Robert Tenzer

Global maps of the CRUST 2.0 crustal components stripped gravity disturbances

We use the CRUST 2.0 crustal model and the EGM08 geopotential model to compile global maps of the gravity disturbances corrected for the gravitational effects (attractions) of the topography and of the density contrasts of the oceans, sediments, ice, and the remaining crust down to the Moho discontinuity. Techniques for a spherical harmonic analysis of the gravity field are used to compute both the gravity disturbances and the topographic and bathymetric corrections with a spectral resolution complete to degree 180 of the spherical harmonics. The ice stripping correction is computed with a spectral resolution complete to degree 90. The sediment and consolidated crust stripping corrections are computed in spatial form by forward modeling their respective attractions. All data are evaluated on a 1 × 1 arc degree grid at the Earths surface and provided in Data Sets S1–S5 in the auxiliary material for the scientific community for use in global geophysical studies. The complete crust-stripped gravity disturbances (globally having a range of 1050 mGal) contain the gravitational signal coming dominantly from the global mantle lithosphere (upper mantle) morphology and density composition and partially from the sublithospheric density heterogeneities. Large errors are expected because of uncertainties of the CRUST 2.0 model (i.e., deviations of the CRUST 2.0 model density from the real Earths crustal density heterogeneities and the Moho relief uncertainties).

Spatial and Spectral Analysis of Refined Gravity Data for Modelling the Crust–Mantle Interface and Mantle-Lithosphere Structure

We analyse spatial and spectral characteristics of various refined gravity data used for modelling and gravimetric interpretation of the crust–mantle interface and the mantle-lithosphere structure. Depending on the purpose of the study, refined gravity data have either a strong or weak correlation with the Moho depths (Moho geometry). The compilation of the refined gravity data is purely based on available information on the crustal density structure obtained from seismic surveys without adopting any isostatic hypothesis. We demonstrate that the crust-stripped relative-to-mantle gravity data have a weak correlation with the CRUST2.0 Moho depths of about 0.02. Since gravitational signals due to the crustal density structure and the Moho geometry are subtracted from gravity field, these refined gravity data comprise mainly the information on the mantle lithosphere and sub-lithospheric mantle. On the other hand, the consolidated crust-stripped gravity data, obtained from the gravity field after applying the crust density contrast stripping corrections, comprise mainly the gravitational signal of the Moho geometry, although they also contain the gravitational signal due to anomalous mass density structures within the mantle. In the absence of global models of the mantle structure, the best possible option of computing refined gravity data, suitable for the recovery/refinement of the Moho interface, is to subtract the complete crust-corrected gravity data from the consolidated crust-stripped gravity data. These refined gravity data, that is, the homogenous crust gravity data, have a strong absolute correlation of about 0.99 with the CRUST2.0 Moho depths due to removing a gravitational signal of inhomogeneous density structures within the crust and mantle. Results of the spectral signal decomposition and the subsequent correlation analysis reveal that the correlation of the homogenous crust gravity data with the Moho depths is larger than 0.9 over the investigated harmonic spectrum up to harmonic degree 90. The crust-stripped relative-to-mantle gravity data correlate substantially with the Moho depths above harmonic degree 50 where the correlation exceeds 0.5.

The spherical harmonic representation of the gravitational field quantities generated by the ice density contrast

The spherical harmonic representation of the gravitational field quantities generated by the ice density contrast We derive the expressions for computing the ice density contrast stripping corrections to the topography corrected gravity field quantities by means of the spherical harmonics. The expressions in the spectral representation utilize two types of the spherical functions, namely the spherical height functions and the newly introduced lower-bound ice functions. The spherical height functions describe the global geometry of the upper topographic bound. The spherical lower-bound ice functions combined with the spherical height functions describe the global thickness of the continental ice sheet. The newly derived formulas are utilized in the forward modelling of the gravitational field quantities generated by the ice density contrast. The 30×30 arc-sec global elevation data from GTOPO30 are used to generate the global elevation model (GEM) coefficients. The spatially averaged global elevation data from GTOPO30 and the 2×2 arc-deg ice-thickness data from the CRUST 2.0 global crustal model are used to generate the global lower-bound ice model (GIM) coefficients. The mean value of the ice density contrast 1753 kg/m3 (i.e., difference of the reference constant density of the continental upper crust 2670 kg/m3 and the density of glacial ice 917 kg/m3) is adopted. The numerical examples are given for the gravitational potential and attraction generated by the ice density contrast computed globally with a low-degree spectral resolution complete to degree and order 90 of the GEM and GIM coefficients.

