Reformulation of the Vening-Meinesz Moritz Inverse Problem of Isostasy for Isostatic Gravity Disturbances

The isostatic gravity anomalies have been traditionally used to solve the inverse problems of isostasy. Since gravity measurements are nowadays carried out together with GPS positioning, the utilization of gravity disturbances in various regional gravimetric applications becomes possible. In global studies, the gravity disturbances can be computed using global geopotential models which are currently available to a relatively high accuracy and resolution. In this study we facilitate the definition of the isostatic gravity disturbances in the Vening-Meinesz Moritz inverse problem of isostasy for finding the Moho depths. We further utilize uniform mathematical formalism in the gravimetric forward modelling based on methods for a spherical harmonic analysis and synthesis of gravity field. We then apply both mathematical procedures to determine globally the Moho depths using the isostatic gravity disturbances. The results of gravimetric inversion are finally compared with the global crustal seismic model CRUST2.0;the RMS fit of the gravimetric Moho model with CRUST2.0 is 5.3 km. This is considerably better than the RMS fit of 7.0 km obtained after using the isostatic gravity anomalies.

Glacial Isostasy:Regional—Not Global

The load of the continental ice caps of the Ice Ages deformed the bedrock, and when the ice melted in postglacial time, land rose. This process is known as glacial isostasy. The deformations are compensated either regionally or globally. Fennoscandian data indicate a regional compensation. Global sea level data support a regional, not global, compensation. Subtracting GIA corrections from satellite altimetry records brings—for the first time—different sea level indications into harmony of a present mean global sea level rise of 0.0 to 1.0 mm/yr.

Determining the effective elastic thickness through cross-correlation between isostatic disturbances

The elastic thickness parameter was estimated using the mobile correlation technique between the observed isostatic disturbance and the gravity disturbance calculated through direct gravimetric modeling. We computed the vertical flexure value of the crust for a specific elastic thickness using a given topographic dataset. The gravity disturbance due to the topography was determined after the calculation. A grid of values for the elastic thickness parameter was generated. Then, a moving correlation was performed between the observed gravity data(representing actual surface data) and the calculated data from the forward modeling. The optimum elastic thickness of the particular point corresponded to the highest correlation coefficient. The methodology was tested on synthetic data and showed that the synthetic depth closely matched the original depth, including the elastic thickness value. To validate the results, the described procedure was applied to a real dataset from the Barreirinhas Basin, situated in the northeastern region of Brazil. The results show that the obtained crustal depth is highly correlated with the depth from known models. Additionally, we noted that the elastic thickness behaves as expected, decreasing from the continent towards the ocean. Based on the results, this method has the potential to be employed as a direct estimate of crustal depth and elastic thickness for any region.

Anthropogenic Earth-Change： We Are on a Slippery Slope, Breaking New Ground and It＇s Our Fault---A Multi-disciplinary Review and New Unified Earth-System Hypothesis

Human activity could be changing the Earth＇s foundations themselves, as we affect multiple systems interacting in feedback mechanisms changing the atmosphere, hydrosphere, cryosphere, biosphere, and even the lithosphere （solid surface） and asthenosphere （deformable semi-molten rock layer beneath）. Anthropogenic movement of ice, water and sediment alters viscosity and movement of the asthenosphere; this induces earthquakes, tsunamis, volcanism and rifting, and may induce plate-tectonic-change. These processes may account for the timing of unexplained contemporary Icelandic, New Zealand, Chilean, Japanese and Indonesian seismicity, volcanism and magma movement. Climate-change and sea-level rise are creating： slip-planes from differential water pore-pressures and/or weakening of previous fault-planes; sediment-change and altered hydrology and reservoir-mass, inducing isostasy and further change in pore-pressure. Loss of plant biomass and diversity alter hydrology, precipitation and transpiration, causing isostasy and further sediment- and climate-change. Increased ocean-mass, temperatures and acidity, reduced oceanic oxygenation, and increased transport of （organic） sediments elevate the production and destabilisation of gas-hydrates, causing slumps and tsunamis. Isostasy and altered viscosity of the asthenosphere increase seismicity, slope and faulting, which are the prime triggers for slumping and tsunamis. Altered asthenosphere flows hasten subduction and rifting landward of subduction, enhancing volcanism. All of these processes predominantly coincide, temporally and spatially, in the coasts and continental margins, and the Pacific ring-of-fire, although response times and extents may vary from immediate to multi-millennial scales and from negligible to catastrophic. Contemporary Icelandic seismic and volcanic activity is explained by depleted magma reserves on the north-western side of the mid-ocean ridge as asthenosphere moves from the constructive boundary under deglaciating and rising Greenland.

