Methods for a spherical harmonic analysis and synthesis of global gravitational and lithospheric structure models are applied to compile the mantle and sub-lithospheric mantle gravity maps. Both ...gravity maps are then interpreted and assessed by means of their accuracy. The mantle gravity map exhibits a gravitational signature that mainly reflects a thermal state of the lithospheric mantle. This is particularly evident over the oceanic lithosphere, with gravity lows along mid-oceanic spreading ridges. The increasing gravity signal with the ocean-floor age is attributed to conductive cooling of the oceanic lithosphere. Gravity lows extend along continental rift systems. Gravity lows also mark active convergent tectonic margins (in Pacific, Mediterranean, and Caribbean). The old, cold and tectonically stable cratonic mantle is typically characterized by gravity highs. A thermal signature of upwelling mantle under mid-oceanic spreading ridges clearly manifests (by gravity lows) also in the sub-lithosphere mantle gravity map. Nevertheless, the overall signature of conductive cooling is less pronounced in this gravity map, and a thermal signature of the asthenosphere under most of the continental lithosphere is weak. This indicates that a lateral thermal gradient within the asthenosphere tends to be weaker than within the overlying lithospheric mantle. The most pronounced feature in this gravity map is the signature of subducted slabs in West Pacific, marked by gravity highs. An antipodal signature of two large low shear-velocity provinces in both mantle gravity maps is absent, while its long-wavelength pattern could clearly be recognized in the free-air gravity map. We explain this finding by the fact that gravity-stripping procedures applied in this study superpose a gravitational signature of an intermediate layer, in this case the lithospheric mantle and the asthenosphere, over a much weaker signature of deeper mantle density heterogeneities. Moreover, the interpretational quality of both mantle gravity maps is considerably worsen by the LITHO1.0 lithospheric model uncertainties, especially within a more complex structure of the continental lithosphere. As a result, some spatial features in presented gravity maps could be artefacts rather than a real gravity signal. Despite accuracy limitations of currently available lithospheric density models, such types of gravity maps provide a useful information for various purposes in geophysics, among others gravimetric interpretations of Earth's inner structure or a separation of gravitational signals from different sources. In geodesy, a primary motivation is related to a compilation of Earth's synthetic density model based on the condition of fulfilling the total mass budget for testing numerical techniques applied in gravimetric forward modelling by means of solving Newton's volume integral.
A long-wavelength geoidal geometry characterizes the most pronounced features of the Indian Ocean geoid low and the West Pacific and North Atlantic geoid highs. These large geoid undulations ...(globally roughly within ±100 m) are mainly attributed to a deep mantle structure and large lithospheric density and geometry variations (such as the African superswell), while maximum geoid modifications by a topographic relief of Himalaya and Tibet are up to ~30 m. To enhance the mantle signature in a long-wavelength geoidal geometry, gravimetric, isostatic, and spectral decomposition methods can be applied. In this study, we demonstrate that isostatic schemes yield isostatic geoid models that closely resemble a long-wavelength geoidal geometry. The gravimetric method, on the other hand, modifies the mantle geoid significantly. Further modifications of the mantle geoid by removing gravitational contributions of lithospheric mantle density and lithospheric thickness variations should (optimally) enhance the signature of the deep mantle in the sub-lithospheric mantle geoid. Our results confirm this assumption by revealing (large-scale) positive anomalies in the Central Pacific and along the Atlantic Ocean that are coupled by two negative anomalies in the East Pacific and South Eurasia. A gravimetric method thus better enhances the mantle signature in the geoidal geometry than isostatic and spatial decomposition methods. Nonetheless, our results also indicate the presence of possibly large errors in geoid modelling results that limit their full implementation in gravimetric studies of the Earth’s mantle density structure without using tomographic images of the mantle and additional geophysical, geothermal, and geochemical constraints.
It is a well-known fact that the long-wavelength terrestrial geoid undulations are mainly attributed to deep mantle density heterogeneities, while more detailed features in the geoid geometry are ...associated with the topography and the lithospheric density structure. To enhance a gravitational signature of mantle density heterogeneities below the lithosphere, the gravitational contributions of topography and lithospheric density heterogeneities should be modelled and subsequently removed from Earth's gravity field. The refined gravity field obtained after this numerical procedure is more suitable for a recovery of a mantle density structure (below the lithosphere). Following this idea, methods for a spherical harmonic analysis and synthesis of gravity field and lithospheric density structures are presented, and a theoretical relation between gravity field and mass density structure is formulated. Since a gravimetric recovery of inner density structure has a non-unique solution, we propose an alternative method based on a conversion of seismic velocities to mass densities. A forward modelling approach is then employed to find the mantle density configuration that generates the gravitational field that best approximates the corresponding refined gravitational field obtained from observed gravity field after subtracting the gravitational signal of the lithosphere.
