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1.
Seismic waves in a stratified half space   总被引：5，自引：0，他引：5  
Summary. For a buried source in a stratified elastic half space, the surface displacements are calculated by numerical integration of the Fourier–Bessel transform of the response. In the transform space this response is conveniently represented in terms of the reflection and transmission properties of the half space. For a layered medium this procedure avoids all problems associated with growing exponential terms in the evanescent regime. A slightly attenuative medium is assumed, so that the surface wave poles are shifted off the real slowness axis and thus a contour of integration along this axis may be employed. A general point source is represented by an arbitrary moment tensor.
The procedure is illustrated by calculations of three component seismograms including all P , SV and SH contributions for body and surface waves at moderate ranges. For local earthquakes we illustrate the striking effect of focal depth and also show the effect of sedimentary cover on strong ground motion.  相似文献   

2.
Summary. High-frequency reflection and refraction seismograms for laterally variable multi-layered elastic media are computed by using the frequency domain elastic Kirchhoff–Helmholtz (KH) theory of Frazer and Sen. Both source and receiver wavefields are expanded in series of generalized rays and then elastic (KH) theory is applied to determine the coupling between each source ray and each receiver ray at each interface. The motion at the receiver is given as a series of integrals, one for each generalized ray. We use geometrical optics and plane wave reflection and transmission coefficients for rapid evaluation of the integrand. When the source or the receiver ray field has caustics on the surface of integration geometrical ray theory breaks down and this gives rise to singularities in the KH integrand. We repair this using methods suggested by Frazer and Sen.
Examples of reflection seismograms for 2-D structures computed by elastic KH theory are shown. Those for a vertical fault scarp structure are compared with the seismograms obtained by physical modelling. Then OBS data obtained from the mid-America trench offshore Guatemala area are analysed by computing KH synthetics for a velocity model that has been proposed for that area. Our analysis indicates the existence of a small low-velocity zone off the trench axis.
No head wave arrivals are obtained in our KH synthetics since we do not consider multiple interactions of a ray with an interface. The nearly discontinuous behaviour of elastic R/T coefficients near the critical angle causes small spurious phases which arrive later than the correct arrivals.  相似文献   

3.
Seismic body waves in anisotropic media: synthetic seismograms   总被引：5，自引：0，他引：5  
Summary. Synthetic seismograms and particle motion diagrams are computed for simple, layered Earth models containing an anisotropic layer. The presence of anisotropy couples the P, SV and SH wave motion so that P waves incident on the anisotropic layer from below produce P, SV and small-amplitude SH waves at the surface both the P velocity and the amplitudes of the converted phases vary with azimuth. Significant SH amplitudes may be generated even when the wavelength of the P wave is much greater than the thickness of the anisotropic layer. Incident SV or SH waves may each generate large amplitudes of both SV and SH motion. This strong coupling is largely independent of the degree of velocity anisotropy of the medium. The arrivals from short-period S waves exhibit S-wave splitting, but arrivals from longer period S waves superpose into a modified waveform. This strong coupling does not allow the arrival of separate phases with pure SV and SH polarization except along directions of symmetry where the motion decouples.  相似文献   

4.
P-SH conversion is commonly observed in teleseismic P waves, and is often attributed to dipping interfaces beneath the receiver. Our modelling suggests an alternative explanation in terms of flat-layered anisotropy. We use reflectivity techniques to compute three-component synthetic seismograms in a 1-D anisotropic layered medium. For each layer of the medium, we prescribe values of seismic velocities and hexagonally symmetric anisotropy about a common symmetry axis of arbitrary orientation. A compressional wave in an anisotropic velocity structure suffers conversion to both SV -and SH -polarized shear waves, unless the axis of symmetry is everywhere vertical or the wave travels parallel to all symmetry axes. The P-SV conversion forms the basis of the widely used 'receiver function' technique. The P-SH conversion occurs at interfaces where one or both layers are anisotropic. A tilted axis of symmetry and a dipping interface in isotropic media produce similar amplitudes of both direct ( P ) and converted ( Ps ) phases, leaving the backazimuth variation of the P-Ps delay as the main discriminant. Seismic anisotropy with a tilted symmetry axis leads to complex synthetic seismograms in velocity models composed of just a few flat homogeneous layers. It is possible therefore to model observations of P coda with prominent transverse components with relatively simple 1-D velocity structures. Successful retrieval of salient model characteristics appears possible using multiple realizations of a genetic-algorithm (GA) inversion of P coda from several backazimuths. Using GA inversion, we determine that six P coda recorded at station ARU in central Russia are consistent with models that possess strong (> 10 per cent) anisotropy in the top 5 km and between 30 and 43 km depth. The symmetry axes are tilted, and appear aligned with the seismic anisotropy orientation in the mantle under ARU suggested by SKS splitting.  相似文献   

