Pre event record of a digital accelerograph is modelled as coloured noise and a scheme is developed which uses adaptive filter to remove instrument and the background noise from the record of digital accelerographs. The effectiveness of the proposed scheme is shown by analysing a record of digital accelerograph. In this example it is first shown that the pre event of the record can be modelled as coloured noise. The proposed scheme is then used to remove the noise adaptively from the recorded acceleration. Comparison of Fourier spectra of pre event record, uncorrected and corrected accelerogram show that noise which was pesent in the uncorrected accelerogram has been satisfactorily removed. Although in this work the scheme has been implemented off-line but it can be used as on-line filter in digital accelerographs. This is perhaps one of the ways by which an accelerograph can also perform the function of a micro earthquake recorder.