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Applying local Green’s functions to study the influence of the crustal structure on hydrological loading displacements
Abstract and Figures
The influence of the elastic Earth properties on seasonal or shorter periodic surface deformations due to atmospheric surface pressure and terrestrial water storage variations is usually modeled by applying a local half-space model or an one dimensional spherical Earth model like PREM from which a unique set of elastic load Love numbers, or alternatively, elastic Green's functions are derived. The first model is valid only if load and observer almost coincide, the second model considers only the response of an average Earth structure. However, for surface loads with horizontal scales less than 2500 km², as for instance, for strong localized hydrological signals associated with heavy precipitation events and river floods, the Earth elastic response becomes very sensitive to inhomogeneities in the Earth crustal structure.
We derive a set of local Green's functions defined globally on a 1° × 1° grid for the 3-layer crustal structure TEA12. Local Green's functions show standard deviations of ±12% in the vertical and ±21% in the horizontal directions for distances in the range from 0.1° to 0.5°. By means of Green's function scatter plots, we analyze the dependence of the load response to various crustal rocks and layer thicknesses. The application of local Green's functions instead of a mean global Green's function introduces a variability of 0.5–1.0 mm into the hydrological loading displacements, both in vertical and in horizontal directions. Maximum changes due to the local crustal structures are from −25% to +26% in the vertical and −91% to +55% in the horizontal displacements. In addition, the horizontal displacement can change its direction significantly. The lateral deviations in surface deformation due to local crustal elastic properties are found to be much larger than the differences between various commonly used one-dimensional Earth models.
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... Recent studies suggest that displacements produced by changes in surface mass can be highly sensitive to the local material properties and structural features of the crust and upper mantle, especially for surface loading occurring at relatively fine spatial scales (e.g.,< 2,500 km 2 ) (e.g., Dill et al., 2015;. For example, computed sensitivity kernels for the load Love number (LLNs) and load Green's function (LGFs), which describe the deformation response of the Earth to an applied unit point load, by systematically perturbing the elastic and density structure of PREM through the crust and upper mantle, finding the LGFs to be predominately sensitive to variations in elastic material properties in the upper 500 km of the Earth. ...
... For example, computed sensitivity kernels for the load Love number (LLNs) and load Green's function (LGFs), which describe the deformation response of the Earth to an applied unit point load, by systematically perturbing the elastic and density structure of PREM through the crust and upper mantle, finding the LGFs to be predominately sensitive to variations in elastic material properties in the upper 500 km of the Earth. Further, Dill et al. (2015) quantified the effect of sensitivities to local crustal structure on the deformation response to surface loading using grids of local LGFs, finding magnitudes of differences up to 25% for vertical displacement and 91% for horizontal displacement. Such sensitivities offer the possibility of tomographic studies to refine seismologically derived Earth models' structural properties when the loading source is reasonably constrained, such as the Earth's ocean tides (e.g., Ito & Simons, 2011). ...
... The uncertainty of TWS estimates associated with choice of Earth structure has only recently begun to be explored (e.g., Argus et al., 2017;Dill et al., 2015). For example, Wang et al. (2015) estimated the effect of assumed Earth structure on estimates of TWS derived from synthetic displacement and gravity observations for the Tibetan Plateau. ...
Geodetic methods can monitor changes in terrestrial water storage (TWS) across large regions in near real‐time. Here, we investigate the effect of assumed Earth structure on TWS estimates derived from Global Navigation Satellite System (GNSS) displacement time series. Through a series of synthetic tests, we systematically explore how the spatial wavelength of water load affects the error of TWS estimates. Large loads (e.g., >1,000 km) are well recovered regardless of the assumed Earth model. For small loads (e.g., <10 km), however, errors can exceed 75% when an incorrect model for the Earth is chosen. As a case study, we consider the sensitivity of seasonal TWS estimates within mountainous watersheds of the western U.S., finding estimates that differ by over 13% for a collection of common global and regional structural models. Errors in the recovered water load generally scale with the total weight of the load; thus, long‐term changes in storage can produce significant uplift (subsidence), enhancing errors. We demonstrate that regions experiencing systematic and large‐scale variations in water storage, such as the Greenland ice sheet, exhibit significant differences in predicted displacement (over 20 mm) depending on the choice of Earth model. Since the discrepancies exceed GNSS observational precision, an appropriate Earth model must be adopted when inverting GNSS observations for mass changes in these regions. Furthermore, regions with large‐scale mass changes that can be quantified using independent data (e.g., altimetry, gravity) present opportunities to use geodetic observations to refine structural properties of seismologically derived models for the Earth's interior structure.
