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1

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A NON-GEOMETRICAL SH-ARRIVAL (1988)

DALEY, P. F. ; HRON, F.

Oxford, UK : Blackwell Publishing Ltd

Geophysical prospecting 36 (1988), S. 0

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ISSN: 1365-2478

Source: Blackwell Publishing Journal Backfiles 1879-2005

Topics: Geosciences , Physics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1111/j.1365-2478.1988.tb02172.x

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2

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WAVEFRONT DIVERGENCE, MULTIPLES, AND CONVERTED WAVES IN SYNTHETIC SEISMOGRAMS (1983)

HRON, F. ; COVEY, J. D.

Oxford, UK : Blackwell Publishing Ltd

Geophysical prospecting 31 (1983), S. 0

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ISSN: 1365-2478

Source: Blackwell Publishing Journal Backfiles 1879-2005

Topics: Geosciences , Physics

Notes: Synthetic seismograms can be very useful in aiding understanding of wave propagation through models of real media, verification of geologic models derived from interpretation of field seismic data, and understanding the nature and complexity of wave phenomena. If meaningful results are to be obtained from synthetic seismograms, the method of their computation must, in general, include three-dimensional geometrical spreading of wavefronts associated with highly concentrated (i.e., point) sources. The method should also adequately represent the seismic response of solid-layered media by including enough primaries, multiples, and converted phases to accurately approximate the total wavefield. In addition to these features, it is also very helpful, although not always essential, if the method of seismogram computation provides for explicit identification of wave type and ray path for each arrival. Various seismograms, computed via asymptotic ray theory and an automatic ray generation scheme, are presented for a highly simplified North Sea velocity structure. This is done to illustrate the importance of the above features and to demonstrate the inadequacy of the plane-wave synthesis method of seismogram computation for point sources and the limitations of acoustic models of solid-layered media.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1111/j.1365-2478.1983.tb01062.x

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ON THE ROLE OF PARTIAL RAY EXPANSION IN THE COMPUTATION OF RAY SYNTHETIC SEISMOGRAMS FOR LAYERED STRUCTURES (1989)

COVEY, J. D. ; HRON, F. ; PEACOCK, K. L.

Oxford, UK : Blackwell Publishing Ltd

Geophysical prospecting 37 (1989), S. 0

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ISSN: 1365-2478

Source: Blackwell Publishing Journal Backfiles 1879-2005

Topics: Geosciences , Physics

Notes: This paper presents results of testing an efficient ray generation scheme needed whenever ray synthetic seismograms are to be computed for layered models with more than 10‘ thick’layers. Our ray generation algorithm is based on the concept of kinematically equivalent waves (the kinematic analogs) having identical traveltimes along different ray-paths between the source and the receiver, both located on the surface of the model. These waves, existing in any medium composed of laterally homogeneous parallel layers, interfere at any location along the recording surface, thereby producing a composite wavelet whose amplitude and shape depend directly on the number of kinematic analogs (the multiplicity factor). Hence, explicit knowledge of the multiplicity factor is crucial for any analysis based on the amplitude and shape of individual wavelets, such as wavelet shaping, Q estimation, or linearized wavelet inversion.For unconverted waves, such as those discussed in this paper, the multiplicity factor can be computed analytically using formulae given in the Appendix; for converted waves, the multiplicity factor should be computed numerically, using the algorithm employed for the computation of the seismograms presented in a previous paper by one of the authors.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1111/j.1365-2478.1989.tb02240.x

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4

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Effects of anelasticity on reflection and transmission coefficients[ Received ] (1997)

Nechtschein, S. ; Hron, F.

