SUMMARY
Gravimetry is a technique widely used to image the structure of the Earth. However, inversions are ill-posed and the imaging power of the technique rapidly decreases with depth. To overcome ...this limitation, muography, a new imaging technique relying on high energy atmospheric muons, has recently been developed. Because muography only provides integrated densities above the detector from a limited number of observation points, inversions are also ill-posed. Previous studies have shown that joint muographic and gravimetric inversions better reconstruct the 3-D density structure of volcanic edifices than independent density inversions. These studies address the ill-posedness of the joint problem by regularizing the solution with respect to a prior density model. However, the obtained solutions depend on some hyperparameters, which are either determined relative to a single test case or rely on ad-hoc parameters. This can lead to inaccurate retrieved models, sometimes associated with artefacts linked to the muon data acquisition. In this study, we use a synthetic example based on the Puy de Dôme volcano to determine a robust method to obtain the resulting model closest to the synthetic model and devoid of acquisition artefacts. We choose a Bayesian approach to include an a priori density model and a smoothing by a Gaussian spatial correlation function relying on two hyperparameters: an a priori density standard deviation and an isotropic spatial correlation length. This approach has the advantage to provide a posteriori standard deviations on the resulting densities. Using our synthetic volcano, we investigate the most reliable criterion to determine the hyperparameters. Our results suggest that k-fold Cross-Validation Sum of Squares and the Leave One Out methods are more robust criteria than the classically used L-curves. The determined hyperparameters allow to overcome the artefacts linked to the data acquisition geometry, even when only a limited number of muon telescopes is available. We also illustrate the behaviour of the inversion in case of offsets in the a priori density or in the data and show that they lead to recognizable structures that help identify them.
SUMMARY
The Ice, Cloud and land Elevation Satellite 2 (ICESat-2) laser altimetry mission, launched in September 2018, uses six parallel lidar tracks with very fine along-track resolution (15 m) to ...measure the topography of ice, land and ocean surfaces. Here we assess the ability of ICESat-2 ocean data to recover oceanographic signals ranging from surface gravity waves to the marine geoid. We focus on a region in the tropical Pacific and study photon height data in both the wavenumber and space domain. Results show that an ICESat-2 single track can recover the marine geoid at wavelengths >20 km which is similar to the best radar altimeter data. The wavelength and propagation direction of surface gravity waves are sometimes well resolved by using a combination of the strong and weak beams, which are separated by 90 m. We find higher than expected power in the 3–20 km wavelength band where geoid and ocean signals should be small. This artificial power is caused by the projection of 2-D surface waves with ∼300 m wavelengths into longer wavelengths (5–10 km) because of the 1-D sampling along the narrow ICESat-2 profile. Thus ICESat-2 will not provide major improvements to the geoid recovery in most of the ocean.
Satellite altimetry cannot accurately derive the short-wavelength component of ocean gravity anomaly. Since the short-wavelength seabed topography affects the gravity anomaly, we can forward the ...short-wavelength gravity anomaly by using seabed topography to make up for the shortcomings of altimetry. Based on the Global Marine Gravity Anomaly version 1 (GMGA1) previously released by our group, and on Parker's formula, the short-wavelength gravity anomaly is forwarded by using the seabed topographic model SRTM15+V2.4, and a new product, Global Marine Gravity Anomaly Version 2 (GMGA2), is obtained. Compared with internationally recognized gravity field products such as SIO V32.1 and DTU17, the accuracy of GMGA2 is 2.5mGal, which is 0.7 mGal higher than GMGA1, and the absolute differences smaller than 5mGal account for more than 96%. An evaluation using ship-borne gravity data showed the accuracy of GMGA2 is 4.8 mGal, which is 0.3 mGal higher than GMGA1. It is concluded from the above results that using the forward method with water depth data significantly improves the short-wavelength gravity anomaly of the altimetry-derived gravity field model, and the accuracy of GMGA2 is close to that of the advanced international level.
The background field of marine gravity anomaly from satellite altimetry is an important data support for gravity-aided navigation of underwater vehicles. To achieve long-endurance and high-precision ...navigation and positioning, an interpolation algorithm based on ensemble learning is proposed, and an adaptive matching navigation method is designed. First, the common interpolation theories of the marine gravity anomaly background field are introduced, and the advantages and disadvantages of these theories are analyzed. The BP-Bagging ensemble learning algorithm for marine gravity anomaly background field interpolation is designed, and the reliability is verified by two satellite altimetric gravity anomaly datasets from the western Pacific Ocean. Then, a matching navigation algorithm based on the calculation method of gravity gradient deviation on the survey line is proposed, which can evaluate the matching capability online according to the position of the underwater vehicle and adaptively adjust the filter feedback coefficients. Finally, the performance of the method is verified by field tests. The matching results show that the proposed method improves navigation accuracy while enhancing the adaptive capability of the matching algorithm and providing better overall performance. Meanwhile, the gravity background field with high resolution yields better matching results.
