Keywords: correction, filter, seismic, wavelet, de-noising, recursive, least squares, band-pass, filtering, inverse filter, convolve, de-convolve.

This method was used on synthetic and real seismic data [1,2] in order to determine its sensitivity to bursts of noise. These can be of short duration but large amplitude, which would usually be associated with unstable instrument operation, but can also occur as a naturally occurring transient. In this case the iterative re-weighted least squares (IRLS) method is applied as a general deconvolution technique [3,4,5] for de-coupling the instrument response from the seismic data in order to obtain an estimate of the true ground motion.

The least squares approach uses optimisation, however the IRLS is an algorithm for determining optimisations where . The algorithm applies different weighting at each iteration of the algorithm. The optimisation problem may be stated as however at each iteration the weights are calculated from the residuals, , the difference between the desired and predicted.

The seismic data used for the analysis is chosen as far as possible such that instrument parameters were available in the seismic record [6,7]. In particular this includes data from the SMART-1 array in Taiwan which provide some details of the anti-alias filter used. For other digital records without details of any anti-alias filter, these can be inferred from the sampling rate, on the assumption that an anti-alias with a cut-off at half the sampling rate would have been used.

The IRLS was applied to the seismic data after wavlet de-noiseing and correcting for the baseline, but without any frequency selective filtering. In addition wavelet decomposition is used for further analysis of seismic data by showing separately more of the low and high frequency details of the data.

1

J.B. Bednar, R. Yarlagadda, T. Watt, " Deconvolution and its Application to Seismic Signal Processing", IEEE Trans. on Acoustics, Speech and Sig Proc", Vol. ASSP-4, No. 6 pp 1655-58, December 1986. doi:10.1109/TASSP.1986.1165004

2

R. Yarlagadda, J.B. Bednar, T. Watt, "Fast Algorithm for Deconvolution", IEEE Trans Acoust., Speech, Signal Processing, vol ASSP-33 pp 174-182, Febb 1985. doi:10.1109/TASSP.1985.1164508

3

A. Chanerley, N. Alexander, "Using the Method of Total Least Squares for Seismic Correction", Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing, B.H.V. Topping, (Editor), Civil-Comp Press, Stirling, UK, paper 217, 2005. doi:10.4203/ccp.81.217

4

A. Chanerley, N. Alexander, "Novel Seismic Correction approaches without instrument data, using adaptive methods and de-noising", 13th World Conference on Earthquake Engineering, Vancouver, Canada, August 1st -6th, 2004, paper 2664.

5

A. Chanerley, N. Alexander, "A New Approach to Seismic Correction using Recursive Least Squares and Wavelet de-noising", Proceedings of the Ninth International Conference on Civil and Structural Engineering Computing, B.H.V. Topping, (Editor), Civil-Comp Press, Stirling, UK, paper 107, 2003. doi:10.4203/ccp.77.107

6

N. Ambraseys, et al "Dissemination of European Strong Motion Data", CD collection. European Council, Environment and Climate Research programme, 2000.

7

A.M. Converse, "BAP: Basic Strong-Motion Accelerograms Processing Software; Version 1.0", USGS, Denver, Colorado. Open-file report 92(296A), 1992.

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