Gravimetric Solution Research Articles

Moho depths for Antarctica Region by the inversion of ground-based gravity data

SUMMARYIn the last years the scientific literature has been enriched with new models of the Moho depth in the Antarctica Continent derived by the seismic reflection technique and refraction profiles, receiver functions and seismic surface waves, but also by gravimetric observations over the continent. In particular, the gravity satellite missions of the last two decades have provided data in this remote region of the Earth and have allowed the investigation of the crust properties. Meanwhile, other important contributions in this direction has been given by the fourth International Polar Year (IPY, 2007–2008) which started seismographic and geodetic networks of unprecedented duration and scale, including airborne gravimetry over largely unexplored Antarctic frontiers. In this study, a new model for the Antarctica Moho depths is proposed. This new estimation is based on no satellite gravity measures, thanks to the availability of the gravity database ANTGG2015, that collects gravity data from ground-base, airborne and shipborne campaigns. In this new estimate of the Moho depths the contribution of the gravity measures has been maximized reducing any correction of the gravity measures and avoiding constraints of the solution to seismological observations and to geological evidence. With this approach a pure gravimetric solution has been determined. The model obtained is pretty in agreement with other Moho models and thanks to the use of independent data it can be exploited also for cross-validating different Moho depths solutions.

A New Model of Quasigeoid for the Baltic Sea Area

The Space Research Centre in Warsaw is participating in the ESA project “Geodetic SAR for Height System Unification and Sea Level Research”. To observe the absolute sea level and enable the unification of the height systems, the physical heights of the tide gauge stations referring to a common equipotential surface (quasigeoid/geoid) are needed. This paper describes the new quasigeoid model for the area of the Baltic sea. The quasigeoid calculation was carried out according to the Helmert method, in which the topography is condensed on a layer lying on the geoid. Airborne gravity anomalies from the Baltic area and terrestrial anomalies from Sweden, Finland, Denmark, Lithuania, Latvia, and Poland were used. The necessary terrain corrections have been computed from a digital terrain model based on the SRTM30 model. To compute the long-wavelength part of the quasigeoid, the geopotential models GOCE-DIR6, GOCO06s, and EIGEN-6C4 were used; therefore, the three solutions have been obtained. All calculations were done in a zero-tide system. The new quasigeoid model is obtained on a regular 1.5’ × 3.0’ grid in the GRS80 reference system, covering the Baltic Sea and the surrounding area 52° < ϕ < 68° and 11° < λ < 30°. These gravimetric quasigeoids were compared to quasigeoid undulations derived at 29 GNSS/leveling points of the ASG-EUPOS permanent network, located in the study area. Our calculations show that the accuracy of the calculated quasigeoids is almost the same in all three cases and is about ±0.04 meters. Finally, quasigeoid anomalies were interpolated at the Polish tide gauge stations. The new gravimetric quasigeoid solution could be very important for height system unification, for geophysical purposes as well as for engineering purposes.

New N-Heterocyclic Compounds Based on 8-Hydroxyquinoline as Efficient Corrosion Inhibition for Mild Steel in HCl Solution: Experimental and Theoretical Assessments

Both new benzimidazole derivatives based on 8-hydroxyquinoline, namely 4-(1-((4-hydroxynaphthalen-1-yl)methyl)-5-methyl-1H-benzo[d]imidazol-2-yl)benzoic acid (QN1) and 4-(1-((4-hydroxynaphthalen-1-yl)methyl)-1H-benzo[d]imidazol-2-yl)benzoic acid (QN2), were synthesized and characterized, and their corrosion inhibition behavior as well as the mechanism of inhibition was investigated by different techniques. Structural characterization includes NMR, IR and elemental analysis. The anticorrosive activity of these compounds was evaluated by the potentiodynamic polarization and impedance spectroscopy. Experimental data show that the QN1 and QN2 are effective against corrosion of steel in 1.0 M HCl and that the inhibitory efficiency reached at an optimum value of 97.7% for the QN1 compound at 1 mm. Polarization Tafel curves show that QN11 and QN2 act as a mixed type of inhibitors. After evaluating the anticorrosive activity of these two compounds, we used the surface techniques, namely SEM coupled with EDS and the gravimetric solutions were analyzed by UV–visible spectrometry. Quantum mechanical investigations density functional theory calculations and the Monte Carlo simulation on corrosion behavior of QN1 and QN2 compounds were also conducted, and satisfying correlation was noticed between the results of corrosion measurement methods and quantum mechanical evaluations.

