Transient SH-waves in a wedge-shaped layer

Summary. A generalized ray theory for transient SH -waves in a wedge-shaped layer over an elastic half-space is developed in this paper. The ray integrals for multiply reflected waves in the layer are derived in terms of two systems of coordinates and two sets of local wavenumbers, one along the free surface and the other along the sloped interface. All local wavenumbers are then transformed to a common wavenumber in all ray integrals which are evaluated by the Cagniard method. Results for the first motion approximation are in agreement with previous investigations.     

Teleseismic body wave radiation from a seismic source in a layered medium

Summary. A simple method is presented which combines the reciprocity theorem and the flat layer theory to yield teleseismic body wave radiation from seismic sources embedded in the Earth's crust. The source is represented by its equivalent body forces and can be quite general. The effect of Yucca Flat geology on explosion signals is studied in detail. In particular, the m _b— M _s relation is shown to be dependent on detonation medium and source depth. Application to shallow earthquake faults demonstrates the strong influence of free surface and layering on the shape of P- and S-wave teleseismic spectra.     

Full reconstruction of a layered elastic medium from P-SV slant-stack data

Summary. We develop a méthod of reconstructing the elastic paraméters as functions of depth, for a horizontally stratified, isotropic elastic half-space. Unlike previous schemes, which have been able to retrieve the shear wave speed and density from SH seismograms slant stacked at two angles, our méthod makes use of P - SV data at a single stacking paraméter to obtain all three elastic constants. The data required are the elements of the full reflection matrix at the surface, corresponding to measurements of two separate components of the response to two independent sources, one explosive, the other generating shear waves.
In developing this inverse scheme fundamental differences emerge between the acoustic or SH problem, and the coupled P - SV case, the most important being in the nature of the interfacial scattering matrix. We show that it is not possible to make use of the downward reflection data for an interface to determine directly the remaining reflection and transmission coefficients, but that the scattering data may be completed by applying a simple iterative procedure at each interface.
We show the result of applying our inverse scheme to seismograms generated for a six-layered model, including a low-velocity layer. We are able to reconstruct both wave speeds and the density as functions of depth, all quantities being in close agreement with the original model.     

SH-waves scattering from a partially filled semi-circular alluvial valley

A series solution of the plane SH-waves incident on a partially filled semi-circular alluvial valley imbedded in a half-space is presented. Based on the region-matching method, the analysed region is decomposed into two subregions by the interface between two media. The antiplane displacement field of each subregion is expressed in terms of an infinite series of cylindrical wavefunctions with unknown expansion coefficients. After imposing the traction-free condition on the curved valley surface and the matching conditions on the interface with the aid of Graf's addition theorem, the unknown coefficients are obtained. Both the frequency- and time-domain responses are evaluated. In the theoretical derivation of this work, two classical exact series solutions are also included, so the present series solution is more general than those given before. Visible effects of different physical parameters on ground surface motions are illustrated in graphical form.     

Ray-reflectivity method for SH-waves in stacks of thin and thick layers

Summary Reflectivity and ray theories are united to produce a hybrid technique of computing synthetic seismograms for a plane layered medium in subcritical regions. Numerical experiments have indicated that this technique is useful when the depth structure is one composed of thick layers separated by finely layered zones. As the theory for wave propagation in a plane layered medium is well known, the simple SH case is investigated so that the basic idea of the method may be conveyed without an excess of mathematics that would be necessitated if the P-SV problem were considered.
In computing the ray-reflectivity seismogram, the thick layers are treated using asymptotic ray theory while the thin-layered zones are treated as quasiinterfaces where analogues of reflection and transmission coefficients called reflectivities and transmittivities are calculated utilizing a Thomson-Haskell formulation. A stationary phase approximation is employed when evaluating the integral which gives the displacement due to an arbitrary ray propagating in the thick layers of the above-mentioned medium, and the validity of this approximation is discussed.
A comparison of ray, numerical integration (reflectivity) and ray-reflectivity synthetic sections indicates that this method yields quite acceptable results for subcritical reflection work and is suitable for application in seismic interpretation as individual arrivals associated with ray-paths in the thick layers may be identified. Furthermore, the method is quite cost efficient and may be extended to a medium where the thick layers are non-planar using asymptotic ray theory in these layers.     

Acoustic-Gravity Wave Propagation in a Measured Atmosphere

Summary An atmosphere is modelled by averaging measurements taken at eight locations for 1968 September 9. The effectiveness of the modelling is evaluated by comparing the atmospheric dispersion properties determined from an experimentally recorded signal resulting from a nuclear explosion on that date and those computed from the model atmosphere. The effects of atmospheric winds are shown to change the dispersion properties.
A theoretical barogram is synthesized for a receiver located 7930 km from the source and is compared to the recorded signal for the event. Barograms are synthesized for two different source functions and the source functions are discussed.