Comment on "An Upper Bound on Rg to Lg Scattering Using Modal Energy Conservation" by Jeffry L. Stevens, Heming Xu, and G. Eli Baker

Reply to "Comment on 'An Upper Bound on Rg to Lg Scattering Using Modal Energy Conservation' by Jeffry L. Stevens, Heming Xu, and G. Eli Baker" by Howard Patton and Indra N. Gupta

“…Patton and Gupta's (2009) equation 5 is identical to Stevens et al's (2009) equation 19 for a step function explosion source (Patton and Gupta [2009] also include a Mueller-Murphy source spectral shape, so results will differ slightly for larger events). It should be remembered, however, that this is an upper bound based on 100% energy conversion, not a prediction for the actual size of the signal.…”

“…As Patton and Gupta (2009) point out, there is a great deal of variability in shallow structure, particularly at the NTS, and in general velocities are lower at shallower depths. However, Patton and Gupta (2009) attribute an unphysical seismic amplification to these shallow, low-velocity layers, and we do not think their source model is meaningful. Specifically, we refer to their placement of the CLVD and spherical explosion source components in media of dramatically different velocities without adjusting the moments.…”

“…Specifically, we refer to their placement of the CLVD and spherical explosion source components in media of dramatically different velocities without adjusting the moments. The hypothesis of Patton and Gupta (2009) is that the moment of the secondary source is constant, independent of material properties above the source, which would imply very large differences in Lg excitation across NTS due to the variability of material properties at shallow depths.…”

“…In our paper (Stevens et al, 2009), we put the CLVD at 2=3 of the explosion depth because that was consistent with those results; and, given the shape of the nonlinear deformation region due to the change in overburden pressure with depth, we would expect the CLVD to be shallower than the explosion source. Patton and Gupta (2009) add a very-low-velocity surface layer in the upper 550 meters and put the CLVD source at 300 meters with the explosion source in the higher velocity medium below, retaining the moments for both explosion and CLVD that we used in our calculations. This is not the same source.…”

“…To see the effect of this, consider the far-field P waves generated by these two sources. Figure 1 shows the far-field P wave from explosion and CLVD sources at 600 and 300 meters depth, respectively in our structure and the structure from Patton and Gupta (2009). These are downgoing P waves leaving the bottom of each structure toward a distant station generated using the method of Bache and Harkrider (1976).…”