Multiple reflections constitute an important source of "noise" on seismograms. Because multiples are related to the primary reflectivity function r(t) in a very complicated way, the suppression of all multiple reflections on a single seismic trace is unlikely without a detailed knowledge of the reflectivity function itself.This paper describes a series of approximations in which multiple reflections are decomposed into component subsets. For certain types of velocity functions, one or two of these subsets form a sufficiently good approximation to the complete multiple process to at least predict the strongest multiples present on a field seismogram. The subset approximations to the complete multiple function include the first-order surface multiples, i.e., three-bounce multiples having a second reflection at the surface. The expression for this set of multiples is m s1 (t) = -R o r(t)*r(t), where the * stands for convolution, and R o is the surface reflection coefficient. Computations of this set are compared with the complete multiple function for logs from Alberta, Canada, and southern Mississippi. A further approximation, called the M s1 (t), is valid in areas where a few reflection coefficients, r(t), are responsible for the bulk of the multiple noise. M s1 (t) consists of all first-order surface multiples which have a contribution from the r(t) zone. The above-mentioned velocity logs are used to illustrate the M s1 (t) approximation. The M s1 (t) function is compared with the complete first-order surface multiple function for the two logs. A method for suppressing the multiples described by the approximations is proposed. The technique is illustrated for the M s1 (t) approximation but can be extended to higher-order approximations. It consists of a positive feedback circuit in which a reflectivity function is simulated along with appropriate time-variant gain adjustments. In order to realize the computation, it is necessary to find the time and amplitude of the reflection coefficients responsible for the large-amplitude multiple reflections. Several methods for providing this information are discussed and a correlation search technique is illustrated with examples. Finally, the suppression technique is illustrated with live seismic data on two record sections from two different areas showing data before and after multiple suppression. In both cases the M s1 (t) approximation was adequate.

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