A COMPARISON OF THE MASLOV INTEGRAL SEISMOGRAM AND THE FINITE-DIFFERENCE METHOD

The Maslov asymptotic method addresses some of the problems with stand ard ray theory, such as caustics and shadows. However, it has been app lied relatively little, perhaps because its accuracy remains untested. In this study we examine Maslov integral. (MI) seismograms by compari ng them with finite-difference (FD) seismograms for several cases of i nterest, such as iii velocity gradients generating traveltime triplica tions and shadows, (2) wave-front bending, kinking and folding in a lo w-velocity waveguide, and (3) wavefield propagation perturbed by a hig h-velocity slab, The results show that many features of high-and inter mediate-frequency waveforms are reliably predicted by Maslov's techniq ue, but also that it is far less reliable and even fails for low frequ encies. The terms 'high' and 'low' are model-dependent, but we mean th e range over which it is sensible to discuss signals associated with i dentifiable wave fronts and local (if complicated) effects that potent ially can be unravelled in interpretation, Of the high-and intermediat e-frequency wave components, those wave-front anomalies due to wave-fr ont bending, kinking, folding or rapid ray divergence can be accuratel y given by MI, True diffractions due to secondary wave-front sections are theoretically not included in Maslov theory (as they require true diffracted rays), but in practice they can often be satisfactorily pre dicted. This occurs roughly within a wavelength of the truncated geome trical wave front: where such diffractions are mast important since th eir amplitudes may still be as large as half that on the geometrical w ave front itself. Outside this region MI is inaccurate (although then the diffractions are usually small), thus waveforms of high and interm ediate frequencies are essentially controlled by classical wave-front geometry. Our results also show that the accuracy of MI can be improve d by rotating the Maslov integration axis so that the nearest wave-fro nt anomaly is adequately 'sampled', This rotation can be performed aft er ray tracing and it can serve to avoid pseudo-caustics by using it i n conjunction with the phase-partitioning approach. The effort needed in phase partitioning has been reduced by using an interactive graphic s technique. It is difficult to formulate a general rule prescribing t he limitations of MI accuracy because of model dependency. However, ou r experiences indicate that two space-and two timescales need to be co nsidered, These are the pulse width in space, the length scale over wh ich the instantaneous wave-front curvature changes, and the timescales of pulse width and significant features in the ray traveltime curve. It seems, from our examples, that when these scales are comparable, th e Maslov method gives very acceptable results.