- See Section 2.99.
- Response parameter is pseudo-acceleration for 5% damping.
- Ground-motion model for PSA to PGA ratio is:
- Regress on ratio of PSA to PGA ratio because more stable than regression on absolute values.
- Choice of functional form guided by numerical simulations and previous empirical studies. Numerical simulations suggest that strike-slip events maybe more likely to show near-field directivity effects at long periods than dip-slip events.
- Data does not allow magnitude dependency to be reliably determined hence not modelled.
- Judge whether long period motion is realistic based on consistency of amplitudes and timing of long period energy and that of higher frequency motions. Expect that seismic ground motions have consistent phase structure at long periods whereas noise will have random phase. Examine the analytical derivative of the phase with respect to frequency and chose the upper period of reliable PSAs based on the period at which the phase derivative becomes more random.
- Only use PSAs for frequencies greater than 1.25 times the high-pass filter corner frequency and for periods less than the shortest period at which phase derivative is not well behaved. Note that these criteria tend to bias regression to larger spectral values because these will be above noise level more often than smaller motions. Do not try to correct for this bias.
- For ≥ 10s insufficient data to yield stable coefficients. Based on numerical simulations, find response spectra are approximately flat for > 8s and M < 7.5 and, therefore, extend model to 20s by assuming constant spectral displacement. Note that may not be appropriate for M > 7.5.
- Note that Loma Prieta is major contributor to dataset, which may explain strong distance dependency of spectral shape.