Bathymetry predicted from vertical gravity gradient anomalies and ship soundings

In this paper, the admittance function between seafloor undulations and vertical gravity gradient anomalies was derived. Based on this admittance function, the bathymetry model of 1 minute resolution was predicted from vertical gravity gradient anomalies and ship soundings in the experimental area from the northwest Pacific. The accuracy of the model is evaluated using ship soundings and existing models, including ETOPO1, GEBCO, DTU10 and V15.1 from SIO. The model＇s STD is 69. 481m, comparable with V15.1 which is generally believed to have the highest accuracy.

Early Cenozoic rapid flight enigma of the Indian subcontinent resolved:Roles of topographic top loading and subcrustal erosion

Intrinsic magmatic processes are considered as critical operators of plate movements. Here we demonstrate the role of extrinsic processes consequent to intrinsic processes as a catalyst for anomalous rapid plate movement. The rapid and accelerated flight of the Indian subcontinent since Deccan volca- nism until its collision with Eurasia remains as one of the geological conundrums. Data on seismic to- mography, peninsular geomorphology and inferences on continuum of subcrustal structures are utilized to address this enigma. We propose geomorphic isostasy as the mechanism that has driven this fastest drift ever recorded in geological history. It was initiated by sudden instability after the Deccan volcanism and resultant extensive accumulation of lava pile over continental lithosphere of northern India, northern-eastern tilt due to crustal thickness heterogeneity and subcrustal thermal stratification. The drift was sustained by Carlsberg and Central Indian ridge-push until collision and sediment top loading at northeast thenceforth. These inferences and geomorphic isostasy as a catalytic mechanism necessitate variability of drift rates as integral inputs for any continental scale modeling.

CRUSTAL CONFIGURATION OF NW HIMALAYA: EVIDENCES FROM THE ISOSTATIC AND FLEXURAL ANALYSIS OF GRAVITY DATA

With an objective of better understanding the nature of India\|Eurasia collision process, as manifest in the NW part of the Himalaya, gravity and GPS aided geodetic studies were carried out during the summers of 1994 through 1996. The area covered includes the Ladakh Himalaya, Indus suture zone (ISZ) and entire NW Himalaya between 74°～80° longitude and 30°～37° latitude. Gravity survey was carried out at 1～2km interval along Kiratpur—Leh—Panamik transect. Four different profiles viz., Kargil—Panikhar; Karu—Tangtse; Mahe—Sumdo and Nyoma—Kyon Tso were also taken. GPS was used, in fast\|static mode for 3\|d position determination of the gravity stations. The collected data were reduced to mean sea level using a new technique of terrain correction (Banerjee, 1998). The collected data was further combined with the published gravity data of SOI (Gulatee, 1956, Chug, 1978); ONGC (Raiverman et al., 1994) and Jin et al., 1994 to produce a new BA map for the NW Himalaya at 10mGal interval. Isostatic anomaly map of the region was also prepared using the BA map and ETOPO\|5 global elevation data set. On the IA map, an isostatic high of about 80mGal is evident over the entire course of the higher Himalaya. This elongated pattern of the gravity high aligns itself over the exposed rocks of central crystallines where the average elevation is 4500m. This 80mGal isostatic high may have been caused due to the fact that isostasy does not strictly prevail in the higher Himalaya and these are in a state of under\|compensation. This IA high has been interpreted in terms of upwarping in the Moho beneath the higher Himalaya. The IA analysis has also led to the depth of Moho to be 36～37km under the foothills, 60～65km under the higher Himalaya and 70～75km under the ISZ and beyond. Doubling of the crustal thickness is evident from the IA analysis and they are in general, in agreement with the DSS results of the Kashmir Himalaya.

Contribution to the Investigation of Structure and Origin of the East African Graben by Gravi metry

For our investigation we have 235 measurements done in the east part of Democratic Republic of Congo by P.Herrinck during a magnetic survey including the graben region from the parallel joining Goma city and Mahagi city, the region between Albert and Aka lakes, and the route from Aba to Kinsagani. During the surveys the density of recording points has been selected according to the importance of anomalies. In this way, the offset was 1 km where the disturbance was high in Goma city and 20 km have been sufficient along the route from Aba to Kinsagani. For the topographic and isostatic reductions only one cartographic document has been chosen that was the international map of the scale 1/1 000 000 which presents a certain characteristic of homogeneity.

