Mohammad Bagherbandi

A synthetic Earth gravity model based on a topographic-isostatic model

The Earth’s gravity field is related to the topographic potential in medium and higher degrees, which is isostatically compensated. Hence, the topographic-isostatic (TI) data are indispensable for extending an available Earth Gravitational Model (EGM) to higher degrees. Here we use TI harmonic coefficients to construct a Synthetic Earth Gravitational Model (SEGM) to extend the EGMs to higher degrees. To achieve a high-quality SEGM, a global geopotential model (EGM96) is used to describe the low degrees, whereas the medium and high degrees are obtained from the TI or topographic potential. This study differes from others in that it uses a new gravimetric-isostatic model for determining the TI potential. We test different alternatives based on TI or only topographic data to determine the SEGM. Although the topography is isostatically compensated only to about degree 40–60, our study shows that using a compensation model improves the SEGM in comparison with using only topographic data for higher degree harmonics. This is because the TI data better adjust the applied Butterworth filter, which bridges the known EGM and the new high-degree potential field than the topographic data alone.

Crustal thickness recovery using an isostatic model and GOCE data

One of the GOCE satellite mission goals is to study the Earth’s interior structure including its crustal thickness. A gravimetric-isostatic Moho model, based on the Vening Meinesz-Moritz (VMM) theory and GOCE gradiomet ric data, is determined beneath Iran’s continental shelf and surrounding seas. The terrestrial gravimetric data of Iran are also used in a nonlinear inversion for a recovering-Moho model applying the VMM model. The newly-computed Moho models are compared with the Moho data taken from CRUST2.0. The root-mean-square (RMS) of differences between the CRUST2.0 Moho model and the recovered model from GOCE and that from the terrestrial gravimetric data are 3.8 km and 4.6 km, respectively.

Signature of the upper mantle density structure in the refined gravity data

The gravitational signal of the upper mantle density structures is investigated in the refined gravity data which are corrected for the gravitational contributions of the crust density structures and the Moho geometry. The gravimetric forward modeling is applied to compute these refined gravity data globally on a 1 × 1 arcdeg grid using the global geopotential model (EGM2008), the global topographic/bathymetric model (DTM2006.0) including the ice-thickness data, and the global crustal model (CRUST2.0). The characteristics of the upper mantle density structures are further analyzed in association with the Moho parameters (i.e., Moho depths and density contrast). The 1 × 1 arcdeg global data of the Moho parameters are estimated by applying the combined least-squares approach based on solving Moritz’s generalization of the Vening–Meinesz inverse problem of isostasy. The refined gravity data exhibit mainly the mantle lithosphere structures attributed to the global mantle convection. A significant correlation found over oceans between the refined gravity data and the Moho density contrast is explained by the increasing density of the oceanic lithosphere with age. Despite the lithosphere structures attributed to the global mantle convection are confirmed also in the refined gravity data over continents, the significant correlation between the refined gravity data and the Moho parameters is in this case absent. Instead, the significant proportion of lateral variations of the Moho density contrast within the continental lithosphere is attributed to the depth-dependant density changes due to pressure and thermal gradient.

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.

Moho depth uncertainties in the Vening-Meinesz Moritz inverse problem of isostasy

We formulate an error propagation model based on solving the Vening Meinesz-Moritz (VMM) inverse problem of isostasy. The system of observation equations in the VMM model defines the relation between the isostatic gravity data and the Moho depth by means of a second-order Fredholm integral equation of the first kind. The corresponding error model (derived in a spectral domain) functionally relates the Moho depth errors with the commission errors of used gravity and topographic/bathymetric models. The error model also incorporates the non-isostatic bias which describes the disagreement, mainly of systematic nature, between the isostatic and seismic models. The error analysis is conducted at the study area of the Tibetan Plateau and Himalayas with the world largest crustal thickness. The Moho depth uncertainties due to errors of the currently available global gravity and topographic models are estimated to be typically up to 1–2 km, provided that the GOCE gravity gradient observables improved the medium-wavelength gravity spectra. The errors due to disregarding sedimentary basins can locally exceed ∼2 km. The largest errors (which cause a systematic bias between isostatic and seismic models) are attributed to unmodeled mantle heterogeneities (including the core-mantle boundary) and other geophysical processes. These errors are mostly less than 2 km under significant orogens (Himalayas, Ural), but can reach up to ∼10 km under the oceanic crust.

