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Science, Volume 384, Issue 6700, Page 1054-1054, June 2024.

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Science, Volume 384, Issue 6700, Page 1057-1057, June 2024.

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Science, Volume 384, Issue 6700, Page 1078-1080, June 2024.

Abstract

Physical geodesy applies potential theory to study the Earth’s gravitational field in space outside and up to a few km inside the Earth’s mass. Among various tools offered by this theory, boundary-value problems are particularly popular for the transformation or continuation of gravitational field parameters across space. Traditional problems, formulated and solved as early as in the nineteenth century, have been gradually supplemented with new problems, as new observational methods and data are available. In most cases, the emphasis is on formulating a functional relationship involving two functions in 3-D space; the values of one function are searched but unobservable; the values of the other function are observable but with errors. Such mathematical models (observation equations) are referred to as deterministic. Since observed data burdened with observational errors are used for their solutions, the relevant stochastic models must be formulated to provide uncertainties of the estimated parameters against which their quality can be evaluated. This article discusses the boundary-value problems of potential theory formulated for gravitational data currently or in the foreseeable future used by physical geodesy. Their solutions in the form of integral formulas and integral equations are reviewed, practical estimators applicable to numerical solutions of the deterministic models are formulated, and their related stochastic models are introduced. Deterministic and stochastic models represent a complete solution to problems in physical geodesy providing estimates of unknown parameters and their error variances (mean squared errors). On the other hand, analyses of error covariances can reveal problems related to the observed data and/or the design of the mathematical models. Numerical experiments demonstrate the applicability of stochastic models in practice.

Abstract

To take the sphericity of the Earth into account, tesseroids are often utilized as grid elements in large-scale gravitational forward modeling. However, such elements in a latitude–longitude mesh suffer from degenerating into poorly shaped triangles near poles. Moreover, tesseroids have limited flexibility in describing laterally variable density distributions with irregular boundaries and also face difficulties in achieving completely equivalent division over a spherical surface that may be desired in a gravity inversion. We develop a new method based on triangular spherical prisms (TSPs) for 3D gravitational modeling in spherical coordinates. A TSP is defined by two spherical surfaces of triangular shape, with one of which being the radial projection of the other. Due to the spherical triangular shapes of the upper and lower surfaces, TSPs enjoy more advantages over tesseroids in describing mass density with different lateral resolutions. In addition, such an element also allows subdivisions with nearly equal weights in spherical coordinates. To calculate the gravitational effects of a TSP, we assume the density in each element to be polynomial along radial direction so as to accommodate a complex density environment. Then, we solve the Newton’s volume integral using a mixed Gaussian quadrature method, in which the surface integral over the spherical triangle is calculated using a triangle-based Gaussian quadrature rule via a radial projection that transforms the spherical triangles into linear ones. A 2D adaptive discretization strategy and an extension technique are also combined to improve the accuracy at observation points near the mass sources. The numerical experiments based on spherical shell models show that the proposed method achieves good accuracy from near surface to a satellite height in the case of TSPs with various dimensions and density variations. In comparison with the classical tesseroid-based method, the proposed algorithm enjoys better accuracy and much higher flexibility for density models with laterally irregular shapes. It shows that to achieve the same accuracy, the number of elements required by the proposed method is much less than that of the tesseroid-based method, which substantially speeds up the calculation by more than 2 orders. The application to the tessellated LITHO1.0 model further demonstrates its capability and practicability in realistic situations. The new method offers an attractive tool for gravity forward and inverse problems where the irregular grids are involved.

Abstract

With the support of inter-satellite link technology, GNSS can theoretically achieve the distributed autonomous orbit determination (AOD) function. Traditional AOD operation generally utilizes the forecast ephemeris uploaded by operational control segment (OCS) as the filter reference orbits or to constrain the orbit systematic errors, especially for constellation overall rotation effects in Earth-centered inertial (ECI) coordinate system. To get rid of the dependency on forecast trajectories for saving the OCS workload and also reduce the onboard storage and computation burden, we use a sequential extended Kalman filter to estimate the orbit parameters and consider main perturbation forces acting on satellites in the AOD solution. In particular, for modeling solar radiation pressure (SRP), an empirical prediction function derived by historical SRP estimates is introduced. Using the proposed scheme, the orbit 3D accuracy and user range error (URE) of the first 180-day distributed AOD solution for BeiDou-3 MEOs with precise Earth rotation parameters (ERPs) can reach about 2.10 and 0.43 m, respectively. The constellation rotation errors implied in AOD orbits around the X-, Y- and Z-axis of ECI system are less than 15.0, 11.7 and 15.2 mas, respectively. For real-world AOD scenarios, precise ERP is not available for satellites. With the 180-day prediction ERP, the orbit 3D errors and URE due to the gradually increased UT1-UTC error can be elevated to 14.62 and 2.91 m during our AOD experiments. Result analysis shows if OCS can upload latest prediction ERP at a frequency of once a week, the 180-day distributed AOD is expected to consistently produce real-time orbits preferable to broadcast ephemeris derived by the traditional region L-band tracking network.