Simple preparation and characterization of novel 8-Hydroxyquinoline derivatives as effective acid corrosion inhibitor for mild steel: Experimental and theoretical studies

The primary objectives of the project are the synthesis of new families of heterocyclic compounds based on 8-hydroxyquinolinenamely: 5-((2-bromoethoxy) methyl) quinolin-8-ol (QC2-Br) and 5-((3-bromopropoxy) methyl) quinolin-8-ol (QC3-Br) and their evaluations as inhibitors of acid corrosion (1.0 M HCl).The synthesis of this series of compounds was carried out by a very simple and effective method, but with very good yield and with very good solubility in common organic solvents.The characterization of these new compounds carried out by infrared (FT-IR), nuclear magnetic resonance (1H and 13C NMR) and elementary analysis (EA).The anticorrosion activity was evaluated by gravimetric (WL), electrochemical methods (PDP and EIS) and theoretical studies (DFT, MC and MD). The inhibitors studied adsorbed on the metal surface according to Langmuir isotherm and act on the metal surface as inhibitors mixed type. The thermodynamic parameters show that the two inhibitors adsorb on the metal surface by chemical bonds (chemisorptions).A CPE, Q determined by fit and graphical methods plotted by synthetic data, was utilized.The statistical studies were carried out to confirm the gravimetric tests.Gravimetric solutions were analyzed by Inductively Coupled Plasma-Optical Spectroscopy (ICP-OES) and UV-visible spectrometry (UV-vis). The surface morphology was characterized by Scanning electronic spectroscopy (SEM) coupled with energy dispersive spectroscopy (EDS) and Infrared spectroscopy (FT-IR).The analysis of gravimetric solutions by ICP-OES and UV-visible show that the two inhibitors capable of making chemical bonds with ferric ions and decrease the dissolution of iron in the corrosive solution.The theoretical, experimental results and surface characterization methods show that the two compounds have a good inhibitor of acid corrosion and the inhibitory efficacy exceeds 96% for the two compounds at a concentration of 1 mM.

Synthesis of new epoxy glucose derivatives as a non-toxic corrosion inhibitors for carbon steel in molar HCl: Experimental, DFT and MD simulation

Abstract The purpose of this study was to examine the effect of inhibiting corrosion of two biodegradable newly synthesized compound derivatives of D-glucose for carbon steel in 1 M HCl. These compounds were characterized by infrared (IR), Nuclear magnetic resonance (1H and 13C NMR) and Elementary analysis (EA) spectroscopy. The evaluation of the corrosion inhibiting effect was studied using Usual electrochemical methods, DFT calculations and MD simulations. The morphology of the metal surface was characterized by SEM/EDS. However, the gravimetric solutions were analyzed by ICP-OPS and UV-visible spectrometry. This study has shown that these compounds provide good protection for carbon steel against corrosion inhibition in the 1 M HCl. Analyzes by scanning electron spectroscopy coupled with energy dispersion spectroscopy (SEM/EDS) show that the two inhibitors have been well adsorbed on the metal surface. The theoritical studies are in good agreement with those obtained from Electrochemical methods.

