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M. J. KUHN 《Geophysical Prospecting》1985,33(8):1103-1137
This paper considers propagation of elastodynamic waves in an imperfectly elastic half-space. Two different excitation modes are investigated: a buried source of compressional waves and a vertically directed areal load applied to the surface. Numerical integration of the analytical solution of the wave equation allows study of the vertical and horizontal components of displacement and/or particle velocity anywhere in the half-space. One case of particular interest concerns the examination of particle displacement and velocity at the surface in a circular area above the source. In another application seismograms generated by an explosive buried source are contrasted with seismograms generated by the transient application of a vertically directed load to the free surface. Still another application of considerable practical interest concerns the study of the nongeometrical pS—wave, in particular its characteristics as functions of range and depth. Finally, in the last application the behavior of a rarely observed wave (denoted here by the letter U) is studied in both elastic and visco-elastic half-spaces. 相似文献
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M. J. KUHN 《Geophysical Prospecting》1987,35(2):167-186
The propagation of transient acoustic pressure waves in a layer enclosed between two, not necessarily identical, half-spaces is considered. The source and the receivers are always located in the same half-space and at the same depth. The source excitation function is a narrow causal spike. Several thicknesses of the layer are examined including the case in which the embedded layer vanishes. The phenomena of ‘constricted’ head waves and wide-angle reflections in the layer are examined in detail using a ‘numerical experimentation’ approach. First, a closed-form solution is numerically evaluated. Then this solution is developed in series and each term is evaluated separately using the same numerical techniques. When the contribution of an individual high-order term becomes unimportant, all higher order terms are discarded, and the response is constructed by superposition of the previously computed low-order terms only. Propagation by wide-angle reflections from inside the layer is of interest. When the thickness of the layer is reduced to a fraction of the wavelength, these events consist typically of a low amplitude, high frequency, geometrical acoustics arrival, followed by higher amplitude, low frequency, non-geometrical coda. When all important low-order terms are added, the non-geometrical events tend to interfere destructively, leaving a waveform nearly identical to that obtained by integration of the closed-form solution. When the thickness of the embedded layer is measured in fractions of the dominant wavelength, none of the individual terms of the series development can be duplicated by asymptotic ray tracing. However, because the codas of the various terms interfere destructively, the total response may be well-represented by the addition of a few low-order rays, using asymptotic approximation. This discovery extends the usefulness of Huygens-Kirchhoff ray tracing to modeling of wave propagation in thin layers. 相似文献
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M. J. KUHN 《Geophysical Prospecting》1979,27(1):62-77
The first part of this paper examines a special case of acoustical imaging in which the source and the receiver coincide. The benefits of weighting and muting are studied in detail by means of computer modeling. The test model consists of a single planar interface z=z1, abruptly terminated at x= o. The amplitude and phase responses are computed in the plane z=z0= o for two separations of neighboring stations, Δx=λ/10 and Δx=λ/2. Six different weighting factors are used in the test. However, in this source-receiver coincident case, three of the weighting factors produce identical responses, so that all six test factors may be represented by only four curves. It is found that when the spatial sampling at the aperture approaches the condition of critical sampling, i.e. Δx=λ/2, only the weighting factor which implicitly takes into account beam steering along the specular reflection path is acceptable. This factor alone keeps the amplitude and the phase curves undistorted until the difference 2 ·ΔR between two neighboring paths reaches approximately λ/2. If we set 2 ·ΔR=λ/2, we may construct a set of curves which we may call quite appropriately muting curves. These curves are physically interpretable only for station separation Δx > λ/4. The muting curves are symmetrical about the line x= 0 and their angular opening depends on spatial separation Δx, depth z, and wavelength λ (which may vary with depth). The second part of this paper suggests how the weighting factor with implicit beam steering can be applied to reconstruction of two and three-dimensional wavefields. Seismic migration of common depth point (CDP) stacked line data is also discussed. This is a hybrid case which presents certain theoretical difficulties. We shall also mention the velocity problem which is inherent to migration of CDP stacked data. The third and final part concerns implementation of the migration of CDP stacked data. When the spatial sampling is between λ/4 and λ/2, the migration process will benefit from beam steering and from muting. The benefits are more subtle when the separation of the traces is less than λ/4. However, in that case the cost of data collection is considerable and often prohibitive. In either case the migration of seismic data can be expedited by use of precalculated tables of migration velocities, ray path distances, and weights (including muting). 相似文献
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Metamorphic Evolution of the Ribeira Belt: Evidence from Outcrops in the Rio de Janeiro Area, Brazil
