abstractWe present a rapid and accurate method of calibrating seismic systems using a random binary calibration signal and cross-spectral techniques. The complex transfer function obtained from the cross spectrum is least-squares fit to the ratio of two polynomials in s(s = iω) whose degrees are determined by a linear systems analysis. This provides a compact representation of the system frequency response. We demonstrate its application to two seismic systems, the IDA and SRO seismomenters. This method yields calibrations to an accuracy of better than 1 per cent in amplitude and 1° in phase.