Skip to main content
NCBI home page
NASA Author Manuscripts logoLink to NASA Author Manuscripts
. Author manuscript; available in PMC: 2018 Jan 9.
Published in final edited form as: Geophys Res Lett. 2016 Jan 21;43(2):600–610. doi: 10.1002/2015GL067439

New Antarctic Gravity Anomaly Grid for Enhanced Geodetic and Geophysical Studies in Antarctica

M Scheinert 1, F Ferraccioli 2, J Schwabe 1,12, R Bell 3, M Studinger 4, D Damaske 5, W Jokat 6,7, N Aleshkova 8, T Jordan 2, G Leitchenkov 8,9, D D Blankenship 10, T M Damiani 11, D Young 10, J R Cochran 3, T D Richter 10
PMCID: PMC5759340  NIHMSID: NIHMS931291  PMID: 29326484

Abstract

Gravity surveying is challenging in Antarctica because of its hostile environment and inaccessibility. Nevertheless, many ground-based, airborne and shipborne gravity campaigns have been completed by the geophysical and geodetic communities since the 1980s. We present the first modern Antarctic-wide gravity data compilation derived from 13 million data points covering an area of 10 million km2, which corresponds to 73% coverage of the continent. The remove-compute-restore technique was applied for gridding, which facilitated levelling of the different gravity datasets with respect to an Earth Gravity Model derived from satellite data alone. The resulting free-air and Bouguer gravity anomaly grids of 10 km resolution are publicly available. These grids will enable new high-resolution combined Earth Gravity Models to be derived and represent a major step forward towards solving the geodetic polar data gap problem. They provide a new tool to investigate continental-scale lithospheric structure and geological evolution of Antarctica.

1. Introduction

The gravity field of the Earth is a key quantity of interest to geodesy and to other fields of geosciences. Being a distinguished equipotential surface of the gravity potential, the geoid serves as a reference surface for the realization of physical heights, which is an important task of geodesy [Forsberg et al., 2005]. In oceanography the geoid serves as a reference for the determination of the (mean) sea-surface topography. In polar regions where the ocean is partly covered by sea ice, icebergs or ice shelves, the geoid also provides a link between the surface ellipsoidal height and the freeboard height, which in turn can be used to infer the thickness of the floating ice. Determining an equipotential surface is also of significance for Antarctic subglacial lake studies [Ewert et al., 2012]. In geophysics, analyses of gravity anomalies yield insight into the structure of the lithosphere and into tectonic and geodynamic processes that shape the continents and surrounding oceans.

Huge progress in mapping the global Earth gravity field has been made in recent years aided in particular by the satellite gravity missions GRACE and GOCE which enable a coherent coverage and consistent accuracy up to an unprecedented resolution of 130 km and 90 km, respectively. This long- to medium-wavelength field resolved by satellite gravimetry is of considerable usefulness to study deeper lithospheric features or large-scale regional to continental scale geoid patterns. However, it is the terrestrial data that critically augment our knowledge of the shorter wavelengths anomalies which are a key for studying crustal features and for a higher resolution view of the geoid. In order to obtain such a higher resolution (up to 10 km) terrestrial gravity compilations can be utilized over most continents and oceans, including the Arctic [Kenyon et al., 2008]. However, Antarctica remains the most difficult-to-access region on Earth and, therefore, still suffers from considerable gravity data coverage gaps. Nevertheless, over the years a considerable number of gravity surveys have successfully been completed in Antarctica. Aerogravimetry in particular has enabled a huge step forward in Antarctic data coverage.

While major efforts have been made to compile all available Antarctic bedrock topography [Fretwell et al., 2013] and magnetic data [Golynsky et al., 2013] no modern continental-scale compilation of gravity data exists to date. Recognising the pressing need for such a gravity compilation, in 2003 the International Association of Geodesy (IAG) launched an initiative which is now organised within Subcommission 2.4f “Gravity and Geoid in Antarctica” (AntGG). Here we present the major outcome of this international multidisciplinary initiative, the first continental-scale gravity anomaly grid for Antarctica.

Enhanced geodetic applications include the development of next generation Earth Gravity Models and a new Antarctic geoid derivation, while geophysical studies will greatly benefit from these gravity grids, too. A higher resolution crustal thickness and elastic thickness estimation will become possible by combining gravity and seismic data compilations [Ferraccioli et al., 2011; An et al., 2015]. The gravity compilation will also shed new light onto the extent of major sedimentary basins and provides a new foundation to study the architecture and the evolution of the continent, including the processes of subduction, collision, continental rifting and intraplate features.

2. Gravity surveys in Antarctica

The acquisition of terrestrial gravity data in Antarctica is challenging because the continent and its surrounding ocean represent a hostile and remote environment. Conventional marine and land gravity surveying techniques are limited by sea ice and ice shelves and by the vast extension, remoteness and inaccessibility of the Antarctic ice sheet, respectively. Most surveying activities are restricted to the Antarctic summer season but adverse weather conditions can occur also during the summer making ground-operations challenging. Moreover, major logistic efforts are required to realize Antarctic surveys. Airborne gravimetry is the only viable method which is capable of dealing with these conditions and enables much larger areas to be surveyed in one season. Airborne surveys often comprise a suite of geophysical-geodetic equipment such as gravimeters, magnetometers to measure the Earth’s near-lithosphere magnetic field, radio echo sounding (RES) to measure internal ice layers and subglacial topography, lasers to measure ice-surface height and roughness, inertial navigation system (INS) to measure aircraft attitude and support the determination of the flight trajectory, and global navigation satellite system (GNSS) antennas and receivers to derive the flight trajectory and kinematic accelerations.

The International Polar Year 2007/2008 (IPY) [Krupnik et al., 2011] provided a springboard to launch major new airborne geophysical surveys, including airborne gravimetry over largely unexplored Antarctic frontiers, such as the Gamburtsev Subglacial Mountains [Ferraccioli et al., 2011; Bell et al., 2011], and Wilkes Land in East Antarctica [Aitken et al., 2014]. Another project providing extensive new airborne gravity data coverage for Antarctica is NASA’s Operation IceBridge (OIB) that aims to bridge the gap between the satellite laser altimetry missions ICESat and ICESat-2 [Studinger et al., 2010]. In East Antarctica a long-term airborne project was conducted by German institutions to unravel the largely unexplored Dronning Maud Land [Riedel et al., 2012]. Over time a large number of gravimetric datasets have been collected in Antarctica by the international geosciences community and incorporated into the AntGG database that is being maintained at TU Dresden [Scheinert, 2012].

