# Application of Dynamic Time Warping to Determine the Shear Wave Velocity from the Down-Hole Test
); [EMAIL_ADDRESS] (M.S. ); [EMAIL_ADDRESS] (M.S. ); [EMAIL_ADDRESS] (M.S. ); [EMAIL_ADDRESS] (M.S.) 2 KGH O/ZH Polska Miedz SA, 59-306 Rudna, Poland; [EMAIL_ADDRESS] 2  
[PERSON]  
1 KGH O/ZH Polska Miedz SA, 59-306 Rudna, Poland; [EMAIL_ADDRESS] 2  
[PERSON]  
1 KGH O/ZH Polska Miedz SA, 59-306 Rudna, Poland; [EMAIL_ADDRESS] 2  
[PERSON]  
1 KGH CUPRUM Sp. z.o.o.--Research and Development Centre, 53-659 Wroclaw, Poland; [EMAIL_ADDRESS] (W.K. ); [EMAIL_ADDRESS] (P.S. ); [EMAIL_ADDRESS] (S.A.); [EMAIL_ADDRESS] (M.S.) 2 KGH O/ZH Polska Miedz SA, 59-306 Rudna, Poland; [EMAIL_ADDRESS] 2  
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Footnotewhere \(\rho\) is the soil density [5]. This parameter holds significant importance in earthquake ground reaction analysis because the stiffness of the material affects the way the soil reacts to seismic vibrations and the distribution of stresses and strains in the soil. Correlating wave velocity with measurements from other tests may provide opportunities to extend or replace some of these tests. This dependence can be examined for, among others, the cone penetration resistance from a CPT, the standard penetration test blow count from an SPT, as well as the effective confining pressure and void ratio from laboratory tests [6]. The benefit of shear wave velocity application in the case of TSF is the ability to use the parameter to assess the seismic resistance of soil to liquefaction [7], which is one of the causes of TSF failures. The speed of the shear wave can be determined through various tests. The two basic tests are the cross-hole test and the down-hole test. Both of these tests are based on the induction of a seismic shear wave that is received by a geophone placed on a probe inserted into the soil. The main difference between these tests is the location of the source of the wave. With the cross-hole method, the source is placed in a second borehole at the same height as the geophone. Due to this, it is only necessary to determine the time of arrival of the wave to the geophone. The ratio of the constant distance between the source and the receiver and the determined time difference enables the calculation of the wave speed. Down-hole test results, where the source is on the surface and is received by two geophones placed at different depths on the probe, are slightly more challenging to interpret. In this case, the crucial task is to determine the difference in the times of the arrival of the wave at both geophones (\(\Delta\)t). The constant difference between the localization of the geophones makes it possible to indicate the wave speed at individual depths. In order to determine \(\Delta\)t, it is necessary to correlate both signals and determine the value of the shift between them. One common method of \(\Delta\)t determination is the cross-correlation method, which is described in more detail in [8]. However, the task can be especially difficult when the signals are noisy or have other irregularities. For this reason, it is necessary to develop an accurate method of determining the value of the shift as well as defining the accuracy of the result obtained. The advantages of the down-hole method over the cross-hole method are that it is less invasive, as it involves making only one well, and it is possible by performing the seismic cone penetration test (SCPT). Our study introduces a novel method for determining the time delay of shear wave arrival using Dynamic Time Warping (DTW), a signal similarity algorithm, to determine the shear wave velocity. This method emphasizes the importance of proper signal preconditioning techniques, such as noise removal, amplitude normalization, trend removal, and the extraction of the informational fragment of the signal.