MODELING OF SURFACE WAVES USING FINITE-DIFFERENCE FORMULATION

MODELING OF SURFACE WAVES USING FINITE-DIFFERENCE FORMULATION O. Ádám, L. Hermann, B. Neducza

Eötvös Loránd Geophysical Institute, P.O.Box 35, Budapest, H-1440, Hungary

The ground roll, in fact, comprises two wave types: The first and of highest intensity is the vertically polarized transverse wave (SV); the second and of lower intensity is the Rayleigh wave consisting of one cycle, eventually of two cycles. The different components of the former travel in different wave–guides and the individual components are results of different phenomena. The ground roll is associated with certain loose unconsolidated young sediments in Hungary. Such are, e.g. the loess covered SW part of the country, and other "rolling" areas of Transdanubia with deep groundwater level. Beside this, there are "ground–rolling" areas in the Great Plain, too, where the groundwater table lies close to the surface, but the very loose and unconsolidated alluvial overburden offers extremely poor energy transfer and it is an excellent ground roll generator. The ground roll – owing to the surface wave character of its components – is attached to the uppermost few m thick weathered layer. Usually the Rayleigh, Sezawa M1, M2 waves and Love wave combinations have been recognized in the model experiments made up to now. Guided waves are rarely mentioned in the literature. The problem has been solved in general only up to the determination of the wave types and their main parameters.
The parameters of the wave–guide are determined by the traveltime curves of a special spread using low frequency vertical geophones (Fig. 1). The traveltime curves can be approximated by a power function (Fig. 2). The velocities of the P and SV waves vary very rapidly near the surface. Different phases of the seismogram show clearly the same curved traveltime curves. That means that all of the phases represent different penetration depths of the wave train, characterized by forward and backward trajectories.
	Figure 1.

Figure 2. Finally, to check the assumption a finite difference algorithm was applied. Results of the finite difference scheme are shown in Figs. 3 and 4. Figure 4 shows the calculated seismogram using a Gaussian beam source in a vertically varying velocity field. Comparison of the two figures demonstrates the very good agreement. The snapshots of calculation are shown in Fig. 3 (at 60, 120, 180 ms). These results verify the validity of guided wave assumption.
	Figure 3.
We are using this software to modeling seismic refraction and reflection method before or after measuring	REFERENCES Ádám, O., 1969, Analysis of the Seismic Ground Roll: Acta Geodaet.: Geophys. et Montanist. Acad. Sci. Hung., 4, pp. 95-133 Kelly et al., 1976, Synthetic seismograms: A finite-difference approach: Geophysics, 41, 2-27 Emerman et al., 1982, An implicit finite-difference formulation of the elastic wave equation: Geophysics, 47, 1521-1526 Jean Virieux, 1986, P-SV wave propagation in heterogeneous media: Velocity-stress finite-difference method: Geophysics, 51, 889-901

Figure 4.
This paper was presented in the poster session at the 2nd EEGS European Section Meeting in Nantes (France), September 2-5, 1996.