A scheme for expressing instrumental responses parametrically

Abstract

This study shows that, provided a seismic instrument as a whole behaves linearly over its response range, and provided its phase response is known accurately, the instrumental responses can be parametrically expressed in terms of transfer functions of linear systems. The scheme is based on the observation that knowing accurately the detailed overall amplitude and phase responses of a linear instrument is tantamount to knowing all the pertinent constants for the construction of its overall transfer function. Because of generally poor quality of empirical phase calibrations, empirical phases are substituted by minimum phases, calculated via a Hilbert transform of amplitude response. Application of the scheme to actual SRO (LP) and USGS (SP) instruments resulted in sufficiently close agreements between parametric and actual responses to warrant the utility of the scheme.