... However, loading effects have global implications, requiring consideration of regional anisotropy on a global scale for unified modeling worldwide. Dill et al. (2015) adopted the same approach as Wang (2000) to calculate sets of LGFs defined globally on a 1°× 1°grid, while the impacts of loading displacements obtained from different sets of LGFs/MGFs on correcting the nonlinear variations of GNSS position time series are still limited so far. Also, there is still a lack of research regarding which of the above regional/global models are more advantageous and how to make an appropriate selection. ...
... It can be found that for both PREMTEA and PREMCRU, MGFs coincides well with their LGFs for distance θ > 1.0°, which is consistent with Dill et al. (2015). However, both two sets of vertical LGFs vary greatly from point to point in the near-field region (distance θ < 0.1°), which confirms that the local crustal structure only affects the near-field part of the GF. ...
... We found that all three components get improved RMSR for both PREMTEA and PREMCRU models and PREMTEA perform slightly better than PREMCRU in all three components, especially in Europe (Section 5.3). Improvements for horizontal components are better than Up components, but we didn't find the phenomenon proposed in Dill et al. (2015) that the phase of LGFs changes of by ±180°, that is, the horizontal ATLD turns to the opposite direction, which may be due to the magnitude of ATLD being smaller to be comparable to hydrological loads. The number of improved stations, with specific counts provided in brackets, is detailed in Table 3 and right panel of Figure 11, the North components exhibit greatest further RMS reduction (85.8% and 84.3% of all 987 stations for PREMTEA and PREMCRU) after using PREMTEA and PREMCRU compared with GB model; followed by the Up components (72.9% and 72.0%) of stations; the improvements for the East components are average (55.8% and 55.5% for PREMTEA and PREMCRU). ...
The Green's function approach is well‐established and widely used for modeling the surface mass loading displacements. Global mean Green's functions (MGFs) are commonly applied without considering local variations of the crustal structure. Derived from the modified layered Earth structure, the local Green's functions (LGFs) are theoretically beneficial to generate more accurate deformation, since they consider interior information of the local crust. This paper analyzed the differences among MGFs from Gutenberg–Bullen A model and two sets of LGFs derived from modified PREM Earth models consolidating with two crust models TEA12 and CRUST1.0, hereafter called PREMTEA and PREMCRU, respectively. Utilizing MGFs and two sets of LGFs, we modeled the corresponding 3D atmospheric loading displacements for 984 ITRF2014 stations and compared them with the ITRF2014 residuals. The results show that LGFs from PREMTEA and PREMCRU perform well in further promoting scatter reduction for ∼72%, ∼56%, and ∼85% of stations for the Up, East and North components, respectively. The improvements for the North components are significant (up to 3.6%). In particular, stations in the east coastal areas of North America and the west edge of Greenland exhibit further promoting scatter reduction for the East components (up to ∼2.5%), while those located in west coastline of North America show better performance for the North components. Nevertheless, there are significant anomalies in northern Europe for PREMCRU, the mutation margin of which should be carefully considered when using a resolution higher than 1°. In the area around station MORP (358.31°W, 55.21°N, sited at coastline of Britain), we suggest using PREMTEA model.
... Surface load change will lead to the Earth's elastic deformation (Farrell, 1972), and the crustal deformation due to multi-component land water loading can be modeled based on the EWH mass change fields in a frame of Green's function (Chanard et al., 2014;Chen, 2015). Considering the non-negligible impact of local crustal structure on loading estimate (Dill et al., 2015;Swarr et al., 2024;Wang et al., 2013), in this study, we perform the deformation convolution using the local Green's functions. Specifically, the 3-D deformation (upward, d u ; northward, d n ; eastward, d e ) at point P with colatitude θ P and longitude λ P due to the surface mass load at point Q with colatitude θ Q and longitude λ Q can be computed by convolving the load mass and the local Green's functions, as follows: ...