These gravity data differ in a number of aspects. Gravimetric surveys were initiated by different nations and programs, had different scientific goals and were realized at different observation epochs (see SI, Table S1). Depending on the applied technique and the positioning method, the accuracy of the gravity data differs over a large range. Issues like the realization of the gravimetric datum or survey layout to enable cross-over calibration also have a strong impact on the final accuracy of an individual survey. The raw data have been treated in different ways, especially with respect to filtering, reductions and/or corrections. For airborne surveys several issues can arise such as an unclear altitude reference of the data or whether a downward continuation was applied or not. These issues are also reflected in incomplete metadata for some of these surveys. In some cases it is also not clear if the term gravity anomaly is correctly referred to, or if – in the geodetic understanding – the data are given as gravity disturbances [Hackney and Featherstone, 2003]. Overlapping or complementary datasets may be internally consistent but can still contain systematic biases such as offsets and tilts. Thus, the large heterogeneity of the gravity data was carefully considered in our new Antarctic compilation.

Overall, more than 13 million gravity data points have been compiled in the AntGG database, originating from terrestrial, airborne and shipborne surveys. More than one million line kilometers of aerogravimetry data are included in our new compilation effort. Altogether, the data compilation covers an area of 10 million km2, corresponding to about 73% of the Antarctic continent including ice shelves. The oceanic area covered by gravity data corresponds to approximately 29% of the Southern Ocean south of 60°S.

3. Global high-resolution determination of the gravity field of the Earth

Global Earth Gravity Models (EGM) are based on satellite data. To obtain a higher resolution than such satellite-only models, terrestrial gravity data have to be included globally which leads to so-called combined EGMs. The term terrestrial data is used here to denote data of ground-based, airborne and shipborne surveys. Combined EGMs reach a half-wavelength resolution of 70 km and better, comparable to harmonic degree and order (d/o) 360 and higher (for the relation of degree and resolution see Barthelmes [2013, p. 20]). Recent high-resolution combined EGMs such as EGM2008 [Pavlis et al., 2008] or EIGEN-6C4 [Förste et al., 2014] reach a resolution of approximately 10 km (d/o 2190) over most parts of the world. However, in Antarctica the resolution is much lower due to two facts: Firstly, the deviation of the satellite orbit inclination from 90° leads to a polar gap in satellite data. Secondly, the largest terrestrial data gaps still exist in Antarctica.

New satellite-based data provide unprecedented accuracy and resolution in the representation of the Earth’s gravity field. The geodetic satellite mission GRACE (GRAvity and Climate Experiment) has been in orbit since March 2002 [Tapley et al., 2004]) while GOCE (Gravity field and steady-state Ocean Circulation Explorer) was launched in March 2009 and fell from orbit in November 2013 [Floberghagen et al., 2011; van der Meijde et al., 2015]). GRACE-based satellite-only global EGMs reach a resolution of 160 to 130 km (d/o 160 to 200) e.g. GGM05S [Tapley et al., 2014]. GOCE has provided significantly higher resolution data to satellite-only EGM. For example, EIGEN-6S2 [Rudenko et al., 2014] combines LAGEOS laser ranging data for the lower degrees 2–30, GRACE range rate data up to d/o 180, and GOCE data resulting in approx. 90 km resolution (d/o 260). However, GOCE has a polar data gap larger than that of GRACE with a diameter of approximately 1,400 km due to its inclination of 96.5°. Therefore, to obtain a stabilized EGM solution, one has to apply a certain type of regularization [Metzler and Pail, 2005; Pail et al., 2011] or to include terrestrial gravity data. However, the latter is not possible yet for Antarctica due to the lack of a continental-scale compilation.

4. Regional gravity field determination in Antarctica and choice of background EGM

In regional gravity field determination the remove-compute-restore (RCR) technique is commonly applied [Forsberg, 1993; Forsberg and Tscherning, 1997; Sansò and Sideris, 2013]. However, as discussed in Section 2, Antarctic gravity data exhibit large heterogeneities and inconsistencies. How heterogeneous gravity data can be utilized to improve the regional geoid has previously been presented for the Weddell Sea [Schwabe and Scheinert, 2014] and Lake Vostok [Schwabe et al., 2014]. The application of a background EGM is a major step of the RCR technique (see Section 5.2).

For this, a satellite-only EGM has to be used since it is independent from terrestrial data. GOCE-based EGMs are favorable for they enable the highest resolution. However, one has to deal with the polar data gap problem. Therefore, the reliability and the applicability of any GOCE-based EGM in the Antarctic interior depends considerably on the regularization technique used in the spherical harmonic analysis. Different approaches are applied in the determination of EGMs such as the European Space Agency’s (ESA) direct, timewise and spacewise models [Pail et al., 2011] or the family of EIGEN [Rudenko et al., 2014; Shako et al., 2014] and GOCO [Pail et al., 2010; Mayer-Gürr, 2012] models. GRACE data were merged up to a certain degree and order to deal with the poor sensitivity of GOCE gravity gradient measurements at long wavelengths. A spherical cap regularization [Metzler and Pail, 2005] was computed in an iterative way as in the ESA direct model ESA-DIR/R5 [Bruinsma et al., 2013, 2014]. (For the sake of briefness, short abbrevations shall be used, like ESA-DIR/R5 for GO CONS GCF 2 DIR R5, ESA’s direct model release 5, and so on.) For the ESA-TIM/R5 a regularization was applied using synthetic signal degree variances due to Kaula’s rule of thumb to constrain zonal and near-zonal coefficients that suffer mostly from the polar data gap [Brockmann et al., 2014].

To investigate the performance of recent EGMs, a comparison was carried out using high-resolution airborne gravity data that can be regarded as providing ground truth for these global models. Our evaluation (see SI, Section S2) considered regions both inside and outside the polar data gap. We concluded that the GOCO03S model [Mayer-Gürr, 2012] utilizes the GOCE observations in an appropriate way with minimum degradation of signals including the interior of the polar gap (which is due to the inclusion of GRACE data). Therefore, it is an appropriate choice to apply GOCO03S as a background EGM to serve as the common reference in adjusting the terrestrial Antarctic gravity datasets.

