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Gravity forward modeling provides important high-resolution information for the development of global gravity models, and can also be applied in many studies, e.g., topographic/isostatic effects computation and Bouguer anomaly maps compilation. In this paper, we present efficient spectral forward modeling approaches in the spheroidal harmonic domain, based on a single layer with constant density or volumetric layers with laterally varying density. With the binomial series expansion applied in spheroidal harmonic gravity forward modeling, the computational cost of these approaches is much lower than similar approaches. In both layering cases, we derive topographic potential models up to degree and order (d/o) 2190 by applying the approaches proposed here. Our methodology is evaluated by comparing these outcome models with other similar topographic potential models derived from spherical harmonic solutions. We find that topographic potentials from spheroidal and spherical harmonic approaches are in great agreement. Finally, the model named EHFM_Earth_7200 with a maximum degree of 7200 was derived by a layer-based approach. The evaluations by ground-truth data show that EHFM_Earth_7200 improves GO_CONS_GCF_2_DIR_R6 by 4% over Antarctica, and improves EGM2008 by ~ 34% over northern Canada. A global map of Bouguer gravity anomaly was also compiled with EHFM_Earth_7200 and EGM2008. As the main conclusion of this work, the new model EHFM_Earth_7200 is beneficial for investigating and modeling the Earth’s external gravity field, the new approaches have comparable accuracy to spherical harmonic approaches and are more suitable for practical use with guaranteed convergence regions because they are performed in the spheroidal harmonic domain.

Previous surveys using the remote sensing (RS) method revealed significant structures in the area of the Western Carpathians. It has not yet been possible to verify and explain the results of these surveys, even though all the phenomena are regional in nature and show many morphological features that clearly indicate recent activity and deformations, including current earthquake foci. The aim of the article was to verify these phenomena and compare them with new findings. A method of combining geomorphological data with satellite image analysis and verification using Global Navigation Satellite Systems (GNSS) and geophysics data was used. In this work, results are presented confirming the existence of a previously identified nonlinear structure—the "gravity nappe" in the western part of the Low Tatras, and the largest tectonic system Muráň—Malcov is analyzed in detail. Similar structures and tectonic zones, on a smaller scale, can also be found in other areas of the Carpathians. For example, the gravity structure in the Lesser Carpathians and the Ukrainian flysch Carpathians or the linear boundaries interpreted as tectonic systems—the Myjava-Subtatrans, Hron and Transgemerian tectonic zones. Recent movement trends have been confirmed by newly unified data from EUREF Permanent Network (EPN) stations and GNSS campaigns carried out in the last two decades in the given area. Both types of analyzed structures are directly related to the occurring foci of earthquakes.

Author(s): Oleg Ilyin

Two-dimensional lattice Boltzmann (LB) models for the Shakhov kinetic equation are developed. In contrast to several previous thermal LB models with variable Prandtl number, the present approach deals with the models on Cartesian lattices. This allows the standard collide-and-stream implementation. …

[Phys. Rev. E 110, 065304] Published Wed Dec 18, 2024

Numerical methods, like the finite element method (FEM) or finite volume method (FVM), are widely used to provide solutions in many boundary value problems. In previous studies, these numerical methods have also been applied in geodesy but demanded extensive computations because the upper boundary condition was usually set up at the satellite orbit level, hundreds of kilometers above the Earth. The relatively large distances between the lower boundary of the Earth's surface and the upper boundary exacerbate the computation loads because of the required discretization in between. Considering that many areas, such as the US, have uniformly distributed airborne gravity data just a few kilometers above the topography, we adapt the upper boundary from the satellite orbit level to the mean flight level of the airborne gravimetry. The significant decrease in the domain of solution dramatically reduces the large computation demand for FEM or FVM. This paper demonstrates the advantages of using FVM in the decreased domain in simulated and actual field cases in study areas of interest. In the simulated case, the FVM numerical results show that precision improvement of about an order of magnitude can be obtained when moving the upper boundary from 250 to 10 km, the upper altitude of the GRAV-D flights. A 2–3 cm level of accurate quasi-geoid model can be obtained for the actual datasets depending on different schemes used to model the topographic mass. In flat areas, the FVM solution can reach to about 1 cm precision, which is comparable with the counterparts from classical methods. The paper also demonstrates how to find the upper boundary if no airborne data are available. Finally, the numerical method provides a 3D discrete representation of the entire local gravity field instead of a surface solution, a (quasi) geoid model.

