Long-period Signals Research Articles

Deep Learning Frequency Loss Functions for Predicting the Seismic Responses of Structures

Novel loss functions for seismic response prediction, such as physics-informed loss functions, have attracted considerable attention. However, existing loss functions are based on the time domain and do not consider the frequency domain differences contained in structure response signals. This study accordingly designed three loss functions based on frequency domain information — one pure frequency domain loss function and two combined frequency- and time-domain loss functions — using Fourier transforms. The proposed loss functions were applied using a trusted publicly available dataset for a frame structure, and their performances were compared with those obtained using the conventional mean squared error (MSE) loss function. The proposed frequency domain loss function exhibited superior performance, accelerating the convergence of learning curves for long-period signals while simultaneously enhancing their frequency domain accuracy and facilitating the prediction of high-sampling-rate response signals. In addition, the designed loss functions exhibited more stable performances and superior accuracy than the MSE when random dataset partitioning was employed. Finally, the combined time- and frequency-domain loss functions were shown to predict the seismic displacement time-history of tall, long-span bridges more accurately than the MSE by training the model to predict structural acceleration responses, then integrating them to predict displacement responses.

The pulse of Yarlung Tsangpo River: Ultra-high-resolution insights into the flow and sediment

Traditional monitoring techniques of flow and sediment are inadequate for the sparsely populated, the rivers in the Qinghai-Tibetan Plateau region which are experiencing amplified climate change. Inspired by the Euchiloglanis fish, this study developed a unique self-contained hydrodynamic observation platform to withstand the high velocities of mountain rivers typically encountered in mountain rivers. The platform, equipped with sensors, was successfully deployed in the Yarlung Tsangpo River, collecting ultra-high-resolution data on flow and sediment over a period of nearly two months. Performance assessments showed that the median value of discharge per unit width measured and suspended sediment concentration by this system were basically consistent with those daily measurements from the hydrological station. Meanwhile, the superiority of the system was reflected in the more significant daily average change, especially at the flooding period. The data unveiled significant minute-level hydrological fluctuations and a complex interplay of factors affecting the river’s flow and sediment transport. A wavelet coherence analysis revealed asynchrony changes in short-period flow and sediment variables. Persistent short-period and coherent long-period signals are significantly displayed during flood events. The platform promises future applications, such as automated benthic observations and replacing traditional ’lead-line’ methods. Despite acknowledging system limitations of underwater attitude, burying tendency, and real-time data transmission capabilities, the study highlighted the crucial role of this system in understanding and managing river dynamics, particularly amid escalating environmental threats.

Horizontal Scales of Small‐ and Meso‐Scale Field‐Aligned Current Structures at Middle and Low Latitudes

AbstractBy utilizing the close orbital separation between Swarm A and C during the Counter Rotation Orbit phase, we check the agreement and stationarity between the FAC‐associated magnetic signatures at the two spacecraft through cross‐correlation analysis. When the agreement and stationarity are passed, the magnetic signature is considered suitable for small and meso‐scale Field‐aligned currents (FAC) estimates with dual‐spacecraft technique. It is found that at low and middle latitudes the dayside wave structure with apparent periods of about 10–60s can be observed around 90% of the time during all seasons. From those 90% can be identified as quasi‐static current structures. On the nightside, the shorter period signatures dominate the apparent period spectrum. At about 30% of the time structures with 1–7s periods are observed. For the longer period signals the proportion is reduced greatly. About 80% of these signatures with periods longer than 3s are identified as quasi‐static current structures. By taking advantage of the constantly changing longitudinal orbit separation during the considered time intervals, we can determine the mean separation at which the correlation breaks down. This provides FAC scale sizes in east‐west direction separately for FACs of various latitudinal wavelengths. The result shows that typical east‐west scale sizes of FAC structures with latitudinal wavelength of 10–400 km range from 10 to 60 km, respectively. FAC‐related structures on the nightside have been associated with medium‐scale traveling ionospheric disturbances and structures on the dayside primarily with FACs driven by atmospheric gravity waves.