Migmatitic granulites and arc-related felsic intrusives of Pan-Africanage form the bedrock in the Rio de Janeiro area, SE Brazil.These rocks preserve a partial record of three parageneses.The earliest assemblage (M1) grew during fabric formation inthe rocks (D1) and is characterized by the mineral assemblagePl + Bt + Sil + Kfs + Qtz. Peak metamorphic conditions (M2)are characterized by the assemblage Bt + Crd + Kfs + Pl + Grt+ liq + Qtz and are inferred to have developed during D2 foldingof the rocks at T = 750–800°C and P = 7 kbar. M3 reactiontextures overprint the M2 assemblage and comprise symplectiticintergrowth of cordierite(II) and quartz that formed after garnet,whereas secondary biotite formed as a result of reactions betweengarnet and K-feldspar. By comparing the observed modal abundanceswith modal contours of garnet, cordierite and quartz on therelevant pseudosection a post M2 P–T vector indicatingcontemporaneous cooling and decompression can be deduced. Theinferred equilibrium assemblage and reaction textures are interpretedto reflect a clockwise P–T path involving heating followedby post-peak decompression and associated cooling. We inferthat metamorphism occurred in response to advective heatingby the abundant syn-collisional (arc-related) I-type granitoidsin the region, consistent with the unusually high peak T/P ratio. KEY WORDS: advective heating; Ribeira belt; granulite; partial melting; P–T pseudosection 相似文献
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In this study we derive expressions for particle displacement or particle velocity anywhere inside a stratified earth and at its surface due to horizontal torque source located in the top layer. Equivalently, invoking Green's function reciprocity theorem, the solution applies also to the case of a surface or subsurface source when the resulting displacement or velocity is measured within the top layer. In order to evaluate the closed-form analytical solution economically and accurately it is advisable to introduce inelastic attenuation. Causal inelastic attenuation also lends the necessary realism to the computed seismic trace. To provide proof that the analytical solution is indeed correct and applicable to the multilayer case, a thick uniform overburden was assumed to consist of many thin layers. The correctness of the computed particle velocity response can be very simply verified by inspection. The computed response can also serve as a check on other less accurate methods of producing synthetic seismograms, such as the techniques of finite differences, finite elements, and various sophisticated ray-tracing techniques. It is not difficult to construct horizontal surface torque source. It appears that such source is well suited for seismic exploration in areas with a high-velocity surface layer. A realistic source function is analyzed in detail and normalized displacement response evaluated at different incidence angles in the near and the far fields. In an effort to distinguish the features of an SH torque seismogram from a pressure seismogram two models with identical layerings and layer parameters have been set up. As expected the torque seismogram is very different from the compressional seismogram. One desirable feature of a torque seismogram is the fast decay of multiples. Exact synthetic seismograms have many uses; some of them, such as the study of complex interference phenomena, phase change at wide angle reflection, channeling effects, dispersion (geometrical and material), absolute gain, and inelastic attenuation, can be carried out accurately and effortlessly. They can also be used to improve basic processing techniques such as deconvolution and velocity analysis. The numerical evaluation of the analytical solution of the wave equation as described in this paper has a long history. Most of the work leading to this paper was carried out by one of us (M. J. K.) in the years 1957 to 1968 at the Geophysical Research Corporation. However, the full testing of the various computer codes was carried out only very recently at the Phillips Petroleum Company. 相似文献
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In the atmospheric surface layer, it is widely accepted that ejection andsweep eddy motions, typically associated with coherent structures, areresponsible for much of the land-surface evaporation, sensible heat, andmomentum fluxes. The present study analyzes the ejection-sweep propertiesusing velocity and scalar fluctuation measurements over tall natural grassand bare soil surfaces. It is shown that momentum ejections and sweeps occurat equal frequencies (D eject D sweep 0.29) irrespective of surfaceroughness length or atmospheric stability conditions. Also, their magnitudesare comparable to values reported from open channel velocity measurements (Dsweep 0.33; D eject : 0.30). The scalar D eject is constant andsimilar in magnitude to the momentum D eject( 0.29) over both surfacesand for a wide range of atmospheric stability conditions, in contrast to thescalar D sweep. The scalar sweep frequency is shown to depend on the scalarskewness for the dynamic convective and free convective sublayers, but isidentical to D eject for the dynamic sublayer. The threshold scalar skewnessat which the D sweep dependence occurs is 0.25, in agreement with theaccepted temperature skewness value at near-neutral conditions. In contrastto a previous surface-layer experiment, this investigation demonstrates thatthe third-order cumulant expansion method (CEM) reproduces the measuredrelative flux contribution of ejections and sweeps (S0) for momentumand scalars at both sites. Furthermore, a linkage between S0 and thescalar variance budget is derived via the third-order CEM in analogy tomomentum. It is shown that S0 can be related to the flux divergenceterm and that such a relationship can be estimated from surface-layersimilarity theory, and the three sublayer model of Kader and Yaglom andproposed similarity functions. 相似文献
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U. NICKUS M. KUHN U. BALTENSPERGER R. DELMAS H. GÄGGELER A. KASPER H. KROMP-KOLB F. MAUPETIT A. NOVO F. PICHLMAYER S. PREUNKERT H. PUXBAUM G. ROSSI W. SCHÖNER M. SCHWIKOWSKI P. SEIBERT M. STAUDINGER V. TROCKNER D. WAGENBACH W. WINIWARTER 《Tellus. Series B, Chemical and physical meteorology》1997,49(1):56-71
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