共查询到20条相似文献，搜索用时 703 毫秒
1.
Effects of the free surface on shear wavetrains 总被引：1，自引：0，他引：1
Russ Evans 《Geophysical Journal International》1984,76(1):165-172
Summary. The behaviour of shear-waves is of great importance in identifying and investigating seismic anisotropy in the Earth. However, shear wavetrains recorded at the Earth's surface do not always reflect the motion at depth, introducing practical problems of interpretation. Shear wavetrains incident on the surface of an isotropic half-space at angles less than critical (about 35°) are broadly preserved, but at greater angles substantial distortions can occur. For stations situated close to the source, as in local earthquake studies, the local SP phase, a radially polarized precursor to S , may occur. The behaviour at the surface of an anisotropic half-space is further complicated by the divergence of phase and energy propagation vectors. All of these complications suggest that detailed seismogram modelling is essential to any study of shear wave propagation in the Earth, and in particular to investigations of anisotropy-induced shear-wave splitting. 相似文献
2.
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
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
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.
Adopting Born and ray approximations, time-domain synthetic seismograms for P-P and P-S scattering from a plane wave incident on a thin, laterally heterogeneous layer are presented in this paper. The time-domain P coda is a convolution between a structure function and the second-order derivative of the time function of the incident P wave. Examples of synthetic seismograms are given using a time function from a computed short-period seismogram for a point explosive source in a half-space. These show that it is impossible, with realistic values of the parameters involved, to generate significant codas when only single scattering is involved. 相似文献
5.
Implementation of perfectly matched layers in an arbitrary geometrical boundary for elastic wave modelling 总被引：1，自引：0，他引：1
The perfectly matched layer (PML) absorbing boundary condition is incorporated into an irregular-grid elastic-wave modelling scheme, thus resulting in an irregular-grid PML method. We develop the irregular-grid PML method using the local coordinate system based PML splitting equations and integral formulation of the PML equations. The irregular-grid PML method is implemented under a discretization of triangular grid cells, which has the ability to absorb incident waves in arbitrary directions. This allows the PML absorbing layer to be imposed along arbitrary geometrical boundaries. As a result, the computational domain can be constructed with smaller nodes, for instance, to represent the 2-D half-space by a semi-circle rather than a rectangle. By using a smooth artificial boundary, the irregular-grid PML method can also avoid the special treatments to the corners, which lead to complex computer implementations in the conventional PML method. We implement the irregular-grid PML method in both 2-D elastic isotropic and anisotropic media. The numerical simulations of a VTI lamb's problem, wave propagation in an isotropic elastic medium with curved surface and in a TTI medium demonstrate the good behaviour of the irregular-grid PML method. 相似文献
6.
Joseph Ha 《Geophysical Journal International》1984,79(3):863-873
Summary. A set of recurrence relations which are computationally more efficient than those of the reflection matrix method of Kennett & Kerry is presented for P - and SV -wave generation in a ( n + 1) layered medium. The recurrence relations contain no growing terms and thus provide a stable algorithm for computing complete P and SV synthetic seismograms. Our algorithm requires a fewer algebraic operations for computing the reflectivity and transmissivity coefficients, ranging from 15 per cent less for a source in the half-space to 30 per cent less for a source in the top layer, than the reflection matrix method. 相似文献
7.
Summary. The polarizations of shear waves recorded by networks of digital three-component seismometers immediately above small earthquakes near the North Anatolian Fault in Turkey display shear-wave splitting on almost all shear-wave seismograms recorded within the shear-wave window. This splitting is incompatible with source radiation-patterns propagating through simple isotropic structures but is compatible with effective anisotropy of the internal structure of the rock along the ray paths. This paper interprets the phenomena in terms of widespread crack-induced anisotropy. Distributions of stress-induced cracks model many features of the observations, and synthetic polarization diagrams calculated for propagation through simulated cracked rock are similar to the observed patterns. This evidence for widespread crack-induced anisotropy lends strong support to the hypothesis of extensive-dilatancy anisotropy (EDA) suggested by laboratory experiments in subcritical crack-growth. The crucial evidence confirming some form of EDA would be observations of temporal changes in shear-wave splitting as the stress field alters the crack density and crack geometry. There is some weak evidence for such temporal changes at one site, but further analysis of suitable digital three-component seismometer networks in seismic areas is required to confirm EDA. 相似文献
8.
