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  • 1
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 115 (1993), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: Using first-order ray perturbation theory and the paraxial ray approximation, a linear relation is derived that describes the first-order perturbation in amplitude due to slowness perturbations along a ray. The method is valid for smooth media, without interfaces. The method allows for an efficient calculation of Frechet derivatives for body wave amplitudes. This makes it possible to add body wave amplitude data to large-scale tomographic inversions for slowness distributions in the Earth. Depending directly on the derivatives of the slowness field, body wave amplitudes provide a constraint on the velocity distribution independent of traveltime data. For a realistic slowness distribution in the upper mantle, examples show that the region of applicability of the linearized perturbation theory to the calculation of amplitude perturbations may become very small due to the non-linear dependence of amplitudes on slowness perturbations. Traveltimes show a more linear dependence on slowness perturbations. The examples suggest that when amplitudes and traveltimes are combined in an inversion for the velocity structure of the upper mantle, a non-linear traveltime inversion must be performed before amplitude data are included. This ensures that the non-linear behaviour of amplitudes due to ray shift induced by slowness perturbations are minimized.
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  • 2
    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: Many geophysical problems involve inverting data in order to obtain meaningful descriptions of the Earth's interior. One of the basic characteristics of these inverse problems is their non-uniqueness. Since computation power has increased enormously in the last few years, it has become possible to deal with this non-uniqueness by generating and selecting a number of models that all fit the data up to a certain tolerance. In this way a solution space with acceptable models is created. The remaining task is then to infer the common robust properties of all the models in the ensemble. In this paper these properties are determined using empirical orthogonal function (EOF) analysis. This analysis provides a method to search for subspaces in the solution space (ensemble) that correspond to the patterns of minimum variability. In order to show the effectiveness of this method, two synthetic tests are presented. To verify the applicability of the analysis in geophysical inverse problems, the method is applied to an ensemble generated by a Monte Carlo search technique which inverts group-velocity dispersion data produced by using vertical-component, long-period synthetic seismograms of the fundamental Rayleigh mode. The result shows that EOF analysis successfully determines the well-constrained parts of the models and in effect reduces the variability present in the original ensemble while still recovering the earth model used to generate the synthetic seismograms. Finally, an application of the method to examine the contrast in upper-mantle S-wave velocity across the Tornquist-Tesseyre Zone is presented, indicating a significant change in S-wave velocity in the upper mantle beneath this zone bordering the East European Platform and Tectonic Europe, and a significantly thicker crust beneath the East European Platform.
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  • 3
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 115 (1993), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: Seismic waves in a random medium (with standard deviation ε and correlation distance a of the relative slowness fluctuations) prefer fast paths, and therefore the apparent velocity of wave propagation is larger than the velocity which corresponds to the volume average of slowness. This velocity shift can be determined by ray perturbation theory (Snieder & Sambridge 1992), by the Huygens method (Podvin & Lecomte 1991) and by wave theory (Müller, Roth & Korn 1992). We apply all three methods to plane-wave propagation through a 2-D acoustic medium with Gaussian or exponential autocorrelation function of the slowness fluctuations. Ray perturbation theory gives numerical and analytical results, but has path-length (L) limitations. The Huygens method, which also gives the ray-theoretical velocity shift, can be used for L/a ratios of seismological interest. Wave theory shows that the velocity shift also depends on the wavelength λ and that for λ/a less than about 0.1 the velocity shift agrees with the result of the Huygens method. For λ/a= 1 the wave-theoretical (i.e. true) shift is lower than the Huygens-method shift by a factor of 0.25 to 0.5. Simple formulae for the ε dependence of the Huygens-method shift at long path lengths (L/a≤ 80) are given, and a correction factor is derived which approximately transforms plane-wave 2-D into spherical-wave 3-D velocity shifts; the latter correspond to 3-D two-point ray tracing.For short-period seismic waves, propagating to teleseismic distances, mantle heterogeneity with ε= 1 per cent and a= 100 km produces a velocity shift of about 0.2 per cent. Shifts of this order can explain the difference in earth models, derived from free oscillations on the one hand and from short-period body waves on the other. A velocity shift (or velocity dispersion) due to anelasticity would be additional.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 103 (1990), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: A time- and frequency-dependent polarization method is applied to synthetic and observational data in order to investigate effects of lateral heterogeneity on surface wave polarization. It is shown that interference of surface wave signals can produce artifacts in the polarization as determined for the dominant signal present in the data.The time- and frequency-dependent polarization technique is applied to surface waves recorded in Iberia to investigate the character of the recorded wavetrains. Rayleigh waves with a southwest backazimuth recorded in the south of Spain appear strongly attenuated relative to other locations in Iberia. By analysing their polarizations, it can be inferred that these surface waves are highly distorted, implying that scattering mechanisms must be operative in the south of Spain. Strong scattering is one of the mechanisms that might explain the observed amplitude reduction, although other mechanisms like intrinsic scattering or defocusing may also contribute. With the present data and the present technique it is not possible to determine the relative contributions of each of these mechanisms.
