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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Physics and chemistry of minerals 26 (1999), S. 406-414 
    ISSN: 1432-2021
    Keywords: Key words Lawsonite ; Equation of state ; X-ray diffraction ; High-pressure ; High-temperature
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract  A pressure-volume-temperature data set has been obtained for lawsonite [CaAl2Si2O7(OH)2.H2O], using synchrotron X-ray diffraction and an externally heated diamond anvil cell. Unit-cell volumes were measured to 9.4 GPa and 767 K by angle dispersive X-ray diffraction using imaging plates. Phase changes were not observed within this pressure-temperature range, and lawsonite compressed almost isotropically at constant temperature. The P-V-T data have been analyzed using a Birch- Murnaghan equation of state and a linear equation of state expressed as β=–1/V0 (∂V/∂P) T . At room temperature, the derived equation of state parameters are: K 0=124.1 (18) GPa K'0 set to 4) and β–1=142.0(24) GPa, respectively. Our results are intermediate between previously reported measurements. The high-temperature data show that the incompressibility of lawsonite decreases with increasing temperature to ∼500 K and then increases above. Hence, the second order temperature derivative of the bulk modulus is taken into account in the equation of state; a fit of the volume data yields K 0=123.9(18) GPa, (∂K/∂T)P=–0.111(3) GPa K–1, (∂2 K/∂T 2)P=0.28(6) 10–3 GPa K–2, α0=3.1(2) 10–5 K–1, assuming K'0=4.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of geodesy 73 (1999), S. 109-117 
    ISSN: 1432-1394
    Keywords: Key words. Multivariate Gauss ; Markoff model ; Eigenvalue decomposition ; Principal-component analysis ; Data reduction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. Geodetic adjustment problems frequently require the solution of large systems of linear equations. An approximation method is presented based on the decomposition of the estimated covariance matrix of the observation matrix, calculated in a pre-processing step, into a system of eigenvalues and eigenvectors. Neglecting the non-dominant eigenvalues and the assigned eigenvectors, the matrix of the residuals is approximated applying the synthesis formula of principal-component analysis. Although the number of observation vectors in the multivariate Gauss–Markoff model is drastically reduced, all unknown parameters are estimated approximately. The described method is tested using a numerical example of satellite altimetry.
    Type of Medium: Electronic Resource
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