Abstract

The European Space Agency (ESA) is preparing a satellite mission called GENESIS to be launched in 2027 as part of the FutureNAV program. GENESIS co-locates, for the first time, all four space geodetic techniques on one satellite platform. The main objectives of the mission are the realization of the International Terrestrial Reference Frames and the mitigation of biases in geodetic measurements; however, GENESIS will remarkably contribute to the determination of the geodetic parameters. The precise GENESIS orbits will be determined through satellite-to-satellite tracking, employing two GNSS antennas to observe GPS and Galileo satellites in both nadir and zenith directions. In this research, we show results from simulations of GENESIS and Galileo-like constellations with joint orbit and clock determination. We assess the orbit quality of GENESIS based on nadir-only, zenith-only, and combined nadir–zenith GNSS observations. The results prove that GENESIS and Galileo joint orbit and clock determination substantially improves Galileo orbits, satellite clocks, and even ground-based clocks of GNSS receivers tracking Galileo satellites. Although zenith and nadir GNSS antennas favor different orbital planes in terms of the number of collected observations, the mean results for each Galileo orbital plane are improved to a similar extent. The 3D orbit error of Galileo is improved from 27 mm (Galileo-only), 23 mm (Galileo + zenith), 16 mm (Galileo + nadir), to 14 mm (Galileo + zenith + nadir GENESIS observations), i.e., almost by a factor of two in the joint GENESIS + Galileo orbit and clock solutions.

SummaryThe aim of this study is to investigate the aftershock sequence data recorded by a dense temporary seismological network deployed in the epicentral area of the 2013 April 9 Shonbeh (Kaki) earthquake, located in the south of the Simply Folded Belt of the Zagros (Iran). For a comprehensive understanding, coseismic displacements of the Shonbeh earthquake have been investigated using Interferometric Synthetic Aperture Radar (InSAR) data. The epicentral distribution of high-resolution relocated aftershocks shows NW-SE and N-S trending of seismicity. The aftershocks are confined between ∼3 and ∼14 km depth, which implies that the rupture occurred mostly within the sedimentary cover beside the fault parameters retrieved from InSAR modeling. Projection of precisely located aftershocks on NE-oriented section and InSAR ground displacement data are consistent with both NW-trending NE- and SW-dipping fault segments. We observe a NNW-SSE right-lateral strike-slip motions that accommodate oblique convergence and differential motion between the North and Central Zagros. The spatial pattern and focal mechanisms of aftershocks are consistent with a distributed deformation between NW-SE trending reverse and N-S trending right-lateral strike-slip fault segments in the south of the Kazerun transition zone that accommodates a wide shear zone.

SummaryThe solution of the remote reference method, a frequently used technique in magnetotelluric data processing, can be viewed as a product of the two-input-multiple-output relationship between the local electromagnetic field and the reference field at a remote station. By applying a robust estimator to the two-input-multiple-output system, one can suppress the influence of outliers in the local magnetic field as well as those in the local electric field based on regression residuals. Therefore, this study develops a new robust remote reference estimator with the aid of robust multivariate linear regression. By applying the robust multivariate regression S-estimator to the multiple-output system, the present work derives a set of equations for robust estimates of the transfer function, noise variances, and the scale of the Mahalanobis distance simultaneously. The noise variances are necessary for the multivariate analysis to normalize the residuals of dependent variables. The Mahalanobis distance, a distance measure for multivariate data, is a commonly-used indicator of outliers in multivariate statistics. By updating those robust estimates iteratively, the new robust remote reference estimator seeks the transfer function that minimizes the robust scale estimate of the Mahalanobis distance. The developed estimator can avoid bias in the magnetotelluric transfer function even if there are significant noises in the reference magnetic field and handle outlying data more robustly than previously proposed robust remote reference estimators. The authors applied the developed method to a synthetic dataset and real-world data. The test results demonstrate that the developed method downweights outliers in the local electric and magnetic fields and gives an unbiased transfer function.