The GAPS Programme at TNG

Context. The atmospheric characterisation of hot and warm Neptune-size exoplanets is challenging mainly due to their relatively small radius and atmospheric scale height, which reduce the amplitude of atmospheric spectral features. The warm-Neptune HAT-P-11 b is a remarkable target for atmospheric characterisation because of the large brightness of its host star (V = 9.46 mag; H = 7.13 mag). Aims. The aims of this work are to review the main physical and architectural properties of the HAT-P-11 planetary system, and to probe the presence of eight molecular species in the atmosphere of HAT-P-11 b through near-infrared (NIR) high-resolution transmission spectroscopy. Methods. We reviewed the physical and architectural properties of the HAT-P-11 planetary system by analysing transits and occultations of HAT-P-11 b from the Kepler data set as well as HIRES at Keck archival radial-velocity data. We modelled the latter with Gaussian-process regression and a combined quasi-periodic and squared-exponential kernel to account for stellar variations on both (short-term) rotation and (long-term) activity-cycle timescales. In order to probe the atmospheric composition of HAT-P-11 b, we observed four transits of this target with the NIR GIANO-B at TNG spectrograph and cross-correlated the data with template atmospheric transmission spectra. Results. We find that the long-period radial-velocity signal previously attributed to the HAT-P-11 c planet (P ~ 9.3 yr; Mp sin i ~ 1.6 MJ; e ~ 0.6) is more likely due to the stellar magnetic activity cycle. Nonetheless, the HIPPARCOS-Gaia difference in the proper-motion anomaly suggests that an outer-bound companion might still exist. For HAT-P-11 b, we measure a radius of Rp = 0.4466 ± 0.0059 RJ, a mass of Mp = 0.0787 ± 0.0048 MJ, a bulk density of ρp = 1.172 ± 0.085 g cm−3, and an orbital eccentricity of e = 0.2577−0.0025+0.0033. These values are compatible with those from the literature. Probing its atmosphere, we detect the presence of two molecular species, H2O and NH3, with a S/N of 5.1 and 5.3, and a significance of 3.4 σ and 5.0 σ, respectively. We also tentatively detect the presence of CO2 and CH4, with a S/N of 3.0 and 4.8, and a significance of 3.2 σ and 2.6 σ, respectively. Conclusions. We revisit the HAT-P-11 planetary system, confirm the presence of H2O, and report the detection of NH3 in the atmosphere of HAT-P-11 b, also finding hints for the presence of CO2 and CH4 that need to be confirmed by further observations.

Very-long-period signal reveals lava lake sloshing and its interaction with a deep reservoir in Nyiragongo volcano

The longevity of lava lakes in open-vent volcanoes reflects a hydraulic connection between the lake and the deep part of the magma plumbing system. Constraining the size of the shallow magmatic system and resolving the rheology of magma filling in the system is essential to evaluate potential hazards like lava flow and other activities. As the lava lake is often perturbed by degassing bursts, rockfall, and even convection, seismic waves radiated from the oscillation of fluid and its mechanical coupling with the surrounding solid walls provide invaluable information on probing system geometry and magma rheology. In this report, I show the first observation of very long-period signals in Nyiragongo volcano, to uncover the sloshing of the world's largest known lava lake and its dynamic interaction with a deep reservoir during the relatively quiet period. The signal is manifested as the ground oscillations with two isolated spectral peaks at ∼15 s and ∼16 s sustaining up to half an hour and a spectral peak at a longer period of ∼76 s. The radiated seismic energy can be well recognized by the stations with distances of <50 km to the lava lake. The traveling time, particle-motion polarization, and deformation inversion suggest that the 15 s' and 16 s' modes are related to two orthogonal horizontal forces at a very shallow depth, likely pointing to the sloshing dynamics of the lava lake. The 76 s' mode is considered as the dynamic coupling between the lake bottom to a deep reservoir at a depth of 8–16 km through a conduit driven by the sloshing. The dynamic modeling of the 76 s' mode points to a deep reservoir storativity of ∼8 m3/Pa and a spherical reservoir with a radius of ∼7.5 km. High-frequency seismic waves before the onset of the 15 s' and 16 s' modes suggest that the signals may be excited by rigorous degassing or rockfall. Variations in the period and quality factor of the modes reflect the changes in the lake/reservoir geometry and magma rheology. This finding may improve our ability to understand the magmatic plumbing system, track magma evolution in Nyiragongo, and further probe the formation of lava lakes in active volcanoes.

