1887
Volume 36 Number 4
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

The existence of‘*‐waves’has, in recent years, prompted a renewed interest in these non‐geometrical arrivals, which are generated by point sources located adajcent to plane interfaces. It has led to the re‐evaluation of seismic data aquisition techniques and to the question of how to use this real phenomena in enhancing existing seismic interpretation methods.

This paper considers a non‐geometrical SH‐arrival which is generated by a point torque source unrealistically buried within a half‐space. The method of solution is essentially the same as presented in an earlier paper, with the modification that the limitation placed on the distance of the source from the interface has been removed in the saddle point method used to obtain a high‐frequency approximate solution. In the earlier paper, a preliminary assumption forced the saddle point, which corresponded to the *‐wave arrival, to be real when it is generally complex. However, for offsets removed from the distinct ray, the imaginary part of this complex quantity is negligible.

A problem which arose when comparing exact synthetic traces with those obtained using zero‐order saddle point methods, was the inability to match either the amplitude or phase of the geometrical arrival in the range of offsets when the *‐wave and this corresponding geometrical ray were well separated. For this range of offsets the geometrical arrival was approaching grazing incidence and another term in the saddle point expansion of the integral was necessary to rectify this error. This method is also being used to validate the results for higher order terms obtained using asymptotic ray theory.

Analytical formulae are given for both the *‐wave and the higher order expansion of the geometrical event, together with a comparison of synthetic seismograms using the method developed here and a numerical integration algorithm.

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2006-04-27
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