Gravity Observations Research Articles

Modified Bott-Parker Method for Gravimetric Moho Modeling

Determining the detailed Moho topography is crucial for understanding the Earth's geodynamic processes. Inversion of the Moho depth in the frequency-domain from gravity observations is an effective tool for this purpose. However, existing inversion methods such as the Parker-Oldenburg (P-O) and Bott-Parker (B-P) methods face challenges including non-convergence and noise amplification. We have developed a modified B-P (mB-P) method to estimate the Moho depth with variable density contrast from gravity data. The proposed method casts exponential density-based Parker’s formula into the iterative continuation theoretical framework, allowing the use of an adaptive filter that has been proven effective in iterative continuation studies. This modification retains the efficiency of the B-P method while offering improved control over solution stability. Gauss-Fast Fourier Transform was adopted to improve the precision of the forward and inverse Fourier transforms in the inversion process. Furthermore, the mathematical connection between the P-O and B-P methods was established. Specifically, the B-P method acts as a low-pass filter to reduce the downward continuation effect in the P-O method and recovers the nonlinear topography through the nonlinearity of the fitting function. Synthetic inversion tests demonstrate that the proposed method achieves superior inversion accuracy compared to the P-O and B-P methods under 3% gravity observations noise and significantly outperforms the P-O method in terms of computational efficiency. We applied the mB-P method to estimate the Moho depth beneath the Tibetan Plateau using satellite gravity data and seismic data, achieving reasonable agreement between the gravimetric model and seismic data.

Accurate prediction of the 2022 MS 6.9 Menyuan and MS 6.8 Luding earthquake epicentres

In 2022, the MS 6.9 Menyuan (Qinghai Province) and MS 6.8 Luding (Sichuan Province) earthquakes occurred successively on China’s North–South seismic belt. Both earthquakes caused serious property losses, and the Luding earthquake caused 100 + casualties. Gravity observations performed in the North–South Seismic Belt before the two earthquakes indicate that gravity changes occurred near the epicentres and exhibited four-quadrant distributions. In this study, We reviewed the successful prediction of these two earthquakes by using gravity data. The distances between the actual and predicted epicenters of the two earthquakes were < 56 km in 2022 and < 10 km in 2021. Before both earthquakes, gravity changes first showed as a gradient zone consistent with the strike of seismogenic fault, and then subsequently exhibited a four-quadrant distribution around the epicentral regions. The earthquakes occurred near the centres of the four-quadrant change and the zero isoline of gravity change. In summary, the gravity data reflected both earthquakes well. The findings indicate that such four-quadrant distributions and gravity change high-gradient zone may be precursor information of earthquake preparation. The results of this study provide a reference for future earthquake monitoring and prediction, with implications for earthquake hazard assessment.

Efficiency of Optimized Approaches for Gravity Operator Modeling

Numerical tesseroid and radial-type approaches are presented and compared in terms of their efficiency for deriving the regional geoid height, vertical gravity, and gradiometric anomalies from sea floor topography grids. The vertical gradient function is particularly suitable for representing shorter wavelengths of gravity, typically less than 10 km. These two modeling methods were applied to the Great Meteor guyot in the Atlantic Ocean using its bathymetry. To optimize the computation of high-resolution gravity anomalies, the Armadillo, GSL, and OpenMP libraries were used to provide an environment for fast vector implementation, numerical integration for tesseroid calculation, and parallelization for loop iterations, resulting in a computation speed increase. The tesseroid and radial methods remain equivalent up to a resolution of about 1 min, with the radial method being faster when dealing with a large number of model points for the geoid. Aside from optimization enabling high-resolution gravity simulations, these fast modeling data can be used as the main operators in gravimetric inversion or to reduce the terrain effects in gravity observations, revealing gravity and sedimentary layers.

Expected constraints on Phobos interior from the MMX gravity and rotation observations

The origin of the Martian moons is still uncertain, and knowledge about their interior could provide support to some of its leading theories. In preparation for the JAXA Martian Moons eXploration (MMX) mission, we review our current knowledge on the interior of Phobos, and provide synthetic tests showing how the gravity and rotation determination could allow the detection of specific interior-structure properties. The inversion of the geodetic observables for the retrieval of the internal mass distribution of a set of synthetic interior models is performed via non-linear least-squares, where the interior parameterization is based on the level-set method. We additionally provide simple expressions allowing to relate some of these interior models to the geodetic observables of Phobos. The results, based on realistic measurement resolution and noise scenarios, show good retrievals for most of the models at the data resolutions expected from MMX. Specifically, we find the gravity information is realistically sufficient for the detection of mass anomalies below the Stickney crater, as well as large scale heterogeneous regions within plausible rubble-pile structures. Libration helps retrieve the more degenerate models for gravity, such as those with concentric layers or with density varying linearly with depth. The incremental improvement from further adding a hypothetical mean obliquity measurement is marginal. Finally, we apply the level-set inversion and the analytical formulas to estimate possible interior characteristics of the ‘real’ Phobos from the currently-available scarce geodetic observables. The level-set solutions for the real-data inversion generally converge to a higher mass concentration towards the surface in the equatorial region. Markov chain Monte Carlo estimations of parameters relative to a simple 2-layer model or a radial density distribution similarly hint at a lighter region inside of Phobos.

