A Maslov-Kirchhoff seismogram method

Abstract

When synthetic seismograms are computed for complicated velocity models using asymptotic methods based on ray theory, the caustic and/or pseudo-caustic geometrical catastrophes that often occur in the ray manifolds can cause many difficulties, because ray amplitudes can become infinite, inaccurate or vanish in such situations. The longer the propagation path relative to the scale of the velocity inhomogeneities and the more the propagation tends to be oblique rather than normal to velocity variations, the more troublesome the catastrophes become. Although the Maslov integral method (MI) largely cures the problems of the classical geometric ray theory (GRT) at caustics (where nearby rays in geometrical space cross) and in geometric shadow zones, it suffers from serious artefacts at pseudo-caustics (the crossing points of rays drawn in the mixed geometrical and slowness space of the Maslov integral). Some methods have been devised to overcome this limitation, but none is satisfactory when it is necessary to compute automatically large suites of seismograms for complex models without continuous intervention from a skilled seismologist. In this paper, we demonstrate how combining the Maslov integral method with a stage of Kirchhoff integration can greatly reduce MI's pseudocaustic problems while retaining MI's ability to overcome the caustic and shadow problems of GRT. In many cases, the additional computational burden increases by one order of magnitude but is still much less than that required in a finite-difference modelling, and is not great for a common workstation. The Maslov—Kirchhoff (MK) technique is shown to be substationally more accurate than ordinary Maslov integration when pseudo-caustics are present. Furthermore, it is more robust and automated than the phase-partitioning technique in curing the problem of joint caustics and pseudo-caustics. We also show that the MK scheme can be more efficient than other Kirchhoff modelling techniques where the kernel of integration is obtained by GRT.