Is ray theory adequate for reflection seismic modelling? (A survey of modelling methods)

The region of the Earth of interest far reflection seismology is characterised by rapid fluctuations in properties with depth superimposed on a smoother trend of general increase in seismic velocity with depth, together with significant horizontal variations. Since most hydrocarbon deposits are to be sought in traps formed by lateral contrasts it is most important that modelling techniques should give as accurate a representation of the seismic wave field as possible in a complex medium. In deep reflection seismology designed to look at the whole crust, the principal features of interest, such as thrusts, have often to be mapped by their expression in terms of horizontal changes in reflection character. Any successful modelling scheme must therefore be able to cope, at the very least, with major horizontal and vertical variations in seismic properties. Incorporating fine-scale structure is difficult and for the time being may have to be done via the use of one-dimensional models (adjusted for appropriate ray paths) or by the association of reflection sequences with interfaces. At 30 Hz a typical P-wavelength would be 100 m, which is larger than the scale on which both horizontal and vertical resolution is desired. We are therefore in a rather 'grey' zone, ill-served by current mathematical techniques for wave propagation, At high frequencies ray based methods are appropriate, and at low frcquencies purely numerical approaches such as finite differences are effective, but in the intermediate regime we face an awkward problem for detailed modelling. Any successful modelling scheme must include an accurate model of the radiation from the source (including any angle dependent effects for source arrays) and the interaction of the arriving waves with the receiver configuration which is also commonly an array of sensors. Here, however, we will concentrate on the propagation of energy between souree and receiver and discuss how far ray based ideas can be exploited to give a reasonable treatment of seismic wave propagation in heterogeneous media.