... where ψ PQ is the spherical distance between P, that is, (θ P , λ P ) and Q, that is, (θ Q , λ Q ); α is the azimuth of the direction from Q to P; αG v and G h are the vertical and horizontal local Green's functions respectively, which vary with both ψ PQ and the location of P. We adopt the local Green's functions from Dill et al. (2015), which are generated in the CF (center of surface figure) reference frame (Blewitt, 2003) based on the combination of the Preliminary Reference Earth Model (PREM; Dziewonski & Anderson, 1981) and a laterally variable continental crust model (named TEA12; Tesauro et al., 2012); ΔH represents the EWH fields obtained in Section 2.1, ρ is the density of water, and therefore ρΔH gives the surface density as defined in Wahr et al. (1998); R is the radius of the Earth, Ω represents the projection of the integral surface onto the unit sphere with dΩ = sinθQdθQdλQ, and therefore R 2 dΩ gives the area of the minimum integral tile. The integral surface, in our study, covers the entire TP, and a 2°(∼200 km) buffer (see Figure 1) is used to eliminate the boundary effect. ...
Plain Language Summary
The crustal kinematic characteristics and uplift mechanism of the Tibetan Plateau (TP) have been widely studied based on the three‐dimensional deformation velocity field from Global Positioning System (GPS) measurements. However, except for tectonic signal, the land water loading effect is also involved in GPS observation and may lead to the biased tectonic interpretation of GPS deformation velocity field. In this study, we construct a set of three‐dimensional crustal loading deformation velocity fields for the TP based on the state‐of‐the‐art multi‐component land water mass change fields constrained by multi‐source data spanning ∼20 years. Results reveal that the loading signal strength of the six land water components ranks from largest to smallest as groundwater, glacier, lake, soil water, permafrost, and snow. We find that all land water components can achieve a strong enough vertical loading velocity exceeding the present‐day GPS vertical velocity at some sites, but show very limited horizontal loading. Our results could provide loading correction reference for the construction of high‐accuracy TP tectonic deformation velocity field.
... On the other hand, the global mean Green's function is derived from the Earth's average structural response (e.g., the PREM Earth model). However, for surface loads with a horizontal scale smaller than 2500 km 2 , such as strong local hydrological signals related to intense precipitation and river flooding, the Earth's response is highly sensitive to uneven crustal structures [100]. This sensitivity hinders the application of the global mean Green's function to obtain realistic local environmental loading displacements [101]. ...
... Although it is neither a layered model nor does it consider the curvature of the Earth's surface, it allows the application of local elastic properties rather than globally averaged properties, as is the case for the Preliminary Reference Earth Model (PREM) (Dziewonski & Anderson, 1981). Notably, the accuracy of PREM reduces in the Earth's outermost 50 km due to the heterogeneity of the crust and the uppermost mantle (D'Urso & Marmo, 2013;Dill et al., 2015). Here, we examine two sets of half-space Green's functions characterized by endmember Young's modulus of 6 and 50 MPa as lower and upper bounds, consistent with local geology and subsoil beneath Mexico City, which is dominated by fine-grained material, mostly silt and soft clay with lenses of sand, gravel, and hard clay (Vázquez-Guillén & Auvinet-Guichard, 2019). ...
Plain Language Summary
Groundwater overdraft in Mexico City results from excessive freshwater demand and unsustainable water resource management in a subtropical environment with warm summers and dry winters. Groundwater depletion can result in ground surface deformation and changes in the gravity field, observable by Sentinel‐1 and GRACE satellites. Here, we examine data from both satellite missions between November 2014 and October 2021 to determine groundwater volume loss. Using GRACE, which has a footprint of ∼350 km, we quantify groundwater volume loss to a rate of 0.85–3.87 km³ per year in the broader area surrounding Mexico City. Analysis of high‐resolution Sentinel‐1 synthetic aperture radar images shows land sinks at a rate of 35 cm/yr within the city and surrounding areas uplifts at a rate of ∼2 cm/yr. While the subsidence is a consequence of aquifer compaction, the uplift represents an elastic unloading response of the Earth's crust to water mass loss. Using geophysical models informed by local geology, we show that the region loses groundwater at rates of 0.86–12.57 km³/yr. Our results emphasize the need for groundwater monitoring in Mexico City to assist with managing freshwater resources.
