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  • 1
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 124 (1996), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: If body-wave phases in laterally heterogeneous media are modelled by surface-wave mode summation, mode coupling is required to bring out the ray character of the body-wave phases. However, it is frequently assumed that in laterally heterogeneous media surface-wave modes propagate without interacting with other modes. The effects of neglecting surface-wave mode coupling on the results from waveform inversions including body-wave arrivals have been studied by performing inversions with and without taking surface-wave mode coupling into account. The two inversion schemes are similar to the Partitioned Waveform Inversion (Nolet 1990) but differ in the approximations used to compute the synthetics: WKBJ, which neglects mode coupling, or SEA (Marquering & Snieder 1995), which does take mode coupling into account.Synthetic inversion experiments show that neglecting mode coupling can lead to biases in the deeper part of the model. Their most striking feature is that for ‘real’ shallow lateral heterogeneities, artificial anomalies with an opposite sign may show up in the deeper part of the model. When mode coupling is taken into account, as in the SEA inversion scheme, these biases do not occur.We have also studied possible bias effects as the result of using WKBJ in the EUR-S91 model of Zielhuis & Nolet (1994), which is characterized by strong velocity anomalies extending as deep as the transition zone. One of the most striking features in this model is the region of low velocities at larger depths beneath the fast Russian platform on the eastern side of the Tornquist–Teisseyre Zone (TTZ). Nolet & Zielhuis (1994) suggested that these low velocities are an indication for injection of water in the mantle by an earlier subduction. Our results show that the neglect of mode coupling indeed does bias the model towards a larger reversal of velocities with depth, and heterogeneities show up even where the S ray does not sample the mantle. However, low velocities deep below the eastern part of the TTZ persist even when mode coupling is taken into account.
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  • 2
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 96 (1989), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: The reflection and transmission of plane P- and S-waves by a laterally homogeneous band is discussed. A dyadic representation of a ‘plane wave Green's tensor’ is derived, which is used to describe the reflection and transmission of plane waves by a thin homogeneous layer in the first Born approximation. From this, the reflection and transmission by an arbitrarily thick continuously stratified band is derived using invariant imbedding. We derive an exact set of matrix Ricatti equations which describe the reflection and transmission of plane waves by the laterally homogeneous band. These equations remain regular at turning points, and incorporate both homogeneous and inhomogeneous waves within the heterogeneity. It is not necessary for the band to be stratified; the density and the elasticity tensor of the band may have an arbitrary depth dependence. It is shown that in case the band is a smooth heterogeneity without turning points, its only effect is a phase shift of the transmitted wave. In a numerical example for the analogue case of 1-D scattering in quantum mechanics the behaviour of homogeneous and inhomogeneous (tunneling) waves is illustrated.
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  • 3
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 120 (1995), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: The importance of surface-wave mode coupling in the modelling of body-wave phases by surface-wave mode summation is studied by means of sensitivity kernels obtained with the Born approximation and exact solutions of the Invariant Imbedding Technique. It is shown that, independent of the character of the lateral heterogeneity, surface-wave mode coupling is required to model body-wave phase perturbations and that neglecting intermode coupling, as in the WKBJ method for surface waves, can lead to large biases. Because methods which describe surfacewave mode coupling in an exact fashion are computationally too expensive to use in inversion schemes, the Scalar Exponent Approximation (SEA) is presented, which is a computationally efficient method and takes mode coupling into account. Since, instead of Earth normal modes, surface-wave modes are used, the summation over the angular order l is carried out analytically. This means that the number of modes and mode interactions needed is significantly reduced which assures an efficient manner of modelling. It is shown that the SEA is accurate in modelling body-wave phase perturbations for geophysically realistic configurations. Because, in contrast to the WKBJ sensitivity kernels, mode coupling introduces sensitivity kernels which also depend on the position along the source-receiver path, the SEA requires a larger model parameter set in inversions. A procedure is presented which reorganizes the model parameter set and leads to a reduced set of physically relevant model parameters. The combination of the SEA and the reorganization of the model parameters can be used efficiently in large-scale 3-D inversions which incorporate the important effects of surface-wave mode coupling.