The Bathymetric Stripping Corrections to Gravity Field Quantities for a Depth-Dependent Model of Seawater Density

In geophysical studies investigating the lithosphere structure, topographic, bathymetric, and density contrasts stripping corrections are applied to gravity data. The ocean density contrast is typically calculated as the difference between the mean densities of crust and seawater. The approximation of the actual seawater density by its mean value yields relative errors up to 2%. To reduce these errors, we adopt a depth-dependent seawater density model to account for increasing density with pressure/depth. This approximation reduces errors to less than 0.1%. This density model is utilized in newly derived expressions for the bathymetric stripping corrections.

A digital rock density map of New Zealand

Digital geological maps of New Zealand (QMAP) are combined with 9256 samples with rock density measurements from the national rock catalogue PETLAB and supplementary geological sources to generate a first digital density model of New Zealand. This digital density model will be used to compile a new geoid model for New Zealand. The geological map GIS dataset contains 123 unique main rock types spread over more than 1800 mapping units. Through these main rock types, rock densities from measurements in the PETLAB database and other sources have been assigned to geological mapping units. A mean surface rock density of 2440kg/m^3 for New Zealand is obtained from the analysis of the derived digital density model. The lower North Island mean of 2336kg/m^3 reflects the predominance of relatively young, weakly consolidated sedimentary rock, tephra, and ignimbrite compared to the South Islands 2514kg/m^3 mean where igneous intrusions and metamorphosed sedimentary rocks including schist and gneiss are more common. All of these values are significantly lower than the mean density of the upper continental crust that is commonly adopted in geological, geophysical, and geodetic applications (2670kg/m^3) and typically attributed to the crystalline and granitic rock formations. The lighter density has implications for the calculation of the geoid surface and gravimetric reductions through New Zealand.

A global correlation of the step-wise consolidated crust-stripped gravity field quantities with the topography, bathymetry, and the CRUST 2.0 Moho boundary

A global correlation of the step-wise consolidated crust-stripped gravity field quantities with the topography, bathymetry, and the CRUST 2.0 Moho boundary We investigate globally the correlation of the step-wise consolidated cruststripped gravity field quantities with the topography, bathymetry, and the Moho boundary. Global correlations are quantified in terms of Pearsons correlation coefficient. The elevation and bathymetry data from the ETOPO5 are used to estimate the correlation of the gravity field quantities with the topography and bathymetry. The 2×2 arc-deg discrete data of the Moho depth from the global crustal model CRUST 2.0 are used to estimate the correlation of the gravity field quantities with the Moho boundary. The results reveal that the topographically corrected gravity field quantities have the highest absolute correlation with the topography. The negative correlation of the topographically corrected gravity disturbances with the topography over the continents reaches -0.97. The ocean, ice and sediment density contrasts stripped and topographically corrected gravity field quantities have the highest correlation with the bathymetry (ocean bottom relief). The correlation of the ocean, ice and sediment density contrasts stripped and topographically corrected gravity disturbances over the oceans reaches 0.93. The consolidated crust-stripped gravity field quantities have the highest absolute correlation with the Moho boundary. In particular, the global correlation of the consolidated crust-stripped gravity disturbances with the Moho boundary is found to be -0.92. Among all the investigated gravity field quantities, the consolidated crust-stripped gravity disturbances are thus the best suited for a refinement of the Moho density interface by means of the gravimetric modeling or inversion.

A mathematical model of the bathymetry-generated external gravitational field

A mathematical model of the bathymetry-generated external gravitational field The currently available global geopotential models and the global elevation and bathymetry data allow modelling the topography-corrected and bathymetry stripped reference gravity field to a very high spectral resolution (up to degree 2160 of spherical harmonics) using methods for a spherical harmonic analysis and synthesis of the gravity field. When modelling the topography-corrected and crust-density-contrast stripped reference gravity field, additional stripping corrections are applied due to the ice, sediment and other major known density contrasts within the Earths crust. The currently available data of global crustal density structures have, however, a very low resolution and accuracy. The compilation of the global crust density contrast stripped gravity field is thus limited to a low spectral resolution, typically up to degree 180 of spherical harmonics. In this study we derive the expressions used in forward modelling of the bathymetry-generated gravitational field quantities and the corresponding bathymetric stripping corrections to gravity field quantities by means of the spherical bathymetric (ocean bottom depth) functions. The expressions for the potential and its radial derivative are formulated for the adopted constant (average) ocean saltwater density contrast and for the spherical approximation of the geoid surface. These newly derived expressions are utilized in numerical examples to compute the gravitational potential and attraction generated by the ocean density contrast. The computation is realized globally on a 1 x 1 arc-deg geographical grid at the Earths surface.

