4.42 Dahle et al. (1991)

• Ground-motion model is:
  
  this equation assumes spherical spreading (S waves) to R₀ and cylindrical spreading with dispersion (Lg waves) for larger distances.
• Response parameter is pseudo-velocity for 5% damping.
• All data from solid rock sites.
• Follow-on study to Dahle et al. (1990b) and Dahle et al. (1990a) but remove Chinese and Friuli data and data from border zone of Eurasian plate, so data is a more genuine intraplate set.
• Use 395 records from Norwegian digital seismograms. Require that the Lg displacement amplitude spectra should have a signal-to-noise ratio of a least 4 in the frequency range 1–10Hz, when compared to the noise window preceding the P-wave arrival.
• For the selected seismograms the following procedure was followed. Select an Lg window, starting at a manually picked arrival time and with a length that corresponds to a group velocity window between 2.6 and 3.6km∕s. Apply a cosine tapering bringing the signal level down to zero over a length corresponding to 5% of the data window. Compute a Fast Fourier Transform (FFT). Correct for instrument response to obtain true ground motion displacement spectra. Bandpass filter the spectra to avoid unreasonable amplification of spectral estimates outside the main response of the instruments. Passband was between 0.8Hz and 15 or 20Hz, dependent on sampling rate. The amplitude spectra obtained using the direct method, using A = Δt where Δt is time step and Z is Fourier transformed time-history and Z^* is its complex conjugate. Convert instrument corrected displacement Lg Fourier transforms to acceleration by double differentiation and an inverse FFT.
• Use 31 accelerograms from eastern N. America, N. Europe and Australia.
• Use R₀ = 100km although note that R₀ may be about 200km in Norway.
• Correlation in magnitude-distance space is 0.20.
• Use a variant of the two-stage method to avoid an over-representation of the magnitude scaling terms at small magnitudes. Compute average magnitude scaling coefficients within cells of 0.2 magnitude units before the second stage.
• Resample data to make sure all the original data is used in a variant of the one-stage method. Compute new (resampled) data points as the average of one or more original points within a grid of cells 160km by 0.4 magnitude units. Correlation in resampled magnitude-distance space is 0.10.
• Find estimated ground motions from one-stage method systematically higher than those from two-stage method particularly at short distances and large magnitudes. Effect more significant for low frequencies. Find that this is because one-stage method gives more weight to supplementary accelerograph data from near field of large earthquakes.
• Standard deviations similar for one- and two-stage equations.
• Scatter in magnitude scaling coefficients from first stage of two-stage method is greater for strong-motion data.
• Try fixing the anelastic decay coefficient (c₄) using a previous study’s results. Find almost identical results.
• Remove 1 record from Nahanni earthquake (M_s = 6.9) and recompute; only a small effect.
• Remove 17 records from Saguenay earthquake (M_s = 5.8) and recompute; find significant effect for large magnitudes but effect within range of variation between different regression methods.