Sample synthesis, characterization, experimental and theoretical study of the inhibitory power of new 8-hydroxyquinoline derivatives for mild steel in 1.0 M HCl

Some new compounds which are derived from 8-hydroxyquinoline were both prepared and characterized by IR, NMR spectroscopy and elemental analysis. After the successful synthesis, we tested these products as corrosion inhibitors of mild steel (MS) in 1.0 M HCl at 298 K ± 1. The anticorrosive property was achieved by electrochemical and theoretical methods such as potentiodynamic polarization (PDP), the spectroscopy impedance (EIS), density functional theory (DFT) calculations and the Monte Carlo simulation (MC). The experimental and theoretical results obtained show that these products have an excellent anticorrosive property for the MS. The thermodynamic parameters show that all the compounds adsorb to the metal surface by chemical bonds according to the Langmuir adsorption isotherm. The surface morphology was investigated using scanning electron spectroscopy (SEM) coupled with energy dispersive spectroscopy (EDS) and the FT-IR analysis. The gravimetric solutions after 6 h of immersion were analyzed by the UV–Visible spectrometry.

New Epoxy sugar based glucose derivatives as eco friendly corrosion inhibitors for the carbon steel in 1.0 M HCl: Experimental and theoretical investigations

In this study, we chose to synthesize new sugar based glucose derivatives as ecological corrosion inhibitors for carbon steel in acidic medium. The products obtained in the form of syrupy liquids, and the purity of obtained compounds was characterized by NMR spectroscopy analysis. The corrosion inhibition activities for both compounds were evaluated by electrochemical and rheological methods. Thus, the results of the experimental tests have been confirmed by theoretical studies ( DFT , MC and MD simulations). The surface study of carbon steel has been characterized by the scanning electron spectroscopy ( SEM ). The gravimetric solutions were identified using UV-Vis spectroscopy and Inductively Coupled Plasma-Optical Spectroscopy ( ICP-OES ). • Newly both glucose derivatives was synthesized and evaluated as corrosion inhibitor for steel in acidic medium. • Adsorption of G-C 12 and G-C 6 , obeyed the Langmuir adsorption isotherm model their adsorption was supported by SEM and UV-vis spectroscopic analyses. • The experimental results were correlated with DFT and MC stimulation results.

A recovered Moho model by integrated inversion of gravity and seismic depths in Iran

This research aims to define the depth of Moho in Iran by collocation method using gravimetric data with seismic information. The definition of the Moho in the Iranian region is of considerable importance due to the geological complexity of the area also characterized by tectonic and orogenic events of particular uniqueness. We applied the collocation method to Moho recovery using the gravity data generated by GOCO03S model reduced by topography/bathymetry, sediment and consolidated crust effects from CRUST1.0. These data have been complemented with seismic Moho depth estimates. A compilation of 213-points seismic depth has been collected over Iran and used in the integrated gravimetric-seismic inversion. Among them, 140 seismic points have been selected completely random and included as data in the integrated collocation approach for Moho depth estimation. The 73 remaining seismic points have been used as checking points for validating the estimated Moho. In the first run, gravity data only have been considered to collocation Moho recovery. When comparing this gravimetric solution with the 73 seismic checking points, a standard deviation of 6.2 km was found. In case of considering the regional seismic depths into the collocation approach, the standard deviation of the residuals between our results and seismic checking Moho depths improved to 4.9 km. It must be stated that, even in the integrated inversion, a significant discrepancy between the seismic and the integrated gravimetric-seismic Moho is present in the South Caspian Basin. Low quality of CRUST1.0 could explain this inconsistency in this area.

Synthetic, spectroscopic characterization, empirical and theoretical investigations on the corrosion inhibition characteristics of mild steel in molar hydrochloric acid by three novel 8-hydroxyquinoline derivatives

The newly synthesized quinoline derivatives were characterized using FTIR, NMR, and elemental analysis, and then they were evaluated as inhibitors against corrosion of mild steel (MS) in 1.0 M HCl. The corrosion testing and evaluation were performed thoroughly employing the weight loss method, electrochemical measurements, and surface analysis. We have demonstrated also that the 8-hydroxyquinoline derivatives react as mixed-type inhibitors. Experimental data show that the three inhibitors are effective against corrosion of steel in 1.0 M HCl and that the inhibitory efficiency reached at an optimum value of 96% for the Q-CH3 compound. In addition, the surface of the MS has been analyzed by SEM-EDS and the dissolution of steel in the gravimetric solution was analyzed by UV-visible spectrometry (UV-vis). The DFT calculations and Monte Carlo (MC) simulations were performed to understand the mechanism of inhibition of compounds with steel.

