1/f Geology and Seismic Deconvolution

Abstract

The reflection seismic problem in geophysics involves the generation near the surface of a seismic wavelet which propagates downwards to reflect from layers in the ground. The returning reflections carry information about depth and velocities but they also generate multiple reflections, making the resulting trace at the surface very hard to interpret. The signal must be deconvolved with an appropriate filter. The common practice in seismic deconvolution is to assume that the reflection sequence is uncorrelated; that is, it has a white power spectrum and a delta function auto-correlation. This means that the acoustic impedance function must have a spectrum proportional to 1/f2 (where f is frequency) which is characteristic of a non-stationary Brownian process. We propose that the power spectrum of the acoustic impedance function is 1/f, which is stationary. This corresponds to a reflection sequence having a power spectrum proportional to f and a negative auto-correlation at small lags. This behaviour in reflection sequences has been seen before and we show it again in a well off Newfoundland.