5. Derivation of a new Antarctic gravity anomaly grid

In the compilation we focus primarily on continental surveys in order to close data gaps as best as currently possible. The original gravity datasets made available to AntGG comprise point-wise data, profile-wise data (as it is mostly the case for airborne and shipborne surveys), and gridded datasets. The original preprocessed gravity data were preserved as much as possible. In view of the large amount of data records (see Section 2) and due to the generally poor linkage between the different datasets we did not attempt to mitigate all problematic issues in the individual datasets.

Shipborne data are only considered in some regions, since in general they show big gaps, incomplete metadata and sometimes unclear referencing. Also, they are not that crucial since in the ocean areas satellite altimetry allows to derive adequate gravity information for most geodetic and geophysical applications [Andersen et al., 2014; Sandwell et al., 2014].

5.1. Compilation of gravity data and metadata

For every campaign metadata were compiled as accurately as possible. The reliability of this process depends to a large extent on the information provided with the original gravity datasets. As a general rule, data of airborne surveys (where a GNSS referenced trajectory is available) were assigned gravity disturbances δg (cf. Section 2), while shipborne and land data were treated as gravity anomalies Δg. In most of the surveys the gravity formula of GRS80 [Moritz, 1984] was taken to compute normal gravity. Where the older GRS67 formula was used, we applied a correction term [Anderson et al., 1984] which almost results in a constant offset on the level of 1 mGal. If the gravity reference is unknown (because it was not possible to connect to an absolute gravity point), a bias was introduced. As reference surface for ellipsoidal heights the WGS84 ellipsoid [NIMA, 2000] was taken (which is the standard for GNSS positioning; deviations from the GRS80 ellipsoid can be neglected).

To characterize the accuracy of each individual dataset – and to make the datasets comparable to each other at least in a relative sense – an a priori standard deviation σ0 was allocated to each dataset. In some cases it could be deduced from the metadata. If no information was available, we utilized pre-comparisons like cross-over computations or previous investigations incorporating independent data, see e.g. Schwabe and Scheinert [2014]. Thus, a standard value of 3 mGal was allocated to airborne gravity surveys where no other value was given. The spatial resolution of airborne campaigns depends mainly on the line spacing which varies from typically only a few km to 30 km (see Table S1). Aircraft speed and respective filtering limit the along-line resolution which, however, is normally still higher than that resulting from the line spacing. Whereas the ground-based surveys ADGRAV-ROSS #23 and GEOMAUD #24 are assigned a priori standard deviations of 5 mGal and 1 mGal, respectively, the BAS survey #25 was given a higher value of 20 mGal according to previous investigations [Schwabe et al., 2012]. The PMGE/VNIIO compilation #26 was assigned a value of 10 mGal since the data were mostly acquired before GNSS positioning became available. Also, due to unknown smoothing and gridding procedure this dataset exhibits a lower spatial resolution of about 25 to 30 km and biases of up to 25 mGal [see also Studinger, 1998; Schwabe and Scheinert, 2014].

Information on the datasets incorporated into the Antarctic gravity anomaly grid are summarized in Table S1, including metadata and a priori standard deviation σ0. In case of aerogravimetry, approximate total length of survey flights per campaign and line spacing are given. The individual gravimetric surveys are not discussed in this paper. Instead, one may refer to the relevant references reported in Table S1. Figure S1 shows location and spatial extension of the individual datasets. Multiple coverage of same areas by different surveys leads to overlaps as illustrated in Figure S2.

5.2. Processing and gridding procedure

From the mostly irregularly distributed data a regular gravity anomaly grid needed to be derived. To facilitate gridding on an equidistant rectangular grid centered at the South Pole we used the polar stereographic projection (based on the WGS84 ellipsoid, true scale at parallel 71°S, using Generic Mapping Tools (GMT) [Wessel et al., 2013]). The grid spacing was chosen to be 10 km. Due to uncertainties and heterogeneities in the data as well as due to signal damping with increasing flight height and heterogeneous line spacing of aerogravimetry, a higher resolution grid mesh was not warranted at continental scale. The choice of a 10 km grid mesh provides a reasonable compromise between the older, more widely-spaced, ground-based surveys and newer and higher-resolution airborne geophysical campaigns.

Biases of the individual datasets were taken into account as well as the heterogeneous accuracy by introducing an a priori standard deviation for each dataset. To consider these aspects accordingly the RCR technique is utilized which is a common method of physical geodesy (Section 4). The RCR technique uses a residual disturbing potential δT which enables to apply spherical approximations and linearized functionals. The residual disturbing potential is made up of the remainder after the long-wavelength part is accounted for by a global EGM, and the short-wavelength part is accounted for by topography. Here, we are using solely (irregularly distributed) gravity anomalies which can be regarded as a functional F of T, i.e. Δg = F(T). Thus, the remove step reads

F(δT)=F(T)-F(TEGM)-F(Ttopo) (1)

Subsequently, a compute step is applied to the residual functional which should be formally denoted by C

[F(δT)]=CF(δT) (2)

Normally, on the left-hand side of this equation δT is standing alone. For example, in case of solving the gravimetric boundary value problem, C might designate the (modified) Stokes integral. Now, the parentheses [*] shall denote values given at the regular grid. After the compute step, the long-wavelength part and shorth-wavelength part are restored in the grid points:

[F(T)]=[F(δT)]+[F(TEGM)]+[F(Ttopo)] (3)

As background EGM in the remove and restore steps (eqs. 1 and 3, respectively) GOCO03S [Mayer-Gürr, 2012] was used up to d/o 250. Topography is usually considered in a residual terrain model (RTM) approach [Forsberg and Tscherning, 1997], which should have a smoothing effect on the data [ibid]. Here, we carried out test calculations using the latest publically available Bedmap2 compilation [Fretwell et al., 2013] including both ice-surface heights and bedrock topography. However, the resulting residual anomalies did not represent an improvement over residual free-air anomalies. Where Bedmap2 has lower accuracies (data-void areas or areas with accuracies of only some hundred or even thousand meter), errors in bedrock topography would directly enter into residual gravity. Therefore, we decided not to apply the topographic reduction (in the RTM sense). Thus, the entire procedure comprises the following steps:

  1. Remove step: The contribution of the background EGM (GOCO03S) was computed in each observation point at flight altitude (if given, see Table S1) or at the surface and subsequently subtracted from the original data (eq. 1). As a result of this step we obtain residual gravity anomalies δ(Δg)(i) for each individual survey (i) still given at irregularly distributed observation points. Gravity disturbances (where clearly identified) were converted to gravity anomalies in advance, estimating the difference (Δg – δg) using the same EGM. At the long wavelengths the downward continuation is implicitly done using the EGM. A further step of downward continuation was not considered. Most data were taken at the surface or close to the surface anyway, as also airborne surveys were flown in altitudes such that the height above ground was small. It can be shown that the vertical gradient of residual gravity anomalies at flight altitude is close to zero, and that the remaining effect of the downward continuation is of the order of magnitude of less than 0.1 mGal with a standard deviation of less than 1 mGal. Moreover, it should be emphasized that most airborne surveys were conducted over the Antarctic ice sheet, which means that ice thickness still adds to the distance from the ground (the ice surface) to bedrock topography. (The Antarctic ice sheet has a mean thickness of 2,126 m [Fretwell et al., 2013].)