    Type of Medium: Electronic Resource
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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: Power spectra of tomographic models of the entire earth and of models of Europe and the Mediterranean area are compared. This comparison reveals a discrepancy (a factor 15–30) between the power of both kinds of models at intermediate spherical-harmonic degrees (around l = 30). Two possible explanations for this discrepancy are given: first, the fact that Europe is more complex than the global average; and second, the lack of resolution in the inversions. Another approach to the problem of the power spectrum of heterogeneities of intermediate length scale is the study of multipathing of long-period surface waves. The multipathing observed in the recordings of these waves, which manifests itself as an increasing complexity of their amplitude spectra due to increasing interference of spectral components with increasing epicentral distance, cannot be explained by present-day global earth models. The gradients in the models are simply not strong enough. However, random models with more power at intermediate scales, and consequently stronger gradients, are able to explain the observed multipathing. It is concluded that the global models underestimate the power in the heterogeneities of intermediate-scale structure in the earth. Finally, an explanation is given why current global models, although they do not contain sufficient power at shorter scales, do explain the traveltime and dispersion data used for the construction of the models.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Physics of the Earth and Planetary Interiors 79 (1993), S. 1-2 
    ISSN: 0031-9201
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Physics of the Earth and Planetary Interiors 44 (1986), S. 226-241 
    ISSN: 0031-9201
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Wave Motion 20 (1994), S. 89-98 
    ISSN: 0165-2125
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 35 (1987), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: A seismic survey was carried out on a tidal flat in the SW-Netherlands in order to determine shear-wave velocities in sediments by means of higher-mode Rayleigh waves. The dispersion properties of these Rayleigh waves were measured in the 2-D amplitude spectrum–or f, k-spectrum–and resulted in phase velocities for six different modes as a function of frequency (5–30 Hz). These observed phase velocities were inverted for a nine-layer model for the shear-wave velocity to a depth of 50 m.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Geologische Rundschau 86 (1997), S. 446-463 
    ISSN: 0016-7835
    Keywords: Key words Earthquakes ; Forecasting ; Hazard ; risk ; Decision making
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Abstract  Earthquake prediction is an area of research of great scientific and public fascination. The reason for this is not only that earthquakes can cause extremely large numbers of fatalities in a short time, but also because earthquakes can have a large social and economic impact on society. Earthquake prediction in the sense of making deterministic predictions about the place, time, and magnitude of earthquakes may very well be fundamentally impossible. However, based on a variety of data, earth scientists can make statements about the probability that earthquakes with a certain size will occur in a certain region over a specified time period. In this context one speaks of “earthquake forecasting.” A number of methods to achieve this are presented. However, it is not obvious how society should respond to these forecasts. It is shown that there is a fundamental dilemma for decision makers that statements of scientists concerning earthquake occurrence either contain very specific information but are very uncertain, or contain very general information but are very certain. Earthquake hazard can to a large extent be reduced by formulating and enforcing appropriate building codes. However, given the fact that the majority of the population that is threatened by earthquakes is living in the third world, it is clear that this cannot easily be realized. For these reasons, earthquake prediction is not only a scientific problem: it also has a complex political dimension.
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