5.
A lower mantle S-wave triplication and the shear velocity structure of D"   总被引：6，自引：0，他引：6  
Summary. A lower mantle S-wave triplication detected with short- and long-period WWSSN and CSN recordings indicates a substantial shear velocity discontinuity near 280 km above the core–mantle boundary. The triplication can be observed in rotated SH seismograms from intermediate and deep focus events throughout the distance range from 70° to 95°. Three distinct source region–receiver array combinations that have been investigated in detail demonstrate consistent travel time and relative amplitude behaviour of the triplication, with slight systematic shifts in the triplication indicating up to 40 km variations in the depth of the discontinuity. Modelling of the observations with synthetic seismograms produced with the Cagniard de Hoop and reflectivity methods constrains the shear velocity increase to be 235 ± 0.25 per cent, comparable to upper mantle discontinuities. Short-period observations indicate that the velocity increase may be a sharp first-order discontinuity, or may extend over a transition zone no more than 50 km thick. The shear velocity gradient below the discontinuity, within the D" layer, is not well-constrained by the SH data, but slightly positive or near zero velocity gradients are consistent with the long-period amplitude ratios of ScSH/SH .  相似文献   

6.
Summary. The method of finite differences is applied to the elastic wave equation to generate synthetic seismograms for laterally varying seafloor structures. The results are compared with borehole seismic data from the Gulf of California (Deep Sea Drilling Project Site 485) in which lines were shot over flat and rough topography. The significant new phenomenon observed in both the synthetic seismograms and the field data is the generation of a 'double head wave' due to the interaction of the incident wavefront with the side of a hill and the flat seafoor adjacent to the hill.
In these models the hills are on the order of a seismic wavelength in height and steep velocity gradients occur over distances comparable to wavelengths. Ray theoretical methods would not be suitable for studying such structures. True amplitude record sections are obtained by the finite difference method, which show for these models that the head wave generated at the flat seafloor adjacent to the hill is lower in amplitude than if the hill were not present and is lower in amplitude than the head wave generated at the hill.
A second feature which is important for borehole receivers is the existence of the 'direct wave root' in the upper basement. This energy occurs below the sharp interface when the direct wave impinges on the interface from above. There is no corresponding Snell's law ray path for this energy and the energy is evanescent with depth in the lower medium.
The properties of both the double head wave and the direct wave root are clearly demonstrated in the finite difference 'snapshot' displays.  相似文献   

7.
Summary. The three-dimensional (3-D) shear wave structure of the mantle, down to the depth of about 900 km, is obtained by inverting waveforms of radial component seismograms. Radial component seismograms contain large amplitude overtone signals which circle the Earth as wave packets and are sometimes called X1, X2, X3, … We use data which contain R1, X1 and X2 and filtered between 2 and 10mHz. It is shown that, unless each seismogram is weighted, all seismograms are not fitted uniformly. Only data from large earthquakes are fitted and the final velocity anomalies are biased by the small number of large earthquake data. Resolution is good at shallow depths, becomes worse in the intermediate depth range between about 400 and 500 km and then becomes better at greater depth ranges (600–900km). Even though we use only spheroidal mode data, velocity anomalies in the shallow structure show excellent correlation with the age of the surface rocks of the Earth. In the deeper regions, between about 600 and 900km, South America shows a fast velocity anomaly which may indicate the slab penetration beyond 700 km there. Another region which shows a fast velocity anomaly is the Mariana trench, but other subduction regions do not show such features.  相似文献   