Oxford, UK : Blackwell Science Ltd

Geophysical prospecting 45 (1997), S. 0

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ISSN: 1365-2478

Source: Blackwell Publishing Journal Backfiles 1879-2005

Topics: Geosciences , Physics

Notes: It is known that the reflection and transmission coefficients used in the zeroth order approximation of asymptotic ray theory (ART) are identical to those obtained for the plane wave impinging on a plane interface separating two perfectly elastic half-spaces. We have used ART to compute reflection and transmission coefficients for two viscoelastic media separated by a plane interface. Our method is different from the plane-wave approach because the ART approach requires only a local application of the boundary conditions both for the eikonal and the ray amplitudes.Several types of viscoelastic media were studied. For a given model, the elastic case was emulated by setting all the quality factors Q equal to each other. Several anelastic cases were computed by keeping the same velocities and densities while changing the Qs. The quality factor is a relatively difficult parameter to measure exactly. Hence elastic coefficients are used in most synthetic seismogram computations, and the quality factors are chosen from experimental measurements or simply estimated.From these computations, amplitude and phase differences between elastic coefficients and coefficients for dissipative media are observed in some cases. These differences show the importance of knowing the exact values of Q. Incorrect Q values can lead to unrealistic moduli and to noticeable phase differences of these viscoelastic coefficients.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1046/j.1365-2478.1997.590288.x

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Blind prediction of the site effects at Ashigara Valley, Japan, and its comparison with reality (1994)

Zahradník, J. ; Moczo, P. ; Hron, F.

Springer

Natural hazards 10 (1994), S. 149-170

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ISSN: 1573-0840

Keywords: Finite-difference method ; numerical predictions ; site effects ; earthquake ground motions

Source: Springer Online Journal Archives 1860-2000

Topics: Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences

Notes: Abstract Weak and strong ground motions were numerically predicted for three stations of the Ashigara Valley test site. The prediction was based on the records from a rock-outcrop station, one weak-motion record from a surface-sediments station, and the standard geotechnical model. The data were provided by the Japanese Working Group on the Effects of Surface Geology as a part of an international experiment. The finite-difference method for SH waves in a 2-D linear viscoelastic medium (a causalQ model) was employed. Comparison with the real records shows that at two stations the predictions fit better than at the third one. Strangely, the two better predictions were for stations situated at larger distances from the reference rock station (one station was on the surface, the other in a borehole). The strong ground motion (the peak acceleration of about 200 cm s−2) was not predicted qualitatively worse than the weak motion (8 cm s−2). A less sophisticated second prediction (not submitted during the experiment), in which we did not attempt to fit the available weak-motion record at the sedimentary station, agrees with the reality significantly better.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00643449

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6

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Tutorial on the numerical modeling of edge diffracted waves by the ray method (1995)

Hron, F. ; Chan, G. H.

Springer

Studia geophysica et geodaetica 39 (1995), S. 103-137

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ISSN: 1573-1626

Keywords: Diffracetd waves ; Asymptotic Ray Theory ; Synthetic seismograms ; Numerical modeling of seismic waves

Source: Springer Online Journal Archives 1860-2000

Topics: Architecture, Civil Engineering, Surveying , Geosciences , Physics

Notes: Summary The concept of diffracted rays introduced by Keller (1962) opened the way for a ray approach in the numerical modeling of the diffraction phenomena frequently seen in the seismic field records. Unlike the computation of travel times, which has never caused any difficulties being governed by the same eikonal equation as are the rays of ordinary seismic body waves, the evaluation of the diffracted ray amplitude has been another story. In this paper we give a tutorial account of a highly promising technique for the computation of the ray amplitude of seismic waves diffracted by linear edges on seismic interfaces originally presented by Klem-Musatov (1980, 1995). We demonstrate the adequacy of this technique on a series of SH synthetic traces containing diffracted arrivals, some of them diffracted more than once. Our computer program is based on a successful combination of Klem-Musatov's approach with the zero order approximation of the Asymptotic Ray Theory (Červený and Hron, 1980). We showed in the paper that both techniqúes are ideally suited for such a combination, since the ray amplitude evaluation in each of them is based on the same transport equation. In our tutorial review we present all formulae which are needed for a practical implementation of the method and provide their physical interpretation, wherver possible, by using the numerical examples presented in the paper.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02296070

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