Ray amplitudes in a three-dimensional inhomogeneous medium

Summary A system of five ordinary differential equations of the first order to compute the geometrical spreading of the wave front of seismic body waves in a three-dimensional medium is suggested.     

Influence of geological factors on seismic ground-motions (seismic microzoning of Prague)

Summary Seismic microzoning of Prague was performed using geological data and seismic response (ground shaking) computations. The Prague territory was covered by a square grid, each square 250 m×250 m being characterized by a simplified geological cross-section from the Earth's surface to the bedrock boundary. The data were obtained from detailed engineering-geological maps 1:5000. The geological cross-sections were transformed into a set of layered models, specified by the thicknesses of individual layers and corresponding compressional and shear-wave velocities, densities and parameters of the causal absorption. The seismic responses were computed by the matrix method. The main amplitude and frequency characteristics of the responses are demonstrated in the form of microzoning maps. The maps do not depend on the specific type of seismic excitation. They make it possible to predict the relative amplification of P and S waves, with respect to the bedrock outcrop, all over the city.     

Computation of ray amplitudes of seismic body waves in vertically inhomogeneous media

Summary Standard methods of interpolating the velocity-depth distribution v=v(z) do not guarantee the continuity of the first and second derivatives of velocity and generate false interfaces of a higher order. These false interfaces cause anomalies in the amplitude-distance curves. It is suggested to apply the smoothed spline approximation to the depth-velocity distribution z=z(v). In this case, the ray integrals can be evaluated in a closed form. The amplitude-distance curves become quite smooth and stable. All necessary formulae and numerical examples are presented.     

Computation of diffracted rays in inhomogeneous media with curved interfaces

Summary A method for computing certain types of diffracted rays and corresponding travel-time curves in laterally inhomogeneous media with slightly curved interfaces is suggested. Numerical examples are presented.Dedicated to Academician Alois Zátopek on His 65th Birthday     

Analytical expressions for Fresnel volumes and interface fresnel zones of seismic body waves. Part 2: Transmitted and converted waves. Head waves

Summary Fresnel volumes and interface Fresnel zones of transmitted and head waves are studied. The relation derived for transmitted waves may also be used for converted reflected waves. Considerable attention is devoted to the penetration of Fresnel volumes across structural interfaces, particularly for head waves.     

Fast computation of ray synthetic seismograms in vertically inhomogeneous media

Summary A procedure of fast computation of body-wave ray synthetic seismograms in vertically inhomogeneous media is suggested. The procedure uses a special approximation of the velocitydepth distribution which guarantees continuity of the first and second derivatives of velocity and does not generate false low-velocity layers (oscillations in the velocity-depth function). The ZESY82 program package, which is based on the suggested procedure, is described. The point source with an arbitrary radiation pattern may be situated at any points of the model, the receivers are situated regularly or irregularly along any profile on the Earth's surface, containing the epicentre. Numerical examples of the synthetic record sections for a model of the Earth's crust and the uppermost mantle are given.

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Numerical modelling of time-harmonic seismic wave fields in simple structures by the gaussian beam method. part I

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