  2. Compute step – project: This step is also done for each dataset individually. The observation points originally given by geographical coordinates were mapped by polar-stereographic projection into points on the plane. Then, the residual gravity anomalies were interpolated from the irregularly distributed points onto a regular grid with 10 km spacing. For this, we used the Generic Mapping Tool (GMT) [Wessel et al., 2013]. Routine blockmean was used as a pre-processing step to avoid aliasing of shorter wavelengths. It computes the mean position and mean value for every grid cell that is not empty. After that, routine surface was applied to realize the interpolation to the regular grid. This is accomplished by solving
    (1-t)·Δs(Δsz)+t·Δsz=0 (4)

    where Δs denotes the surface Laplacian operator, t a tension factor [Wessel and Smith, 2015], and z = z(x, y) the data to be gridded at rectangular coordinates, i.e., residual gravity anomalies given in terms of polar-stereographic coordinates. A non-zero tension factor relaxes the constraint of minimum curvature that otherwise can result in “undesired oscillations” and “false local maxima and minima” [Smith and Wessel, 1990]. It is recommended to use values of 0.25 … 0.3 for potential field data, whereas a larger tension factor (0.35) should be used for topography data [Wessel and Smith, 2015]. Here, a tension factor of 0.3 was utilized. Depending on the respective (mean) spacing a mask was derived for each dataset considering its effective coverage in order to prevent gaps between profiles or single observation points. Gridded residual gravity anomalies [δ(Δg)(i)] are resulting from this step. Their statistics are given in SI, Table S2.

  3. Compute step – level: In subtracting the respective mean from the residual gravity anomalies (cf. Table S2) each dataset (i) is individually referenced to the background EGM. In this way, systematic effects are accounted for, e.g. biases originating from different gravity datum realizations. This simple ansatz gives comparable results to a more complex computation using least-squares estimation including the estimation of offsets as realized by Schwabe and Scheinert [2014]. Considerable offsets of up to 40 mGal were detected. A higher-order detrending was also tested but omitted, since it can cause additional tilts or a degradation of the relative consistency between two overlapping datasets. As a result levelled residual gravity anomalies [ δ(Δg)0(i)] are obtained.

  4. Compute step – merge: Up to this step the datasets were treated individually. According to coverage, levelled residual gravity anomalies [ δ(Δg)0(i)] of more than one survey could be given in one grid point. Now, the final value is computed by a pointwise weighted mean from the individual gridded residual gravity anomalies:
    [δ(Δg)]=∑pi[δ(Δg)0(i)]∑pi (5)

    Weights were derived taken inverse a priori variances (Table S1): pi=1/σi2. Edge effects may occur where multiple datasets of different accuracy intersect or overlap. However, a filtering was not applied in order not to propagate such effects more widely throughout the grid. This step results in a regular grid of residual gravity anomalies [δ(Δg)].

  5. Restore step: The contribution of the background EGM is restored according to eq. 3. This was accomplished by adding the long-wavelength part evaluated from the background EGM in the points of the regular grid at the surface. This results in the desired regular grid of gravity anomalies [Δg].

5.3. Results

The resulting gridded dataset of (surface) gravity anomalies is the main outcome. In Figure 1 the planar grid was mapped to geographic coordinates by means of inverse polar-stereographic projection. Figure S1 gives the root mean square (RMS) of the weighted mean, propagated from a priori standard deviations as listed in Table S1.

Figure 1.

Figure 1

Open in a new tab

Gridded dataset of surface free-air gravity anomalies in Antarctica.

To evaluate the impact of newer aerogravimetry data, the RMS of residual individual datasets was estimated with respect to the residual gridded dataset (Figure S3). For example, this map clearly demonstrates the consistency of IceBridge data (#22) with other overlapping aerogravimetric data, e.g. in the Weddell Sea and Antarctic Peninsula regions but also at higher latitudes closer to the pole. Vice versa, larger deviations can be detected for the PMGE/VNIIO compilation #26 in East Antarctica (between 60°E and 90°E). A major reason for the lower accuracy lies in the fact that a lot of the data incorporated into this compilation were acquired prior to the availability of GNSS positioning. In the region of the Antarctic Peninsula, larger deviations are partly due to dataset #25 (see discussion in Sect. 5.1). Here, an improvement is likely to occur when accurate topography information is incorporated into the RCR processing scheme.

Finally, from the gridded gravity anomalies, complete Bouguer anomalies (Figure 2) were computed making use of the Bedmap2 dataset [Fretwell et al., 2013]. For this, the GRAVSOFT routine TC [Forsberg and Tscherning, 2008] was utilized applying a spherical prism integration with an integration radius of 300 km. To compute the complete Bouguer anomaly all density discontinuities were taken into account, with (standard) densities of 2670 kg/m3 for rock, 917 kg/m3 for ice, and 1025 kg/m3 for water.

Figure 2.

Figure 2

Open in a new tab

Gridded dataset of complete Bouguer gravity anomalies in Antarctica using Bedmap2 [Fretwell et al., 2013]. See Sect. 5.3 for explanations.

6. Implications for Antarctic geophysics

Our compilation of gravity anomalies provides a new basis for the geophysical community to study large-scale crustal architecture, effective elastic thickness, and isostatic and tectonic processes that shaped the Antarctic continent from the Precambrian to the Cenozoic. The continental-scale gravity compilation will also assist in developing more robust geophysical ties between Antarctica and formerly adjacent continents within the Gondwana, Rodinia and Columbia supercontinents [Aitken et al., 2015].

