Results in the $(p,\tau)$ domain

All the results that I will show in this paper are for a simple two layer model. The bottom half space is isotropic and of very low density so that there is a very high reflectivity for most angles. The surface layer is highly anisotropic. It has orthorhombic symmetry with a horizontal plane of symmetry. The medium is expected to exhibit triplication in the propagation of shear waves. Most of the examples are for the response to a horizontal traction applied along the vertical symmetry plane. In figure  I show the $(p,\tau)$ domain response for a run with no multiples and no direct arrivals. The $(p,\tau)$ domain response is found by taking the inverse fourier transform of the $(p,\omega)$ domain data that I have calculated. The plot shows the x-component of displacement. The uppermost event is the P-P wave reflection. The second event is the P-S and S-P reflections. The third event which exhibits a downwards concavity in the wavefront is the S-S wave reflection. The range of p values used did not extend far enough to observe all of the propagating S-waves. Figure  shows the same model but in this case the direct arrivals have been calculated. Figure  shows the same model with the first order multiples calculated. The P-P-P multiple is almost hidden behind the S-S arrival. The final event is the S-S-S-S arrival, in between there are multiples with mixed wavetypes, P-P-P-S, P-P-S-S, and P-P-P-S. This figure is already somewhat confusing. One advantage of the phase shift method is that I can easily ``turn off'' some of these events to obtain a clearer picture.

 

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Figure 7 Primaries only data in the $p-\tau$ domain. Traction applied along x-axis, velocities measured along x-axis.

 

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Figure 8 Primaries + direct arrivals in the $p-\tau$ domain. Traction applied along x-axis, velocities measured along x-axis.

 

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Figure 9 Primaries and first order multiples in the $p-\tau$ domain. Traction applied along x-axis, velocities measured along x-axis.