Physical seismic modelling of shear-wave singularities on a sphere of orthorhombic phenolic: A research note

R. James Brown and Eric V. Gallant


A great deal of theoretical development and numerical modelling of seismic anisotropic wave propagation has been carried out, particularly within the last decade. Only within the past few years have a half dozen or so institutions begun scaled laboratory experiments, or physical modelling, to determine how well the various numerical schemes predict the actual physical results. A particular numerical modelling algorithm might be inadequate for several possible reasons, for instance: the basic theoretical assumptions on which the model rests may be in partial error or incomplete; the algorithm itself might involve computational approximations, perhaps to make the problem numerically tractable, that introduce significant error; or the routine might be derived on an idealized basis that is somewhat at variance with the physical reality (e.g. an elastic model representing an anelastic reality). There is therefore considerable interest on the part of seismic anisotropists to compare the results of numerical and physical modelling for which "the same medium" is used in the modelling procedure, that is, using input parameter values (e.g. stiffnesses, velocities) for a numerical "experiment" that are identical to those of the particular physical medium used in the corresponding laboratory experiment.

One such area of interest, at present, is in the behaviour of shear waves near special directions of propagation known as singular directions or singularities, which occur at places where the two shear-wave phase-velocity surfaces meet (i.e. touch or intersect). Near the commonest kind of singularity, the point singularity, a shear wave might exhibit anomalous behaviour, such as rapid variation in polarization or amplitude, similar to what might be observed near cusps on the group-velocity surface, even when the anisotropy is not sufficiently strong to cause cusps (Crampin and Yedlin, 1981; Crampin, 1991). Point singularities have now been recognized by Bush and Crampin (1987) and Bush (1990) in VSP data from the Paris Basin, and such observations may become increasingly important in exploration seismology, not least because point singularities may well occur along nearly vertical raypaths in sedimentary basins. If it were possible to determine the directions of such singularities, it could place tight constraints upon the nature of the internal anisotropy of the rockmass (Crampin, 1991).

Our objectives in this physical modelling work are, in the short term, to look for singular directions in an orthorhombic modelling medium, to examine the variations in polarization and amplitude near such directions, and to compare our physical results with numerical results obtained by collaborators; and in the long term, to elaborate how one might use singularity-related observations in exploration and/or development, and to develop the necessary processing code required to this end.

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