Recent continental-scale estimations of crustal thickness variations beneath Antarctica have relied mainly on inversions of satellite gravity [Block et al., 2009; O’Donnell and Nyblade, 2014] or compilations of relatively sparse and mostly passive seismic arrays [An et al., 2015]. Our new free-air and Bouguer anomaly grids are capable of resolving much shorter wavelength features related for example to major sedimentary basins and other intracrustal density variations. By incorporating the more regional-scale flexural responses to these intracrustal loads [Watts, 2001] improved crustal thickness estimations and tectonic interpretations for Antarctica will in turn become possible. Deriving improved estimates of crustal and sedimentary basin thickness in Antarctica is important in the quest to better constrain geothermal heat flux variations [Maule et al., 2005] and quantifying their potential influence on subglacial hydrology and ice sheet dynamics [Bell et al., 1998; Schroeder et al., 2014]. Efforts to select the ideal candidate sites for drilling the oldest ice [Fischer et al., 2013] also require an improved knowledge of the crustal structure in East Antarctica, which can influence regional geothermal heat flux patterns and hence the preservation of old basal ice.

The first terrestrial gravity anomaly grids for Antarctica will help shed new light onto the evolution of fundamental large-scale geological processes such as continental rifting in West Antarctica [Damiani et al., 2014; Jordan et al., 2013a; Bingham et al., 2012; Jordan et al., 2010] and intraplate mountain building in the Transantarctic Mountains [Stern and ten Brink, 1989; Studinger et al., 2004, 2006; Jordan et al., 2013b], the Gamburtsev Subglacial Mountains [Ferraccioli et al., 2011] and Dronning Maud Land [Näslund, 2001]. Gravity anomalies can aid studies of subduction and terrane accretion processes [Ferraccioli et al., 2002, 2006] and intraplate basin formation [Ferraccioli et al., 2009]. The availability of new terrestrial gravity anomaly grids for Antarctica will also augment current international efforts to compile almost two million line km of recent magnetic anomaly data for the continent [Golynsky et al., 2013], and together with these data, will provide a window on Antarctic subglacial geology and tectonic evolution [Jokat et al., 2003; Riedel and Jokat, 2007; Ferraccioli et al., 2009; Aitken et al., 2014].

7. Conclusions and Outlook

The first Antarctic-wide gridded dataset of gravity anomalies has been derived by incorporating all available gravity data collected over the continent over the last three decades. In the gridding procedure our aim was to preserve, as much as possible, the features of the original datasets (namely accuracy and variability). The scientific user is provided the grids of (surface) free-air gravity anomalies and of Bouguer anomalies with a grid spacing of 10 km each as well as a grid of accuracy measures (propagated RMS). The Antarctic gravity anomaly grid is ready to be used in the derivation of new global Earth Gravity Models. Also, as a next step of AntGG, an improved continent-wide Antarctic regional geoid will be derived from our new grid. Although the data coverage is still partially incomplete, the new compilation represents the biggest step forward so far towards solving the polar data gap problem. Further gravity surveys (especially airborne campaigns) are to be carried out, especially over the South Pole region, the largest of the gaps that is of significant hindrance, in particular for global models derived from GOCE data. As several international projects are planned in this respect, there is a high probability that the remaining major data gaps will be closed within the next few years. In the course of time, with new data being available, it is anticipated to provide updates of the Antarctic gravity anomaly grid presented here.

Datasets are available at: http://dx.doi.org/10.1594/PANGAEA.848168.

Supplementary Material

Supp1

Keypoints.

  • New 10 km grid of terrestrial gravity anomalies in Antarctica, covering 73% of the continent

  • Enabling determination of new high-resolution combined Earth Gravity Models

  • Providing new tool to investigate lithospheric structure and geological evolution of Antarctica

Acknowledgments

All contributors of gravity data are greatly acknowledged. M.S. thanks all colleagues who have supported the work of AntGG during the last decade, either as active members in the IAG Subcommission 2.4f ”‘Gravity and Geoid in Antarctica”’ and/or in the SCAR Expert Group GIANT or in other ways of collaboration. We thank two anonymous reviewers for their valuable remarks that helped to improve the manuscript.