8.
Summary. Two-dimensional finite element modelling of underground structural anomalies at shallow depths has been done to obtain the response at the ground surface to damped, vertically incident, SH -waves. Power spectral ratios are examined to determine what effects the position, shape, depth and size of the anomaly have on the surface seismograms. Based on the results gathered from a number of models, inferences are made with respect to the inverse problem: given the seismic motion of the ground surface, what can be said about the underground structure?  相似文献   

9.
Summary. A formulation is derived for calculating the energy division among waves generated by plane waves incident on a boundary between generally anisotropic media. A comprehensive account is presented for P, SV and SH waves incident from an isotropic half-space on an orthorhombic olivine half-space, where the interface is parallel to a plane of elastic symmetry. For comparison, a less anisotropic medium having transverse isotropy with a horizontal axis of symmetry is also considered. The particle motion polarizations of waves in anisotropic medium differ greatly from the polarizations in isotropic media, and are an important diagnostic of the presence of anisotropy. Incident P and SV waves generate quasi- SH waves, and incident SH waves generate quasi- P and quasi- SV waves, often of considerable relative magnitude. The direction of energy transport diverges from the propagation direction.  相似文献   

10.
Summary. An algorithm which is part analytical and part numerical is suggested for the computation of complete synthetic seismograms for complex three-dimensional geological structures with radial symmetry. A partial separation of variables based on the combination of a finite Fourier integral transform with respect to the spatial coordinate z together with the finite difference method is the essence of the algorithm. Upon application of the finite transform the problem reduces to solving a system of equations containing only partial derivatives with respect to one spatial coordinate ( r ) and time. As radial symmetry is assumed, there is no functional dependence on φ in the cylindrical system of coordinates ( r , φ, z ). The coefficients of the transformed equations may contain finite Fourier integrals of the z dependence of the elastic parameters. Several examples of synthetic seismograms computed for both SH - and P – SV -waves propagating in complex subsurface geometries are presented and their interpretation discussed.  相似文献   

11.
Shear-coupled PL     
Summary. Observed teleseismic shear-coupled PL -waves ( SPL ) display a variety of waveforms depending on factors such as source depth, source type and velocity structure. Using a WKBJ spectral method for SV -wave propagation, synthetic seismograms of SPL are produced to examine the factors important in SV and SPL excitation. Results show that SPL is preferentially excited by shallow sources compared to deep sources. This is due to large source area reverberations which consequently leak as SV -waves into the mantle. Interaction at the receiver area then sets up the classic prograde elliptical motion by which SPL can be identified. This is in accordance with the teleseismic observations and indicates that most previous models for the propagation of SPL were not appropriate for shallow source since emphasis was placed on wave interactions occurring only near the receiver.  相似文献   

12.
A curious observation has been made on radial receiver functions calculated from teleseisms recorded by 29 broad-band seismometers distributed over Iceland. The arrival time of the direct P phase of the radial receiver functions depends critically upon the azimuth of the teleseismic source. For a seismic station in West Iceland, the direct P  phase of the radial receiver function arrives consistently later for easterly source azimuths than for westerly source azimuths. The reverse applies for stations in East Iceland. In the original seismograms, the delayed P phase of the receiver function appears up to 450 ms later on the radial than on the vertical component. The seismometer locations in East and West Iceland are separated by the Neovolcanic Zone, a constructive plate boundary. The delayed P phases occur for seismic rays travelling across this zone. However, it is not obvious how wave propagation across the plate boundary zone could cause the observed delays. The tentative explanation proposed here involves the regional dip of the Icelandic lava sequences towards the Neovolcanic Zone. A dipping interface at shallow depth results in a P–S converted phase arriving shortly after the P phase. These phases cannot be separated in the radial receiver functions, given the bandwidth of the observed signals. However, a calculation of receiver functions from estimates of the P , SV and SH wavefields clearly reveals a P–S converted phase at about 500 ms for easterly source azimuths in West Iceland and for westerly source azimuths in East Iceland. The amplitudes of the direct P phase and the P–S phase converted at a dipping interface would be expected to vary strongly with azimuth in accordance with the observed behaviour.  相似文献   

