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CivilComp Proceedings
ISSN 17593433 CCP: 77
PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 107
A New Approach to Seismic Correction using Recursive Least Squares and Wavelet DeNoising A.A. Chanerley+ and N.A. Alexander*
+School of Computing & Technology, University of East London, England
A.A. Chanerley, N.A. Alexander, "A New Approach to Seismic Correction using Recursive Least Squares and Wavelet DeNoising", in B.H.V. Topping, (Editor), "Proceedings of the Ninth International Conference on Civil and Structural Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 107, 2003. doi:10.4203/ccp.77.107
Keywords: correction, filter, seismic, wavelet, denoising, recursive, least squares,.
Summary
This paper begins with a brief introduction to some methods used to correct seismic
data [1,2,3]. Most corrected seismic data [3] assume a 2nd order,
singledegreeoffreedom (SDOF) instrument function with which to deconvolve the instrument
response from the ground motion. Other corrected seismic data [7] is not explicitly
deconvolved, citing as reason insufficient instrument information with which to
deconvolve the data. Whereas this latter approach may facilitate ease of processing, the
estimate of the ground motion cannot be entirely reliable. This paper discusses a
relatively straightforward implementation of the wellknown recursive least squares
(RLS) algorithm in the context of a system identification problem. The resulting
inverse filter is then applied to the data in order to deconvolve the instrument
response.
The RLS algorithm was chosen in preference to the least mean squares (LMS) adaptive algorithm. The RLS algorithm has only one parameter to adjust in a relatively straightforward manner. This parameter is exponentially weighted and is called a forgetting factor, , in the literature. On application it reduces the effect due to previous error values. The RLS algorithm is dependent on the incoming data samples rather than the statistics of the ensemble average as in the case of the LMS algorithm. This means that the coefficients will be optimal for the given data without making any assumptions regarding the statistics of the process, also the algorithm has a higher rate of convergence than the LMS. The RLS has a variant, which is used to produce the results in this presentation. It is numerically more stable than the direct algorithm. This is the QR decompositionbased RLS algorithm deduced directly from the squareroot Kalman filter counterpart. The QRRLS adapts by first updating the square root of the correlation matrix, , and then updating the filter weights using . The papers then discuss the implementation of the translation invariant wavelet transform [5,6] in order to denoise [4] rather than filter the resulting seismic data. Ideally, noise errors should be removed before any instrument correction is applied, since deconvolution may amplify the noise within a seismic data set. However standard procedures for correcting seismic data [2,3,4] apply a bandpass filter on the resulting data available, after performing a 2nd order instrument deconvolution. This is necessary since prefiltering first, would render deconvolution after, a redundant exercise. Nevertheless, even postfiltering after deconvolution as is the general case alters the data set and for the same reason, can no longer adequately represents the true ground motion, since the filtering will remove some of the true ground motion data from the seismic set. Wavelet denoising however removes only those signals whose amplitudes are below a certain threshold. Denoising is not frequency selective and cannot affect the data in the same way. Therefore it is proposed that wavelet denoising be implemented prior to deconvolution. It is considered that even if the specification on the type of instrument used to record the seismic event is available, then the QRRLS algorithm is still a better choice for inverse filtering the resulting data to obtain a better representation of the true ground motion. References
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