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Title: Deformation of solid earth by surface pressure: equivalence between Ben-Menahem and Singh’s formula and Sorrells’ formula
SUMMARY Atmospheric pressure changes on Earth’s surface can deform the solid Earth. Sorrells derived analytical formulae for displacement in a homogeneous, elastic half-space, generated by a moving surface pressure source with speed $$c$$. Ben-Menahem and Singh derived formulae when an atmospheric P wave impinges on Earth’s surface. For a P wave with an incident angle close to the grazing angle, which essentially meant a slow apparent velocity $$c_a$$ in comparison to P- ($$\alpha ^{\prime }$$) and S-wave velocities ($$\beta ^{\prime }$$) in the Earth ($$c_a \ll \beta ^{\prime } \lt \alpha ^{\prime }$$), they showed that their formulae for solid-Earth deformations become identical with Sorrells’ formulae if $$c_a$$ is replaced by $$c$$. But this agreement was only for the asymptotic cases ($$c_a \ll \beta ^{\prime }$$). The first point of this paper is that the agreement of the two solutions extends to non-asymptotic cases, or when $$c_a /\beta ^{\prime }$$ is not small. The second point is that the angle of incidence in Ben-Menahem and Singh’s problem does not have to be the grazing angle. As long as the incident angle exceeds the critical angle of refraction from the P wave in the atmosphere to the S wave in the solid Earth, the formulae for Ben-Menahem and Singh’s solution become identical to Sorrell’s formulae. The third point is that this solution has two different domains depending on the speed $$c$$ (or $$c_a$$) on the surface. When $$c/\beta ^{\prime }$$ is small, deformations consist of the evanescent waves. When $$c$$ approaches Rayleigh-wave phase velocity, the driven oscillation in the solid Earth turns into a free oscillation due to resonance and dominates the wavefield. The non-asymptotic analytical solutions may be useful for the initial modelling of seismic deformations by fast-moving sources, such as those generated by shock waves from meteoroids and volcanic eruptions because the condition $$c / \beta ^{\prime } \ll 1$$ may be violated for such fast-moving sources.  more » « less
Award ID(s):
2225216
PAR ID:
10610306
Author(s) / Creator(s):
Publisher / Repository:
Geophysical Journal International
Date Published:
Journal Name:
Geophysical Journal International
Volume:
238
Issue:
2
ISSN:
0956-540X
Page Range / eLocation ID:
820 to 826
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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