... Elastic surface deformations are calculated in the spatial domain by convolving loading Green's function with simulated mass distributions from ECMWF atmospheric surface pressure, MPIOM ocean bottom pressure, LSDM terrestrial water storage, and global mass balance barystatic sea level variations. Spatial calculation is performed on a 0.125 • global grid in the near-field (≤3.5 • ) and on a 2.0 • grid in the far-field (>3.5 • ) (see Dill et al. (2015) for more details). Gridded loading displacements are stored on a regular 0.5 • global grid with 24h sampling for hydrological and sea level loading (HYDL, SLEL) and 3-hourly sampling for nontidal atmospheric and oceanic loading (NTAL, NTOL) according to the time steps of the modeled mass data sets. ...
The Earth System Modelling Group of GeoForschungsZentrum Potsdam (ESMGFZ) provides geodetic products for gravity variations, Earth rotation excitations, and Earth surface deformations related to mass redistributions and mass loads in the atmosphere, ocean, and terrestrial water storage. Earth rotation excitation compiled as effective angular momentum (EAM) functions for each Earth subsystem (atmosphere, ocean, continental hydrology) are important for Earth rotation prediction. Especially the 6-day forecasts extending the model analysis runs offer essential information for the improvement of ultra-short-term Earth rotation predictions. In addition to the individual effective angular momentum function of each subsystem, ESMGFZ calculates a combined EAM prediction product. Adjusted to the official Earth orientation parameter (EOP) products IERS 14C04 and Bulletin A, this EAM prediction product allows to extrapolate the polar motion and Length-of-Day parameter time series for 90 days into the future via the Liouville equation. ESMGFZ submits such an EOP prediction to the 2nd EOPPCC campaign.
Model-based information about the global water cycle, in particular the redistribution of terrestrial water masses, is highly relevant for the understanding of Earth system dynamics. In many geodetic applications, hydrological model results play an important role by augmenting observations with a higher spatio-temporal resolution and gapless coverage. Here we demonstrate the feasibility of the high-resolution, open-source hydrological model OS LISFLOOD to simulate terrestrial water storage (TWS) variations with a spatial sampling of up to about 5 km (0.05○). Validation against data from satellite gravimetry reveals that the choice of the maximum soil depth has a significant impact on long-term trends in TWS, mainly in the deepest soil layer. We find that refining the soil depth definition effectively reduces spurious TWS trends, while preserving accuracy in modeled river discharge. Using the modified model set-up, we show that in many regions TWS from OS LISFLOOD fits better to observations than TWS from the Land Surface Discharge Model (LSDM) routinely operated at the GFZ and used in geodetic applications worldwide. The advantage of the high spatial resolution of the OS LISFLOOD implementation is shown by comparing vertical surface displacements to GNSS observations in a global network of stations. The data set presented here is the first application of OS LISFLOOD to generate quasi-global (regions south of 60○S excluded) daily 0.05○ TWS fields for a 23-year period (2000–2022).
Based on the SNREI model, the loading theory of calculating deformation due to surface and internal mass loads has been thoroughly investigated. However, the real Earth not only features a complex three-dimensional internal structure, but also has complex surface topography. Therefore, the SNREI hypothesis cannot meet the high precision requirement of load gravity effect calculation in gravity observation, highlighting the urgent need for a loading theory that accounts for surface topography. The load gravity effect comprises the direct gravitational effect g^N of the loading mass and the additional effect g^E generated by the earth deformation. In this study, we propose a formulism for calculating the direct gravitational effect on actual topography and approximately considers the additional effect generated by the earth deformation. By analyzing Green's functions and employing two examples, the differences between the direct gravitational and additional effects on a topography are compared, demonstrating the significance influence of topography in load gravity calculations. We use a SRTM terrain model with 1 km spatial resolution to obtain the load gravity effects in the Tibetan Plateau caused by long-term changes in surface mass with a spatial resolution of 0.125° during 2002-2021 with a forward model. The results indicate that the maximum difference in load gravity rate due to topography reaches −1.8 μGal/a in the region along the southern edge of the Tibetan Plateau, where significant glacial retreat has been observed, with its absolute value of 91% of the value calculated using spherical model (1.98 μGal/a). Additionally, by examining the influence of heavy rainfall on a superconducting gravimeter in a cave, we found that the standard deviation of the original residual gravity data can be reduced from 0.288 μGal to 0.076 μGal when applying the load theory that considers the topography, which effectively corrected the rainfall interference. The results of this study emphasize the importance of accounting topography in regional load gravity effect calculations.
