 |
| Titel |
Characterizing the statistical structure of bathymetry and topography as a Matérn process |
| VerfasserIn |
Frederik J. Simons, Sofia C. Olhede, Gabe L. Eggers, Kevin W. Lewis |
| Konferenz |
EGU General Assembly 2014
|
| Medientyp |
Artikel
|
| Sprache |
Englisch
|
| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 16 (2014) |
| Datensatznummer |
250098854
|
| Publikation (Nr.) |
 EGU/EGU2014-14572.pdf |
|
|
|
|
|
| Zusammenfassung |
| Describing and classifying the statistical structure of topography and bathymetry is of much
interest across the geophysical sciences. Oceanographers are interested in the roughness of
seafloor bathymetry as a parameter that can be linked to internal-wave generation and mixing
of ocean currents. Tectonicists are searching for ways to link the shape and fracturing of the
ocean floor to build detailed models of the evolution of the ocean basins in a plate-tectonic
context. Geomorphologists are building time-dependent models of the surface that benefit
from sparsely parameterized representations whose evolution can be described by differential
equations. Geophysicists seek access to parameterized forms for the spectral shape of
topographic or bathymetric loading at various (sub)surface interfaces in order to use the joint
structure of topography and gravity for inversions for the effective elastic thickness
of the lithosphere. Planetary scientists are in need of robust terrain-classification
models to help unravel the cratering history and tectonic evolution of planetary
surfaces, for the selection of suitable landing sites, and for purposes as mundane as the
prediction of wear and tear on rover wheels. Finally, statisticians, mathematicians
and computer scientists are interested in the analysis of texture for purposes of
out-of-sample prediction, extension, and in-painting for application in fields as diverse as
computer graphics and medical imaging. A unified geostatistical framework for the
description, characterization and study of surfaces of these various kinds and for
such a multitude of applications is via the Matérn process, a theoretically well
justified and mathematically attractive parameterized form for the spectral-domain
covariance of Gaussian processes, both in isotropic form and considering various
geometrical kinds anisotropy. We discuss a constructive new estimation technique to
find the parameters of the Matérn forms of topography and bathymetry from small
and possibly irregularly shaped pieces of terrestrial and planetary real estate, via
maximum-likelihood optimization. We discuss whether the Matérn form is appropriate (it is),
how to find the parameters and their associated uncertainties, how well the models
fit the data, and, finally, what they can tell us about the surfaces in question. We
present results that are analytical as well as numerical, backed by extensive testing on
simulated data, and with examples for the terrestrial planets Venus and Mars, as well as
for the seafloor- and subseafloor expression of tectonic and geomorphic processes
on Earth, where we hope that our new methodology will lead to new paradigms. |
|
|
|
|
|
|