We study the effects of structural inhomogeneity on the quasi-static growth of strike-slip faults. A layered medium is considered, made up of an upper layer bounded by a free surface and welded to a lower half-space with different elastic property. Mode III crack is employed as a mathematical model of strike-slip fault, which is nucleated in the lower half-space and then propagates towards the interface. We adopt FEM-β, newly proposed analysis method for failure, to simulate the quasi-statistic crack growth governed by the stress distribution in layered media. Our results show that along planar traces across interfaces a compliant upper layer has significant effects on promoting/suppressing crack growth before/after its extension into the layer and vice versa for a rigid one. This proposes a possibility that surface breaks due to strike-slip faulting could be arrested by deposit layers at the topmost part of the Earth's crust. 相似文献
9.
T. J. Clarke 《Geophysical Journal International》1984,78(3):775-793
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. 相似文献
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. 相似文献
10.
Seismic waves in a stratified half space 总被引：5，自引：0，他引：5
B. L. N. Kennett 《Geophysical Journal International》1980,61(1):1-10
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
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
11.
Summary. There is evidence that the equivalent seismic sources of the Amchitka Island explosions — Longshot, Milrow and Cannikin — depart significantly from the simple model of a point compressional-source in a layered elastic-medium. Consequently modelling the observed seismograms using standard source-models may not be the most efficient method of determining source properties. Here an alternative to modelling is used to obtain information on the seismic sources due to the explosions. Broad-band (BB) estimates of the P signals are obtained from the short-period (SP) seismograms, corrected for attenuation, and interpreted in terms of P, pP and radiation from secondary sources. the main conclusions are:
(i) BB estimates of the radiated displacement from the explosions can be obtained with only a small reduction in the signal-to-noise ratio seen on SP seismograms;
(ii) observations of differences in pulse amplitudes and spectra are not necessarily due to differences in anelastic attenuation;
(iii) P and pP at a given station may differ in shape so that notches in the signal spectrum may not be related to source depth;
(iv) there is evidence of arrivals that others have identified as due to slap-down but which could be interpreted as an overshoot to pP;
(v) direct interpretation of the estimated ground displacement is a better procedure for determining the seismic source properties of explosions than modelling SP seismograms using idealised models as a starting point. 相似文献
(i) BB estimates of the radiated displacement from the explosions can be obtained with only a small reduction in the signal-to-noise ratio seen on SP seismograms;
(ii) observations of differences in pulse amplitudes and spectra are not necessarily due to differences in anelastic attenuation;
(iii) P and pP at a given station may differ in shape so that notches in the signal spectrum may not be related to source depth;
(iv) there is evidence of arrivals that others have identified as due to slap-down but which could be interpreted as an overshoot to pP;
(v) direct interpretation of the estimated ground displacement is a better procedure for determining the seismic source properties of explosions than modelling SP seismograms using idealised models as a starting point. 相似文献
12.
A fault plane solution using theoretical P seismograms 总被引：1，自引：0，他引：1
We use the method of Hudson and Douglas, Hudson & Blarney to compute seismograms which simulate the codas of 10 short period P -wave seismograms from a shallow earthquake. The polarities and relative amplitudes of P and pP measured from seven of the observed seismograms are used to compute a fault plane solution with confidence limits, assuming that the source radiates as a double couple. This solution is in approximate agreement with that given for the same earthquake by Sykes & Sbar, who used only the onset polarities of short-period P waves. The small difference between the two solutions can be explained by interference between the true first motion of P and microseismic noise at two stations.
The results show that, for some shallow earthquakes, the relative amplitude method has the following advantages over the first motions method. First, a P/pP amplitude ratio (with appropriate confidence limits) can always be measured, even in seismograms which are so noisy that the first motion of P is uncertain. Second, the fault plane solutions obtained from relative amplitudes have known confidence limits. Finally, by using more information from each seismogram, the relative amplitude method requires considerably fewer seismograms than the first motions method. 相似文献
The results show that, for some shallow earthquakes, the relative amplitude method has the following advantages over the first motions method. First, a P/pP amplitude ratio (with appropriate confidence limits) can always be measured, even in seismograms which are so noisy that the first motion of P is uncertain. Second, the fault plane solutions obtained from relative amplitudes have known confidence limits. Finally, by using more information from each seismogram, the relative amplitude method requires considerably fewer seismograms than the first motions method. 相似文献
13.