Novel Cu (II) and Zn (II) complexes of 8-hydroxyquinoline derivatives as effective corrosion inhibitors for mild steel in 1.0 M HCl solution: Computer modeling supported experimental studies

In this work, we have synthesized and characterized novel complexes of copper (II) and zinc (II). These complexes were obtained by reacting of 5-azidomethyl-8-hydroxyquinoline with copper chloride dihydrate and zinc chloride dihydrate. The isolated complexes were characterized by UV–visible spectroscopy (UV–Vis), Elemental analysis (EA), Infrared (IR), Mass spectrometry (MS) and 1H and 13C Nuclear Magnetic Resonance (NMR). These complexes were tested as corrosion inhibitors of mild steel in 1.0 M HCl by experimental and theoretical investigations. The surface of the steel before and after corrosion was characterized by the Scanning Electron Microscope coupled with Dispersive Energy Analysis (SEM-EDAX) and the gravimetric solution was analyzed by UV–visible spectrometry. The results of electrochemical and theoretical studies and the surface analysis of the steel show that these two complexes are effective for the protection of steel in 1.0 M HCl, but the high-temperature complexes become less effective, in addition, these complexes are adsorbed to the steel surface following the isotherm of Langmuir.

Evaluation of different gravimetric methods to Moho recovery in Iran

The complexity of geological units in Iran because of several unique events like tectonics and orogenic activities in this region led to extensive investigations for Moho recovery by seismic methods therein. In this research, three gravimetric methods have been evaluated by some point-wise seismic data. We applied collocation method as an iterative process as well as modified forms of Sjoberg and Jeffrey’s theory of isostasy for local Moho depth recovery. The gravity data has been generated by GOCO03S model reduced by topography/bathymetry, sediment and consolidated crust effects. Although the iteration process in collocation approach only slightly changed the estimated depths, this method led to a better agreement with seismic data rather than others. Differences between collocation, Jeffrey and Sjoberg’s solutions with seismic studies are similar but Jeffrey and Sjoberg’s methods displayed a systematic bias. The standard deviations of the residuals among seismic data and gravimetric solutions are around 6 km. Overall, the evaluation of these approaches indicated that Moho from gravimetric approaches reduced only slightly the standard deviation of seismic Moho estimates. Significant discrepancies with seismic data have been detected in Makran subduction zone, Oman Sea, Persian Gulf and Caspian Sea. The explanation of such inconsistency can be partially due to the poor quality of CRUST1.0 data in these areas, as this model has been used to correct the gravity values that were input in the inversion procedures.

GIGJ: A Crustal Gravity Model of the Guangdong Province for Predicting the Geoneutrino Signal at the JUNO Experiment

AbstractGravimetric methods are expected to play a decisive role in geophysical modeling of the regional crustal structure applied to geoneutrino studies. GIGJ (GOCE Inversion for Geoneutrinos at JUNO) is a 3‐D numerical model constituted by ~46 × 103 voxels of 50 × 50 × 0.1 km, built by inverting GOCE (Gravity field and steady‐state Ocean Circulation Explorer) gravimetric data over the 6° × 4° area centered at the JUNO (Jiangmen Underground Neutrino Observatory) experiment, currently under construction in the Guangdong Province (China). The a priori modeling is based on the adoption of deep seismic sounding profiles, receiver functions, teleseismic P wave velocity models, and Moho depth maps, according to their own accuracy and spatial resolution. The inversion method allowed for integrating GOCE data with the a priori information and some regularization conditions through a Bayesian approach and a stochastic optimization. GIGJ fits the highly accurate and homogeneously distributed GOCE gravity data with a ~1 mGal standard deviation of the residuals, compatible with the observation accuracy. GIGJ provides a site‐specific subdivision of the crustal layers masses, of which uncertainties include estimation errors, associated to the gravimetric solution, and systematic uncertainties, related to the adoption of a fixed sedimentary layer. A consequence of this local rearrangement of the crustal layer thicknesses is a ~21% reduction and a ~24% increase of the middle and lower crust geoneutrino signal, respectively. The geophysical uncertainties of geoneutrino signals at JUNO produced by unitary uranium and thorium abundances distributed in the upper, middle, and lower crust are reduced by 77%, 55%, and 78%, respectively. The numerical model is available at this site (http://www.fe.infn.it/radioactivity/GIGJ).