As the largest groundwater drainage region in China, the per capita water resources in the North China Plain (NCP) account for only one-seventh of the country’s available water resources. Currently, the NCP is experiencing a serious water shortage due to the overexploitation of groundwater resources and a subsequent series of natural disasters. Thus, accurate regional assessments and effective water resource management policies are of critical importance. To accomplish this phenomenon, the daily terrestrial water storage anomaly (TWSA) over the NCP is calculated from the combination of the GNSS vertical deformation sequences (seasonal items) and GRACE (trend items). The groundwater storage anomaly (GWSA) in the NCP is obtained by subtracting the canopy water, soil water, and snow water equivalent components from the TWSA. The inversion results of this study are verified by comparisons with the Global Land Data Assimilation System (GLDAS) data products. The elevated annual amplitude areas are located in Beijing and Tianjin, and the Pearson correlation coefficient (PCC), root mean square error (RMSE), and Nash–Sutcliffe efficiency (NSE) between the two GWSA results are 0.67, 4.01 cm, and 0.61, respectively. This indicates that the methods proposed in this study are reliable. Finally, the groundwater drought index was calculated for the period from 2011 to 2021, and the results showed that 2019 was the driest year, with a drought severity index value of −0.12, indicative of slightly moderate drought conditions. By calculating and analyzing the annual GWSA, this work shows that the South–North Water Transfer Project does provide some regional drought mitigation.
Surface deformation of the earth due to a periodic point load on the earth's surface is re-analyzed. Firstly, the equation of motion for deformation of the whole earth due to a periodic zonal harmonic load is solved, and the load Love numbers, which are ratios between the load and the resultant perturbations, are acquired accordingly for the International Association of Seismology and Physics of the Earth's Interior (IASPEI) earth model. The load Green's functions are then evaluated by using the calculated load Love numbers. All the steps are verified, and the characters of the acquired load Love numbers and the load Green's functions are inspected. A comparison is made with former studies that used different earth models.
[1] High-resolution load-induced crustal deformations calculated from numerical models are tested for their ability to predict hydrologically-induced station height variability, as they are known to be large enough to affect epoch-wise parameters obtained from the analysis of global geodetic networks. Loading contributions due to terrestrial water storage as given by global hydrological models are calculated on a 0.5° global regular grid with daily temporal resolution. Apart from the dominant seasonal variations, the hydrological loading signal discloses also rapid changes exceeding 1 mm in several regions that can be associated with major precipitation events and river floods. Locally strong loading signals with exceptionally high amplitudes, in many cases even with nonseasonal nature, occur along the major river channels. Only high-resolution loading calculations considering also the water mass anomalies stored in the model river flow can resolve the correct amplitudes in the surrounded area up to 100 km distance. The comparison of the modeled hydrological surface deformation with GPS station time series shows that high-resolution hydrological loading estimates based on global-scale models are able to explain a considerable fraction (up to 54%) of the observed vertical station movements caused by continental water storage variations.
Love Numbers are computed for several reference Earth models. A Love
number is the proportionality coefficient between the mechanical cause
and its consequence in term of elastic deformation (vertical and
horizontal displacement, gravity perturbation) for a scale given in term
of a spherical harmonics' degree. A practical numerical method for Love
numbers computation is described. Love numbers of low degree (1 and 2)
and high degree (greater than 1,000 and up to 10,000+) are computed.
Their meanings are discussed depending on the effective depth of the
deformation and the rheological properties of the Earth's model.
Internal Love numbers of degree 10, 100, 1000, 10000 and sampling the
Earth's interior every kilometer, show how the Earth's interior is
deformed and which Earth's layers contribute to the global or local
deformation depending on the spherical harmonics' degree. Reference Love
numbers of several reference Earth's models are compared. Site-dependent
Love numbers are computed taking into account the specific radial
Earth's structure below a given site, under the assumption that the
Earth is spherically symmetric. This approach provides an attempt to
estimate the uncertainties of Love numbers relative to the
site-dependent rheology and gain insights in the Earth's elastic
deformation processes.