Deep plutonic bodies over low-frequency earthquakes revealed from receiver-side Green's functions

Seismological heterogeneity in subduction zones provides insights into slow earthquakes and potential megathrust earthquakes. Studies at the Kii Peninsula in the Nankai subduction zone suggest that there are high-density and high-velocity plutonic bodies in the accretionary prism over the subducting slab, potentially influencing megathrust earthquakes. The lateral variation of heterogeneity and the spatial extent of plutonic bodies remain to be investigated well. Our passive-source imaging of receiver-side Green's functions, from widely distributed campaign seismic observations, reveals a sharp negative S-wave velocity contrast on the top surface of the subducting Philippine Sea plate common to all along-dip profiles and a positive phase tilted upward in the forearc crust. The low permeability of the forearc crust prevents the infiltration of slab-dehydrated fluid further into the upper crust. In the western area, we also found positive phases tilted upward in the forearc crust. The negative phase extends towards the deeper extent of slow-earthquake sources. Meanwhile, the positive phase likely represents the top surface of plutonic rocks of the Kumano and Ohmine plutons that span all the way down to the plate interface. Together with observations of gravity anomaly, intraslab seismicity, and seismic tomography, our interpretation supports the presence of plutonic bodies which extend deep beneath the forearc crust as well as laterally over the subducting PHS slab, rather than a serpentinized mantle wedge. The upper plate is generally low in permeability, but areas with localized high permeability may exist on the updip side of tremor sources. This condition, wherein fluid can infiltrate upwards locally, may maintain the relatively less active slow earthquakes in the western area. The lateral variation of the upper-plate lithology likely influences fluid processes and slow earthquake activities.

Relativity of the event: examples in JT gravity and linearized GR

Observables in quantum gravity are famously defined asymptotically, at the boundary of AdS or Minkowski spaces. However, by gauge fixing a coordinate system or suitably dressing the field operators, an approximate, “quasi-local” approach is also possible, that can give account of the measurements performed by a set of observers living inside the spacetime. In particular, one can attach spatial coordinates to the worldlines of these observers and use their proper times as a time coordinate. Here we highlight that any such local formulation has to face the relativity of the event, in that changing frame (= set of observers) implies a reshuffling of the point-events and the way they are identified. As a consequence, coordinate transformations between different frames become probabilistic in quantum gravity. We give a concrete realization of this mechanism in Jackiw-Teitelboim gravity, where a point in the bulk can be defined operationally with geodesics anchored to the boundary. We describe different ways to do so, each corresponding to a different frame, and compute the variances of the transformations relating some of these frames. In particular, we compute the variance of the location of the black hole horizon, which appears smeared in most frames. We then suggest how to calculate this effect in Einstein gravity, assuming knowledge of the wavefunction of the metric. The idea is to expand the latter on a basis of semiclassical states. Each element of this basis enjoys standard/deterministic coordinate transformations and the result is thus obtained by superposition. As a divertissement, we sabotage Lorentz boosts by adding to Minkoswki space a quantum superposition of gravitational waves and compute the probabilistic coordinate transformation to a boosted frame at linear order. Finally, we attempt to translate the relativity of the event into the language of dressed operators.

Separation of earthquake and hydrology signals from GRACE satellites data via independent component analysis: a case study in the Sumatra region