A preliminary study on the lithospheric thermal structure and rheology of the Tibetan plateau

The lithosphere temperature beneath the Tibetan plateau was estimated by local isostasy equilib- rium constrained geothermal calculation. Maps of the lateral temperature variation at depths of 40 km, 70 km, and Moho are presented for the Tibetan plateau, and the thermal thickness of the lithosphere is also presented. The Tibetan plateau has a warm and thick lithospheres, but the thinner lithospheres are identified in the north- ern Tibet and the eastern margin of the plateau. The warm and soft lithospheres in the Tibetan plateau may represent a snapshot of the early stage of convective thinning of the convergent lithosphere. The ＂creme brulee＂ layering demonstrates the rheological behavior of the Tibetan plateau.

A three-dimensional Moho depth model beneath the Yemeni highlands and rifted volcanic margins of the Red Sea and Gulf of Aden, Southwest Arabia

Knowing Moho discontinuity undulation is fundamental to understanding mechanisms of lithosphereasthenosphere interaction, extensional tectonism and crustal deformation in volcanic passive margins such as the study area, which is located in the southwestern corner of the Arabian Peninsula bounded by the Red Sea and the Gulf of Aden. In this work, a 3D Moho depth model of the study area is constructed for the first time by inverting gravity data from the Earth Gravitational Model(EGM2008) using the ParkerOldenburg algorithm. This model indicates the shallow zone is situated at depths of 20 km to 24 km beneath coastal plains, whereas the deep zone is located below the plateau at depths of 30 km to 35 km and its deepest part coincides mainly with the Dhamar-Rada ’a Quaternary volcanic field. The results also indicate two channels of hot magmatic materials joining both the Sana’a-Amran Quaternary volcanic field and the Late Miocene Jabal An Nar volcanic area with the Dhamar-Rada’a volcanic field. This conclusion is supported by the widespread geothermal activity(of mantle origin) distributed along these channels,isotopic data, and the upper mantle low velocity zones indicated by earlier studies.

Optimum choice of parameters and numerical schemes for a regional gravimetric Moho recovery

Despite practical limitations of isostatic theories to model the Moho geometry are well-known,gravimetric methods are often used in terrestrial studies of crustal structure in regions with a low seismic data coverage.Moreover,these methods are indispensable in planetary studies.Various gravimetric methods have been proposed.The Airy and Pratt theories are defined based on adopting a local compensation mechanism.The Vening Meinesz theory assumes a regional isostatic flexural model.The Vening Meinesz regional isostatic model generally describes a respond of the lithosphere to a load more realistically than the Airy model over continents.The Pratt method,on the other hand,better describes a compensation mechanism of the oceanic lithosphere.The application of a particular isostatic model also depends on applied numerical procedures,parameters for inversion,input data specifications,and many other aspects.In this study,we address some basic aspects by applying local and regional isostatic models for a Moho recovery.We also conduct a spectral analysis to assess a spectral resolution of gravity data that is optimal for a Moho recovery.Furthermore,we inspect the influence of low-degree spherical harmonics of gravity field on a Moho geometry.Gravimetric results are validated using seismic data at the European plate.Our results confirm a better performance of a regional compensation principle.We also demonstrate that a different thickness of the oceanic and continental crustal thickness should be taken into account as a priori information.Spectral analysis indicates that gravity data used for a Moho inversion should optimally have a spatial resolution between degrees 60 to 180.Results also show that low-degree spherical harmonics do not modify significantly the Moho geometry,particularly over regions with a relatively homogenous structure of deep mantle.