For about three decades, the Global Navigation Satellite System (GNSS) has been used for high-precision positioning in scientific and engineering applications, such as deformation monitoring for seismicity and volcano eruption. Such high-precision positioning applications require millimeter-level positioning accuracy. There are many man-made and natural reflective surfaces near the GNSS receiving antennas. GNSS signals can be reflected and then arrive at the GNSS antenna. The multipath effect occurs when the direct signal is mixed with the reflected signal at the GNSS receiver. Choke-ring antennas are designed to mitigate the multipath effect of reflected signals from below the horizontal plane of the GNSS receiving antenna. Moreover, GNSS receiving antennas at network/permanent stations are usually installed on tall pillars or monuments to prevent multipath from “ground” reflected signals. However, part of the reflected signals can still arrive at the GNSS antenna center and cause multipath errors in GNSS measurements. How much can the multipath effect be on the real-time GNSS-measured displacements in studies on seismicity and volcano eruption? This work investigates the below-the-horizon multipath effect of choke-ring antennas on GNSS carrier-phase measurements. Here we show the differenced carrier-phase multipath errors of two commonly used GNSS antennas at the International GNSS Service (IGS) tracking stations can reach 8 mm, the maximum, with the mean and SD in a few millimeters at the 95% confidence level. The findings of this work should be applicable to other choke-ring antennas with similar architecture.

The ambiguity resolution (AR) technology effectively accelerates convergence and improves precise point positioning (PPP) accuracy. Many observations involved in the calculation can enhance the accuracy of parameter estimation. Still, it can also introduce unmodeled errors, making it difficult to fix ambiguities, especially in multiple global navigation satellite system (GNSS). This paper presents a novel PPP Partial-AR (PAR) method to enhance Precise Point Positioning (PPP) performance by selecting an ambiguity subset based on the variation of ambiguity check factors, including the ratio, ambiguity dilution of precision (ADOP), and Bootstrapping success rate. The proposed method is validated using post-processing and real-time static and kinematic datasets across five GNSS integration modes involving the global positioning system (GPS) and BeiDou navigation satellite system (BDS), demonstrating that PPP Partial-AR (PAR) outperforms the method that fixes all ambiguities, known as PPP Full-AR (FAR). The static and kinematic post-processing experiment shows that PPP-PAR, compared with PPP-FAR, increases the ambiguity epoch fixing rate from 84.6 and 79.5% to 94.2 and 91.9%, decreases the time to first fix (TTFF) from 21.4 and 31.1 min to 17.7 and 25.4 min, and reduces the root mean square error (RMSE) from 12.7/11.3/32.2 and 21.7/19.4/51.8 mm to 11.5/10.3/30.9 and 19.1/18.1/48.9 mm in the north-east-up directions, respectively. The static and kinematic real-time experiment shows that PPP-PAR, compared with PPP-FAR, increases the ambiguity epoch fixing rate from 80.1 and 71.7% to 91.8 and 86.6%, decreases the TTFF from 29.5 and 35.5 min to 25.2 and 28.7 min, and reduces the RMS from 22.4/19.4/45.9 and 33.8/26.9/65.2 mm to 18.6/17.1/42.0 and 29.2/23.6/60.5 mm in the north-east-up directions, respectively. Moreover, the real-time experiments with actual kinematic data show that the proposed method significantly improves the ambiguity epoch fixing rate from 43.3% for PPP-FAR to 50.7% for PPP-PAR, and increases the positioning accuracy with an RMS value of 0.28/0.21/0.57 m for the PPP float solution, 0.23/0.19/0.55 m for the PPP-FAR solution towards 0.21/0.18/0.53 m for the PPP-PAR solution.

