Band limited ridge regression deconvolution of vibroseis data

Owing to the band limited nature of seismic data, ridge regression plays an important role in the processing and particularly in the deconvolution of seismic sections. To improve the condition number of the autocovariance matrix a ride regression parameter (RRP) is added which is a small fraction of the zero-lag autocovariance value. As pointed out by Berkhout, the size of the RRP is important since it affects the phase of the residual wavelet. In a previous work, Matsuoka and Ulrych explored this property of the RRP by considering the effect of very large values of this parameter on the deconvolution of Vibroseis data. In this paper we briefly summarise our previous findings and extend the method by considering the effect of band limited ridge regression on the deconvolution of Vibroseis data. We call this approach BLRR deconvolution and we develop a theoretical justification for its use. We show that the use of BLRR is effective in the removal of not only short- and long-period multiples, but also in the deconvolution of phase shifted and attenuated wavelets. The latter result is of particular importance, since, as shown by Gibson and Larner, the conventional phase corrected deconvolution is not effective in low-Q environments. The determination of the value of the BLRR parameter in this work is accomplished by monitoring a modified form of the Varimax of the deconvolved trace. The use of the Varimax norm was suggested by Levy and Oldenburg as a measure of phase distortion, and we have found it to be of particular value in deconvolution studies.