Inversion of gravity and topography data for the crust thickness of China and its ad-jacent region

The data of Bouguer gravity and topography are inverted to obtain the crust thickness of China. In order to reduce the effect of regional non-isostasy we corrected the reference Moho depth in the inversion with regional topography relief, and performed multiple iterations to make the result more reliable. The obtained crust thickness of China is plotted on a map in cells of l°×1°. Then we analyzed the correlation between the Bouguer gravity anomaly and fluctuation of the Moho depth. A good linear correlation is found, with a correlation coefficient of -0.993. Different correlation coefficients, 0.96 and 0.91, are found for the data in land and ocean region, respectively. The correlation result also shows that the boundary between land and ocean is generally along the bathymetric line of -800 m. In order to examine the influence of the Earth＇s curvature on the calculated result, we tried two inversion models： the inversion for the whole region and the inversion for 4 sub-regions. The difference in the crust thickness deduced from the two models is less than 5 km. Possible explanation for the difference is discussed. After comparing our result with that of other studies, we suggest that with our method the Bouguer gravity and the topography data can be independently inverted to obtain the crust thickness of China and its adjacency.

Characteristics of isostatic gravity anomaly in Sichuan-Yunnan region,China

Sichuan-Yunnan region in China, a tectonic transition belt where earthquakes occurred frequently and intensely, has a distinct variation characteristic of gradient zone of Bouguer gravity anomaly （BGA）. Many deep faults and epicenters of severe earthquake scatter along the BGA gradient zones. Here we apply two forward models （Airy model and Vening Meinesz model） of isostatic gravity mechanisms （local versus regional） in this region to calculated the isostatic gravity anomaly （IGA）. Afterwards, the relationship between IGA and distribution of faults as well as seismicity is also illustrated. The IGA results show that the two models are similar and most parts of the study area are in an isostatic state. Most featured faults are distributed along the steep anomaly gradient zones; earthquakes tend to occur in the non-isostatic area and steep gradient belt of IGA. The distribution of root thickness based on regional mechanism can be associated with the main trend of BGA variation. The regional mechanism is more plausible and closer to the reality because of its relatively further consideration of the horizontal forces derived from adjacent particles in the crust. Then we analyze the effect of isostasy on the tectonic movements and find that the isostatic adjustment is not the main cause of the continuous uplift process of Longmenshan Mountain fault zone. which is due to the Indian-Eurasian continental collision.

Lithospheric Thermal Isostasy of North Continental Margin of the South China Sea

Accompanied with rifting and detaching of the north continental margin of the South China Sea, the crust and the lithosphere become thinner away from the continental margin resulting from the tectonic activities, such as tensile deformation, thermal uplift, and cooling subsidence, etc.. Integrated with thermal, gravimetric, and isostatic analysis techniques, based on the seismic interpretation of the deep penetration seismic soundings across the northern margin of the South China Sea, we reconstructed the lithospheric thermal structure and derived the variation of the crust boundary in the east and west parts of the seismic profile by using gravity anomaly data. We mainly studied the thermal isostasy problems using the bathymetry of the profiles and calculated the crust thinning effect due to the thermal variety in the rifting process. The results indicate that the thermal isostasy may reach 2.5 km, and the compositional variations in the lithospheric density and thickness may produce a variation of 4.0 km. Therefore, the compositional isostatic correction is very important to recover the relationship between surface heat flow and topography. Moreover, because of the high heat flow characteristic of the continental margin, building the model of lithospheric geotherm in this region is of great importan for studying the Cenozoic tectonic thermal evolution of the north passive continental margin of the South China Sea.

Dynamic mechanisms controlling the topography of Longmenshan area

The Longmenshan fault, which defines the eastern edge of the Tibetan Plateau, is one of the steepest margins of the plateau with a sharp elevation drop of about 4 km over a distance less than 100 km across the Longmenshan fault. The mechanism which is responsible for controlling and maintaining the elevation difference is highly debated. Using multiple observations including seismic velocity model, Moho depth, effective elastic thickness of the lithosphere, we conducted a quantitative study for elucidating the contributions from crust and lithospheric mantle by an integrated analysis of lithospheric isostasy and flexure. It is shown that the topography of the Longmenshan fault is supported by both lithospheric isostasy and flexure statically, and lower crustal channel flow and mantle convection dynamically. Different mechanisms have different weights for contribution to the topography of the Songpan-Ganzi block and the Sichuan Basin. The static and dynamic support contribute roughly the same to the topographic difference of ~4 km between the two sides of the Longmenshan fault. The static topographic difference of ~2 km is mainly resulted from the lithospheric isostasy, while the dynamic one of ~2 km is contributed by the uprising of the accumulated material in the lower crust beneath the Songpan-Ganzi block and the downward drag force caused by the upper mantle convection under the Sichuan Basin. It is thus suggested that the lower crustal flow and upper mantle convection are dynamic forces which should be taken into account in the studies on the dynamics in the Longmenshan and surrounding regions.