Generation Of Scaled Long-Period Ship Waves In A Pump-Driven Flume

Experimental investigations on the generation of long-period, primary ship waves using a pump-driven technique in a closed-circuit flume are presented. Long-period ship waves can have a major impact on river banks and engineering structures. As larger ship dimensions accompanied by a corresponding rise in loads are expected in the future, the characterisation of long-period ship waves and understanding their impact on bank protection and engineering structures is crucial, especially for appropriate design. Our study combines a closed-loop PID controlled wave generation with a numerical finite difference method (FDM) model. This setup offers the advantage of generating repeatable waves at arbitrary positions along the test section of the laboratory flume. The experiments conducted demonstrate a good reproduction of a scaled long-period ship wave signal (1:10) in a distance of approximately 9 m from the flume inlet. The combination of the PID controlled pump-driven technique with a numerical model provides a solid basis for further studies on ship-induced loads, with the aim to predict future wave loads, better understand the wave-structure-interaction and to mitigate potential damage.

The TESS-Keck Survey. XVIII. A Sub-Neptune and Spurious Long-period Signal in the TOI-1751 System

We present and confirm TOI-1751 b, a transiting sub-Neptune orbiting a slightly evolved, solar-type, metal-poor star (T eff = 5996 ± 110 K, log(g)=4.2±0.1 , V = 9.3 mag, [Fe/H] = −0.40 ± 0.06 dex) every 37.47 days. We use TESS photometry to measure a planet radius of 2.77−0.07+0.15R⊕ . We also use both Keck/HIRES and APF/Levy radial velocities (RV) to derive a planet mass of 14.5−3.14+3.15M⊕ , and thus a planet density of 3.6 ± 0.9 g cm−3. There is also a long-period (∼400 days) signal that is observed in only the Keck/HIRES data. We conclude that this long-period signal is not planetary in nature and is likely due to the window function of the Keck/HIRES observations. This highlights the role of complementary observations from multiple observatories to identify and exclude aliases in RV data. Finally, we investigate the potential compositions of this planet, including rocky and water-rich solutions, as well as theoretical irradiated ocean models. TOI-1751 b is a warm sub-Neptune with an equilibrium temperature of ∼820 K. As TOI-1751 is a metal-poor star, TOI-1751 b may have formed in a water-enriched formation environment. We thus favor a volatile-rich interior composition for this planet.

Unravelling the excitation mechanism of very long-period (VLP) tremors in the Gulf of Guinea: evidence for vibrations of thin surface crustal plates

SUMMARY The Gulf of Guinea exhibits a continuous emission of narrow-band and long-period signals (16, 26 and 27 s) on teleseismic records, yet the underlying excitation mechanism remains unclear. This study establishes a connection between these tremors and the vibration of thin, decoupled crustal plates at unexplored volcanoes in the gulf. We first formulate the damped plate oscillation equation, by incorporating the vibration of the thin surface crustal plate and magma flow in the subsurface sill. The findings reveal that a fundamental-mode vibration with a period of several dozen seconds can be induced by a crustal plate that is less than 1.0 km thick but extends over tens of kilometres in both length and width, given a subsurface sill depth exceeding 10.0 cm. The thin plate hypothesis also allows for excitation of a few overtone modes, but such waves in higher frequencies diminish over long distances, leaving only the monotonous fundamental-mode vibration at teleseismic stations. The long duration of Guinea tremors at each recurrence is attributed to the presence of low viscosity basaltic magma, which influences the damping factor. Direct wave loads at the shallow gulf serve as the primary vibration source, accounting for seasonal variations and recurring patterns. Sporadic energy bursts may also occur due to large storms. Radiation patterns of Guinea tremors are linked to the geometric structure of the thin plate. Our theoretical estimates of tremor spectra closely align with observed data, confirming the model’s accuracy in capturing reported Guinea tremor characteristics. This study provides valuable insights into the origins of very long-period tremors at continental volcanoes.