Joseph Ha 《Geophysical Journal International》1984,78(1):291-305
Summary. A set of recurrence relations similar to that of Kennett suitable for SH -wave generation in an ( n + l)-layered half-space is presented. The recurrence relations contain no growing terms, thus providing a stable and efficient algorithm for computing complete SH synthetic seismograms. The complete expansion of these recurrence relations gives the explicit form of the transfer function for SH -waves. The transfer function for a point source in layer s of the stratification is a series of 2 n terms in the denominator and a series of 2 n−s +1 terms in the numerator. The result of Wang from ray summation is shown to be a special case of our general result. Numerical comparison of the algorithm of this paper with the propagator matrix method is also made. 相似文献
14.
Toshiro Tanimoto 《Geophysical Journal International》1982,70(3):639-646
Summary. There are two ways to apply the Cagniard de-Hoop method when generating synthetic seismograms due to a source in a three-dimensional medium. One is the Hankel transform method (hereafter called 'the cylindrical wave representation method'), which utilizes the property of the modified Bessel function. The other is 'the plane wave representation method', which replaces the Bessel function by a superposition of plane waves. In extending a point source to a finite dimensional source, the latter method is extremely useful, because it enables the integrations on the fault surface to be performed analytically.
Using the latter method, expressions for displacements due to a Haskell type vertical fault in a uniform half-space are obtained. A solution is given as a sum of four quadrantal source contributions, which is similar to Madariaga's solution for a source in the whole space. Each contribution consists of a single finite range integration or a single integration plus a pole contribution, depending on the location of the observation point with respect to the source. The procedure can be extended to other fault types. 相似文献
Using the latter method, expressions for displacements due to a Haskell type vertical fault in a uniform half-space are obtained. A solution is given as a sum of four quadrantal source contributions, which is similar to Madariaga's solution for a source in the whole space. Each contribution consists of a single finite range integration or a single integration plus a pole contribution, depending on the location of the observation point with respect to the source. The procedure can be extended to other fault types. 相似文献
15.
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. 相似文献
16.
Summary. Seismic investigations using shear-wave and converted wave techniques show that very often reflected PS - and SS -waves have anomalous polarizations ( accessory components ). This phenomenon cannot be explained in terms of isotropic models with dipping boundaries. Computations of synthetic seismograms of reflected PS - and SS -waves were made for different models of transversely isotropic media with dipping anisotropic symmetry axes not normal to the boundaries. Synthetic seismograms were computed by ray techniques using an optimization algorithm to construct all rays arriving at a given receiver. These computations indicate that accessory components arise when the medium above the boundary is anisotropic, where they are caused by the constructive interference of qSV - and qSH -waves. If a low-velocity layer is present, displacement vectors of both waves have horizontal projections which are approximately orthogonal. The algorithm for wave separation is presented and some results of its use are given. 相似文献
17.
Seismic body waves in anisotropic media: reflection and refraction at a plane interface 总被引：9，自引：0，他引：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
18.
Summary. Analytical results are presented for Love waves generated by sudden changes of the rate of advance of a curved rupture front in an inclined fault plane that is embedded in an elastic half-space. The boundary condition at the surface of the half-space approximates the presence of an overlying layer. The calculation consists of two parts. First, ray theory is used to calculate far-field approximations to the horizontally polarized wavefields which are emitted when the speed of the rupture front suddenly changes. These fields can be expressed as products of emission coefficients (which govern the angular dependence) and propagation terms. Secondly, a representation integral for the Love wave over a surface enclosing the rupture front is constructed, using the emitted signal and an appropriate Green's function. This integral is evaluated asymptotically. The resulting approximate Love-wave spectrum shows an explicit dependence on the nature of the rupture process, on the rupture-front and fault-plane geometry, and on the magnitude of a sudden change in the rate of advance of the rupture front. 相似文献
19.
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. 相似文献
20.
David W. Eaton 《Geophysical Journal International》2006,166(3):1249-1258
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