The evaluation of the New Zealand's geoid model using the KTH method

Abstract We compile a new geoid model at the computation area of New Zealand and its continental shelf using the method developed at the Royal Institute of Technology (KTH) in Stockholm. This method utilizes the least-squares modification of the Stokes integral for the biased, unbiased, and optimum stochastic solutions. The modified Bruns-Stokes integral combines the regional terrestrial gravity data with a global geopotential model (GGM). Four additive corrections are calculated and applied to the approximate geoid heights in order to obtain the gravimetric geoid. These four additive corrections account for the combined direct and indirect effects of topography and atmosphere, the contribution of the downward continuation reduction, and the formulation of the Stokes problem in the spherical approximation. The gravimetric geoid model is computed using two heterogonous gravity data sets: the altimetry-derived gravity anomalies from the DNSC08 marine gravity database (offshore) and the ground gravity measur...

Layer-Based Modelling of the Earth’s Gravitational Potential up to 10-km Scale in Spherical Harmonics in Spherical and Ellipsoidal Approximation

Global forward modelling of the Earth’s gravitational potential, a classical problem in geophysics and geodesy, is relevant for a range of applications such as gravity interpretation, isostatic hypothesis testing or combined gravity field modelling with high and ultra-high resolution. This study presents spectral forward modelling with volumetric mass layers to degree 2190 for the first time based on two different levels of approximation. In spherical approximation, the mass layers are referred to a sphere, yielding the spherical topographic potential. In ellipsoidal approximation where an ellipsoid of revolution provides the reference, the ellipsoidal topographic potential (ETP) is obtained. For both types of approximation, we derive a mass layer concept and study it with layered data from the Earth2014 topography model at 5-arc-min resolution. We show that the layer concept can be applied with either actual layer density or density contrasts w.r.t. a reference density, without discernible differences in the computed gravity functionals. To avoid aliasing and truncation errors, we carefully account for increased sampling requirements due to the exponentiation of the boundary functions and consider all numerically relevant terms of the involved binominal series expansions. The main outcome of our work is a set of new spectral models of the Earth’s topographic potential relying on mass layer modelling in spherical and in ellipsoidal approximation. We compare both levels of approximations geometrically, spectrally and numerically and quantify the benefits over the frequently used rock-equivalent topography (RET) method. We show that by using the ETP it is possible to avoid any displacement of masses and quantify also the benefit of mapping-free modelling. The layer-based forward modelling is corroborated by GOCE satellite gradiometry, by in-situ gravity observations from recently released Antarctic gravity anomaly grids and degree correlations with spectral models of the Earth’s observed geopotential. As the main conclusion of this work, the mass layer approach allows more accurate modelling of the topographic potential because it avoids 10–20-mGal approximation errors associated with RET techniques. The spherical approximation is suited for a range of geophysical applications, while the ellipsoidal approximation is preferable for applications requiring high accuracy or high resolution.

Sub-crustal stress determined using gravity and crust structure models

The sub-crustal stress induced by mantle convection has been traditionally computed using the Runcorn formulae of solving the Navier-Stokes problem. The main disadvantage of this method is a limited spectral resolution (up to degree 25 of spherical harmonics) due to a divergence of the spherical harmonic expression. To improve the spectral resolution, we propose a new method of computing the horizontal components of the sub-crustal stress based on utilising the stress function with a numerical differentiation. According to the proposed method, the stress function is functionally related to the gravity and crust structure models expressed in terms of spherical harmonics, instead of directly relating the stress components with partial derivatives of these spherical harmonics. The stress components are then computed from the stress function by applying a numerical differentiation. This modification increases the degree-dependent convergence domain of the asymptotically convergent series and consequently allows computing the stress components to a higher spectral resolution, which is compatible with currently available global crustal models. We further utilise the solution to the Vening Meinesz-Moritz inverse problem of isostasy in definition of the stress function. This definition facilitates a variable crustal thickness instead of assuming only a constant value adopted in the Runcorn formulae. The crustal thickness and sub-crustal stress are then determined directly from gravity data and a crustal structure model. We apply this numerical approach to compute the sub-crustal stress globally. Regional results are also presented and discussed over study areas of oceanic subduction zones, convergent continent-to-continent collision zones and hotspots. We demonstrate that the largest (in magnitude) sub-crustal stress occurs mainly along seismically active convergent tectonic plate boundaries.