This study is a comprehensive numerical investigation of the Lg-wave geometrical spreading for vertically inhomogeneous media. I modeled a suite of source and path parameters and measured different Lg amplitudes including root-mean-square (rms), peak-to-peak, third-peak (Nuttli, 1980; Patton, 2001), envelope-peak, and spectral amplitudes for analysis.
The main result of this investigation is that the estimation of Lg spreading rates from the rms amplitudes and from the spectral amplitudes yielded the most reliable estimates that are basically independent of almost all the source and path variables within the parameter ranges that I simulated. I obtained a spreading rate of Δ-1.0 for the rms amplitude and a rate of Δ-0.5 for the spectral amplitude across the frequency band of the data. The relationship between the two spreading-rate estimates is consistent with Parseval's theorem.
Spreading-rate estimates from other amplitude measurements show larger variations with the variation of source and path parameters. These variations suggest that the behavior Lg peak amplitudes might be more complex than that of a single-mode Airy phase. The decay of the third-peak amplitudes appears to be less rapid than the decay of the peak-to-peak and envelope-peak amplitudes.
There are no systematic changes in the spreading rates due to the variation of variables such as velocity model, source depth, and source mechanism. The introduction of a gradient zone at the crust-mantle boundary and the earth-flattening transformation did not change the spreading rates significantly, at least not beyond certain source-receiver distances. The most important variable affecting the Lg spreading appears to be the closeness of the source to major velocity discontinuities in the velocity models.