hole tests for three SCPT studies (**a–c**). The color scale from red to green indicates the quality of the signals (red—low quality, green—high quality).  
The results show that, in addition to using a good method for determining the difference in the time of arrival of the wave, it is also very important to evaluate the quality of the measurements in order to avoid erroneous results. Furthermore, having two measurements (left shear wave and right shear wave) and a quality assessment means that the result of a higher-quality measurement can be taken as the final value of the estimated speed.  
As mentioned in the Introduction, a common way of finding \(\Delta\)t is using the cross-correlation method. The disadvantage is that the precision is limited by the signal resolution. Moreover, in more difficult cases, i.e., measurements close to the surface or the deepest ones, the cross-correlation method gave unrealistic results because the shear wave speed was too high [8]. Both methods were tested on the same dataset. The advantages of using the DTW method are its efficacy (i.e., more realistic results in difficult cases) and the precision of the shear wave speed.