Digital calculation of response spectra from strong-motion earthquake records

Abstract

This report presents a numerical method for computing response spectra from strong-motion earthquake records. The method is based on the exact solution to the governing differential equation and gives a three to four-fold saving in computing time compared to a third order Runge-Kutta method of comparable accuracy. An analysis was made of the errors introduced at various stages in the calculation of spectra so that allowable errors could be prescribed for the numerical integration. Using the proposed method of computing or other methods of comparable accuracy, example calculations show that the errors introduced by the numerical procedures are much less than the errors inherent in the digitization of the acceleration record. Included as appendices to the report are computer programs in Fortran IV, with instructions for their use, for computing spectra, for correction of the baseline of the digitized record, and for the computation of ground velocity and displacement.