Hierarchical Velocity Optimization for Connected Automated Vehicles With Cellular Vehicle-to-Everything Communication at Continuous Signalized Intersections

The rapid development of intelligent connected technologies and cellular vehicle-to-everything communication (C-V2X) provide new opportunities to solve the connected automated vehicle (CAV) traffic problem for eco-driving at continuous signalized intersections. With C-V2X, a hierarchical velocity optimization design based on hybrid model predictive control technique (HVO-HMPC) is presented to reduce the fuel consumption and pollution emission. First, a distance–domain velocity optimization problem, with distance as the independent variable, was constructed. Second, a hybrid MPC scheme was developed by combining the multiple shooting method and MPC technique to calculate the optimal velocity profile of a high-level controller, which acts as the reference velocity in a low-level controller. Then, a car-following model was built, the low-level controller tracked the reference velocity with the predictive control as the backbone, and the optimal velocity was calculated while ensuring that the safety velocity constraint is satisfied. Next, the proposed HVO-HMPC was tested in Prescan, and the effect comparisons with different control methods in terms of fuel consumption, pollution emission, braking time, and number of braking applications were studied under different driving scenarios. Results show that once the maximal speed is limited to 40 km/h under short-period signals and 20 km/h under long-period signals, the HVO-HMPC effectively reduces fuel consumption by 27.21%, 25.89%, and pollution emissions by 25.3%, 25.97%, respectively, while achieving best performance. Finally, an experimental prototype is built to confirm the validity of the HVO-HMPC.

Autogenic masking of allogenic inputs: Numerical modelling of signal preservation in deep-water fan strata

Variations in climate, sea-level and tectonic processes can be recorded in various ways in strata, and recognising and measuring such external signals preserved in strata is an important aspect of deciphering Earth history. Key questions are what type of signals are likely to be preserved; how input signals may be shredded, over-printed or otherwise reduced before preservation, by stochastic or autogenic processes; and how allocyclic products may be mimicked and masked by autogenic processes. A reduced-complexity numerical forward model of down-slope sediment erosion, transport and dispersive deposition of submarine fan strata is the simplest-possible formulation that produces reasonably realistic strata that can be robustly analysed for signal content across model realisations with a range of external forcing amplitudes and periods. Three different initial topographic surfaces that include increasing influence of random noise allow comparison of the signal preserved with different levels of random influence on the deterministic model. Spectral analysis, with rigorous testing for statistical significance, shows that the signal recorded depends strongly on the level of noise present in the underlying topography, that short-period high-amplitude allocyclic signals are the most likely to be preserved in this case, and that autogenic dynamics in the modelled system can effectively mask even long-period high-amplitude input signals because they have similar periodicities. Autogenic processes in this model can also produce 5:1 bundling of cyclical strata commonly assumed to be strong evidence for orbital forcing. This analysis suggests that we might be substantially underestimating the complexity involved in extracting a signal of external forcing from strata where any autogenic processes operate, to the extent that the two different effects may often be practically indistinguishable, indicating that a multiple hypothesis approach is important to account for the resulting uncertainty.

Increasing the detectability of long-period and nulling pulsars in next-generation pulsar surveys

Abstract Recent discoveries of multiple long-period pulsars (periods ${\sim}10\,$ s or larger) are starting to challenge the conventional notion that coherent radio emission cannot be produced by objects that are below the many theorised death lines. Many of the past pulsar surveys and software have been prone to selection effects that restricted their sensitivities towards long-period and sporadically emitting objects. Pulsar surveys using new-generation low-frequency facilities are starting to employ longer dwell times, which makes them significantly more sensitive in detecting long-period or nulling pulsars. There have also been software advancements to aid more sensitive searches towards long-period objects. Furthermore, recent discoveries suggest that nulling may be a key aspect of the long-period pulsar population. We simulate both long-period and nulling pulsar signals, using the Southern-sky MWA Rapid Two-meter (SMART) survey data as reference and explore the detection efficacy of popular search methods such as the fast Fourier transform (FFT), fast-folding algorithm (FFA) and single pulse search (SPS). For FFT-based search and SPS, we make use of the PRESTO implementation, and for FFA we use RIPTIDE. We find RIPTIDE’s FFA to be more sensitive; however, it is also the slowest algorithm. PRESTO’s FFT, although faster than others, also shows some unexpected inaccuracies in detection properties. SPS is highly sensitive to long-period and nulling signals, but only for pulses with high intrinsic signal-to-noise ratios. We use these findings to inform current and future pulsar surveys that aim to uncover a large population of long-period or nulling objects and comment on how to make optimal use of these methods in unison.

