Obtaining estimates of the low-frequency ‘fling’, instrument tilts and displacement timeseries using wavelet decomposition

Abstract

This paper proposes a novel, wavelet-based algorithm, which by extracting the low-frequency fling makes it possible to automatically correct for baseline shift and re-integrate down to displacement. The algorithm applies a stationary-wavelet transform at a suitable level of decomposition to extract the low frequency fling model in the acceleration time histories. The low frequency, acceleration fling should be as close as possible to the theoretical type A model, which after correction leads to a pulse-type velocity and ramp-like displacement after first and second integration. The wavelet transform essentially decomposes the seismic record using maximally flat filters and these together with a de-noising scheme form the core of this approach, which is to extract the lower and higher frequency sub-band acceleration, velocity and displacement profiles and correct for baseline shift. The correction automatically selects one time point from the low-frequency sub-band and then zeros the acceleration baseline after the fling. This implies pure, translation without any instrument tilts. Estimates of instrument tilt angles are also obtainable from the wavelet transformed time history as well as estimates of signal-to-noise ratios. The acceleration data used in this study is from station TCU068 in the near-fault region of the Chi-Chi, Taiwan, earthquake of 20th September 1999.

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