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- W2093448980 abstract "Reflection imaging and inversion methods derive their existence from the presence of singularities in the earth’s material properties that carry the waves. Coherent reflections emerge at these singularities and the aim of this paper is (i) to characterize these singularities locally by Holder scaling exponents and globally by multifractal singularity spectra; (ii) to understand how the singularity structure is mapped from space, the medium, to space-time, the wavefield. The types of media under consideration within (exploration) seismology require such a generalized representation – one beyond those defined by piece-wise smooth functions – because of the complexity inherent in the spatial variability of the medium properties. The proposed generalization permits (i) a broader class of singularities; (ii) an accumulation of the singularities. Subsequently this paper addresses the implications of the generalization by (i) empirically establishing a link between the medium’s and reflection wavefield’s global singularity structure; (ii) finding a theoretical explanation for this link. The latter appears to be difficult within the current wave theory which lacks reference to scale. Therefore a critical re-evaluation is made of the assumptions underlying the current wave theory. It is conjectured that the theory may be generalized in order to contain reference to scale and scale dynamics." @default.
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- W2093448980 date "1998-01-01" @default.
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- W2093448980 title "Evidence of scaling for acoustic waves in multiscale media and its possible implications" @default.
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- W2093448980 doi "https://doi.org/10.1190/1.1820248" @default.
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