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Satellite data sets are an asset in global gravity collections; their characteristics vary in coverage and resolution. New collections appear often, and the user must adapt fast to their characteristics. Their use in geophysical modeling is rapidly increasing; with this in mind we compare two of the most densely populated sets: EIGEN-6C4 and GGMplus. We characterize them in terms of their frequency histograms, Free Air anomalies, power spectrum, and simple Bouguer anomalies. The nature of the digital elevation models used for data reduction is discussed. We conclude that the GGMplus data set offers a better spatial resolution. To evaluate their effect in geophysical modelling, we chose an inland region with a prominent volcanic structure in which we perform 3D inversions of the respective Bouguer anomalies, obtaining density variations that in principle can be associated with the geologic materials and the structure of the volcanic edifice. Model results are analyzed along sections of the inverted data; we conclude that the GGMplus data set offers higher resolution in the cases analyzed.

Modeling in Geophysics is a permanent exercise, trying to reproduce, as close as possible, the Earth systems and processes that scientists try to understand. Here we are concerned with one of the Potential Methods used for this purpose: the gravity method. As technology has progressed, determination of the gravity field of the Earth at given locations has also changed. For most of last century gravimetric determinations were mainly performed on the surface of the Earth, with oceanic measurements occurring along ships’ navigation trajectories, including a few aerial acquisitions. The process was usually slow, expensive, and limited in extent. By the end of the century a radical change occurred, and satellites were incorporated to gravimetric data acquisition, introducing global data coverage [

The EIGEN-6C4 gravimetric satellite data model is the highest resolution model with the highest coverage worldwide. Many studies have proven the value of their data for numerous regional tectonic studies, e.g., [

The gravimetric satellite models used for evaluation in this study are: the EIGEN-6C4 model, made available through International Centre for Global Earth Models (ICGEM, [

For the calculation of the Bouguer Anomaly (AB) at a given location, it is necessary to use the elevation at the given point. The elevation is provided by a digital elevation model (DEM). In this work we used 3 DEMs with different resolutions. The ETOPO1 topography model (National Center for Environmental Information; NOAA; https://ngdc.noaa.gov/mgg/global/global.html), with 1 arcminute resolution, sampled to 0.009˚ resolution (approximately 1 km), the maximum resolution for the EIGEN-6C4. The SRTM15 topography model https://topex.ucsd.edu/cgi-bin/get_srtm15.cgi; [

For the direct comparison of the GGMplus model it is necessary to obtain the Free Air (FA) anomaly of the EIGEN-6C4; to this end, we will use the ETOPO DEM, and the EIGEN-6C4 data. We calculate the FA anomaly of Model EIGEN-6C4 with:

FA = G o b s − G t h e o ± C a l t (1)

For a direct comparison of the G_{obs} of the EIGEN-6C4 model with the GGMplus model, it is necessary to convert the GGMplus model (FA anomaly) to an observed gravity value at ground surface (G_{obs}); this is done using the elevation of the station or, in general, the elevation provided by a DEM. The precision of the G_{obs} will depend, thus, on the precision of the DEM used to obtain it. In the case of the GGMplus model, the DEM has a resolution of approximately 7.5 arc-sec (or 200 m approximately [_{obs}

G o b s = FA − G t h e o ± C a l t (2)

Gravity on Earth is distributed in a similar way as it would be in a sphere, but with a slight increase towards the geographical poles, due to the flattening of the terrestrial spheroid [_{theo}). To calculate the theoretical gravity at any point on the planet we need Equation (2) (Geodetic Reference System of 1980, GRS80).

G t e o = 978032.7 ( 1 + 0.0053024 sin λ 2 + 0.000058 sin λ 4 ) mGal (3)

The altitude correction (C_{alt}) is applied to correct the distance of the measurement to the reference level; therefore, it has a + or - sign depending on whether the altitude is less or greater than the reference level. The equation for calculating the simplified height correction is [

C a l t = − 0.3086 ∗ h (4)

where h is the station elevation of the DEM. From (3) and (4) in (2) we obtain the value of G_{obs}:

G o b s = ± 0.3086 ∗ h + FA + G t h e o (5)

Since satellites acquire data at several hundred kilometers above the ground surface, when computing the gravity field, a new type of correction must be included, corresponding to the weight of the column of air between ground and the satellite position, and it is also necessary to consider the sphericity of the Earth in the calculation. In [

We perform 3D gravity inversions using the method described by [^{3}. The code is implemented in the Oasis Montaj program of Seequent. To represent geologic volumes, the program uses a Cartesian Cut Cell algorithm (CCC); to match the observed result with the calculated one, within established error limits, the inversion program uses an Iterative Reweighting Inversion algorithm (IRI) [

Since GGMplus is a Free Air anomaly model (FA), we shall start by comparing it with other FA models, for a preliminary evaluation.

can be readily appreciated comparing the low-gravity regions on the west side of the maps.

