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    Band-limited topographic mass distribution generates full-spectrum gravity field: Gravity forward modeling in the spectral and spatial domains revisited

    200750_132576_Hirt_Band-limited_topographic_mass_distribution.pdf (1.509Mb)
    Access Status
    Open access
    Authors
    Hirt, Christian
    Kuhn, Michael
    Date
    2014
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Hirt, C. and Kuhn, M. 2014. Band-limited topographic mass distribution generates full-spectrum gravity field: Gravity forward modeling in the spectral and spatial domains revisited. Journal of Geophysical Research: Solid Earth. 119 (4): pp. 3646-3661.
    Source Title
    Journal of Geophysical Research: Solid Earth
    DOI
    10.1002/2013JB010900
    ISSN
    2169-9313
    School
    Department of Spatial Sciences
    Remarks

    Copyright © 2014 American Geophysical Union

    URI
    http://hdl.handle.net/20.500.11937/40151
    Collection
    • Curtin Research Publications
    Abstract

    Most studies on gravity forward modeling in the spectral domain truncate the gravitational potential spectra at a resolution commensurate with the input topographic mass model. This implicitly assumes spectral consistency between topography and implied topographic potential. Here we demonstrate that a band-limited topographic mass distribution generates gravity signals with spectral energy at spatial scales far beyond the input topography's resolution. The spectral energy at scales shorter than the resolution of the input topography is associated with the contributions made by higher-order integer powers of the topography to the topographic potential. The pth integer power of a topography expanded to spherical harmonic degree n is found to make contributions to the topographic potential up to harmonic degree p times n. New numerical comparisons between Newton's integral evaluated in the spatial and spectral domain show that this previously little addressed truncation effect reaches amplitudes of several mGal for topography-implied gravity signals. Modeling the short-scale gravity signal in the spectral domain improves the agreement between spatial and spectral domain techniques to the μGal level, or below 10−5 in terms of relative errors. Our findings have important implications for the use of gravity forward modeling in geophysics and geodesy: The topographic potential in spherical harmonics must be calculated to a much higher harmonic degree than resolved by the input topography if consistency between topography and implied potential is sought. With the improved understanding of the spectral modeling technique in this paper, theories, and computer implementations for both techniques can now be significantly better mutually validated.

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