Published laboratory investigations suggest an association exists between the ratio of seismic compressional and shear‐wave velocities [Formula: see text] and sedimentary rock lithology. Comparisons of some theoretical models with these laboratory studies suggest that crack, or pore, geometry has a stronger effect on observed [Formula: see text] values than elastic constants of the minerals comprising the matrix. Further, it can be inferred that the observed association between lithology and [Formula: see text] is a result of an association between lithology and distribution of pore and crack shapes. Direct observation of crack shapes for a variety of lithologies is a next step in strengthening these inferences. The present study reviews the empirical relations between [Formula: see text] and lithology and examines two published theoretical models of cracked elastic media. The models suggest that seismic velocities of sandstones may be controlled by cracks and pores with aspect ratios in the range of [Formula: see text] to 1, dolomite in the range of [Formula: see text] to [Formula: see text], and dense limestones, of generally low porosity, in the range of [Formula: see text] to [Formula: see text]. Direct observations of the aspect ratio of cracks and pores in sedimentary rocks would test these inferences and offer a basis for physical and geologic insight into lithologic interpretations of [Formula: see text] ratios.
A laboratory study of the effects of oriented pennyshaped inclusions embedded in a solid matrix on the propagation of seismic shear waves shows good agreement with theoretical predictions for some polarizations and poor agreement for polarizations at large crack densities. The models are constructed of solid matrix of epoxy resin with inclusions of thin rubber discs of approximately equal cross-sectional areas. The theoretical basis for these experiments is the theory of Hudson, in which the wavelength is greater than the dimensions of the individual cracks and their separation distance, and the cracks are in dilute concentration. By a pulse transmission method, seismograms were gathered in models free of inclusions and models with inclusions. Seismic measurements of velocity anisotropy, for variations in both a polarization and propagation direction, were performed on physical models with inclusions (cracks) representing five different crack densities (1, 3, 5, 7, and 10 percent). Variations in velocity anisotropy at different crack densities have been evaluated by using Thomsen’s parameter (γ) which relates velocities to their elastic constants, [Formula: see text]. Comparisons between experimental and theoretical results indicate that with the waves polarized parallel to the aligned inclusions, [Formula: see text] agree well with the theoretical model. However, shear waves for the same propagation direction but polarized perpendicular to the plane containing the inclusions [Formula: see text] produced results that agree well with the theory for crack densities up to 7 percent, but disagree for higher crack densities. The deviation of γ at 10 percent crack density suggests that crack‐crack interaction and their coalescence may be observable and could lead to seismic techniques to differentiate between microcracks and larger macrocracks.
Theoretically and experimentally, the shear‐wave velocity of a porous rock has been shown to be less sensitive to fluid saturants than the compressional wave velocity. Thus, observation of the ratio of the seismic velocities for waves which traverse a changing or laterally varying zone of undersaturation or gas saturation could produce an observable anomaly which is independent of the regional variation in compressional wave velocity. One source of shear‐wave data in reflection seismic prospecting is mode conversion of P waves to shear waves in marine areas of high water bottom P-wave velocity. A relatively simple interpretative technique, based on amplitude variation as a function of the angle of incidence, is a possible discriminant between shear and multiple compressional arrivals, and data for a real case are shown. A normal moveout velocity analysis, carefully coupled with this offset discriminant, leads to the construction of a shear‐wave reflection section which can then be correlated with the usual compressional wave section. One such a section has been constructed, the variation in the ratio of the seismic velocities can be mapped, and potentially anomalous subsurface regions observed.
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