We compare vertical seasonal loading deformation observed by continuous
GPS stations in southern Alaska and modeled vertical displacements due
to seasonal hydrological loading inferred from GRACE. Seasonal
displacements are significant, and GPS-observed and GRACE-modeled
seasonal displacements are highly correlated. We define a measure called
the WRMS Reduction Ratio to measure the fraction of the position
variations at seasonal periods removed by correcting the GPS time series
using a seasonal model based on GRACE. The median WRMS Reduction Ratio
is 0.82 and the mean is 0.73 ± 0.26, with a value of
1.0 indicating perfect agreement of GPS and GRACE. The effects of
atmosphere and non-tidal ocean loading are important; we add the AOD1B
de-aliasing model to the GRACE solutions because the displacements due
to these loads are present in the GPS data, and this improves the
correlations between these two geodetic measurements. We find weak
correlations for some stations located in areas where the magnitude of
the load changes over a short distance, due to GRACE's limited spatial
resolution. GRACE models can correct seasonal displacements for campaign
GPS measurements as well.
Three different environmental loading methods are used to estimate surface displacements and correct non-linear variations in a set of GPS weekly height time series. Loading data are provided by (1) Global Geophysical Fluid Center (GGFC), (2) Loading Model of Quasi-Observation Combination Analysis software (QLM) and (3) our own daily loading time series (we call it OMD for optimum model data). We find that OMD has the smallest scatter in height across the selected 233 globally distributed GPS reference stations, GGFC has the next smallest variability, and QLM has the largest scatter. By removing the load-induced height changes from the GPS height time series, we are able to reduce the scatter on 74, 64 and 41 % of the stations using the OMD models, the GGFC model and QLM model respectively. We demonstrate that the discrepancy between the center of earth (CE) and the center of figure (CF) reference frames can be ignored. The most important differences between the predicted models are caused by (1) differences in the hydrology data from the National Center for Atmospheric Research (NCEP) vs. those from the Global Land Data Assimilation System (GLDAS), (2) grid interpolation, and (3) whether the topographic effect is removed or not. Both QLM and GGFC are extremely convenient tools for non-specialists to use to calculate loading effects. Due to the limitation of NCEP reanalysis hydrology data compared with the GLDAS model, the GGFC dataset is much more suitable than QLM for applying environmental loading corrections to GPS height time series. However, loading results for Greenland from GGFC should be discarded since hydrology data from GLDAS in this region are not accurate. The QLM model is equivalent to OMD in Greenland and, hence, could be used as a complement to the GGFC product to model the load in this region. We find that the predicted loading from all three models cannot reduce the scatter of the height coordinate for some stations in Europe.
Temporal mass variations in the continental hydrosphere and in the atmosphere lead to changes in the gravitational potential field that are associated with load-induced deformation of the Earth's crust. Therefore, models that compute continental water storage and atmospheric pressure can be validated by measured load deformation time series. In this study, water mass variations as computed by the Water-GAP Global Hydrology Model (WGHM) and surface pressure as provided by the reanalysis product of the National Centers for Environmental Prediction describe the hydrological and atmospheric pressure loading, respectively. GPS observations from 14 years at 208 stations world-wide were reprocessed to estimate admittance factors for the associated load deformation time series in order to determine how well the model-based deformation fits to real data. We found that such site-specific scaling factors can be identified separately for water mass and air pressure loading. Regarding water storage variation as computed by WGHM, weighted global mean admittances are 0.74 +/- 0.09, 0.66 +/- 0.10, 0.90 +/- 0.06 for the north, east and vertical component, respectively. For the dominant vertical component, there is a rather good fit to the observed displacements, and, averaged over all sites, WGHM is found to slightly overestimate temporal variations of water storage. For Europe and North America, with a dense GPS network, site-specific admittances show a good spatial coherence. Regarding regional over- or underestimation of WGHM water storage variations, they agree well with GRACE gravity field data. Globally averaged admittance estimates of pre-computed atmospheric loading displacements provided by the Goddard Geodetic VLBI Group were determined to be 0.88 +/- 0.04, 0.97 +/- 0.08, 1.13 +/- 0.01 for the north, east and vertical, respectively. Here, a relatively large discrepancy for the dominant vertical component indicates an underestimation of corresponding loading predictions.
We analyze continuous GPS measurements in Nepal, southern side of the
Himalaya, and compare GPS results with GRACE observations in this area.
