The high-degree constituents of the bathymetric stripping Corrections to gravity field

quantities

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 depth-dependent seawater density model.

• All computations were realized globally on a 5×5 arc-min grid at the Earth’s surface.

MotivationIn 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).

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 depth-dependent 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.

Fig. 2 The complete bathymetric stripping correction to gravity anomalies (min = -752 mGal, max = 405 mGal, mean = -374 mGal, STD =110 mGal).

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).

Robert Tenzer, Gladkikh VladislavNational School of Surveying, Division of Sciences, University of Otago,

Dunedin, New ZealandPavel Novák Department of Mathematics, University of West Bohemia, Plzeň, Czech

Republic

Fig. 8 The correlation coefficients of the bathymetric and topographic potential values with the EGM2008 gravity potential.

Objectives • Computation of the bathymetric stripping corrections.• Application of the bathymetric stripping corrections to

the topography corrected gravity field quantities.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 Geospatial-Intelligence Agency EGM development team).

Fig. 1 The bathymetric stripping correction to gravity disturbances (min = 113 mGal, max = 1230 mGal, mean = 335 mGal, STD =169 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).

ReferencesHinze WJ (2003) Bouguer reduction density, why 2.67? Geophysics 68(5): 1559-1560Pavlis 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