13.
We present approximate displacement and energy PP and PS reflection/transmission coefficients for weak-contrast interfaces in general weakly anisotropic elastic media. The coefficients were obtained by applying first-order perturbation theory and then expressed in a compact and relatively simple form. The formulae can be used for arbitrary orientations of the incidence plane and interface, without the need to transform the elasticity parameters to a local Cartesian coordinate system. The accuracy of the approximate formulae is illustrated for the PS reflection coefficient for two synthetic models. For these models, we also study the possibility of using the approximate PP reflection coefficient in the inverse problem.  相似文献   

14.
The Kirchhoff (or tangent plane) approximation, derived from the theoretically complete Kirchhoff–Helmholtz integral representation for the seismic wavefield, has been used extensively for the analysis of seismic-wave scattering from irregular interfaces; however, the accuracy of this method for curved interfaces has not been rigorously established. This paper describes an efficient Kirchhoff algorithm to simulate scattered waves from an arbitrarily curved interface in an elastic medium. Synthetic seismograms computed using this algorithm are compared with exact synthetics computed using analytical formulae for scattering of plane P waves by a spherical elastic inclusion. A windowing technique is used to remove strong internal reverberations from the analytical solution. Although the Kirchhoff method tends to underestimate the total scattering intensity, the accuracy of the approximation improves with increasing value of the wavenumber-radius product, kR . The arrival times and pulse shapes of primary reflections from the sphere are well approximated using the Kirchhoff approach regardless of curvature of the scattering surface, but the amplitudes are significantly underestimated for kR ≤ 5. The results of this work provide some new guidelines to assess the accuracy of Kirchhoff-synthetic seismograms for curved interfaces.  相似文献   

15.
We have been developing an accurate and efficient numerical scheme, which uses the finite-difference method (FDM) in spherical coordinates, for the computation of global seismic wave propagation through laterally heterogeneous realistic Earth models. In the field of global seismology, traditional axisymmetric modeling has been used widely as an efficient approach since it can solve the 3-D elastodynamic equation in spherical coordinates on a 2-D cross-section of the Earth, assuming structures to be invariant with respect to the axis through the seismic source. However, it has the severe disadvantages that asymmetric structures about the axis cannot be incorporated and the source mechanisms with arbitrary shear dislocation have not been attempted for a long time. Our scheme is based on the framework of axisymmetric modeling but has been extended to treat asymmetric structures, arbitrary moment-tensor point sources, anelastic attenuation, and the Earth center which is a singularity of wave equations in spherical coordinates. All these types of schemes which solve 3-D wavefields on a 2-D model cross-section are classified as 2.5-D modeling, so we have named our scheme the spherical 2.5-D FDM. In this study, we compare synthetic seismograms calculated using our FDM scheme with three-component observed long-period seismograms including data from stations newly installed in Antarctica in conjunction with the International Polar Year (IPY) 2007–2008. Seismic data from inland Antarctica are expected to reveal images of the Earth's deep interior with enhanced resolution because of the high signal-to-noise ratio and wide extent of this region, in addition to the rarity of sampling paths along the rotation axis of the Earth. We calculate synthetic seismograms through the preliminary reference earth model (PREM) including attenuation using a moment-tensor point source for the November 9, 2009 Fiji earthquake. Our results show quite good agreement between synthetic and observed seismograms, which indicates the accuracy of observations in the Antarctica, as well as the feasibility of the spherical 2.5-D modeling scheme.  相似文献   

16.
Summary. The rather abrupt changes in velocity gradient which have sometimes been proposed, notably in the upper mantle and near the base of the mantle, have an effect equivalent to that of one or more second-order discontinuities, where partial reflection occurs due to a change in curvature of the wavefront across these discontinuities. The effect is ignored in the classical WKBJ approximation to the wave functions, but it can be explicitly demonstrated by applying the extended WKBJ method (Langer's approximation) to a piecewise smooth layered model. For the purpose of this study it is convenient to represent the response of such a modelby a generalized reflection coefficient. For a model of one or a system of several second-order discontinuities (approximating a change in velocity gradient over a finite depth interval), the reflection coefficient can be perhaps surprisingly large for long-period waves near their turning point. It is shown that this effect can significantly alter the amplitude decay of SH waves diffracted around the core, in models where a change in velocity gradient near the core—mantle boundary constitutes a low-velocity zone at the base of the mantle; such models have recently been proposed. With the same velocity gradients, the effect on P diffraction is less important. The results for SH diffraction in these models support the conclusion that a small amplitude decay must be explained by a velocity decrease with depth, i.e. a low-velocity zone at the base of the mantle.  相似文献   