Combined Gravimetric-Seismic Moho Model of Tibet

Substantial progress has been achieved over the last four decades to better understand a deep structure in the Himalayas and Tibet. Nevertheless, the remoteness of this part of the world still considerably limits the use of seismic data. A possible way to overcome this practical restriction partially is to use products from the Earth’s satellite observation systems. Global topographic data are provided by the Shuttle Radar Topography Mission (SRTM). Global gravitational models have been derived from observables delivered by the gravity-dedicated satellite missions, such as the Gravity Recovery and Climate Experiment (GRACE) and the Gravity field and steady-state Ocean Circulation Explorer (GOCE). Optimally, the topographic and gravity data should be combined with available results from tomographic surveys to interpret the lithospheric structure, including also a Moho relief. In this study, we use seismic, gravity, and topographic data to estimate the Moho depth under orogenic structures of the Himalayas and Tibet. The combined Moho model is computed based on solving the Vening Meinesz–Moritz (VMM) inverse problem of isostasy, while incorporating seismic data to constrain the gravimetric solution. The result of the combined gravimetric-seismic data analysis exhibits an anticipated more detailed structure of the Moho geometry when compared to the solution obtained merely from seismic data. This is especially evident over regions with sparse seismic data coverage. The newly-determined combined Moho model of Tibet shows a typical contrast between a thick crustal structure of orogenic formations compared to a thinner crust of continental basins. The Moho depth under most of the Himalayas and the Tibetan Plateau is typically within 60–70 km. The maximum Moho deepening of ~76 km occurs to the south of the Bangong-Nujiang suture under the Lhasa terrane. Local maxima of the Moho depth to ~74 km are also found beneath Taksha at the Karakoram fault. This Moho pattern generally agrees with the findings from existing gravimetric and seismic studies, but some inconsistencies are also identified and discussed in this study.

Regional gravity field recovery using the GOCE gravity gradient tensor and heterogeneous gravimetry and altimetry data

AbstractA regional approach using Poisson wavelets is applied for gravity field recovery using the GOCE (Gravity Field and Steady‐State Ocean Circulation Explorer) gravity gradient tensor, heterogeneous gravimetry data, and altimetry measurements. The added value to the regional model introduced by GOCE data is validated and quantified. The performances of the solutions modeled with different diagonal components of GOCE data and their combinations are investigated. Numerical experiments in a region in Europe show that the effects introduced by GOCE data demonstrate long‐wavelength patterns on the centimeter scale in terms of quasi‐geoid heights, which may allow reducing the remaining long‐wavelength errors in ground‐based data, and improve the regional model. The accuracy of the gravimetric quasi‐geoid computed with a combination of three diagonal components is improved by 0.6 cm (0.5 cm) in the Netherlands (Belgium) compared to that derived from gravimetry and altimetry data alone, when GOCO05s is used as the reference model. Moreover, the added value from GOCE data reduces the mean values of the misfit between the gravimetric solution and GPS/leveling data. Performances of different components and their combinations are not identical, and the solution with vertical gradients is best when a single component is used. The incorporation of multiple components shows further improvements, and the combination of three components best fits the local GPS/leveling data. Further comparison shows that our solution is the highest quality and may be substituted for existing models for engineering purposes and geophysical investigations over the target area.