Author(s): E. A. Sorokina and V. I. Ilgisonis

The fundamental theoretical problem of the existence of plasma equilibrium in a nonsymmetric magnetic field with nested magnetic surfaces is resolved. The lack of examples of smooth solutions to the equilibrium equations with no symmetry of the configuration has for many years served as the argument…

[Phys. Rev. E 110, 065209] Published Tue Dec 17, 2024

Author(s): Felipe Veloso, Vicente Rosales, Mario Favre, and Julio Valenzuela

We have experimentally studied the formation of shock waves in a laser-induced annular configuration. By locating an aluminum target in the focal plane of a 109W/cm2 laser, an annular plasma is formed that acts as a piston for a shock wave in a background gas composed by either argon or nitrogen. Ac…

[Phys. Rev. E 110, 065210] Published Tue Dec 17, 2024

Author(s): Yunuo Xiong, Shujuan Liu, and Hongwei Xiong

Recently, fictitious identical particles have provided a promising way to overcome the fermion sign problem and have been used in path integral Monte Carlo to accurately simulate warm dense matter with up to 1000 electrons [T. Dornheim et al., J. Phys. Chem. Lett. 15, 1305 (2024)]. The inclusion of…

[Phys. Rev. E 110, 065303] Published Tue Dec 17, 2024

The Kalman filter stands as one of the most widely used methods for recursive parameter estimation. However, its standard formulation typically assumes that all state parameters avail initial values and dynamic models, an assumption that may not always hold true in certain applications, particularly in global navigation satellite system (GNSS) data processing. To address this issue, Teunissen et al. (2021) introduced a generalized Kalman filter that eliminates the need for initial values and allows linear functions of parameters to have dynamic models. This work proposes a least-squares approach to reformulate the generalized Kalman filter, enhancing its applicability to GNSS data processing when the parameter dimension varies with satellite visibility changes. The reformulated filter, named generalized least-squares filter, is equivalent to the generalized Kalman filter when all state parameters are recursively estimated. In this case, we demonstrate how both the generalized Kalman filter and the generalized least-squares filter adaptatively manage newly introduced or removed parameters. Specifically, when estimation is limited to parameters with dynamic models, the generalized least-squares filter extends the generalized Kalman filter by allowing the dimension of estimated parameters to vary over time. Moreover, we introduce a new element of least-squares smoothing, creating a comprehensive system for prediction, filtering, and smoothing. To verify, we conduct simulated kinematic and vehicle-borne kinematic GNSS positioning using the proposed generalized least-squares filter and compare the results with those from the standard Kalman filter. Our findings show that the generalized least-squares filter delivers better results, maintaining the positioning errors at the centimeter level, whereas the Kalman-filter-based positioning errors exceed several decimeters in some epochs due to improper initial values and dynamic models. Moreover, the normal equation reduction strategy employed in the generalized least-squares filter improves computational efficiency by 23% and 32% in simulated kinematic and vehicle-borne kinematic positioning, respectively. The generalized least-squares filter also allows for the flexible adjustment of smoothing window lengths, facilitating successful ambiguity resolution in several epochs. In conclusion, the proposed generalized least-squares filter offers flexibility for various GNSS data processing scenarios, ensuring both theoretical rigor and computational efficiency.

Author(s): David R. Blackman, Vladimir Tikhonchuk, Ondrej Klimo, and Stefan Weber

Broadband lasers have been suggested as a useful tool to suppress laser-plasma instabilities. However, this study shows that in the kinetic inflation regime broadband lasers are ineffective in suppressing backward stimulated Raman scattering (SRS). The role of electron trapping is pivotal in the persistence of SRS despite the increased laser bandwidth.

[Phys. Rev. E 110, 065207] Published Mon Dec 16, 2024

Author(s): M. Pouyez, A. A. Mironov, T. Grismayer, A. Mercuri-Baron, F. Perez, M. Vranic, C. Riconda, and M. Grech

Electromagnetic showers developing from the collision of an ultraintense laser pulse with a beam of high-energy electrons or photons are investigated under conditions relevant to future experiments on multipetawatt laser facilities. A semianalytical model is derived that predicts the shower multipli…

