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CivilComp Proceedings
ISSN 17593433 CCP: 81
PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 217
Using the Method of Total Least Squares for Seismic Correction A.A. Chanerley+ and N.A. Alexander*
+School of Computing and Technology, University of East London, United Kingdom
A.A. Chanerley, N.A. Alexander, "Using the Method of Total Least Squares for Seismic Correction", in B.H.V. Topping, (Editor), "Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 217, 2005. doi:10.4203/ccp.81.217
Keywords: correction, filter, seismic, wavelet, denoising, recursive, least squares, bandpass, filtering, filter, inverse filter, convolve, deconvolve.
Summary
Typical techniques used for seismic correction are necessary to: (i) digitise, that is equiand
upsample the data, (ii) detrend, (iii) denoise using the wavelet transform or bandpass
filter [1], using digital Butterworth, Chebyshev filters or digital Finite Impulse
Response (FIR) filters [8,9,10,11] (iv) correct for instrument characteristics (v)
downsample to an appropriate sampling rate. The sequence of the components (ii) to
(v) and the exact algorithms used in these correction techniques may vary significantly, as
can the resulting recaptured original ground motion itself.
Recent methods, which describe the deconvolution of an instrument response from seismic data, apply a leastsquares based, inverse, system identification method [1,3] with which to deconvolve the instrument response from the ground motion. Previous methods assume a second order, singledegreeoffreedom (SDOF) [8,10] instrument function and apply an inverse filter in the time or frequency domain, with which to deconvolve the instrument. Whereas in other cases, corrected seismic data [4] are not explicitly deconvolved, as a consequence of insufficient instrument parameter data. The advantage of the leastsquares based method is that it does not require any information regarding the instrument; it only requires the data, which the instrument has provided, from which to determine an estimate of the inverse of the instrument response. However, the least squares solution which minimises has been sought with the assumption that the data matrix is 'correct' and that any errors in the problem are in the vector . This paper applies the method of total least squares (TLS), [2,5,6,7] which allows for the fact that both and may be in error. A range of instruments and their performance are compared using Icelandic seismic data, digitally recorded and with instrument parameters included. These parameters are the viscous damping ratio and the instruments natural frequency. Four instrument types were compared, SMA1, DCA333, A700 and SSA1, each seismic record has details of the instrument parameters, but only one has some details of the antialias filter used in the instrument. Instrument performance was based on a comparison of instrument frequency responses obtained by deconvolution in the time domain using the QRRLS, deconvolution in the frequency domain using instrument parameters in the second order SDOF equation and the method of Total Least Squares (TLS). Correlation was good up to the cutoff frequencies, thereafter the rolloff between the methods differed in gradient, with both the TLS and QRRLS showing steeper gradients than that for the second order, SDOF response. This is consistent with the fact that digital instruments would have an antalias filter whose impression is embedded in the data. Details of such filters are not always included in the record. References
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