A brief review of instrument de-convolution of seismic data

Most corrected seismic data assume a 2nd order, single-degree-of-freedom (SDOF) instrument function with which to de-convolve the instrument response from the ground motion. Other corrected seismic data is not explicitly de-convolved, citing as reason insufficient instrument information with which to de-convolve the data. Whereas this latter approach may facilitate ease of processing, the estimate of the ground motion cannot be entirely reliable and therefore methods of deconvolution have been suggested and described in [1, 2, 4 ,5]]. This paper reviews a relatively straightforward implementation of the well-known recursive least squares (RLS) algorithm in the context of a system identification problem [4]. The paper then goes on to discuss the order in which implementation of the RLS algorithm should be applied when correcting seismic data. Noise reduction is typically achieved by de-noising using the discrete wavelet transform [8, 9] or filtering the resulting de-convolved seismic data. De-noising removes only those signals whose amplitudes are below a certain threshold and is not therefore frequency selective. Standard band-pass filtering methods on the other hand are frequency selective, but different cut-off frequencies for band-pass filters are applied in different parts of the world when correcting seismic events. These give rise to substantial differences in power spectral density characteristics of the corrected seismic data