References

  1. Aitken A, Betts P, Young D, Blankenship D, Roberts J, Siegert M. The Australo-Antarctic Columbia to Gondwana transition. Gondwana Res. 2015 doi: 10.1016/j.gr.2014.10.019. (online; article in press) [DOI] [Google Scholar]
  2. Aitken ARA, Young DA, Ferraccioli F, Betts PG, Greenbaum JS, Richter TG, Roberts JL, Blankenship DD, Siegert MJ. The subglacial geology of Wilkes Land, East Antarctica. Geophys Res Lett. 2014;41(7):2390–2400. doi: 10.1002/2014GL059405. [DOI] [Google Scholar]
  3. An M, Wiens DA, Zhao Y, Feng M, Nyblade AA, Kanao M, Li Y, Maggi A, Lvque J-J. S-velocity model and inferred Moho topography beneath the Antarctic Plate from Rayleigh waves. J Geophys Res. 2015;120(2014JB011332):359–383. doi: 10.1002/2014JB011332. [DOI] [Google Scholar]
  4. Andersen OB, Knudsen P, Kenyon S, Holmes S. Global and Arctic Marine Gravity Field From Recent Satellite Altimetry (DTU13). 76th EAGE Conference and Exhibition; 2014. [DOI] [Google Scholar]
  5. Anderson DL, et al. Geophysik der festen Erde, des Mondes und der Planeten. In: Fuchs K, Soffel H, editors. Landolt-Börnstein, Neue Serie, Gruppe V: Geophysik und Weltraumforschung. 2/a. Springer-Verlag; Berlin–Heidelberg–New York: 1984. [Google Scholar]
  6. Barthelmes F. Scientific Technical Report STR09/02. Helmholtz-Zentrum Potsdam Deutsches GeoForschungsZentrum; 2013. Definition of Functionals of the Geopotential and Their Calculation from Spherical Harmonic Models. (revised edition) [Google Scholar]
  7. Bell RE, Blankenship DD, Finn CA, Morse DL, Scambos TA, Brozena JM, Hodge SM. Influence of subglacial geology on the onset of a West Antarctic ice stream from aerogeophysical observations. Nature. 1998;394:58–62. doi: 10.1038/27883. [DOI] [Google Scholar]
  8. Bell RE, Ferraccioli F, Creyts TT, Braaten D, Corr H, Das I, Damaske D, Frearson N, Jordan T, Rose K, Studinger M, Wolovick M. Widespread Persistent Thickening of the East Antarctic Ice Sheet by Freezing from the Base. Science. 2011;331(6024):1592–1595. doi: 10.1126/science.1200109. [DOI] [PubMed] [Google Scholar]
  9. Bingham RG, Ferraccioli F, King EC, Larter RD, Pritchard HD, Smith AM, Vaughan DG. Inland thinning of West Antarctic Ice Sheet steered along subglacial rifts. Nature. 2012;487(7408):468–471. doi: 10.1038/nature11292. [DOI] [PubMed] [Google Scholar]
  10. Block AE, Bell RE, Studinger M. Antarctic crustal thickness from satellite gravity: Implications for the Transantarctic and Gamburtsev Subglacial Mountains. Earth Plan Sci Lett. 2009;288(1–2):194–203. doi: 10.1016/j.epsl.2009.09.022. [DOI] [Google Scholar]
  11. Brockmann JM, Zehentner N, Höck E, Pail R, Loth I, Mayer-Gürr T, Schuh W-D. EGM TIM RL05: An independent geoid with centimeter accuracy purely based on the GOCE mission. Geophys Res Lett. 2014;41(22):8089–8099. doi: 10.1002/2014GL061904. [DOI] [Google Scholar]
  12. Bruinsma SL, Förste C, Abrikosov O, Marty J-C, Rio M-H, Mulet S, Bonvalot S. The new ESA satellite-only gravity field model via the direct approach. Geophys Res Lett. 2013;40(14):3607–3612. doi: 10.1002/grl.50716. [DOI] [Google Scholar]
  13. Bruinsma SL, Foerste C, Abrikosov O, Lemoine J-M, Marty J-C, Mulet S, Rio M-H, Bonvalot S. ESA’s satellite-only gravity field model via the direct approach based on all GOCE data. Geophys Res Lett. 2014;41(21):7508–7514. doi: 10.1002/2014GL062045. [DOI] [Google Scholar]
  14. Damiani TM, Jordan TA, Ferraccioli F, Young DA, Blankenship DD. Variable crustal thickness beneath Thwaites Glacier revealed from airborne gravimetry, possible implications for geothermal heat flux in West Antarctica. Earth Plan Sci Lett. 2014;407(0):109– 122. doi: 10.1016/j.epsl.2014.09.023. [DOI] [Google Scholar]
  15. Ewert H, Popov S, Richter A, Schwabe J, Dietrich R, Scheinert M. Precise analysis of ICESat altimetry data and assessment of the hydrostatic equilibrium for subglacial Lake Vostok, East Antarctica. Geophys J Int. 2012 doi: 10.1111/j.1365-246X.2012.05649.x. [DOI] [Google Scholar]
  16. Ferraccioli F, Bozzo E, Capponi G. Aeromagnetic and gravity anomaly constraints for an early Paleozoic subduction system of Victoria Land, Antarctica. Geophys Res Lett. 2002;29(10):44-1–44-4. doi: 10.1029/2001GL014138. [DOI] [Google Scholar]
  17. Ferraccioli F, Jones P, Vaughan A, Leat P. New aerogeophysical view of the Antarctic Peninsula: More pieces, less puzzle. Geophys Res Lett. 2006;33:L05, 310. doi: 10.1029/2005GL024636. [DOI] [Google Scholar]
  18. Ferraccioli F, Armadillo E, Jordan T, Bozzo E, Corr H. Aeromagnetic exploration over the East Antarctic Ice Sheet: A new view of the Wilkes Subglacial Basin. Tectonophys. 2009;478(1–2):62– 77. doi: 10.1016/j.tecto.2009.03.013. [DOI] [Google Scholar]
  19. Ferraccioli F, Finn C, Jordan T, Bell R, Anderson L, Damaske D. East Antarctic rifting triggers uplift of the Gamburtsev Mountains. Nature. 2011;479(7373):388–392. doi: 10.1038/nature10566. [DOI] [PubMed] [Google Scholar]
  20. Fischer H, Severinghaus J, Brook E, Wolff E, Albert M, Alemany O, Arthern R, Bentley C, Blankenship D, Chappellaz J, Creyts T, Dahl-Jensen D, Dinn M, Frezzotti M, Fujita S, Gallee H, Hindmarsh R, Hudspeth D, Jugie G, Kawamura K, Lipenkov V, Miller H, Mulvaney R, Parrenin F, Pattyn F, Ritz C, Schwander J, Steinhage D, van Ommen T, Wilhelms F. Where to find 1.5 million yr old ice for the IPICS “Oldest-Ice” ice core. Clim Past. 2013;9(6):2489–2505. doi: 10.5194/cp-9-2489-2013. [DOI] [Google Scholar]
  21. Floberghagen R, Fehringer M, Lamarre D, Muzi D, Frommknecht B, Steiger C, Piñeiro J, da Costa A. Mission design, operation and exploitation of the gravity field and steady-state ocean circulation explorer mission. J Geod. 2011;85(11):749–758. doi: 10.1007/s00190-011-0498-3. [DOI] [Google Scholar]
