Theoretical and observed depth correction for Ms

Modal summation technique is used to generate 5000, three-component theoretical seismograms of Love and Rayleigh waves, assuming modi®ed PREM (PREM-C) and AK135F global earth models. The focal depth h and the geometrical fault parameters are randomly chosen so as to uniformly cover possible source mechanisms and obtain uniform distribution of log h in the interval 1 < h < 600 km. The amplitudes of 20 2-s waves measured on each of the synthetic seismograms yield curves of amplitude vs. depth, and consequently the theoretical surface waves magnitude depth correction for all three components of ground motion. Predicted surface wave amplitudes are practically constant for h < 20 km, then decrease with the focal depth. This decrease is not uniform, and depends on the excitation level of higher modes. For PREM-C model and for shallow sources, computed Love wave amplitudes are nearly an order of magnitude larger than those of Rayleigh waves, which is why the AK135F model is given preference over PREM-C. The theoretical depth correction ranges between zero, for shallow sources, to about +1 magnitude unit, for the deepest ones. The theoretical results are compared with 74,480 individual station measurements of 20-s surface wave amplitudes reduced to the same distance, period and seismic moment. It is found that empirical data closely match the predictions made by using the AK135F model.