Isostatic GOCE Moho model for Iran

One of the major issues associated with a regional Moho recovery from the gravity or gravity-gradient data is the optimal choice of the mean compensation depth (i.e., the mean Moho depth) for a certain area of study, typically for orogens characterised by large Moho depth variations. In case of selecting a small value of the mean compensation depth, the pattern of deep Moho structure might not be reproduced realistically. Moreover, the definition of the mean compensation depth in existing isostatic models affects only low-degrees of the Moho spectrum. To overcome this problem, in this study we reformulate the Sjöberg and Jeffrey’s methods of solving the Vening-Meinesz isostatic problem so that the mean compensation depth contributes to the whole Moho spectrum. Both solutions are then defined for the vertical gravity gradient, allowing estimating the Moho depth from the GOCE satellite gravity-gradiometry data. Moreover, gravimetric solutions provide realistic results only when a priori information on the crust and upper mantle structure is known (usually from seismic surveys) with a relatively good accuracy. To investigate this aspect, we formulate our gravimetric solutions for a variable Moho density contrast to account for variable density of the uppermost mantle below the Moho interface, while taking into consideration also density variations within the sediments and consolidated crust down to the Moho interface. The developed theoretical models are applied to estimate the Moho depth from GOCE data at the regional study area of the Iranian tectonic block, including also parts of surrounding tectonic features. Our results indicate that the regional Moho depth differences between Sjöberg and Jeffrey’s solutions, reaching up to about 3km, are caused by a smoothing effect of Sjöberg’s method. The validation of our results further shows a relatively good agreement with regional seismic studies over most of the continental crust, but large discrepancies are detected under the Oman Sea and the Makran subduction zone. We explain these discrepancies by a low quality of seismic data offshore.

Moho Density Contrast in Central Eurasia from GOCE Gravity Gradients

Seismic data are primarily used in studies of the Earth’s inner structure. Since large parts of the world are not yet sufficiently covered by seismic surveys, products from the Earth’s satellite observation systems have more often been used for this purpose in recent years. In this study we use the gravity-gradient data derived from the Gravity field and steady-state Ocean Circulation Explorer (GOCE), the elevation data from the Shuttle Radar Topography Mission (SRTM) and other global datasets to determine the Moho density contrast at the study area which comprises most of the Eurasian plate (including parts of surrounding continental and oceanic tectonic plates). A regional Moho recovery is realized by solving the Vening Meinesz-Moritz’s (VMM) inverse problem of isostasy and a seismic crustal model is applied to constrain the gravimetric solution. Our results reveal that the Moho density contrast reaches minima along the mid-oceanic rift zones and maxima under the continental crust. This spatial pattern closely agrees with that seen in the CRUST1.0 seismic crustal model as well as in the KTH1.0 gravimetric-seismic Moho model. However, these results differ considerably from some previously published gravimetric studies. In particular, we demonstrate that there is no significant spatial correlation between the Moho density contrast and Moho deepening under major orogens of Himalaya and Tibet. In fact, the Moho density contrast under most of the continental crustal structure is typically much more uniform.

Implementation of a rigorous least-squares modification of Stokes’ formula to compute a gravimetric geoid model over Saudi Arabia (SAGEO13)

A gravimetric geoid model (SAGEO13) is computed for the Kingdom of Saudi Arabia using a rigorous stochastic computational method. The computational methodology is based on a combination of least-squares (LS) modification of Stokes’ formula and the additive corrections for topographic, ellipsoidal, atmospheric, and downward continuation effects on the geoid solution. In this study, we used terrestrial gravity data, a digital elevation model (SRTM3), and seven global geopotential models (GGMs) to compute a new geoid model for Saudi Arabia. The least-squares coefficients are derived based on the optimisation of the input modification parameters. The gravimetric solution and its additive corrections are computed based on the optimum LS coefficients. Compared to GPS-levelling data, SAGEO13 shows a fit of 18 cm (RMS) after using a 4-parameter fitting model.

