A homomorphic system is used to map the convolution of a source function with the impulse response of the earth into the sum of the log spectra of the source function and the earth's response. If the source function is considered stationary and the earth's response spatially nonstationary, by averaging the log spectra of several reflection records, the log spectrum of the source function will be enhanced and the log spectrum of the earth's response will average out. An inverse homomorphic system maps the average log spectrum to an estimate of the source function. The source function is then deconvolved from reflection records. Application of log spectral averaging as a method of deconvolution to a seismic reflection profile obtained in a shallow water-geologically complex area indicates the homomorphic technique to be an effective method for suppressing the air gun bubble pulse oscillation.

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