Statistical features of sea-floor topography

Bell, Thomas H.

doi:10.1016/0011-7471(75)90090-x

Cited by 78 publications

(110 citation statements)

References 14 publications

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“…Goff and Jordan, 1988). In such places, stochastic models are appropriate for use because the frequency power spectra of deepocean bathymetry follow well-defined parametric relationships (Bell, 1975). Specifically, the high-frequency tail of the power spectra is characterised by power law relationships (i.e.…”

Section: Stochastic Modelsmentioning

confidence: 99%

“…This spectral behaviour is common across other types of natural terrain, and consequently spectral analysis of natural terrain often focuses upon establishing the transition between high-and low-frequency behaviour, and the characterisation of the high-frequency power law relationships (Shepard et al, 2001). Whilst the spectral properties of mid-ocean bathymetry (Bell, 1975;Goff and Jordan, 1988) and subglacial channels (Goff et al, 2014) have been assessed, to the best of our knowledge this has not been done for fjord bathymetry. As part of this study, we use data that are available from surveyed fjords to constrain the stochastic models of the bathymetry of many Greenland fjords.…”

Section: Stochastic Modelsmentioning

confidence: 99%

“…Our analysis is based upon analogous analysis of abyssal-hill features in the mid-ocean (Bell, 1975;Goff and Jordan, 1988), although it is simpler in the respect that fjord bathymetry is approximated as a one-dimensional problem. Using the centreline mapping approach presented in Sect.…”

Section: Stochastic Modelling Of Fjord Bathymetrymentioning

confidence: 99%

“…Power spectra for each fjord were then obtained from the square of the complex modulus, and arithmetically averaged over the nine selected fjord profiles, to create a composite power spectra. This arithmetic averaging approach is as described in Bell (1975) for mid-ocean bathymetry and enables longer wavelength features to be statistically constrained along with the higher-frequency features that are repeatedly sampled.…”

Section: Stochastic Modelling Of Fjord Bathymetrymentioning

confidence: 99%

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Generating synthetic fjord bathymetry for coastal Greenland

et al. 2017

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Abstract. Bed topography is a critical boundary for the numerical modelling of ice sheets and ice-ocean interactions. A persistent issue with existing topography products for the bed of the Greenland Ice Sheet and surrounding sea floor is the poor representation of coastal bathymetry, especially in regions of floating ice and near the grounding line. Sparse data coverage, and the resultant coarse resolution at the iceocean boundary, poses issues in our ability to model ice flow advance and retreat from the present position. In addition, as fjord bathymetry is known to exert strong control on ocean circulation and ice-ocean forcing, the lack of bed data leads to an inability to model these processes adequately. Since the release of the last complete Greenland bed topography-bathymetry product, new observational bathymetry data have become available. These data can be used to constrain bathymetry, but many fjords remain completely unsampled and therefore poorly resolved. Here, as part of the development of the next generation of Greenland bed topography products, we present a new method for constraining the bathymetry of fjord systems in regions where data coverage is sparse. For these cases, we generate synthetic fjord geometries using a method conditioned by surveys of terrestrial glacial valleys as well as existing sinuous feature interpolation schemes. Our approach enables the capture of the general bathymetry profile of a fjord in north-west Greenland close to Cape York, when compared to observational data. We validate our synthetic approach by demonstrating reduced overestimation of depths compared to past attempts to constrain fjord bathymetry. We also present an analysis of the spectral characteristics of fjord centrelines using recently acquired bathymetric observations, demonstrating how a stochastic model of fjord bathymetry could be parameterised and used to create different realisations.