The general aspect of the anomaly (

The Observed Gravity (G_{obs}) is the gravity that is measured in the surface of the Earth, which is the value of the GGMplus model we compared with the EIGEEN-6C4 model. We calculate the G_{obs} of the GGMplus model according to Equation (5) (

A comparison of the radial power spectrum of GGMplus and EIGEN-6C4 on a land region, shows additional differences between the depth sources of the anomalies as shown in

Inversions corresponding to EIGEN-6C4 and GGMplus data sets are in the black

polygon of

A preliminary assessment can be made considering the front sections along the X-axis (

Another difference is appreciated in the surface distribution of density not shadowed by the displayed DEM. The EIGEN model shows rather uniform portions of green, whilst the GGMplus model shows a speckled surface with a distribution of cells with lower density values (blue).

Sections along the Y-axis of EIGEN-6C4 and GGMplus appear in

in the latter it appears of smaller size and fragmented. In the south portion of the sections appears an unexpected, low-density anomaly of large dimensions (yellow arrows); we shall discuss the volcanic implications of this anomaly elsewhere. In this study, we will only compare its manifestations in the two cases under comparison. The EIGEN-6C4 section shows the anomaly as an ellipse, whilst the GGMplus section shows a wider anomaly, divided in the surface by a higher density region.

To inspect in more detail the results of the inversions, we compare cross-sections along lines N-S and E-W of

The cross-section corresponding to GGMplus exhibits important differences. The volcano anomaly shows its center closer to the surface by almost 2 km (i.e., at sea level) and a high-density gradient underneath the center; this may have important implications for the location of a magma chamber. The verticality of the anomaly is modified to a south-dipping anomaly. In addition, a bifurcation is observed, divided by a small, higher-density region in the surface, in agreement with the observation made in

Cross-sections corresponding to line E-W appear in

In the use of the gravity satellite model, the correct choice of the DEM allows to

get the most out of the data. For example, the ideal case is to use a DEM that has the same spatial resolution as the gravimetric model.

In the use of the gravity satellite model, the correct choice of the DEM allows to get the most out of the data. For example, the ideal case is to use a DEM that has the same spatial resolution as the gravimetric model. In

A brief discussion of the BA in

We selected a region in which geologic differences are present, expecting that they would be reflected in the rock-density variations associated with the intervening geologic sources. We selected a voxel for the inversion with cells of 1 km on the side. The results obtained belong to this spatial resolution; they can be increased or diminished varying those dimensions. We would expect that the larger the cell dimensions the smaller the differences between the 3D inversions with the BA of both data sets. If cell dimensions are diminished, the better resolution of GGMplus is expected to yield more accurate results.

After evaluation of the frequency histograms, the Free Air anomalies, the radial power spectrum, and the simple Bouguer anomalies of the EIGEN-6C4 and GGMplus data sets, we concluded that the latter has a better spatial resolution. We infer that for wavelengths of 5 - 3.5 CYL/K_unit, the former can produce better results with respect to the location of the deep sources of the gravitational field, while the GGMplus model could represent better results for shallower sources. The effects on models built from 3D inversions were evaluated under conditions of complete equality, except for the BA for each data set. The GGMplus model indicated that its resolution advantages are maintained in the modeling process.

The GGMplus model indisputably demonstrated that it achieves a higher spectral resolution in shallow cortical elements, which is reflected in a better identification of local elements. In addition, it is observed that it maintains the regional tectonic trends presented by the EIGEN-6C4 model, which makes it ideal for regional and local gravimetric studies. The biggest problem with the GGMplus model is still its limited coverage, since it only presents data up to 10 km from the coastline, which is why it is suggested to be combined with the EIGEN-6C4 model for study areas that include marine regions.

The use of DEMs with a higher sampling resolution than the resolution of the gravimetric model, allows the overestimation of AB of the model to be reduced by a fraction. However, they generate a random and chaotic high-frequency noise pattern, for this reason their use is discouraged, although it can be corrected using band-pass filters. The use of DEMs of lower resolution than the gravimetric model is discouraged since it generates blurring of the anomalies.

A comparison of the radial power spectrum of GGMplus and EIGEN-6C4, on a land region, shows additional differences between the depth sources of the anomalies; the difference is particularly relevant for the depth sources between approximately 15 and 1 km. This change between spectra is of interest in studies that try to model the depths of sources according to the power spectrum radial average method [

During development of this work, MC received support from Consejo Nacional de Ciencia y Tecnología (CONACYT, México. This study has been supported by IIMAS, UNAM; we acknowledge material support from both institutions. Comments of one anonymous reviewer helped improve the original manuscript. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

The authors declare no conflicts of interest regarding the publication of this paper.

Camacho, M. and Alvarez, R. (2021) Geophysical Modeling with Satellite Gravity Data: Eigen-6C4 vs. GGM Plus. Engineering, 13, 690-706. https://doi.org/10.4236/eng.2021.1312050