S* - shear energy from a P-wave source

P. F. Daley


The existence of an apparent source of V S waves propagating in the underlying homogeneous isotropic medium resulting from an explosive P wave point source in the immediate vicinity of an interface, most often the earth's surface, has been shown in the literature to be a mathematical, numerical, and physical reality. This arrival, when observed on synthetic sections computed using the hybrid finite integral transform - finite-difference method, was designated as the S* arrival. It had no true geometrical ray path, but rather an apparent path of energy transport and was termed, appropriately, a non-geometrical or inhomogeneous arrival. Its theoretical existence was subsequently confirmed by analytical methods using a zero order saddle point approximation to the Sommerfeld integral. These first analytical methods made a simplifying assumption that the saddle point was constrained to be on the real axis in the complex slowness (p) plane, even though it was known at the time that this was an idealized solution. However, the numerical results from this simplified solution showed reasonably good agreement with the purely numerical results, and as is often the case, the problem was not pursued further.

In the twenty years that have passed since this original investigation significant advances in data acquisition have been made and interest in this shear wave generation phenomenon has been shown. This has prompted a more mathematically intensive study of the problem with the idea that some of the original conjectures regarding the properties of this type of arrival be investigated in the light of a more comprehensive mathematical analysis. The investigation presented here of the S* arrival indicates other instances where the zero-order asymptotic expansion, which is dependent on plane-wave reflection and transmission coefficients, to describe the particle displacement of body waves, is inadequate.

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