Experimental Study on the Performance of Steel Electrodes for Long-term Monitoring

Long-term monitoring of electromagnetic (EM) fields requires dense arrays of electrode buried underground for a long time. Steel electrodes are cheap and easy to deploy but are well known to be prone to the noise due to the electrochemical reaction on the metal-fluid interface. In this experiment, we bury an array of steel and non-polarizable electrodes in a realistic monitoring setting, and investigate the performance of steel electrodes with the non-polarizable electrodes as reference. The pilot experiment of 8 days has found significant drift in the data from the steel electrodes, but a detrending process that removes the long-period signals can make the steel and non-polarizable electrode data more consistent at the time scale of a few minutes. The results show that the steel electrodes can have performance comparable with that of the non-polarizable electrodes if signals at relatively short periods are concerned. This study offers inspiration of collecting electrical field data by dense steel electrode arrays for a variety of monitoring applications.

Enhancing multi-class SSVEP classification performance using regularized covariance estimators, spatiotemporal beamforming, and short-time EEG trials

One of the main challenges in BCI technologies is the problem of poor information transfer rate (ITR) of BCI systems and its effect on reducing the commands users can give. At the state of the art, the Linearly Constrained Minimum Variance (LCMV) beamformer is one of the most effective strategies that can provide satisfactory performance in the analysis of steady-state visual evoked potentials (SSVEP). When only a short-period SSVEP signal is available, a poor estimate of the covariance matrix used in the original LCMV method is obtained. Therefore, the main drawback of the conventional LCMV beamformer and its spatiotemporal form (LCMVst) is that they require a long-period SSVEP signal to achieve a reliable estimate for the beamformer weights. To cope with the mentioned problems, this paper presents two types of regularized estimators to achieve a robust estimate for the covariance matrix when only a short-period SSVEP signal is available. These two types, which are user-independent, include the convex combination (CC) and general linear combination (GLC) methods. In the next step, in order to provide suitable beamformer weights, the CC and GLC covariance estimators are combined with the original LCMVst beamformer. Furthermore, two new subject-based electrode selection algorithms, i.e., sequential forward electrode selection (SFES) algorithm and common spatial pattern (CSP) based technique, are applied to pick out the best collection of electrodes and to maximize the classification accuracy. The introduced methods were assessed using a four-class SSVEP dataset recorded on 20 subjects. Experimental results indicate that the proposed estimators optimally classify SSVEPs by estimating proper beamformer weights. The proposed LCMVst-CC and LCMVst-GLC beamformers improved the average classification accuracy by about 27.75% in comparison to the original LCMV-based beamformer at the 0.25-second segment length. Using SSVEP stimulations, we show that our proposed beamformers offer a better classification performance than the conventional LCMV-based spatiotemporal beamformer for all stimulation times.

Microscopic defect dynamics during a brittle-to-ductile transition

Deformation of all materials necessitates the collective propagation of various microscopic defects. On Earth, fracturing gives way to crystal-plastic deformation with increasing depth resulting in a "brittle-to-ductile" transition (BDT) region that is key for estimating the integrated strength of tectonic plates, constraining the earthquake cycle, and utilizing deep geothermal resources. Here, we show that the crossing of a BDT in marble during deformation experiments in the laboratory is accompanied by systematic increase in the frequency of acoustic emissions suggesting a profound change in the mean size and propagation velocity of the active defects. We further identify dominant classes of emitted waveforms using unsupervised learning methods and show that their relative activity systematically changes as the rocks cross the brittle-ductile transition. As pressure increases, long-period signals are suppressed and short-period signals become dominant. At higher pressures, signals frequently come in avalanche-like patterns. We propose that these classes of waveforms correlate with individual dominant defect types. Complex mixed-mode events indicate that interactions between the defects are common over the whole pressure range, in agreement with postmortem microstructural observations. Our measurements provide unique, real-time data of microscale dynamics over a broad range of pressures (10 to 200 MPa) and can inform micromechanical models for semi-brittle deformation.