  22. Forsberg R. Modelling the fine-structure of the geoid: Methods, data requirements and some results. Surv Geophys. 1993;14:403–418. [Google Scholar]
  23. Forsberg R, Tscherning C. Topographic effects in gravity field modelling for BVP. In: Sansò F, Rummel R, editors. Geodetic Boundary Value Problems in View of the One Centimeter Geoid, Lecture Notes in Earth Sciences. Vol. 65. Springer; 1997. pp. 241–272. [Google Scholar]
  24. Forsberg R, Tscherning CC. An overview manual for the GRAVSOFT geodetic gravity field modelling programs. 2 2008. [Google Scholar]
  25. Forsberg R, Sideris MG, Shum CK. The gravity field and GGOS. J Geodyn. 2005;40(4–5):387–393. doi: 10.1016/j.jog.2005.06.014. [DOI] [Google Scholar]
  26. Förste C, Bruinsma SL, Abrikosov O, Lemoine J-M, Schaller T, Götze H-J, Ebbing J, Marty JC, Flechtner F, Balmino G, Biancale R. EIGEN-6C4: The latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse, pres. 5th GOCE User Workshop; Paris. 25–28 Nov 2014.2014. [Google Scholar]
  27. Fretwell P, Pritchard HD, Vaughan DG, Bamber JL, Barrand NE, Bell R, Bianchi C, Bingham RG, Blankenship DD, Casassa G, Catania G, Callens D, Conway H, Cook AJ, Corr HFJ, Damaske D, Damm V, Ferraccioli F, Forsberg R, Fujita S, Gim Y, Gogineni P, Griggs JA, Hindmarsh RCA, Holmlund P, Holt JW, Jacobel RW, Jenkins A, Jokat W, Jordan T, King EC, Kohler J, Krabill W, Riger-Kusk M, Langley KA, Leitchenkov G, Leuschen C, Luyendyk BP, Matsuoka K, Mouginot J, Nitsche FO, Nogi Y, Nost OA, Popov SV, Rignot E, Rippin DM, Rivera A, Roberts J, Ross N, Siegert MJ, Smith AM, Steinhage D, Studinger M, Sun B, Tinto BK, Welch BC, Wilson D, Young DA, Xiangbin C, Zirizzotti A. Bedmap2: improved ice bed, surface and thickness datasets for Antarctica. The Cryosphere. 2013;7(1):375–393. doi: 10.5194/tc-7-375-2013. [DOI] [Google Scholar]
  28. Golynsky A, Bell R, Blankenship D, Damaske D, Ferraccioli F, Finn C, Golynsky D, Ivanov S, Jokat W, Masolov V, Riedel S, von Frese R, Young D. Air and shipborne magnetic surveys of the Antarctic into the 21st century. Tectonophys. 2013;585:3– 12. doi: 10.1016/j.tecto.2012.02.017. [DOI] [Google Scholar]
  29. Hackney RI, Featherstone WE. Geodetic versus geophysical perspectives of the ’gravity anomaly’. Geophys J Int. 2003;154:35–43. [Google Scholar]
  30. Jokat W, Boebel T, Knig M, Meyer U. Timing and geometry of early Gondwana breakup. J Geophys Res. 2003;108(B9) doi: 10.1029/2002JB001802. [DOI] [Google Scholar]
  31. Jordan T, Ferraccioli F, Vaughan D, Holt J, Corr H, Blankenship D, Diehl T. Aerogravity evidence for major crustal thinning under the Pine Island Glacier region (West Antarctica) GSA Bulletin. 2010;122(5–6):714–726. doi: 10.1130/B26417.1. [DOI] [Google Scholar]
  32. Jordan T, Ferraccioli F, Armadillo E, Bozzo E. Crustal architecture of the Wilkes Subglacial Basin in East Antarctica, as revealed from airborne gravity data. Tectonophys. 2013a;585:196–206. doi: 10.1016/j.tecto.2012.06.041. [DOI] [Google Scholar]
  33. Jordan T, Ferraccioli F, Ross N, Siegert M, Corr H, Leat P, Bingham R, Rippin D, le Brocq A. Inland extent of the Weddell Sea Rift imaged by new aerogeophysical data. Tectonophys. 2013b;585:137–160. doi: 10.1016/j.tecto.2012.09.010. [DOI] [Google Scholar]
  34. Kenyon S, Forsberg R, Coakley B. New Gravity Field for the Arctic. Eos, Trans AGU. 2008;89(32):289–290. doi: 10.1029/2008EO320002. [DOI] [Google Scholar]
  35. Krupnik I, Allison I, Bell R, Cutler P, Hik D, López-Martínez J, Rachold V, Sarukhanian E, Summerhayes C, editors. Understanding Earths Polar Challenges: International Polar Year 2007–2008. CCI Press, Edmonton, Alberta and University of the Arctic; Rovaniemi, Finland: 2011. (printed version) and ICSU/WMO Joint Committee for International Polar Year 20072008. [Google Scholar]
  36. Maule CF, Purucker ME, Olsen N, Mosegaard K. Heat Flux Anomalies in Antarctica Revealed by Satellite Magnetic Data. Science. 2005;309(5733):464–467. doi: 10.1126/science.1106888. [DOI] [PubMed] [Google Scholar]
  37. Mayer-Gürr T. The new combined satellite only model GOCO03S. presentation at GGHS 2012; Venice. October 2012.2012. [Google Scholar]
  38. Metzler B, Pail R. GOCE Data Processing: The Spherical Cap Regularization Approach. Stud Geophysica et Geodaetica. 2005;49(4):441–462. doi: 10.1007/s11200-005-0021-5. [DOI] [Google Scholar]
  39. Moritz H. Geodetic Reference System 1980. Bull Géod. 1984;58:395–405. [Google Scholar]; J Geod. 58(3):388–398. doi: 10.1007/BF02519014. [DOI] [Google Scholar]
  40. Näslund J-O. Landscape development in western and central Dronning Maud Land, East Antarctica. Ant Science. 2001;13(3):302–311. doi: 10.1017/S0954102001000438. [DOI] [Google Scholar]
  41. NIMA. NIMA Techn Rep 8350.2. 3. 2000. Department of Defense World Geodetic System 1984 – Its Definition and Relationships with Local Geodetic Systems. foreword by W. M. Mularie. [Google Scholar]
  42. O’Donnell JP, Nyblade AA. Antarctica’s hypsometry and crustal thickness: Implications for the origin of anomalous topography in East Antarctica. Earth Plan Sci Lett. 2014;388:143– 155. doi: 10.1016/j.epsl.2013.11.051. [DOI] [Google Scholar]
  43. Pail R, Goiginger H, Schuh W-D, Höck E, Brockmann J, Fecher T, Gruber T, Mayer-Gürr T, Kusche J, Jäggi A, Rieser D. Combined satellite gravity field model GOCO01S derived from GOCE and GRACE. Geophys Res Lett. 2010;37(20):L20, 314. doi: 10.1029/2010GL044906. [DOI] [Google Scholar]
  44. Pail R, Bruinsma S, Migliaccio F, Förste C, Goiginger H, Schuh W-D, Höck E, Reguzzoni M, Brockmann JM, Abrikosov O, Veicherts M, Fecher T, Mayrhofer R, Krasbutter I, Sansò F, Tscherning CC. First GOCE gravity field models derived by three different approaches. J Geod. 2011;85(11):819–843. doi: 10.1007/s00190-011-0467-x. [DOI] [Google Scholar]