Theoretical Deficiencies of Isostatic Schemes in Modeling the Crustal Thickness along the Convergent Continental Tectonic Plate Boundaries

The results of global and regional studies often show significant disagreement between the Moho depths determined using seismic and isostatic models. In this study, we estimate the differences between these two models in central Eurasia. The Vening Meinesz-Moritz （VMM） inverse problem of isostasy is utilized to determine the isostatic Moho depths. The estimated VMM Moho depths are then corrected for the sediment density contrast. The application of this correction improves the agreement between the isostatic and seismic Moho models. The existing discrepancies between the isostatic and seismic models are finally modeled by applying the non-isostatic correction, which accounts for the unmodelled mantle density heterogeneities and other geodynamic processes, which are not taken into account in classical isostatic models. Our results reveal that the non-isostatic correction still cannot fully describe mechanisms affecting the Moho geometry along the convergent continent-tocontinent tectonic plate boundaries occurring beneath Himalayas despite an overall good performance of the applied method.

3D palaeogeographic reconstructions of the Phanerozoic versus sea-level and Sr-ratio variations:Discussion

Verard et el. （2015, Journal of Palaeogeography, 4（1 ）： 64-84） claim that their global geodynamic model allows one to reconstruct the surface features of topography on rand and in adjacent oceans （i.e., pateobathymetry） anywhere on the gtobe and at any geological time during the past 600 miltion years （Ma）. Such a grand model requires a rigorous scrutiny. The purpose of this discussion is to illustrate that the modet suffers from （1） the selective omission of real-world datasets that do not fit the model, （2） the inclusion of datasets without revealing their original sources or without citing relevant peer-reviewed publications, （3） the emphasis on ＇unpublished＇ internal company datasets that disallow open access to the international scientific community, and （4） the use of poorly understood concepts without providing the basic conceptual clarity. These deficiencies undermine the credibility of the heuristic modet.

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 solv- ing a non-linear Fredholm integral equation of the first kind. Here solutions to the two Moho parame- ters 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 1°×1°. The numerical results show that the estimated Moho density contrast varies from 21 to 637 kg/m3, with a global average of 321 kg/m^3, 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 least-squares 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.

The deep thermal structure of the lithosphere in the northwestern South China Sea and its control on the shallow tectonics

The northwestern sub-basin of South China Sea(SCS)is a unique tectonic unit formed in the early spreading of the SCS.The northwestern Sub-basin has a series of complex geological structures such as seamounts and fault zones surrounded by the Xisha Trough,the Zhongsha Massif,and the Pearl River Valley.These extensional structures and magmatic activity in the northwestern sub-basin are closely related to the lithospheric structure and its deformation.However,details of the deep lithosphere structure are still poorly known.Here,we obtained detailed data of water and Moho depth using sonar buoys,Extended Spread Profiles(ESP),Ocean Bottom Seismometer(OBS),both Multi-beam and land-sea joint seismic surveys in the northwestern sub-basin and its surrounding areas.Then we adopted a thermal isostasy method to calculate the depth of the Lithosphere-Asthenosphere Boundary(LAB)in the northwestern sub-basin of the SCS and its surrounding regions.Results show that the range of LAB depth is~25–110 km.The shallowest burial depth is 25–60 km occurring in the ocean basin.The depth increases to 60–110 km toward the continental margin.The lithospheric structure on the north and south sides of the Xisha Trough is symmetrical and shows the deep structure and thermal features of aborted rifts.The LAB depth in the Zhongsha Trough and the Zhongsha Massif increased from 60 to 70 km southwestwards,consistent with the trend of surface morphology.The LAB depth to the west side of the Pearl River Valley is 60–80 km,and the thinning of the lithosphere is related to the distribution of faults,depressions and the magmatic activity.The LAB depth in the northwestern sub-basin and the eastern subbasin is less than 60 km with the thinnest part being less than 46 km.Combining ocean drilling,seismic investigation,and seafloor topography,we show that the ocean basin of the northwestern sub-basin of the SCS locates within the 46 km isobath of the LAB.The formation of the rifted valleys and discrete blocks surrounding the ocean basins is both controlled by the regional tectonic movement and the deep thermal state,where their lithospheric structures show strong heterogeneity.