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  • 4
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 125 (1996), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: Geometric ray theory is an extremely efficient tool for modelling wave propagation through heterogeneous media. Its use is, however, only justified when the inhomogeneity satisfies certain smoothness criteria. These criteria are often not satisfied, for example in wave propagation through turbulent media. In this paper, the effect of velocity perturbations on the phase and amplitude of transient wavefields is investigated for the situation that the velocity perturbation is not necessarily smooth enough to justify the use of ray theory. It is shown that the phase and amplitude perturbations of transient arrivals can to first order be written as weighted averages of the velocity perturbation over the first Fresnel zone. The resulting averaging integrals are derived for a homogeneous reference medium as well as for inhomogeneous reference media where the equations of dynamic ray tracing need to be invoked. The use of the averaging integrals is illustrated with a numerical example. This example also shows that the derived averaging integrals form a useful starting point for further approximations. The fact that the delay time due to the velocity perturbation can be expressed as a weighted average over the first Fresnel zone explains the success of tomographic inversions schemes that are based on ray theory in situations where ray theory is strictly not justified; in that situation one merely collapses the true sensitivity function over the first Fresnel zone to a line integral along a geometric ray.
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  • 5
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 123 (1995), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: It is generally believed that azimuthal seismic anisotropy is an important property of the subcontinental mantle, and that this is a relatively small-scale phenomenon compared with anisotropy of the oceanic mantle. During recent years, shear-wave splitting has come to be viewed as the most direct diagnostic of azimuthal anisotropy. The magnitude of the splitting delay times can often rule out a crustal source of anisotropy; however, it is not yet clear whether the source of anisotropy lies within the lithosphere or the sublithosphere. It is essential to know the scale of lateral variations and the distribution of anisotropy with depth in order to understand the origin of this phenomenon. Here we describe a way to constrain the depth of the anisotropy, by studying the lateral variation of the splitting parameters at neighbouring seismic stations. We use SKS and SKKS phases recorded at the NARS-NL array, a relatively dense network of broad-band stations separated by about 50 km. Fresnel zones at different depths are calculated for these phases. The depth of the anisotropy is constrained by the criterion that Fresnel zones corresponding to different splitting observations should not overlap. Variability in the splitting measurements for events with different directions of approach recorded at one station, and for single events recorded at various stations, provides evidence for a non-homogeneously distributed source of anisotropy, located below the array at different depths. We show that this variability in the measurements cannot be due to effects of crustal scattering. Our results indicate that the anisotropy is partly located in the sublithospheric mantle at about 400 km depth. This suggests that the deformation in this region is subject to significant lateral variations.
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  • 6
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: The stable, Precambrian East European Platform adjoins the younger, tectonically active regions of central and western Europe along a distinct crustal boundary, the Tornquist-Teisseyre Zone (TTZ). Seismic body- and surface-wave studies indicate that there may be a significant change in S-wave velocity at the top of the mantle in the region of the TTZ, with higher velocities under the East European Platform. to confirm these results we use a genetic algorithm (GA) to invert fundamental Rayleigh group-velocity estimates for wave paths across western and central Europe and across the East European Platform to determine ‘average’layered S-velocity models separately for each region. the use of the GA method allows identical model parametrizations and broad parameter search ranges to be used for both regions so that a relatively unbiased estimate of the difference in structure can be obtained.The GA is a guided search technique which requires neither a linearized forward method nor a single starting model and which can be applied to very large model-spaces. Consequently, fewer assumptions and physical approximations are required and a greater range of possible solutions is examined than with many other inversion methods. Here we employ the GA to produce a large set of acceptable solutions and associated misfit values, in contrast to inversion for a single, ‘optimum’solution. the scatter in the set of acceptable solutions gives an estimation of uncertainty, resolution and parameter trade-offs of the non-linear inversion.The scatter of the solutions for the dispersion data shows velocity-depth trade-offs around the Mohorovičić discontinuity, indicates the maximum depth resolution of the inversion, and shows the uncertainty in upper mantle S-velocity estimates. the results indicate a thicker crust and up to 0.3 km s-1 (7 per cent) higher ‘average’S-wave velocities in the upper 100km of the mantle under the East European Platform than under western and central Europe.