It is acknowledged that a classical definition of the geoid-to-quasigeoid separation as a function of the simple planar Bouguer gravity anomaly is compatible with Helmert's definition of orthometric ...heights. According to Helmert, the mean actual gravity along the plumbline between the geoid and the topographic surface in the definition of orthometric height is computed approximately from the measured surface gravity by applying the Poincaré-Prey gravity reduction. This study provides theoretical proof and numerical evidence that this assumption is valid. We demonstrate that differences between the normal and (Helmert) orthometric corrections are equivalent to the geoid-to-quasigeoid separation differences computed for individual levelling segments. According to our theoretical estimates, maximum differences between these 2 quantities should be less than ±1 mm. By analogy, differences between the Molodensky normal and Helmert orthometric heights at levelling benchmarks should be equivalent to the geoid-to-quasigeoid separation computed from the Bouguer gravity data. Both theoretical findings are inspected numerically by using levelling and gravity data along selected closed levelling loops of the vertical control network in Hong Kong. Results show that values of the geoid-to-quasigeoid separation at levelling benchmarks differ less than ±0.1 mm from differences between the normal and orthometric corrections. Relatively large differences (slightly exceeding 2 mm) between values of the geoid-to-quasigeoid separation and differences between the normal and (Helmert) orthometric heights at levelling benchmarks are explained by errors in levelling measurements rather than by inconsistencies in computed values of the geoid-to-quasigeoid separation and (Helmert) orthometric correction.
The Earth's synthetic density and gravitational models can be used to validate numerical methods for global (or large-scale) gravimetric forward and inverse modelling formulated either in the spatial ...or spectral domains. The Preliminary Reference Earth Model (PREM) density parameters can be adopted as a 1-D reference density model and further refined using more detailed 2-D or 3-D crust and mantle density models. Alternatively, the AK135-F density parameters can be used for this purpose. In this study, we investigate options for a refinement of the Earth's synthetic density model by assessing the accuracy of available 1-D density models, specifically the PREM and AK135-F radial density parameters. First, we use density parameters from both models to estimate the Earth's total mass and compare these estimates with published results. We then estimate the Earth's gravity field parameters, particularly the geoidal geopotential number W
and the mean gravitational attraction and compare them with published values. According to our results, the Earth's total mass from the two models (the PREM and the AK135-F) differ less than 0.02% and 0.01%, respectively, when compared with the value adopted by the International Astronomical Union (IAU). The geoidal geopotential values of the two models differ from the value adopted by the IAU by less than 0.1% and 0.04%, respectively. The values of the mean gravitational attraction of the two models differ less than 0.02% and 0.08%, respectively, when compared with the value obtained from the geocentric gravitational constant and the Earth's mean radius. These numerical findings ascertain that the PREM and AK135-F density parameters are suitable for defining a 1-D reference density model.
The Earth’s synthetic gravitational and density models can be used to validate numerical procedures applied for global (or large-scale regional) gravimetric forward and inverse modeling. Since the ...Earth’s lithospheric structure is better constrained by tomographic surveys than a deep mantle, most existing 3D density models describe only a lithospheric density structure, while 1D density models are typically used to describe a deep mantle density structure below the lithosphere-asthenosphere boundary. The accuracy of currently available lithospheric density models is examined in this study. The error analysis is established to assess the accuracy of modeling the sub-lithospheric mantle geoid while focusing on the largest errors (according to our estimates) that are attributed to lithospheric thickness and lithospheric mantle density uncertainties. Since a forward modeling of the sub-lithospheric mantle geoid also comprises numerical procedures of adding and subtracting gravitational contributions of similar density structures, the error propagation is derived for actual rather than random errors (that are described by the Gauss’ error propagation law). Possible systematic errors then either lessen or sum up after applying particular corrections to a geoidal geometry that are attributed to individual lithospheric density structures (such as sediments) or density interfaces (such as a Moho density contrast). The analysis indicates that errors in modeling of the sub-lithospheric mantle geoid attributed to lithospheric thickness and lithospheric mantle density uncertainties could reach several hundreds of meters, particularly at locations with the largest lithospheric thickness under cratonic formations. This numerical finding is important for the calibration and further development of synthetic density models of which mass equals the Earth’s total mass (excluding the atmosphere). Consequently, the (long-to-medium wavelength) gravitational field generated by a synthetic density model should closely agree with the Earth’s gravitational field.
The high-resolution Moho depth model is required in various geophysical studies. However, the available models’ resolutions could be improved for this purpose. Large parts of the world still need to ...be sufficiently covered by seismic data, but existing global Moho models do not fit the present-day requirements for accuracy and resolution. The isostatic models can relatively reproduce a Moho geometry in regions where the crustal structure is in an isostatic equilibrium, but large segments of the tectonic plates are not isostatically compensated, especially along active convergent and divergent tectonic margins. Isostatic models require a relatively good knowledge of the crustal density to correct observed gravity data. To overcome the lack of seismic data and non-uniqueness of gravity inversion, seismic and gravity data should be combined to estimate Moho geometry more accurately. In this study, we investigate the performance of two techniques for combining long- and short-wavelength Moho geometry from seismic and gravity data. Our results demonstrate that both Butterworth and spectral combination techniques can be used to model the Moho geometry. The results show the RMS of Moho depth differences between our model and the reference models are between 1.7 and 4.7 km for the Butterworth filter and between 0.4 and 4.1 km for the spectral combination.
