A note on correction of strong-motion accelerograms for instrument response

Two methods for accelerometer instrument correction are described: (1) a direct numerical differentiation of recorded accelerograms from which high-frequency digitization errors have been filtered out and (2) an ideal "mathematical accelerometer" with a natural frequency significantly higher than the natural frequency of the recording instrument. Although both methods give good results, the first one is recommended for standard use. of critical. The recorded relative instrument response approximates accurately the ground acceleration in the frequency range from 0 cps to about ½ to ¼ of the natural frequency of the transducer. Thus, the direct instrument output can be used to represent ground acceleration up to about 5 to 15 cps. If information on higher frequencies is required, instrument correction of the recorded accelerogram must be performed. Modern computational methods in the dynamics of structures now require the accurate high-frequency part of the accelerogram, in order to determine the response of the higher modes of vibration. Detailed studies of earthquake source parameters and especially the studies aimed at the determination of the size of the earthquake dislocation surface and the effective stress call for the maximum possible accuracy in the high-frequency end of the Fourier amplitude spectrum of ground acceleration. Unlike the baseline correction of accelerograms (Trifunac 1970) considered by many investigators, the instrument correction problem was studied by only a few. Jenschke and Penzien (1964) proposed an approximate method for the accelerograph instrument cor- rection in response-spectrum calculations. Their method was based on a numerical approximation of the first derivative of an accelerograph transducer's recorded relative response, whereas McLennan (1969) derived an exact method to correct for accelero- meter error in the dynamic response calculations. The disadvantage in both of these methods was that they were designed to correct the response spectra and not the recorded accelerogram that serves as the basic input for all computations. In this paper, we present two different types of accelerometer instrument corrections. The first method, based on our previous work (Trifunac and Hudson 1970), uses direct numerical differentiation of an instrument response. This differentiation is performed after high-frequency digitization errors are filtered out from digitized data. The second method is the extension of McLennan's (1969) approach. It consists of computing the response of a high-frequency oscillator that has a natural frequency significantly higher than the accelerometer frequency.