Quality description for gravimetric and seismic moho models of fennoscandia through a combined adjustment

The gravimetric model of the Moho discontinuity is usually derived based on isostatic adjustment theories considering floating crust on the viscous mantle. In computation of such a model some a priori information about the density contrast between the crust and mantle and the mean Moho depth are required. Due to our poor knowledge about them they are assumed unrealistically constant. In this paper, our idea is to improve a computed gravimetric Moho model, by the Vening Meinesz-Moritz theory, using the seismic model in Fennoscandia and estimate the error of each model through a combined adjustment with variance component estimation process. Corrective surfaces of bi-linear, bi-quadratic, bi-cubic and multi-quadric radial based function are used to model the discrepancies between the models and estimating the errors of the models. Numerical studies show that in the case of using the bi-linear surface negative variance components were come out, the bi-quadratic can model the difference better and delivers errors of 2.7 km and 1.5 km for the gravimetric and seismic models, respectively. These errors are 2.1 km and 1.6 km in the case of using the bi-cubic surface and 1 km and 1.5 km when the multi-quadric radial base function is used. The combined gravimetric models will be computed based on the estimated errors and each corrective surface.

Comparative analysis of Vening-Meinesz Moritz isostatic models using the constant and variable crust-mantle density contrast – a case study of Zealandia

We compare three different numerical schemes of treating the Moho density contrast in gravimetric inverse problems for finding the Moho depths. The results are validated using the global crustal model CRUST2.0, which is determined based purely on seismic data. Firstly, the gravimetric recovery of the Moho depths is realized by solving Moritz’s generalization of the Vening-Meinesz inverse problem of isostasy while the constant Moho density contrast is adopted. The Pratt-Hayford isostatic model is then facilitated to estimate the variable Moho density contrast. This variable Moho density contrast is subsequently used to determine the Moho depths. Finally, the combined least-squares approach is applied to estimate jointly the Moho depths and density contract based on a priori error model. The EGM2008 global gravity model and the DTM2006.0 global topographic/bathymetric model are used to generate the isostatic gravity anomalies. The comparison of numerical results reveals that the optimal isostatic inverse scheme should take into consideration both the variable depth and density of compensation. This is achieved by applying the combined least-squares approach for a simultaneous estimation of both Moho parameters. We demonstrate that the result obtained using this method has the best agreement with the CRUST2.0 Moho depths. The numerical experiments are conducted at the regional study area of New Zealand’s continental shelf.

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.

Evaluation of gravitational gradients generated by Earth's crustal structures

Spectral formulas for the evaluation of gravitational gradients generated by upper Earths mass components are presented in the manuscript. The spectral approach allows for numerical evaluation of global gravitational gradient fields that can be used to constrain gravitational gradients either synthesised from global gravitational models or directly measured by the spaceborne gradiometer on board of the GOCE satellite mission. Gravitational gradients generated by static atmospheric, topographic and continental ice masses are evaluated numerically based on available global models of Earths topography, bathymetry and continental ice sheets. CRUST2.0 data are then applied for the numerical evaluation of gravitational gradients generated by mass density contrasts within soft and hard sediments, upper, middle and lower crust layers. Combined gravitational gradients are compared to disturbing gravitational gradients derived from a global gravitational model and an idealised Earths model represented by the geocentric homogeneous biaxial ellipsoid GRS80. The methodology could be used for improved modelling of the Earths inner structure.

Combined Moho parameters determination using CRUST1.0 and Vening Meinesz-Moritz model

According to Vening Meinesz-Moritz (VMM) global inverse isostatic problem, either the Moho density contrast (crust-mantle density contrast) or the Moho geometry can be estimated by solving a non-linear Fredholm integral equation of the first kind. Here solutions to the two Moho parameters are presented by combining the global geopotential model (GOCO-03S), topography (DTM2006) and a seismic crust model, the latter being the recent digital global crustal model (CRUST1.0) with a resolution of 1º×1º. The numerical results show that the estimated Moho density contrast varies from 21 to 637 kg/m3, with a global average of 321 kg/m3, and the estimated Moho depth varies from 6 to 86 km with a global average of 24 km. Comparing the Moho density contrasts estimated using our leastsquares method and those derived by the CRUST1.0, CRUST2.0, and PREM models shows that our estimate agrees fairly well with CRUST1.0 model and rather poor with other models. The estimated Moho depths by our least-squares method and the CRUST1.0 model agree to 4.8 km in RMS and with the GEMMA1.0 based model to 6.3 km.