Influence of a thin layered viscoelastic surface zone on seismic traces recorded at the earth's surface
P. F. Daley, Edward S. Krebes
The influence of a thin layered viscoelastic surface zone on the reflected SH wavefield in a simple model consisting of a single layer over a halfspace is investigated. This thin weathering zone is generally assumed to be composed of any number of layers as long as the "thin" assumption is retained. The free surface vacuum - solid interface is replaced by this zone of finite thickness, which is assumed small when compared with the predominant wavelength which is defined in terms of the predominant frequency of the band limited wavelet employed and the near surface velocity. A ray-reflectivity analogue of the surface conversion coefficient is derived and comparisons of synthetic traces computed for an elastic and viscoelastic thin surface zone are made. For surface receiver seismology the effect of the viscoelastic versus elastic response detected by the receivers should be examined in that all deeper reflections within the structure must pass through this layer before being recorded at the geophones and all are consequently affected in some manner.
The seismic velocity of the surface layer is very often the lowest when compared with the velocities in the underlying geological structure and it is not uncommon for the impedance contrast of the weathering layer and the subsequent layer to be relatively high. As matrix methods are employed to obtain an analogous expression for the traditional surface coefficient, the full seismic response of the thin layered zone is inherent in the expression. Combining this with a high impedance contrast and the frequency, incident angle and zone thickness dependence of the surface conversion coefficient analogue could possibly lead to a ringing event being recorded at the surface. There could also be gaps in the frequency amplitude spectrum due to so-called "tuning" effects.
SH wave propagation is used to explore this problem due to its simpler nature when compared with the coupled P-SV problem. As might be expected there is a trade off in that the effects of introducing this concept into the P-SV case can be much more pronounced than those for the SH case. However, it is necessary to introduce displacement potentials in the P-SV case to determine the thin layer propagator matrices, introducing added complication into an already complex problem. In the SH derivation this step is bypassed, after a fashion, as the results obtained using potentials are the same as those using displacements.