Abstract

The use of normal modes to represent the propagation of elastic waves at large horizontal offset is well known. By addition of the relevant leaky modes, the mode theory is shown to be useful for representation of the seismograms at shorter range. A theoretical model consisting of a 2-cm brass layer over a steel half-space is considered. Dispersion curves and excitation functions are computed for the first four normal modes and the first three PL modes. Attenuation as a function of frequency also is computed for the PL modes. A suite of seismograms is computed for the distance range 50-70 cm, showing each mode individually and their sum (the total seismogram). It is found that, for the distances used, the individual modes do not approximate transients with a definite 'arrival' time. Only their sum is required to exhibit this physical behavior. In addition, at short distances, the dispersion of a single mode is not visually obvious although the dispersion curve may be recovered by use of Fourier transform methods. Determination of the dispersion curves from the total seismogram is more difficult and requires some separation of the modes, as they overlap in frequency and velocity. This work shows the preponderance of the leaky modes in the early part of the seismogram and indicates their importance in the later part of the seismogram for short horizontal offset.

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