17.
Experimental study of shear-waves from shots in anisotropic media   总被引：1，自引：0，他引：1  
Summary. A complex array of vertical-seismic-profiles and reflection surveys in the Taman Peninsula, Krasnodar, using geophones with inclined axes, is used to investigate shear-wave splitting in thick Maikopian clays characterised by pronounced diapirism. The shear waves split into SH (faster) and SV (slower) components and display transverse isotropy with a vertical axis of symmetry with a maximum shear-wave delay of up to 0.5 s . Within the accuracy of the observations there is no azimuthal anisotropy.  相似文献   

18.
We investigate large-amplitude phases arriving in the P -wave coda of broad-band seismograms from teleseisms recorded by the Gräfenberg array, the German Regional Seismic Network and the Global Seismic Network. The data set consists of all events m b≤ 5.6 from the Aleutian arc between 1977 and 1992. Earthquakes with large-amplitude coda waves correlate with the presence of oceanic crust in the source region. The amplitudes sometimes approach those of the P wave, much larger than predicted by theory. Modelling indicates that phases in the P -wave coda cannot be P -wave multiples beneath the source and receiver, or underside reflections, which precede PP , from upper-mantle discontinuities. Among the events, seismograms are very similar, where the arrival times of the unusual phases agree approximately with the predicted times of S -to- P conversions from the upper-mantle discontinuities under the source. Because the large-amplitude phases in the P -wave coda have little, if any, dependence on event depth and have predominantly an SV -wave radiation pattern towards the receiver, we suggest that they originate as SV and/or Rayleigh waves and are enhanced by lateral heterogeneity and multipathing from the subducting Aleutian slab.  相似文献   

19.
Summary. Data from a refraction and a reflection seismic survey in the Black Forest, southwest Germany, are used for extensive one- and two-dimensional modelling. The data are available along approximately the same line, and therefore the same piece of crust is probed by two seismic methods. We utilize this favorable circumstance for detailed model calculations concerning both data sets. Lower crustal properties vary on the scale of a wavelength and thus full solutions of the elastic equations are required: the Reflectivity Method for the evaluation of refraction seismograms and numerical solutions of the acoustic wave equation for the reflection response. Details of the geometry and physical properties of the lamination are derived. Vertical layering on a scale of 100 m is found; horizontal extent of reflecting elements is in the range of a few hundreds of meters; rocks with velocities between 5.6 and 7.2 km/s constitute the lower crust.  相似文献   

20.
Summary. The propagation of a pulsed elastic wave in the following geometry is considered. An elastic half-space has a surface layer of a different material and the layer furthermore contains a bounded 3-D inhomogeneity. The exciting source is an explosion, modelled as an isotropic pressure point source with Gaussian behaviour in time.
The time-harmonic problem is solved using the null field approach (the T matrix method), and a frequency integral then gives the time-domain response. The main tools of the null field approach are integral representations containing the free space Green's dyadic, expansions in plane and spherical vector wave functions, and transformations between plane and spherical vector wave functions. It should be noted that the null field approach gives the solution to the full elastodynamic equations with, in principle, an arbitrarily high accuracy. Thus no ray approximations or the like are used. The main numerical limitation is that only low and intermediate frequencies, in the sense that the diameter of the inhomogeneity can only be a few wavelengths, can be considered.
The numerical examples show synthetic seismograms consisting of data from 15 observation points at increasing distances from the source. The normal component of the velocity field is computed and the anomalous field due to the inhomogeneity is sometimes shown separately. The shape of the inhomogeneity, the location and depth of the source, and the material parameters are all varied to illustrate the relative importance of the various parameters. Several specific wave types can be identified in the seismograms: Rayleigh waves, direct and reflected P -waves, and head waves.  相似文献   

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