  45. Pavlis NK, Holmes SA, Kenyon SC, Factor JK. An Earth Gravitational Model to Degree 2160: EGM2008. presentation at EGU General Assembly; Vienna. April 13–18, 2008.2008. [Google Scholar]
  46. Riedel S, Jokat W. A compilation of new airborne magnetic and gravity data across Dronning Maud Land, Antarctica. In: Cooper A, Raymond C, Diggles M, Mautner S, editors. Antarctica: A Keystone in a Changing World, Online Proc 10th ISAES, USGS Open-File Report. 2007. [DOI] [Google Scholar]
  47. Riedel S, Jokat W, Steinhage D. Mapping tectonic provinces with airborne gravity and radar data in Dronning Maud Land, East Antarctica. Geophys J Int. 2012;189(1):414–427. doi: 10.1111/j.1365-246X.2012.05363.x. [DOI] [Google Scholar]
  48. Rudenko S, Dettmering D, Esselborn S, Schöne T, Förste C, Lemoine J-M, Ablain M, Alexandre D, Neumayer K-H. Influence of time variable geopotential models on precise orbits of altimetry satellites, global and regional mean sea level trends. Adv Space Res. 2014;54(1):92–118. doi: 10.1016/j.asr.2014.03.010. [DOI] [Google Scholar]
  49. Sandwell DT, Müller RD, Smith WHF, Garcia E, Francis R. New global marine gravity model from CryoSat-2 and Jason-1 reveals buried tectonic structure. Science. 2014;346(6205):65–67. doi: 10.1126/science.1258213. [DOI] [PubMed] [Google Scholar]
  50. Sansò F, Sideris MG, editors. Geoid Determination – Theory and Methods. Springer-Verlag; Berlin Heidelberg: 2013. [DOI] [Google Scholar]
  51. Scheinert M. Progress and prospects of the Antarctic Geoid Project (Commission Project 2.4) In: Kenyon S, Pacino M, Marti U, editors. Geodesy for Planet Earth, International Association of Geodesy Symposia. Vol. 136. Springer; Berlin Heidelberg: 2012. pp. 451–456. [DOI] [Google Scholar]
  52. Schroeder DM, Blankenship DD, Young DA, Quartini E. Evidence for elevated and spatially variable geothermal flux beneath the West Antarctic Ice Sheet. Proc Nat Ac Sci. 2014;111(25):9070–9072. doi: 10.1073/pnas.1405184111. [DOI] [PMC free article] [PubMed] [Google Scholar]
  53. Schwabe J, Scheinert M. Regional geoid of the Weddell Sea, Antarctica, from heterogeneous ground-based gravity data. J Geod. 2014;88(9):821–838. doi: 10.1007/s00190-014-0724-x. [DOI] [Google Scholar]
  54. Schwabe J, Scheinert M, Dietrich R, Ferraccioli F, Jordan T. Regional Geoid Improvement over the Antarctic Peninsula Utilizing Airborne Gravity Data. In: Kenyon S, Pacino M, Marti U, editors. Geodesy for Planet Earth, International Association of Geodesy Symposia. Vol. 136. Springer; Berlin Heidelberg: 2012. pp. 457–464. [DOI] [Google Scholar]
  55. Schwabe J, Ewert H, Scheinert M, Dietrich R. Regional geoid modeling in the area of subglacial Lake Vostok, Antarctica. J Geodyn. 2014;75:9–21. doi: 10.1016/j.jog.2013.12.002. [DOI] [Google Scholar]
  56. Shako R, Förste C, Abrikosov O, Bruinsma S, Marty J-C, Lemoine J-M, Flechtner F, Neumayer H, Dahle C. EIGEN-6C: A High-Resolution Global Gravity Combination Model Including GOCE Data, in Observation of the System Earth from Space - CHAMP, GRACE, GOCE and future missions. In: Flechtner F, Sneeuw N, Schuh W-D, editors. Advanced Technologies in Earth Sciences. Springer; Berlin Heidelberg: 2014. pp. 155–161. [DOI] [Google Scholar]
  57. Smith WHF, Wessel P. Gridding with continuous curvature splines in tension. Geophysics. 1990;55:293305. [Google Scholar]
  58. Stern TA, ten Brink US. Flexural uplift of the Transantarctic Mountains. J Geophys Res. 1989;94:10,315–10,330. [Google Scholar]
  59. Studinger M. Berichte zur Polar-forschung (Reports on Polar Research) Alfred Wegener Institute for Polar and Marine Research; Bremerhaven: 1998. Compilation and analysis of potential field data from the Weddell Sea, Antarctica: Implications for the break-up of Gondwana; p. 276. [Google Scholar]
  60. Studinger M, Bell R, Buck W, Karner G, Blankenship D. Sub-ice geology inland of the Transantarctic Mountains in light of new aerogeophysical data. Earth Planet Sci Lett. 2004;220:391–408. doi: 10.1016/S0012-821X(04)00066-4. [DOI] [Google Scholar]
  61. Studinger M, Bell RE, Fitzgerald PG, Buck WR. Crustal architecture of the Transantarctic Mountains between the Scott and Reedy Glacier region and South Pole from aerogeophysical data. Earth Plan Sci Lett. 2006;250(1–2):182– 199. doi: 10.1016/j.epsl.2006.07.035. [DOI] [Google Scholar]
  62. Studinger M, Koenig L, Martin S, Sonntag J. Operation IceBridge: Using instrumented aircraft to bridge the observational gap between IceSat and IceSat-2. IEEE International; Geoscience and Remote Sensing Symposium (IGARSS); 2010.2010. pp. 1918–1919. [DOI] [Google Scholar]
  63. Tapley BD, Bettadpur S, Watkins M, Reigber C. The gravity recovery and climate experiment: Mission overview and early results. Geophys Res Lett. 2004;31(9) doi: 10.1029/2004GL019920. [DOI] [Google Scholar]
  64. Tapley BD, Flechtner F, Bettadpur SV, Watkins MM. The GRACE Mission: Status and Future Activities, abstract G23C-03. presented at 2014 Fall Meeting; 15–19 Dec 2014.San Francisco, CA: AGU; 2014. [Google Scholar]
  65. van der Meijde M, Pail R, Bingham R, Floberghagen R. GOCE data, models, and applications: A review. Int J Appl Earth Obs Geoinf. 2015;35:4–15. doi: 10.1016/j.jag.2013.10.001. [DOI] [Google Scholar]
  66. Watts AB. Isostasy and Flexure of the Lithosphere. Cambridge University Press; 2001. p. 480. [Google Scholar]
  67. Wessel P, Smith WHF. Technical Reference, Cookbook and Manpages. 2015. The Generic Mapping Tool GMT, Version 4.5.14. [Google Scholar]
  68. Wessel P, Smith WHF, Scharroo R, Luis J, Wobbe F. Generic Mapping Tools: Improved Version Released. Eos, Trans AGU. 2013;94(45):409–410. doi: 10.1002/2013EO450001. [DOI] [Google Scholar]

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supp1
NIHMS931291-supplement-Supp1.pdf (682.3KB, pdf)

RESOURCES