Synthetic seismograms that include multiples and transmission coefficients have been obtained by solving the boundary value problem for the multilayered half-space exactly for the plane wave case at normal incidence. The computations of 4 seismograms of interest have been programmed for the IBM 704. The seismograms differ in location of source and detector, i.e., whether buried or at the surface of the half space and whether or not this surface is a stress free surface. Evaluation of the computer programs prior to synthesizing seismograms is accomplished by comparing computer with analytical solutions of simple problems. The significance of multiples to the total reflected signal depends on the vertical distribution of acoustic impedance. For small contrasts in acoustic impedance distributed throughout the section, multiples are relatively insignificant. For moderate contrasts similarly distributed, multiples can produce discrete events, cause phase shifts in large amplitude direct reflections, and alter the frequency of weak direct reflected signal. If the near-surface contrasts are large, then multiples within these layers can mask a direct reflected signal from depth by producing "ringing" or "wave training." The present analysis gives a more reasonable explanation of "ringing" records than has been given heretofore. It is evident when comparing synthetic seismograms, including multiples with field seismograms, that the predicted multiple contribution in many cases is greater than actually present, indicating that the mathematical model on which computation is based is not yet adequately realistic.

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