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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of geodesy 72 (1998), S. 294-303 
    ISSN: 1432-1394
    Keywords: Key words Wavelets ; B-splines ; Gravity tides
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. In this contribution we introduce the concept of multiresolution analysis (MRA) and give an explanation of the relationship between MRA and orthonormal wavelet basis. The construction of the orthonormal B-spline wavelet bases is described in detail. We extend the B-splines to `non-integral order' cases and thus obtain a new family of orthonormal wavelet bases for the space L 2(R). Some good properties of the new wavelets are demonstrated. The new wavelet family gives satisfactory performances in our research projects including seismic signal compression and gravity tide data processing.
    Type of Medium: Electronic Resource
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  • 2
    Publication Date: 2019-07-10
    Description: The conventional Lorenz-Mie formalism is extended to the scattering process associated with a coated sphere embedded in an absorbing medium. It is shown that apparent and inherent scattering cross sections of a scattering particle, which are identical in the case of transparent host medium, are different if the host medium is absorptive. Here the inherent single-scattering properties are derived from the near-field information whereas the corresponding apparent counterparts are derived from the far-field asymptotic form of the scattered wave with scaling of host absorption that is assumed to be in an exponential form. The formality extinction and scattering efficiencies defined in the same manner as in the conventional sense can be unbounded. For a nonabsorptive particle embedded in an absorbing medium, the effect of host absorption on the phase matrix elements associated with polarization is significant. This effect, however, is largely reduced for strongly absorptive particles such as soot. For soot particles coated with water, the impurity can substantially reduce the single-scattering albedo of the particle if the size parameter is small. For water-coating soot and hollow ice spheres, it is shown that the phase matrix elements -P(sub 12)/P(sub 11) and P(sub 33)/P(sub 11) are unique if the shell is thin, as compared with the case for thick shell. Furthermore, the radiative transfer equation regarding a multidisperse particle system in an absorbing medium is discussed. It is illustrated that the conventional computation algorithms can be applied to solve the multiple scattering process if the scaled apparent single-scattering properties are applied.
    Keywords: Communications and Radar
    Format: application/pdf
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