[Phys. Rev. E 110, 065208] Published Mon Dec 16, 2024

The Radio & Plasma Wave Investigation (RPWI) onboard the ESA JUpiter ICy moons Explorer (JUICE) is described in detail. The RPWI provides an elaborate set of state-of-the-art electromagnetic fields and cold plasma instrumentation, including active sounding with the mutual impedance and Langmuir probe sweep techniques, where several different types of sensors will sample the thermal plasma properties, including electron and ion densities, electron temperature, plasma drift speed, the near DC electric fields, and electric and magnetic signals from various types of phenomena, e.g., radio and plasma waves, electrostatic acceleration structures, induction fields etc. A full wave vector, waveform, polarization, and Poynting flux determination will be achieved. RPWI will enable characterization of the Jovian radio emissions (including goniopolarimetry) up to 45 MHz, has the capability to carry out passive radio sounding of the ionospheric densities of icy moons and employ passive sub-surface radar measurements of the icy crust of these moons. RPWI can also detect micrometeorite impacts, estimate dust charging, monitor the spacecraft potential as well as the integrated EUV flux. The sensors consist of four 10 cm diameter Langmuir probes each mounted on the tip of 3 m long booms, a triaxial search coil magnetometer and a triaxial radio antenna system both mounted on the 10.6 m long MAG boom, each with radiation resistant pre-amplifiers near the sensors. There are three receiver boards, two Digital Processing Units (DPU) and two Low Voltage Power Supply (LVPS) boards in a box within a radiation vault at the centre of the JUICE spacecraft. Together, the integrated RPWI system can carry out an ambitious planetary science investigation in and around the Galilean icy moons and the Jovian space environment. Some of the most important science objectives and instrument capabilities are described here. RPWI focuses, apart from cold plasma studies, on the understanding of how, through electrodynamic and electromagnetic coupling, the momentum and energy transfer occur with the icy Galilean moons, their surfaces and salty conductive sub-surface oceans. The RPWI instrument is planned to be operational during most of the JUICE mission, during the cruise phase, in the Jovian magnetosphere, during the icy moon flybys, and in particular Ganymede orbit, and may deliver data from the near surface during the final crash orbit.

Although GNSS (Global Navigation Satellite System) is well-established for outdoor positioning, it still encounters challenges in urban occluded environments. Currently, multi-source fusion positioning has emerged as the primary solution. Since commonly used smartphones can simultaneously receive satellite signals and send 5G signals, researching GNSS/5G fusion positioning based on smartphones is a highly feasible solution. However, existing studies on GNSS/5G fusion positioning primarily rely on simulation data and TOA (Time of Arrival). On the one hand, simulation data often fail to accurately reflect positioning performance in real-world environments. On the other hand, while TOA often struggles to achieve high accuracy due to time synchronization errors, the AOA (Angle of Arrival) method, which does not depend on time synchronization, presents a promising alternative. Therefore, we propose a GNSS/5G tightly coupled fusion positioning method based on AOA measurements and conduct practical tests. For the first time, we use a smartphone to verify the performance of this method in urban occluded environments. The static experimental results indicate that SPP of the smartphone performs poorly in occluded environments. In contrast, AOA positioning demonstrates relatively stable performance. GNSS/5G fusion positioning yields the best positioning results, exhibiting a best improvement of 98.18% over SPP and 70.69% over AOA positioning. For the two dynamic routes with varying levels of occlusion, GNSS/5G fusion positioning shows considerable enhancements, achieving improvements of 39.39% and 9.32% over SPP, and 13.35% and 44.68% over AOA positioning. These results demonstrate that the fusion positioning method can effectively compensate for the shortcomings of satellite positioning in occluded environment.

Author(s): J. W. Li, J. Yan, C. S. Wu, Z. S. Dai, L. F. Wang, J. Qi, B. L. Chen, X. Zhang, G. Li, L. F. Jing, Z. J. Chen, W. Jiang, W. L. Shang, S. Y. Tu, Y. S. Liu, J. Zhang, J. M. Yang, W. H. Ye, W. D. Zheng, M. Wang, W. B. Pei, S. P. Zhu, and X. T. He

In traditional indirect-drive double-shell inertial confinement fusion, high-energy x-ray preheat has always been identified as a major source of degrading implosion performance. However, a significant increase of the neutron yield is observed in ignition-like double-shell implosion experiments perf…

