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The high-degree constituents
of the bathymetric stripping
Corrections to gravity field quantities
Robert Tenzer, Gladkikh Vladislav
National School of Surveying, Division of Sciences, University of Otago, Dunedin,
New Zealand
Pavel Novák
Department of Mathematics, University of West Bohemia, Plzeň, Czech Republic
Motivation
In geophysical studies investigating the lithosphere structure, the
topographic, bathymetric, and consolidated crust density contrast
stripping corrections are computed and applied to observed
gravity data. The gravitational field generated by the ocean
density contrast represents a significant amount of the signal to
be modelled and subsequently removed from the Earth’s gravity
field. The currently available global topographic/bathymetric data
and the Earth’s gravity field models allow modelling the
topography corrected and bathymetry stripped gravity field
quantities to a very high accuracy and resolution (with a spectral
resolution complete to degree 2160 of spherical harmonics).
Objectives
• Computation of the bathymetric stripping corrections.
• Application of the bathymetric stripping corrections to the
topography corrected gravity field quantities.
Fig. 1 The bathymetric stripping correction to gravity
disturbances (min = 113 mGal, max = 1230 mGal, mean = 335
mGal, STD =169 mGal).
Fig. 2 The complete bathymetric stripping correction to gravity
anomalies (min = -752 mGal, max = 405 mGal, mean = -374
mGal, STD =110 mGal).
Fig. 3 The topography corrected gravity disturbances
(min = -1584 mGal, max = 345 mGal, mean = -70 mGal, STD
= 111 mGal).
Fig. 4 The topography corrected gravity anomalies (min = -720
mGal, max = 475 mGal, mean = 42 mGal, STD =76 mGal).
Fig. 5 The topography corrected and bathymetry stripped
gravity disturbances (min = -1443 mGal, max = 1472 mGal,
mean = 265 mGal, STD = 242 mGal).
Fig. 6 The topography corrected and bathymetry stripped
gravity anomalies (min = -766 mGal, max = 342 mGal, mean =
-374 mGal, STD = 108 mGal).
Input data
• EGM2008: Coefficients of the Earth Gravitational Model 2008
(EGM2008) up to degree/order 2160 (Pavlis et al. 2008).
• DTM2006.0: Coefficients of the global topography and
bathymetry model up to degree/order 2160 (publicly released
together with EGM2008 by the U.S. National GeospatialIntelligence Agency EGM development team).
Methodology
• The EGM2008 coefficients complete to degree 2160 of spherical
harmonics were used to compute the gravity disturbances and
gravity anomalies.
• The DTM2006.0 coefficients and the EGM2008 geoid model
coefficients were used to generate coefficients of the global
elevation model (GEM) and the global bathymetric model
(GBM). The GEM and GBM coefficients define the
heights/depths relative to the EGM2008 geoid surface.
• The GEM and GBM coefficients complete to degree 2160 of
spherical harmonics were used to compute the topographic and
bathymetric stripping corrections to the gravity disturbances and
gravity anomalies.
• The reference constant density of 2670 kg/m3 (Hinze 2003) was
adopted for computing the topographical and bathymetric
stripping corrections.
• The ocean density contrast was defined for the depthdependent seawater density model.
• All computations were realized globally on a 5×5 arc-min grid at
the Earth’s surface.
Results
• The bathymetric stripping corrections to gravity values (see Figs.
1 and 2).
• The topography corrected gravity values (see Figs. 3 and 4).
• The topography corrected and bathymetry stripped gravity
values (see Figs. 5 and 6).
• The power spectra and the spectral characteristics of the
bathymetric, topographic, and Earth’s gravity potentials (see
Figs. 7 and 8).
Conclusions
• The approximation of the actual seawater density by its mean value yields a relative
inaccuracy to about 2%. The approximation of the actual seawater density by the depthdependent density model reduces these errors considerably to less than 0.1%.
• The topography corrected and bathymetry stripped gravity field quantities revealed main
structures of the ocean floor relief and the global pattern of the tectonic plates more likely
due to the different density and thickness of the continental and oceanic lithospheric plates.
Moreover, more detailed features due to the inhomogeneities of the density and thickness
within the oceanic lithospheric plates (e.g., Mid-Atlantic Ridge) are pronounced.
• The bathymetric potential Vb has larger degree variances than the topographic potential Vt
and the Earth’s gravity potential W over a substantial part of the considered spherical
harmonic spectrum up to the maximum degree of 2159 (Fig. 7). The correlation between Vb
and W decreases (in an absolute sense) at higher-degrees (approximately from degree 180;
Fig. 8). The (absolute) correlation between Vb and W decreases below 0.3 approximately at
degrees above 1000 that correspond to the equiangular resolution of 10 arc-min (spatial
resolution of about 18 km). The lack of a larger correlation between Vb and W can be
explained by the existence of deep mass anomalies and isostatic compensation phenomena
inside the Earth’s interior that are reflected by the external gravity potential of the Earth.
The topographic potential Vt is significantly correlated with the Earth’s external gravity
potential W at the higher frequencies, while at a long-wavelength part of spectrum
(approximately below the spherical harmonic degree 20) it revealed inhomogeneous density
structures inside the Earth’s mantle (Fig. 8).
Fig. 7 The degree variances of the bathymetric, topographic, and Earth’s gravity potentials.
References
Hinze WJ (2003) Bouguer reduction density, why 2.67? Geophysics 68(5): 1559-1560
Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2008) An Earth Gravitational Model to degree 2160: EGM2008, General
Assembly of the European Geosciences Union, Vienna, Austria, April 13-18, 2008
Fig. 8 The correlation coefficients of the bathymetric and topographic potential values with the
EGM2008 gravity potential.