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•Spherical Slepian functions can determine the regional mass-term sea level.•The land-to-ocean leakage is corrected by optimal buffer zones through simulations.•Selective Gaussian ...smoothing effectively reduces the north–south stripes of GRACE.•Temporal variabilities of our results are comparable with other sea level datasets.•Our results retain spatial sea level features in the gulf and continental shelf.
Treatment of land-to-ocean leakage is crucial in modeling the mass-term sea level (MSL) using the Gravity Recovery and Climate Experiment (GRACE) satellite gravity measurements. In this study, we utilized the Spherical Slepian functions (SSFs) to determine MSL variations in the South China Sea. A sensitivity simulation in terms of trend, annual amplitude, and phase revealed that the SSF solution with a 1° coastal buffer zone provides a better land-to-ocean leakage correction than traditionally used Spherical Harmonics (SH). It was also found that an additional smoothing procedure for SSF with low concentrating energy could significantly reduce the high-frequency noise in GRACE (e.g., the north–south strips). The spatiotemporal characteristics of the true MSL were further compared among GRACE SH and Mascon solutions, model-predicted ocean bottom pressure, and steric-corrected altimetric data (i.e., satellite-altimetric sea level minus steric effect). Results revealed that despite the SSF-inverted regional MSL solution being generally similar to other results, this technique notably recovered the realistic magnitude of detailed features. The apparent MSL signal was, for instance, precisely recovered in the central part of the Gulf of Thailand and the Sunda Shelf by the SSF, while the SH significantly underestimated it due to smoothing. In addition to the seasonality, the interannual signal decomposed from the SSF-inverted residual MSL (by removing the trend and periodic signals) was the strongest and well cross-correlated with the Southern Oscillation Index. With more detailed spatial patterns revealed by MSL from GRACE SSF, our findings demonstrate that SSF is more suitable for regional-scale studies.
The monitoring of water storage variations is essential not only for the management of water resources, but also for a better understanding of the impact of climate change on hydrological cycle, ...particularly in Tibet. In this study, we estimated and analyzed changes of the total water budget on the Tibetan Plateau from the Gravity Recovery And Climate Experiment (GRACE) satellite mission over 15 years prior to 2017. To suppress overall leakage effect of GRACE monthly solutions in Tibet, we applied a forward modeling technique to reconstruct hydrological signals from GRACE data. The results reveal a considerable decrease in the total water budget at an average annual rate of −6.22 ± 1.74 Gt during the period from August 2002 to December 2016. In addition to the secular trend, seasonal variations controlled mainly by annual changes in precipitation were detected, with maxima in September and minima in December. A rising temperature on the plateau is likely a principal factor causing a continuous decline of the total water budget attributed to increase melting of mountain glaciers, permafrost, and snow cover. We also demonstrate that a substantial decrease in the total water budget due to melting of mountain glaciers was partially moderated by the increasing water storage of lakes. This is evident from results of ICESat data for selected major lakes and glaciers. The ICESat results confirm a substantial retreat of mountain glaciers and an increasing trend of major lakes. An increasing volume of lakes is mainly due to an inflow of the meltwater from glaciers and precipitation. Our estimates of the total water budget on the Tibetan Plateau are affected by a hydrological signal from neighboring regions. Probably the most significant are aliasing signals due to ground water depletion in Northwest India and decreasing precipitation in the Eastern Himalayas. Nevertheless, an integral downtrend in the total water budget on the Tibetan Plateau caused by melting of glaciers prevails over the investigated period.
Total basin discharge is a critical component for the understanding of surface water exchange at the land-ocean interface. A continuous decline in the number of global hydrological stations over the ...past fifteen years has promoted the estimation of total basin discharge using remote sensing. Previous remotely sensed total basin discharge of the Yangtze River basin, expressed in terms of runoff, was estimated via the water balance equation, using a combination of remote sensing and modeled data products of various qualities. Nevertheless, the modeled data products are presented with large uncertainties and the seasonal error characteristics of the remotely sensed total basin discharge have rarely been investigated. In this study, we conducted total basin discharge estimation of the Yangtze River Basin, based purely on remotely sensed data. This estimation considered the period between January 2003 and December 2012 at a monthly temporal scale and was based on precipitation data collected from the Tropical Rainfall Measuring Mission (TRMM) satellite, evapotranspiration data collected from the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite, and terrestrial water storage data collected from the Gravity Recovery and Climate Experiment (GRACE) satellite. A seasonal accuracy assessment was performed to detect poor performances and highlight any deficiencies in the modeled data products derived from the discharge estimation. Comparison of our estimated runoff results based purely on remotely sensed data, and the most accurate results of a previous study against the observed runoff revealed a Pearson correlation coefficient (PCC) of 0.89 and 0.74, and a root-mean-square error (RMSE) of 11.69 mm/month and 14.30 mm/month, respectively. We identified some deficiencies in capturing the maximum and the minimum of runoff rates during both summer and winter, due to an underestimation and overestimation of evapotranspiration, respectively.
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