We find both GPS and GRACE show significant seasonal variations. Further
comparison indicates that the observed seasonal GPS height variation and
GRACE-derived seasonal vertical displacement due to the changing
hydrologic load exhibit very consistent results, for both amplitude and
phase. For continuous GPS stations whose observation time span are
longer than 3 years, the average WRMS reduction is ˜45% when we
subtract GRACE-derived vertical displacements from GPS observed time
series. The comparison for annual amplitudes between GPS observed and
GRACE-derived seasonal displacements also shows consistent correlation.
The good seasonal correlation between GPS and GRACE is due to the
improved GPS processing strategies and also because of the strong
seasonal hydrological variations in Nepal. Besides the seasonal signal,
GRACE also indicates a long-term mass loss in the Himalaya region,
assuming no GIA effect. This mass loss therefore will lead to crustal
uplift since the earth behaves as an elastic body. We model this effect
and remove it from GPS observed vertical rates. With a 2D dislocation
model, most GPS vertical rates, especially in the central part of Nepal,
can be interpreted by interseismic strain from the Main Himalayan
Thrust, and several exceptions may indicate the complexity of vertical
motion in this region and some potential local effects.
Following the release of global continental effective elastic thickness
(Te) maps obtained using different approaches, we now have the
opportunity to provide better constraints on Te. We improve previous
estimates of Te derived from thermo-rheological models of lithospheric
strength (or Ter) using new equations that consider
variations of the Young's Modulus in the lithosphere. These new values
are quantitatively compared with those obtained from an inverse approach
(or Tei) based on a comparison of the spectral coherence
between topography and gravity anomalies with the flexural response of
an equivalent elastic plate to loading. The two models show in general a
good agreement, having equal means (at the 95% significance level) in
about half of the continental areas. In other regions Tei
exceeds Ter in about 65% of the data points, showing that
Tei provides an upper bound on Te. The two data sets have a
similar range, but demonstrate different distributions. Ter
has a bimodal distribution, with the two peaks representative of the
cratons and of the areas outside of them. In contrast, Tei
has more uniform distribution without predominant peaks. Our models show
higher similarities in the Meso-Cenozoic orogens than in the Archaean
and Proterozoic shields and platforms, due to the methods employed. For
the regions with the most robust determinations of Ter and
Tei, the relationship between them is close to linear. The
results of this work can be used for further studies on the mechanical
properties of the lithosphere.
The paper deals with large-scale crustal deformation due to hydrological
surface loads and its influence on seasonal variation of GPS estimated
heights. The research was concentrated on the area of Poland. The
deformation caused by continental water storage has been computed on the
basis of WaterGAP Hydrological Model data by applying convolution of
water masses with appropriate Green's function. Obtained site
displacements were compared with height changes estimated from GPS
observations using the Precise Point Positioning (PPP) method. Long time
series of the solutions for 4 stations were used for evaluation of
surface loading phenomena. Good agreement both in amplitude and phase
was found, however some discrepancies remain which are assigned to
single point positioning technique deficiencies. Annual repeatability of
water cycle and demanding procedure for computing site displacements for
each site, allowed to develop a simple model for Poland which could be
applied to remove (or highly reduce) seasonal hydrological signal from
time series of GPS solutions.
The seasonal modulation of seismicity observed in Nepal is given to be
related to subtle stress changes, induced by strong seasonal variations
of ground deformation. Horizontal and vertical seasonal variations are
observed on GPS times series from stations located in Nepal, India and
Tibet (China). We demonstrate that this geodetic deformation is induced
by seasonal variations of continental water storage driven by the
Monsoon. We use data from the Gravity Recovery and Climate Experiment
(GRACE) to determine the time evolution of surface loading. We compute
the expected geodetic deformation assuming a perfectly elastic Earth
model. We consider Green's functions, describing the surface deformation
response to a point load, for an elastic homogeneous half-space model
and for a layered non-rotating spherical Earth model based on the
Preliminary Reference Earth Model (PREM) and a local seismic velocity
model. The amplitude and phase of the seasonal variation of the vertical
and horizontal geodetic positions can be jointly adjusted only with the
layered Earth model. The study emphasizes the importance of using a
realistic Earth elastic structure to model surface displacements induced
by surface loading. The study also shows that the modeling of geodetic
seasonal variations provides a way to probe the Elastic structure of the
Earth, even in the absence of direct measurements of surface load
variations. Finally, it enhances the possibility of evaluating, with
smaller uncertainties, the subtle stress changes given to be responsible
for the seasonal variations of seismicity.