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  • 7
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 127 (1996), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: Waveforms of 449 seismograms have been inverted for S-wave velocity structures beneath Europe, the northeastern Atlantic, and western Asia down to a depth of 670 km. Recorded waveforms were used in the time window starting at the S-wave arrival and ending after the fundamental-mode Rayleigh-wave arrival. The inversion method is based on the partitioned waveform inversion (Nolet 1990), with the difference that synthetic seismograms are calculated taking surface-wave mode coupling into account in order to model body waves in laterally heterogeneous media more accurately. The partitioning of the inversion procedure makes non-linear optimization feasible, even for inversions including surface-wave mode coupling. The non-linear inversion of the waveforms resulted in linear constraints on the 3-D velocity structure. In a second step, these constraints were used in a linear inversion for the 3-D shear-wave velocity model beneath Europe, the northeastern Atlantic and western Asia. The EUR-SC'95 model is presented, which is characterized by a wide range of length-scales of the velocity structures. In central Europe, where the ray density is highest, small-scale structures are recovered, such as the presence of high velocities associated with the Hellenic subduction zone. On the edges of the inversion model, where the ray density (and therefore also the resolution) is poorer, we find larger-scale features, such as the relatively laterally homogeneous high-velocity structure beneath the Russian Platform to a depth of 300 km. In this paper we discuss the inversion method, data processing, parametrization difficulties due to the introduction of surface-wave mode coupling, spatial resolution of the model, and structures in the EUR-SC'95 model.
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  • 8
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 126 (1996), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: The wavelength-smoothing (WS) method was introduced recently (Lomax 1994) as a method for the rapid estimation of the principal features of broad-band wave phenomena in realistic., complicated structures. The WS method is based on the concept that waves at a particular frequency and corresponding wavelength respond to a complicated velocity distribution as if the distribution were smoothed over about a wavelength. This method reproduces several finite-frequency wave phenomena, but has not been given a formal theoretical justification. Here, we use scattering theory and a local, plane-wave approximation to develop a wavelength-averaging (WA) method for modelling finite-frequency wave propagation. The new WA method is similar to the WS method in concept and implementation, but is valid only in a more limited geometry of velocity heterogeneity. In particular, the new formulation performs well for models with complex, but smoothly varying, velocity variations (‘quasi-random’ models), but does less well in models with extensive regions of slowly varying velocity that are separated by strong gradients in velocity (‘deterministic’ models). This limits application of the current formulation of the WA method to predominantly quasi-random structures, although such models may be useful in many problems, particularly for Monte-Carlo-based inversion methods requiring fast forward calculations.
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  • 9
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 98 (1989), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: Surface wave attenuation is usually attributed to inelastic properties of the Earth, but a considerable part of the surface wave attenuation may be due to scattering by lateral heterogeneities. For body waves, the theory describing attenuation due to scattering is well known. In this paper, a similar theory is presented, which describes the attenuation of surface waves due to scattering. The Born approximation is used to derive the scattered wavefield, therefore only weak heterogeneities can be described. Some numerical experiments are performed for periods between 25 and 100 s. For realistic scatterers the conversions from the fundamental mode to the higher modes cannot be neglected. The Q−1 values computed for scattering media are of the same order of magnitude as measured Q−1 data. A whole range of attenuation curves as a function of frequency can be obtained by varying the parameters of the scattering experiment. This leads to believe that Q−1 data inversions to Q−1 depth models should be regarded with some suspicion, because the contribution of scattering to the attenuation cannot be neglected.
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  • 10
    Electronic Resource
    Electronic Resource
    [s.l.] : Macmillan Magazines Ltd.
    Nature 401 (1999), S. 739-740 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Ask your colleagues and students to define a wave, and you may be surprised at the answers you get. Even wave professionals are prone to confusion and vagueness when confronted with such an apparently simple question. Students often begin circularly: “a wave is a solution to the wave ...
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