False Planets around Giant Stars: A Case Study of Sanders 364 in M67

Discovering planets in sparsely populated regions of parameter space is crucial to improving our understanding of planetary formation and evolution. One such region is the subset of planets that orbit giant, evolved stars. However, some of these evolved stars are known to exhibit long-period quasiperiodic radial velocity signals, which can masquerade as signals from orbital motion due to planetary companions. In this paper, we investigate the case of Sanders 364, a K giant star in the old open cluster M67. A paper by Brucalassi et al. reports the discovery of a giant planet with a period of 121 days orbiting Sanders 364. From our analysis of a large set of independent radial velocities, we find no convincing evidence for the giant planet reported by Brucalassi et al. We did identify six long-period radial velocity signals of unclear origin, including the 121 days signal reported by Brucalassi et al., but based on our analysis, we speculate that these are quasiperiodic signals that arise from nonplanetary origins, such as stellar variability or aliasing. The results from our study of Sanders 364 suggest that the detection of true orbital motion from a long-period planetary companion requires extra care when the host star is highly evolved. We conclude by offering recommendations for future study of planetary companions around evolved host stars.

Frequency analysis of the first-overtone RR Lyrae stars based on Extended Aperture Photometry from K2 data

Context. Additional low-amplitude signals have been observed in many RR Lyrae stars separate from pulsations in radial modes. The most common of these are short-period signals forming a period ratio of around 0.60–0.65 with the first overtone and long-period signals forming a period ratio of around 0.68. The RR Lyrae stars may also exhibit quasi-periodic modulation in their light curves, the so-called Blazhko effect. Aims. We used the extensive sample of the first-overtone RR Lyrae stars observed by the Kepler telescope during the K2 mission to search for and characterize additional low-amplitude signals. The K2 data provides space-based photometry for a statistically significant sample. Hence, this data is excellent for studying the pulsation properties of RR Lyrae stars in detail. Methods. We used K2 space-based photometry for RR Lyrae candidates from Campaigns 0–19. We selected RR Lyrae stars pulsating in the first overtone and performed a frequency analysis for each star to characterize their frequency contents. Results. We classified 452 stars as first-overtone RR Lyrae. From that sample, we selected 281 RR0.61 stars, 67 RR0.68 stars, and 68 Blazhko stars. We found particularly interesting stars that show all of the above phenomena simultaneously. We detected signals in RR0.61 stars that form period ratios lower than those observed for the majority of stars of this type. These signals likely form a new sequence in the Petersen diagram, around a period ratio of 0.60. In 32 stars, we detected additional signals that form a period ratio close to that expected in RRd stars, but the classification of these stars as RRd is uncertain. We also report a discovery of additional signals in eight stars that form a new group in the Petersen diagram around the period ratio of 0.465–0.490. The nature of this periodicity remains unknown.

Continuation of Events Detection with Global Long-Period Seismic Data: An Analysis from 2010 to 2022

Abstract We develop an algorithm to detect and locate sources of long-period (25–100 s) seismic signals. Our method is based on the analysis of seismological data recorded at global networks, plus all available stations at latitude larger (smaller) than 60° (−60°). We use a delay and stack method to identify coherent Rayleigh waves generated at the free surface of the Earth. The application of our approach to 13 yr of continuous data permitted us to detect more than 36,000 events. After a precise analysis to classify known events and to remove spurious detections, we report more than 1700 previously unidentified source of long-period seismic signals. Each source is characterized by its location (with associated uncertainty) and moment magnitude. This new catalog mainly reveals sources in the polar regions likely associated with glaciers dynamics but also volcanic activity, landslides, and regular earthquakes located in remote areas of the planet. Our study reveals the importance of maintaining global seismic networks and exploring the recorded data, beyond providing new observations that can be the basis to future studies to better characterize physical processes occurring at the free surface of our planet.

3-D anisotropic modelling of geomagnetic depth sounding based on unstructured edge-based finite-element method

SUMMARY Geomagnetic depth sounding (GDS) is a geophysical electromagnetic (EM) method that studies the deep structure and composition of the Earth by using long-period EM signals from geomagnetic observatories and satellites. In this paper, a 3-D anisotropic GDS modelling algorithm is developed. The curl–curl equation is discretized using the edge-based finite-element method on unstructured tetrahedral grids. In order to solve the computationally demanding problem of EM modelling on a global scale, the complex linear system is first separated into the equivalent real linear systems and then the real system is iteratively solved by the flexible generalized minimum residual method with a block diagonal pre-conditioner. This will greatly reduce the condition number of the linear system and thus speed up the solution process. We verify the accuracy of the proposed algorithm by comparing our results with the existing methods. After that, we design a subduction zone model to simulate the EM responses under isotropic and anisotropic environments, respectively. The numerical results show the high efficiency of the proposed algorithm and the response differences between isotropic and anisotropic models. This research can provide theoretical and technical support for the high-accuracy and efficient inversion of GDS data for the geo-dynamic study.

