Characterizing intrinsic and stratigraphic Q in VSP data with information measures
Short-period multiples in finely layered geological media modify a seismic pulse as it propagates. This effect, called stratigraphic filtering, or extrinsic attenuation, is characterized by strong attenuation and dispersion of seismic amplitudes. It is similar to, and in fact very difficult to distinguish from, the effect produced by processes of seismic amplitude loss due to friction (or intrinsic attenuation). This is an important and difficult fact for interpreters of seismic data, because it means that similar data signatures are produced by very different geological and petrophysical features of the Earth. In this thesis I seek data analysis methods with the ability to amplify small differences produced by the processes of intrinsic attenuation and stratigraphic filtering, with the aim of discriminating between the two. In a zero-offset vertical seismic profiling (VSP) data set, at any instant in time we have access to a snapshot of the seismic wavefield along the principal direction of wave propagation. In practice, such a snapshot has the form of discrete amplitude values being assigned to each of a set of discrete depth values. Regarding this snapshot as a “message”, made up of a sequence of “letters”, or amplitude values, drawn from an “alphabet” of allowable amplitudes, permits the data to be analyzed using information-theoretic methods. For instance, Shannon entropy, which measures the degree of disorder within a message, can be assigned to each snapshot, and the time evolution of this number can be determined directly from a VSP data set. It is hypothesized that processes of intrinsic and extrinsic attenuation cause significant and measurable differences in the evolution of the entropy, which means this information measure could be utilized to help distinguish between the two. I analyze this with synthetic VSPs based on real well-log data, pointing out the important role of amplitude bin size in this information measure and the variability of results that should be expected as bin size changes. I point out with these examples that intrinsic and extrinsic attenuation processes tend to have opposite influences on entropy versus time curves. A field data set example is suggestive that the relative strength of stratigraphic filtering and intrinsic attenuation can be estimated in this way.