Peter Vajda

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.

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.

Global model of the upper mantle lateral density structure based on combining seismic and isostatic models

We compile the global model of the upper mantle lateral density structure with a 2×2 arc-deg spatial resolution using the values of the crust-mantle density contrast estimated relative to the adopted crust density model. The combined least-squares approach based on solving Moritz’s generalization of the Vening-Meinesz inverse problem of isostasy is facilitated to estimate the crust-mantle density contrast. The global geopotential model (EGM08), the global topographic/bathymetric model (DTM2006.0) including ice-thickness data, and the global crustal model (CRUST2.0) are used to compute the isostatic gravity anomalies. The estimated upper mantle densities globally vary between 2751 and 3635 kg/m3. The minima correspond with locations of the divergent oceanic tectonic plate boundaries (along the mid-oceanic ridges). The maxima are found along the convergent tectonic plate boundaries in the Andes and Himalayas (extending under the Tibetan Plateau). A comparison of the estimated upper mantle densities with the CRUST2.0 data shows a relatively good agreement between these two models within the continental lithosphere with the differences typically within ±100 kg/m3. Much larger discrepancies found within the oceanic lithosphere are explained by the overestimated values of the CRUST2.0 upper mantle densities. Our result shows a prevailing pattern of increasing densities with the age of oceanic lithosphere which is associated with the global mantle convection process.

On Gravity Inversion for Point Mass Anomalies by Means of the Truncated Geoid

AbstractThe physical meaning of the truncated geoid, which is defined by the convolution of gravity anomalies with the Stokes function on a spherical cap of specified radius, has been studied by the authors. They investigated its relation to the density distribution, generating the surface gravity, and its potential use in inversion. Some progress results for simulated studies on point mass anomalies are presented. The behavior of the truncated geoid is controlled by the radius of the integration domain, hereinafter referred to as the truncation parameter, which is treated as a free parameter. The change of the truncated geoid in response to the change of the truncation parameter was studied in the context of the simulated mass distributions. By means of such computer simulations we have managed to demonstrate the clear sensitivity of the truncated geoid to the depths, in addition to the horizontal positions, of point mass anomalies generating the synthetic surface gravity. The objective of this paper is to illustrate, with the help of computer simulation as the method of our study, the contribution of the truncated geoid to the solution of the gravimetric inverse problem. Further work towards employing the truncated geoid in gravity exploration is being conducted.

Spectral expressions for modelling the gravitational field of the Earth’s crust density structure

We derive expressions for computing the gravitational field (potential and its radial derivative) generated by an arbitrary homogeneous or laterally varying density contrast layer with a variable depth and thickness based on methods for a spherical harmonic analysis and synthesis of gravity field. The newly derived expressions are utilised in the gravimetric forward modelling of major known density structures within the Earth’s crust (excluding the ocean density contrast) beneath the geoid surface. The gravitational field quantities due to the sediments and crust components density contrasts, shown in numerical examples, are computed using the 2 × 2 arc-deg discrete data from the global crustal model CRUST2.0. These density contrasts are defined relative to the adopted value of the reference crustal density of 2670 kgm−3. All computations are realised globally on a 1 × 1 arc-deg geographical grid at the Earth’s surface. The maxima of the gravitational signal due to the sediments density contrast are mainly along continental shelf regions with the largest sedimentary deposits. The corresponding maxima due to the consolidated crust components density contrast are over areas of the largest continental crustal thickness with variable geological structure.

Depth-dependent density change within the continental upper mantle

Depth-dependent density change within the continental upper mantle The empirical model of the depth-dependent density change within the upper continental mantle is derived in this study. The density of the upper(most) mantle underlying the continental crust is obtained from the estimated values of the crust-mantle (Moho) density contrast. Since the continental crustal thickness varies significantly, these upper mantle density values to a large extent reflect the density changes with depth. The estimation of the Moho density contrast is done through solving Moritzs generalization of the Vening-Meinesz inverse problem of isostasy. The solution combines gravity and seismic data in the least-squares estimation model. The estimated upper mantle density (beneath the continental crust) varies between 2770 and 3649 kg/m3. The upper mantle density increases almost proportionally with depth at a rate of 13 ± 2 kg/m3 per 1 km at the investigated depth interval from 6 to 58 km.

Global atmospheric effects on the gravity field quantities

Global atmospheric effects on the gravity field quantities We compile the global maps of atmospheric effects on the gravity field quantities using the spherical harmonic representation of the gravitational field. A simple atmospheric density distribution is assumed within a lower atmosphere (< 6 km). Disregarding temporal and lateral atmospheric density variations, the radial atmospheric density model is defined as a function of the nominal atmospheric density at the sea level and the height. For elevations above 6 km, the atmospheric density distribution from the United States Standard Atmosphere 1976 is adopted. The 5 × 5 arc-min global elevation data from the ETOPO5 are used to generate the global elevation model coefficients. These coefficients (which represent the geometry of the lower bound of atmospheric masses) are utilized to compute the atmospheric effects with a spectral resolution complete to degree and order 180. The atmospheric effects on gravity disturbances, gravity anomalies and geoid undulations are evaluated globally on a 1 × 1 arc-deg grid.