The CARMENES search for exoplanets around M dwarfs

We present the discovery of an Earth-mass planet (Mb sin i = 1.26 ± 0.21 M⊕) on a 15.6 d orbit of a relatively nearby (d ~ 9.6 pc) and low-mass (0.167 ± 0.011 M⊙) M5.0 V star, Wolf 1069. Sitting at a separation of 0.0672 ± 0.0014 au away from the host star puts Wolf 1069 b in the habitable zone (HZ), receiving an incident flux of S = 0.652 ± 0.029 S⊕. The planetary signal was detected using telluric-corrected radial-velocity (RV) data from the CARMENES spectrograph, amounting to a total of 262 spectroscopic observations covering almost four years. There are additional long-period signals in the RVs, one of which we attribute to the stellar rotation period. This is possible thanks to our photometric analysis including new, well-sampled monitoring campaigns undergone with the OSN and TJO facilities that supplement archival photometry (i.e., from MEarth and SuperWASP), and this yielded an updated rotational period range of Prot = 150–170 d, with a likely value at 169.3−3.6+3.7. The stellar activity indicators provided by the CARMENES spectra likewise demonstrate evidence for the slow rotation period, though not as accurately due to possible factors such as signal aliasing or spot evolution. Our detectability limits indicate that additional planets more massive than one Earth mass with orbital periods of less than 10 days can be ruled out, suggesting that perhaps Wolf 1069 b had a violent formation history. This planet is also the sixth closest Earth-mass planet situated in the conservative HZ, after Proxima Centauri b, GJ 1061 d, Teegarden’s Star c, and GJ 1002 b and c. Despite not transiting, Wolf 1069 b is nonetheless a very promising target for future three-dimensional climate models to investigate various habitability cases as well as for sub-m s−1 RV campaigns to search for potential inner sub-Earth-mass planets in order to test planet formation theories.

Contribution of loading deformation to the GNSS vertical velocity field in the Chinese mainland

SUMMARYTo obtain the deformation of the solid Earth from a global navigation satellite system (GNSS)-observed velocity field, the loading effect of the surface mass variations should be effectively deducted. However, the GNSS-observed velocity field in mainland China is currently limited only to the loading correction calculated using Gravity Recovery and Climate Experiment (GRACE) spherical harmonic coefficients, which is equivalent to the approximately 300-km smoothed result in the spatial domain; thus, the derived tectonic deformation is inaccurate. Therefore, it is important to study and identify a reasonable method for calculating the loading effect of the surface mass change model and to carry out an effective loading correction of the GNSS velocity field. In this study, the performances of two calculation methods, namely the GRACE spherical harmonic coefficient and Green's function, were analyzed and compared. In addition, we constructed a comprehensive model of the global surface mass variations, calculated the vertical load velocity in mainland China using Green's function method and compared the results with those for the GRACE spherical harmonic products. We found that the difference between the results of the GRACE spherical harmonic coefficient and Green's function methods was more than 1 mm/yr in the North China Plain, implying that the GRACE spherical harmonic coefficient method cannot be used for loading correction of the observed GNSS vertical velocity field. In contrast, the loading effect calculated using Green's function method can be more effectively applied for loading correction of the GNSS vertical velocity field in mainland China. The GNSS-observed velocity exhibited a clear uplift in the North China Plain and the west glacier areas; however, the GNSS velocity fields were significantly reduced after the loading correction, indicating that the observed GNSS vertical velocity fields were mainly caused by the surface mass loading due to the negative correlation between the vertical load velocity and the surface mass changes. Moreover, we found that the loading correction accounted for more than 50 per cent of the GNSS vertical velocity field in most of the glaciated regions in eastern and western China, and the maximum value exceeded 300 per cent, indicating that the loading effect was large. Finally, we obtained the GNSS vertical velocity field for mainland China with a loading correction. Additionally, the spectral characteristics of the time-varying gravity field in mainland China were investigated. The results showed that clear annual, semi-annual and 10-year medium- and long-period signals exist.