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  • conditional simulation  (2)
  • Kriging  (1)
  • 1
    ISSN: 1573-8868
    Keywords: simulation ; conditional simulation ; fourier methods ; band-limited fractal ; variogram ; fast kriging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract We evaluate the performance and statistical accuracy of the fast Fourier transform method for unconditional and conditional simulation. The method is applied under difficult but realistic circumstances of a large field (1001 by 1001 points) with abundant conditioning criteria and a band limited, anisotropic, fractal-based statistical characterization (the von Kármán model). The simple Fourier unconditional simulation is conducted by Fourier transform of the amplitude spectrum model, sampled on a discrete grid, multiplied by a random phase spectrum. Although computationally efficient, this method failed to adequately match the intended statistical model at small scales because of sinc-function convolution. Attempts to alleviate this problem through the “covariance” method (computing the amplitude spectrum by taking the square root of the discrete Fourier transform of the covariance function) created artifacts and spurious high wavenumber content. A modified Fourier method, consisting of pre-aliasing the wavenumber spectrum, satisfactorily remedies sinc smoothing. Conditional simulations using Fourier-based methods require several processing stages, including a smooth interpolation of the differential between conditioning data and an unconditional simulation. Although kriging is the ideal method for this step, it can take prohibitively long where the number of conditions is large. Here we develop a fast, approximate kriging methodology, consisting of coarse kriging followed by faster methods of interpolation. Though less accurate than full kriging, this fast kriging does not produce visually evident artifacts or adversely affect the a posteriori statistics of the Fourier conditional simulation.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 32 (2000), S. 765-786 
    ISSN: 1573-8868
    Keywords: stratigraphy ; bathymetry ; conditional simulation ; spectral modeling ; coherence modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Stratigraphic modeling based on physical and geologic principles has been improved by more sophisticated process models and increased computer power. However, such efforts may reach a limit in their predictive power because of the stochastic, multiscaled nature of the physical processes involved. Building on techniques from the geostatistical literature, a conditional simulation method, dubbed “SimStrat,” has been developed to improve predictions of stratigraphic architecture from limited data. No physical processes are invoked. Rather, the prediction is based solely on geometric and statistical principals. The method takes as input sonar bathymetry, seismically defined stratigraphic horizons, and core-defined horizons. Each stratigraphic horizon is characterized using spectral modeling and coherence modeling for adjacent horizons. Predictions of subsurface horizons are improved where seafloor bathymetry conforms with the underlying strata. Conditional simulations can then be generated that conform to available data constraints and statistical characterization. Tests with synthetic data in one and two dimensions for differing spectral models confirm the reliability of the method.
    Type of Medium: Electronic Resource
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  • 3
    Publication Date: 2022-05-25
    Description: Author Posting. © The Author(s), 2007. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Continental Shelf Research 28 (2008): 614-633, doi:10.1016/j.csr.2007.11.011.
    Description: We present a methodology for statistical analysis of randomly-located marine sediment point data, and apply it to the U.S. continental shelf portions of usSEABED mean grain size records. The usSEABED database, like many modern, large environmental datasets, is heterogeneous and interdisciplinary. We statistically test the database as a source of mean grain size data, and from it provide a first examination of regional seafloor sediment variability across the entire US continental shelf. Data derived from laboratory analyses (“extracted”) and from word-based descriptions (“parsed”) are treated separately, and they are compared statistically and deterministically. Data records are selected for spatial analysis by their location within sample regions: polygonal areas defined in ArcGIS chosen by geography, water depth, and data sufficiency. We derive isotropic, binned semivariograms from the data, and invert these for estimates of noise variance, field variance, and decorrelation distance. The highly erratic nature of the semivariograms is a result both of the random locations of the data and of the high level of data uncertainty (noise). This decorrelates the data covariance matrix for the inversion, and largely prevents robust estimation of the fractal dimension. Our comparison of the extracted and parsed mean grain size data demonstrates important differences between the two. In particular, extracted measurements generally produce finer mean grain sizes, lower noise variance, and lower field variance than parsed values. Such relationships can be used to derive a regionallydependent conversion factor between the two. Our analysis of sample regions on the U.S. continental shelf revealed considerable geographic variability in the estimated statistical parameters of field variance and decorrelation distance. Some regional relationships are evident, and overall there is a tendency for field variance to be higher where the average mean grain size is finer grained. Surprisingly, parsed and extracted noise magnitudes correlate with each other, which may indicate that some portion of the data variability that we identify as “noise” is caused by real grain size variability at very short scales. Our analyses demonstrate that by applying a bias-correction proxy, usSEABED data can be used to generate reliable interpolated maps of regional mean grain size and sediment character.
    Description: The authors thank the Office of Naval Research for support under grants N00014-05-1-0079 (JAG) and N00014-05-1-0080 (CJJ), and the USGS/Coastal and Marine Geology Program (SJW).
    Keywords: Grain size ; Continental shelf ; Database ; Semivariogram ; Statistical analysis ; Kriging
    Repository Name: Woods Hole Open Access Server
    Type: Preprint
    Format: application/pdf
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