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Section: Stochastic Modelsmentioning

confidence: 99%

Section: Stochastic Modelsmentioning

confidence: 99%

Section: Stochastic Modelling Of Fjord Bathymetrymentioning

confidence: 99%

Section: Stochastic Modelling Of Fjord Bathymetrymentioning

confidence: 99%

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Generating synthetic fjord bathymetry for coastal Greenland

et al. 2017

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“…We first consider the topography which is of particular importance since it is not only relatively well measured, but is a fundamental geophysical field. Starting with Vennig-Meinesz (1951), many spectral analyses of the earth's topography have been made (Balmino et al, 1973;Bell, 1975;Berkson and Matthews, 1983;Fox and Hayes, 1985;Gibert and Courtillot, 1987;Balmino, 1993;Mareschal, 1989;Lavallée et al, 1993;Tchiguirinskaia et al, 2000;Gagnon et al, 2003) all finding approximately power law (isotropic) spectra (also 3/28/07 1…”

Section: Horizontal Structuresmentioning

confidence: 99%

Scaling and multifractal fields in the solid earth and topography

Lovejoy

Schertzer

2007

Nonlin. Processes Geophys.

124

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Abstract. Starting about thirty years ago, new ideas in nonlinear dynamics, particularly fractals and scaling, provoked an explosive growth of research both in modeling and in experimentally characterizing geosystems over wide ranges of scale. In this review we focus on scaling advances in solid earth geophysics including the topography. To reduce the review to manageable proportions, we restrict our attention to scaling fields, i.e. to the discussion of intensive quantities such as ore concentrations, rock densities, susceptibilities, and magnetic and gravitational fields.We discuss the growing body of evidence showing that geofields are scaling (have power law dependencies on spatial scale, resolution), over wide ranges of both horizontal and vertical scale. Focusing on the cases where both horizontal and vertical statistics have both been estimated from proximate data, we argue that the exponents are systematically different, reflecting lithospheric stratification whichwhile very strong at small scales -becomes less and less pronounced at larger and larger scales, but in a scaling manner. We then discuss the necessity for treating the fields as multifractals rather than monofractals, the latter being too restrictive a framework. We discuss the consequences of multifractality for geostatistics, we then discuss cascade processes in which the same dynamical mechanism repeats scale after scale over a range. Using the binomial model first proposed by de Wijs (1951) as an example, we discuss the issues of microcanonical versus canonical conservation, algebraic ("Pareto") versus long tailed (e.g. lognormal) distributions, multifractal universality, conservative and nonconservative multifractal processes, codimension versus dimension formalisms. We compare and contrast different scaling models (fractional Brownian motion, fractional Levy motion, continuous (in scale) cascades), showing that they are all based on fractional integrations of noises built up from singularity Correspondence to: S. Lovejoy (lovejoy@physics.mcgill.ca) basis functions. We show how anisotropic (including stratified) models can be produced simply by replacing the usual distance function by an anisotropic scale function, hence by replacing isotropic singularities by anisotropic ones.

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Theory connecting nonlocal sediment transport, earth surface roughness, and the Sadler effect

Schumer

Taloni

Furbish

2017

Geophysical Research Letters

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Earth surface evolution, like many natural phenomena typified by fluctuations on a wide range of scales and deterministic smoothing, results in a statistically rough surface. We present theory demonstrating that scaling exponents of topographic and stratigraphic statistics arise from long‐time averaging of noisy surface evolution rather than specific landscape evolution processes. This is demonstrated through use of “elastic” Langevin equations that generically describe disturbance from a flat earth surface using a noise term that is smoothed deterministically via sediment transport. When smoothing due to transport is a local process, the geologic record self organizes such that a specific Sadler effect and topographic power spectral density (PSD) emerge. Variations in PSD slope reflect the presence or absence and character of nonlocality of sediment transport. The range of observed stratigraphic Sadler slopes captures the same smoothing feature combined with the presence of long‐range spatial correlation in topographic disturbance.

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Statistical features of sea-floor topography

Cited by 78 publications

References 14 publications

Generating synthetic fjord bathymetry for coastal Greenland

Generating synthetic fjord bathymetry for coastal Greenland

Scaling and multifractal fields in the solid earth and topography

Theory connecting nonlocal sediment transport, earth surface roughness, and the Sadler effect

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