Application of Cesàro mean and the L-curve for the deconvolution problem

Abstract

In this paper, the Cesàro mean technique is applied to regularize the divergent problem which occurs in ground motion deconvolution analysis in geotechnical engineering. To deal with this ill-posed problem, we use the corner of the L-curve as the compromise point to determine the optimal order of Cesàro mean so that the high frequency content can be suppressed instead of engineering judgement using the concept of a cutoff frequency. The fractional order of Cesàro mean has been derived and used to fulfill this purpose. From the examples shown, it is found that the wave form including maximum acceleration can be accurately predicted and that both the high frequency content and divergent results can be avoided by using the proposed regularization technique.