Evaluating uncertainties in the calibration of isotopic reference materials and multi-element isotopic tracers (EARTHTIME Tracer Calibration Part II)

A statistical approach to evaluating uncertainties in the calibration of multi-element isotopic tracers has been developed and applied to determining the isotopic composition of mixed U–Pb (202Pb–205Pb–233U–235U) tracers used for accurate isotope dilution U–Pb geochronology. Our experiment, part of the EARTHTIME initiative, directly links the tracer calibration to first-principles measurements of mass and purity that are all traceable to SI units, thereby quantifying the accuracy and precision of U–Pb dates in absolute time. The calibration incorporates new more accurate and precise purity measurements for a number of commonly used Pb and U reference materials, and requires inter-relating their isotopic compositions and uncertainties. Similar methods can be used for other isotope systems that utilize multiple isotopic standards for calibration purposes. We also detail the inter-calibration of three publicly available U–Pb gravimetric solutions, which can be used to bring the same first-principles traceability to in-house U–Pb tracers from other laboratories. Accounting for uncertainty correlations in the tracer isotope ratios yields a tracer calibration contribution to the relative uncertainty of a 206Pb/238U date that is only half of the relative uncertainty in the 235U/205Pb ratio of the tracer, which was historically used to approximate the tracer related uncertainty contribution to 206Pb/238U dates. The tracer uncertainty contribution to 206Pb/238U dates has in this way been reduced to <300ppm when using the EARTHTIME and similarly calibrated tracers.

Assessment of the direct inversion scheme for the quasigeoid modeling based on applying the Levenberg–Marquardt algorithm

Methods for a spherical harmonic analysis and synthesis are often used in describing the global gravity field by means of spherical harmonics to a certain degree of spectral resolution. In local gravity field modeling, the radial basis functions (RBFs) can be used to parameterize the gravity field with a high spatial/spectral resolution because of their local support. Since the global integration is required in both cases, these two methods are somehow complementary. In physical geodesy, this is done practically by adopting a remove-compute-restore numerical scheme. According to this scheme, a long-wavelength part of the gravity spectrum is defined by means of the spherical harmonics while a residual (high-frequency) gravity contribution is treated based on using the RBFs. To find an optimal parameterization of the gravity field, the number of RBFs and their spatial configuration are optional. Moreover, the regularization is applied to stabilize the (ill-posed) gravity inversion. In this study, we utilize the Levenberg–Marquardt (LM) algorithm for finding the optimal number of RBFs and their 3-D spatial configuration (i.e., horizontal location and depth) simultaneously with a regularization parameter. The optimal choice of these parameters is based on minimizing the least-squares residuals between the predicted and observed values of the potential and gravity field. In numerical experiment, we apply the LM algorithm in two inverse schemes of solving the Molodensky’s problem. The results reveal that a direct inversion of the observed gravity data to the potential field (i.e., quasigeoid heights) yields a systematic bias. Moreover, this gravimetric solution has a low approximation quality in terms of the potential field. The systematic discrepancies are thus modeled and corrected for by combining the gravity and GPS-leveling data. We propose and apply the RBF-parameterization, which again utilizes the LM optimization algorithm in combining these data. We demonstrate that only a two-step approach provides a satisfactory approximation to both the gravity and potential field.

Regional gravity inversion of crustal thickness beneath the Tibetan plateau

We apply a newly developed inversion scheme for a gravimetric determination of the Moho depths. This scheme utilizes the system of observation equations, which relates the complete crust-stripped gravity disturbances (i.e., the gravity disturbances corrected for anomalous crustal density structures) with the (unknown) Moho depths by means of a linearized Fredholm integral equation of the first kind. A point-value discretization scheme is applied, in which the coefficients of a design matrix are calculated using the closed analytical formula for the integral kernel function. The a priori error model is not applied due to the lack of knowledge on the accuracy of crustal density structure model. Tikhonov’s regularization is applied to stabilize the ill-posed solution; the regularization matrix is the identity matrix and the regularization parameter is selected based on an optimal fitting of the gravimetric solution to the a priori seismic Moho model. This method is applied to determine the Moho depths regionally at the study area of the Tibetan plateau and Himalayas characterized by the world largest crustal thickness. A constant value of the crust-mantle density contrast of 485 kg m−3 is assumed in our numerical model. For this density contrast, the estimated maximum Moho depths in central Tibet exceed 80 km.