Strong ground motion scaling relations for the Central United States cannot be obtained by applying regression analysis to the existing, sparse data base. Adaptation of the corresponding Western United States data base must be done carefully because the important problems of differences in regional anelastic attenuation, magnitude scales, and earthquake source physics still have to be resolved. Until this is done, empirical relations have to be adapted, but some test of their validity must be made. Since the Central United States data set is not a valid test, synthetic seismograms can be used to test some of the assumptions and results.
The Central United States ground motion scaling problem differs from usual experience in that the nature of ground motion scaling at distances greater than 100 km from the source is of utmost importance. Numerical techniques are used to generate SH time histories in a four layer Central United States earth model. A study of model parameters indicates that simple deductions based on the scaling of pulses are applicable to the high-frequency surface wave trains at large distances and that spatial attenuation for these waves should be of the form
An attempt to apply the results of the numerical study to the existing Central United States data base is not too impressive because of the limited frequency range of the synthetics and lack of detailed knowledge about earth structure in the Mississippi embayment, from which the actual data were obtained.