Improved Velocity and Displacement Time Histories in Frequency Domain Spectral-Matching Procedures

Existing spectral-matching techniques in the frequency domain distort the displacement time history of the ground motions. In the time domain spectral- matching procedures, scale functions (wavelets) are additive and, with an appropriate scale functional form, extra displacement will not be imposed to the record. However, matching in the frequency domain with a multiplicative scale function applied to the Fourier spectrum requires a special attention in the matching process to have control on the displacement time history. This study shows that thevelocity value at the end of the record is not affected by the Fourier amplitude spectrum scaling, but the displace- ment may linearly increase (or decrease) boundlessly. Two numerical solutions are proposed to solve the displacement drift problem in the frequency domain. Following the proposed frequency domain baseline correction procedure, one does not need to perform baseline correction in the time domain after completing the spectral matching. As a result, acceleration, velocity, and displacement time histories will remain fully compatible, and the boundary conditions of the velocity and displacement time histories will be preserved. The proposed procedure is not limited to spectral-matching methods and can be used with any general filtering process to retain the final dis- placement of the record. The possibility of applying a zero-padding technique to the spectral-matching filter is also discussed. It is shown that applying an appropriate window along with the zero-padding technique can lead to a reasonable displacement time history. The proposed procedures can be easily added to the existing or new frequency domain spectral-matching algorithms without significantly disrupting the spectral-matching process.