Gravity models are powerful tools for mapping tectonic structures, especially in the deep ocean basins where the topography remains unmapped by ships or is buried by thick sediment. We combined new ...radar altimeter measurements from satellites CryoSat-2 and Jason-1 with existing data to construct a global marine gravity model that is two times more accurate than previous models. We found an extinct spreading ridge in the Gulf of Mexico, a major propagating rift in the South Atlantic Ocean, abyssal hill fabric on slow-spreading ridges, and thousands of previously uncharted seamounts. These discoveries allow us to understand regional tectonic processes and highlight the importance of satellite-derived gravity models as one of the primary tools for the investigation of remote ocean basins.
We have used ensemble averages of satellite-derived free-air gravity anomaly data, together with inverse modelling techniques, to determine the effective elastic thickness, Te
, of circum-Pacific ...subducting oceanic lithosphere and its relationship to plate age. Synthetic modelling tests show that Te
can be recovered best using gravity anomaly, rather than bathymetry, data and profiles that are at least 750 km long. Inverse modelling based on a uniform Te
elastic plate suggests that Te
increases with age of the subducting oceanic lithosphere and is given approximately by the depth to the 390 ± 10 °C oceanic isotherm based on a cooling plate model. Misfits between the observed and calculated gravity anomalies are significantly improved if a mechanically weak zone is included between the trench axis and the outer rise. This weak zone is coincident with observations of bend-faulting and seismicity. Inverse modelling shows that Te
landward of the outer rise is generally 40–65 per cent less than the Te
seaward of the outer rise. Both landward and seaward Te
increases with age of the lithosphere and are given by the depth to the 342–349 °C and 671–714 °C oceanic isotherm, respectively. A dependence of Te
on age is consistent with models for the cooling of oceanic lithosphere as it moves away from a mid-ocean ridge and the temperature-dependent ductile creep of oceanic lithospheric minerals such as olivine. By comparing the observed Te
to the predicted Te
based on laboratory-derived yield strength envelopes and an assumption of elastic-perfectly plastic deformation, we have attempted to constrain the rheology of oceanic lithosphere. Regardless of the assumed friction coefficient, the dry-olivine low-temperature plasticity flow laws of Goetze, Evans & Goetze, Raterron et al. and Mei et al. all provide quite a good fit to the observed Te
at circum-Pacific subduction zones. This result contrasts with the Hawaiian Islands, where these flow laws are generally too strong to fit the observations. The discrepancy in rheology within Pacific plate may be caused by differences in the timescale of loading and therefore the amount of viscoelastic stress relaxation that has occurred. Other possibilities include thermal rejuvenation and magma-assisted flexure at the Hawaiian Islands.
SUMMARY
Second- and third-order gravitational potential derivatives can be employed for the determination of the medium- and high-frequency parts of the Earth's gravity field. Due to the Gravity ...field and steady-state Ocean Circulation Explorer mission, second-order derivatives (SOD) in particular, express currently observed functionals of high accuracy and global coverage. Third-order derivatives (TOD), or gravitational curvature data, provide significant gravity field information when applied regionally. The absence of directly observed TOD data underlines the importance of investigating the relationship between SOD and TOD. This paper discusses the combination of simulated SOD in order to obtain TOD at satellite altitude by applying the spectral combination method. For the determination of TOD integral equations are developed that utilize SOD data at satellite altitude, thus extending the well-known Meissl spectral scheme. The performance of the derived mathematical models is investigated numerically for the test area of Himalayas and the Tibet region. Two different TOD computational strategies are examined. First, we define a deterministic approach that recovers TOD data from noise-free simulated SOD data. Results show that retrieved TOD data at satellite level reach an agreement of the level of 1 × 10−17 m−1s−2 when compared with the true TOD data. Secondly, we propose a new mathematical model based on the spectral combination of integral relations and noisy SOD data with Gaussian noise for recovering TOD. Integral estimators of biased and unbiased types are examined in the cases of SOD data at satellite altitude. The used vertical SOD components show differences between the recovered and true vertical TOD components in the order of 1 × 10−17 m−1s−2 in magnitude, proving the vertical–vertical component of SOD as the best for validating purposes.
SUMMARY
Inversion of large-scale gravity data set is generally a challenging problem due to memory requirements and computational costs. In this study, based on VNet, we present an efficient strategy ...for the large-scale gravity inverse problem by simultaneously tackling several base-scale gravity data. We first construct a large number of base-scale geological models including gravity sources, with different shapes and dimensions, and also their forward model data sets. Then, the idea of semantic segmentation is used to train an inversion network. In the next step, a finite number of base-scale and similar size area of gravity data, clipped from the original large data set with a fixed stride, are fed into the trained network. Finally, the individual recovered models are combined to provide the inversion result for the whole subsurface area. The feasibility and effectiveness of the presented inversion algorithm are tested on a large-scale complicated synthetic model. The algorithm is, then, verified for the inversion of the gravity data set obtained over the Morro do Engenho complex in central Brazil.
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