SummaryAtmospheric pressure changes on Earth’s surface can deform the solid Earth. Sorrells derived analytical formulas for displacement in a homogeneous, elastic half-space, generated by a moving surface pressure source with speed c. Ben-Menahem and Singh derived formulas when an atmospheric P-wave impinges on Earth’s surface. For a P-wave with an incident angle close to the grazing angle, which essentially meant a slow apparent velocity ca in comparison to P-wave (α′) and S-wave velocities (β′) in the Earth (ca ≪ β′ < α′), they showed that their formulas for solid-earth deformations become identical with Sorrells’ formulas if ca is replaced by c. But this agreement was only for the asymptotic cases (ca ≪ β′). The first point of this paper is that the agreement of the two solutions extends to non-asymptotic cases, or when ca/β′ is not small. The second point is that the angle of incidence in Ben-Menahem and Singh’s problem does not have to be the grazing angle. As long as the incident angle exceeds the critical angle of refraction from the P-wave in the atmosphere to the S-wave in the solid Earth, the formulas for Ben-Menahem and Singh’s solution become identical to Sorrell’s formulas. The third point is that this solution has two different domains depending on the speed c (or ca) on the surface. When c/β′ is small, deformations consist of the evanescent waves. When c approaches Rayleigh-wave phase velocity, the driven oscillation in the solid Earth turns into a free oscillation due to resonance and dominates the wave field. The non-asymptotic analytical solutions may be useful for the initial modeling of seismic deformations by fast-moving sources, such as those generated by shock waves from meteoroids and volcanic eruptions because the condition c/β′ ≪ 1 may be violated for such fast-moving sources.

SummaryApplications of machine learning in seismology have greatly improved our capability of detecting earthquakes in large seismic data archives. Most of these efforts have been focused on continental shallow earthquakes, but here we introduce an integrated deep-learning-based workflow to detect deep earthquakes recorded by a temporary array of ocean-bottom seismographs (OBSs) and land-based stations in the Tonga subduction zone. We develop a new phase picker, PhaseNet-TF, to detect and pick P- and S-wave arrivals in the time-frequency domain. The frequency-domain information is critical for analyzing OBS data, particularly the horizontal components, because they are contaminated by signals of ocean-bottom currents and other noise sources in certain frequency bands. PhaseNet-TF shows a much better performance in picking S waves at OBSs and land stations compared to its predecessor PhaseNet. The predicted phases are associated using an improved Gaussian Mixture Model Associator GaMMA-1D and then relocated with a double-difference package teletomoDD. We further enhance the model performance with a semi-supervised learning approach by iteratively refining labelled data and retraining PhaseNet-TF. This approach effectively suppresses false picks and significantly improves the detection of small earthquakes. The new catalogue of Tonga deep earthquakes contains more than 10 times more events compared to the reference catalogue that was analyzed manually. This deep-learning-enhanced catalogue reveals Tonga seismicity in unprecedented detail, and better defines the lateral extent of the double-seismic zone at intermediate depths and the location of 4 large deep-focus earthquakes relative to background seismicity. It also offers new potential for deciphering deep earthquake mechanisms, refining tomographic models, and understanding of subduction processes.

Publication date: Available online 28 May 2024

Source: Advances in Space Research

Author(s): Kuan Po Chiu, Cissi Ying-tsen Lin, Yih-Min Chen, Jui-Hong Chou, Chi-Kuang Chao, Tiger J.-Y. Liu

Publication date: Available online 28 May 2024

Source: Advances in Space Research

Author(s): Aqil Tariq, Yan Jianguo, Qingyun Deng, Jean-Pierre Barriot, Kamal Abdelrahaman

Publication date: Available online 28 May 2024

Source: Advances in Space Research

Author(s): Arnaud Masson, Shing F. Fung, Enrico Camporeale, Masha M. Kuznetsova, Stefaan Poedts, Julie Barnum, Rebecca Ringuette, D. De Zeeuw, Shawn Polson, Viacheslav M. Sadykov, Vicente Navarro, Brian Thomas, Ronald M. Caplan, Jon Linker, Lutz Rastaetter, Chiu Wiegand, Ryan M. McGranaghan, Maksym Petrenko, Chinwe Didigu, Jan Reerink