A coda-envelope-inversion technique is developed to image the three-dimensional spatial distribution of relative scattering coefficients. The technique is applied to the Norris Lake Community, Georgia, earthquake swarm of 1993. The relative scattering coefficient is the ratio of the scattering coefficient to a regionally determined average used to normalize the coda amplitudes. The inversion problem was solved using the Algebraic Reconstruction Technique (ART) with the relative scattering coefficient constrained to positive values. Although coda envelope inversion is based on the theory for single scattering, we show that it may with a correction factor be used to characterize the distribution of relative scattering coefficients when multiple scattering contributes significantly to the coda. The coda envelope inversion for the Norris Lake Community earthquake swarm revealed a highly nonuniform distribution of relative scattering coefficients. The zones of strong scattering are correlated with the hypocenters and areas of rough topography. Moreover, at shallow depths the relative scattering coefficients are frequency dependent, with scattered energy increasing with frequency. We interpret this frequency dependence to imply that open fractures less than 250 m in length are responsible for strong scattering in the coda of these shallow earthquakes. At greater depths, scattering is independent of frequency and probably relates to velocity layering. A strong reflecting layer was identified at or below 7 km, which is consistent with the thrust plain identified in the Georgia COCORP reflection lines. The inhomogeneous distribution of scattering strength obtained in this study argues strongly against the observation-based assumption that the scattering structures are uniformly distributed in the crust.

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