[Phys. Rev. E 110, L063201] Published Fri Dec 13, 2024

Vertical land motion and the redistribution of masses within and on the surface of the Earth affect the Earth’s gravity field. Hence, studying the ratio between temporal changes of the surface gravity \(\left( {\dot{g}} \right)\) and height ( \(\dot{h}\) ) is important in geoscience, e.g., for reduction of gravity observations, assessing satellite gravimetry missions, and tuning vertical land motion models. Sjöberg and Bagherbandi (2020) estimated a combined ratio of \(\dot{g}/\dot{h}\) in Fennoscandia based on relative gravity observations along the 63 degree gravity line running from Vågstranda in Norway to Joensuu in Finland, 688 absolute gravity observations observed at 59 stations over Fennoscandia, monthly gravity data derived from the GRACE satellite mission between January 2003 and August 2016, as well as a land uplift model. The weighted least-squares solution of all these data was \(\dot{g}/\dot{h}\)  =  − 0.166 ± 0.011 μGal/mm, which corresponds to an upper mantle density of about 3402 ± 95 kg/m3. The present note includes additional GRACE data to June 2017 and GRACE Follow-on data from June 2018 to November 2023. The resulting weighted least-squares solution for all data is \(\dot{g}/\dot{h}\)  =  − 0.160 ± 0.011 μGal/mm, yielding an upper mantle density of about 3546 ± 71 kg/m3. The outcomes show the importance of satellite gravimetry data in Glacial Isostatic Adjustment (GIA) modeling and other parameters such as land uplift rate. Utilizing a longer time span of GRACE and GRACE Follow-on data allows us to capture fine variations and trends in the gravity-to-height ratio with better precision. This will be useful for constraining and adjusting GIA models and refining gravity observations.

Ionospheric scintillations disrupt the trans-ionospheric satellite signals and cause quandaries in satellite applications typically near the low equatorial sites; GNSS signals are utilized extensively for monitoring such anomalies. This work presents the unique results that confirm the suitability and limitations of a commercial low-cost, GNSS module (Ublox ZED F9P) for amplitude scintillation monitoring from a location in India situated near the EIA crest during the autumnal equinox of 2022 for low to intense amplitude scintillations. Comparison of amplitude scintillation index (S4) and fade rate using concurrent data from a Leica GR50 geodetic receiver and the low-cost module shows fairly good agreement between the results. The findings have practical utility in designing cost, size, and power-efficient GNSS probes using such modules for ionospheric research. Such modules are not a replacement for the traditional receivers but can be utilized to implement a multi-point, autonomous amplitude scintillation monitoring network.

LARES-2 is a new geodetic satellite designed for high-accuracy satellite laser ranging. The orbit altitude of LARES-2 is similar to that of LAGEOS-1, whereas the inclination angle of 70° complements the LAGEOS-1 inclination of 110°; hence, both satellites form the butterfly configuration for the verification of the Lense–Thirring effect. Although the major objective of LARES-2 is testing general relativity, LARES-2 substantially contributes to geodesy in terms of the realization of terrestrial reference frames, recovery of the geocenter motion, pole coordinates, length-of-day, and low-degree gravity field coefficients. We analyze the first 1.5 years of LARES-2 data and test different empirical orbit models for LARES-2 with and without co-estimating low-degree gravity field coefficients to find the best combination strategy with LAGEOS satellites. We found that LARES-2 orbit determination is more accurate than that of LAGEOS-1/2 due to a different satellite construction consisting of a solid sphere with no inner structure. Neither the correction for D0 nor the empirical once-per-revolution along-track accelerations SC/SS have to be estimated for LARES-2 when co-estimating gravity field coefficients. The only empirical parameter needed for LARES-2 is the constant along-track acceleration S0 to compensate for the Yarkovsky–Schach effect. On the contrary, for LAGEOS-1/2, the non-gravitational perturbations affect C30 and Z geocenter estimates when once-per-revolution parameters are not estimated. LARES-2 does not face this issue. LARES-2 improves the formal errors of the Z geocenter component by up to 59% and C20 by up to 40% compared to the combined LAGEOS-1/2 solutions and provides C30 estimates unaffected by thermal orbit modeling issues.

An Erratum to this paper has been published: https://doi.org/10.1134/S1064226924550023