Discussion on the Theoretical Basis for Cross-Over Method Applied to Downhole Wave Velocity Test

Abstract

At engineering practice, the theoretical basis for the cross-over method, used to obtain shear wave arrival time in the downhole method of the wave velocity test by surface forward and backward strike, is that the polarity of P-wave keeps the same, while the polarity of S-wave transforms when the direction of strike inverted. However, the characteristics of signals recorded in tests are often found to conflict with this theoretical basis for the cross-over method, namely, the polarity of the P-wave also transforms under the action of surface forward and backward strike. Therefore, 3D finite element numerical simulations were conducted to study the validity of the theoretical basis for the cross-over method. The results show that both shear and compression waves are observed to be in 180° phase difference between horizontal signal traces, consistent with the direction of excitation generated by reversed impulse. Furthermore, numerical simulation results prove to be reliable by the analytic solution; it shows that the theoretical basis for the cross-over method applied to the downhole wave velocity test is improper. In meanwhile, numerical simulations reveal the factors (inclining excitation, geophone deflection, inclination, and background noise) that may cause the polarity of the P-wave not to reverse under surface forward and backward strike. Then, as to reduce the influence factors, we propose a method for the downhole wave velocity test under surface strike, the time difference of arrival is based between source peak and response peak, and numerical simulation results show that the S-wave velocity by this method is close to the theoretical S-wave velocity of soil.