Computational & Technology Resources
an online resource for computational,
engineering & technology publications
PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping and Z. Bittnar
An Approach to Seismic Correction which includes Wavelet De-noising
A.A. Chanerley and N.A. Alexander
School of Engineering, University of East London, Dagenham, United Kingdom
A.A. Chanerley, N.A. Alexander, "An Approach to Seismic Correction which includes Wavelet De-noising", in B.H.V. Topping, Z. Bittnar, (Editors), "Proceedings of the Sixth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 44, 2002. doi:10.4203/ccp.75.44
Keywords: filters, deconvolution, seismic accelerograms, wavelet, denoising, thresholding.
Seismic accelerograms are the convolution of ground motion with the transfer function of the accelerometer and structure on which the accelerometer is mounted. The accelerometer response can be corrected in the time or frequency domain to recover an estimate of the ground motion of the seismic event. This correction of the accelerogram is essential for non-linear, finite element, timehistory, analysis of various civil engineering structures, as the uncorrected record is modified in amplitude, phase and frequency. This paper briefly discusses issues of the de- convolution of seismic data and then introduces threshold de-noising using the stationary wavelet transform in order to reduce the unwanted frequencies. The results are compared with optimal filters as well as the more standard band-pass filtering techniques.
De-convolution of the instrument response from seismic accelerograms is an essential step in the correction of seismic data and is used in the UEL methods A & B  as well as those of others [2,3,4,5]. Methods of de-convolution include time domain differential mapping  and frequency-domain de-convolution [1,2] using the Fast Fourier Transform (FFT) algorithm. The paper shows that de-convolution using the FFT produces an almost flat response characteristic over a larger frequency range than those methods using differential mapping.
It was demonstrated in , by comparing power spectral densities of various earthquakes, that band-pass filtering can remove too much energy. The consequences of this were manifest in the estimates of the total acceleration response spectra that produced errors of the order of up to 20% for certain seismic data. In order to try and mitigate this error one approach was to implement a least squares adaptive algorithm . Another approach, included and compared in this paper, is the application of the stationary wavelet transform  to de-noise seismic signals. The stationary wavelet transform (SWT) is shift invariant  and has the structure of an un-decimated filter bank  and is better suited to de-noising than the discrete wavelet transform (DWT). The latter is not shift-invariant and would degrade any de-noising using a thresholding  scheme.
In summary, when applied to strong-motion seismic data, the results produced thus far demonstrate that, over the Nyquist cycle, this approach removes less energy as expected with a wavelet transform. Moreover this approach is less computationally intensive than the previous adaptive methods used. Hence it is suggested that using the wavelet transform is a more efficient than adaptive methods and more effective than band-pass methods at removing unwanted frequencies in seismic accelerograms.
purchase the full-text of this paper (price £20)