SUMMARY The Gravity Recovery and Climate Experiment (GRACE) satellites have observed mass migrations caused by megathrust earthquakes. Extracting earthquake-related signals from GRACE data is still a challenge due to the interference from non-earthquake sources such as terrestrial hydrology. Instead of reducing hydrological signals by potentially biased hydrological models, in this study we apply a model-free technique of independent component analysis (ICA), to separate earthquake and non-earthquake signals from non-Gaussian GRACE data. We elucidate the principles and mechanisms of ICA for the separation of earthquake and hydrology signals, employing simulated data to demonstrate the process. Our findings demonstrate that both spatial ICA and temporal ICA are highly effective in discerning earthquake related to 2004 Mw 9.2 event and hydrological signals from GRACE data in the Sumatra region. This stands in stark contrast to principal component analysis, which often encounters challenges with signal intermingling. The utility of ICA is evident in its ability to distinctly delineate coseismic and post-seismic behaviours associated with megathrust events, including the 2004 Sumatra, the 2010 Maule, and the 2011 Tohoku earthquakes. ICA effectively mitigates the potential for misestimation of earthquake signals, an issue that can carry substantial implications. Therefore, employing ICA facilitates the accurate extraction of earthquake-related data from satellite gravity observations—a critical process for refining earthquake source parameters and understanding Earth's rheological properties, especially when non-earthquake signals are significant and cannot be disregarded.

Nubian aquifer linkage to the High Aswan Dam Reservoir: Initial assessments of processes and challenges

Egypt, relying heavily on the Nile as its primary water resource, is facing a rising water budget deficit due to increasing consumption, hydroclimatic changes, and upstream river damming. To address the above, innovative management of High Aswan Dam Reservoir (HADR), the third largest artificial reservoir on Earth, and its exchange with the surrounding groundwater system is suggested to develop new agricultural areas. However, the interconnectivity mechanism between the HADR and the fossil Nubian aquifer, the largest transboundary aquifer in Africa, remains speculative due to the lack of in-situ investigations. To address this deficiency, we perform a geophysical survey using aeromagnetic, time-domain electromagnetic, and vertical electrical resistivity sounding in a 330 km2 pilot area to the northwest of the HADR that is hypothesized to have a dense fracture system that could act as a conduit between these two large water bodies. Our survey results show the presence of normal faults cross the reservoir to the tangential basement and the sedimentary cover that are water-saturated and act as recharges to the Nubian fossil aquifer. These in-situ investigations confirm previous orbital gravity observations by GRACE-FO hypothesizing the interconnectivity between the reservoir and the Nubian aquifer, which was subject to debate. We suggest that such connecting areas between these two water bodies can be optimal sites for future agricultural development using improved management of surface water-groundwater exchanges for irrigation. Finally, our findings highlight upcoming challenges for this linkage if the level of HADR reaches below ∼160 m above mean sea level (amsl) due to upstream dam operation during the Nile’s extended drought periods. Under these conditions, the Nubian aquifer could discharge back into the HADR at the investigated site, changing the water budget of the aquifer and compromising the planned agriculture developments in the adjacent areas, which account for ∼ 10 % of the total arable land in Egypt.

Selection of a calibration system for relative gravimeters and testing of the processing using the example of the Zhetygen calibration baseline in Kazakhstan

This article consolidates and organizes modern methods for calibrating relative gravimeters, aiming to streamline the selection and implementation of effective calibration systems, particularly in Kazakhstan. The concept of the calibration function and various methods for its determination are presented. Practical implementations of laboratory methods relevant to modern high-precision relative gravimeters are discussed, including the tilt, moving mass, artificial acceleration, and line calibration methods. Data processing through least squares adjustment at the calibration line and an overview of existing software packages for gravity observation equalization are explored. The article also covers existing horizontal and vertical calibration systems in different countries, detailing their main characteristics and schematics. Finally, an estimation of scale factors for five years of measurements with Scintrex CG-5 gravimeters at the Zhetygen calibration line in Kazakhstan is provided.

The Planck Computer Is the Quantum Gravity Computer: We Live inside a Gigantic Computer, the Hubble Sphere Computer?

Recent developments in the quantization of general relativity theory provide a new perspective on matter and even the whole universe. Already, in 1922, Eddington suggested that a future quantum gravity theory had to be linked to Planck length. This is today the main view among many working with quantum gravity. Recently, it has been demonstrated how Planck length, the Planck time, can be extracted from gravity observations with no knowledge of G, ℏ, or even c. Rooted in this, both general relativity theory and multiple other gravity theories can be quantized and linked to the Planck scale. A revelation from this is that matter seems to be ticking at the reduced Compton frequency, where each tick can be seen as one bit, and one bit corresponds to a Planck mass event. This new speculative way of looking at gravity can also potentially tell us considerably about what quantum gravity computers are and what they potentially can do. We will conjecture that that all quantum gravity and quantum gravity computers are directly linked to the Planck scale and the Compton frequency in matter, something we will discuss in this paper. Quantum gravity computers, we will see, in many ways, are nature’s own designed computers with enormous capacity to 3D “print” real time. So, somewhat speculatively, we suggest we live inside a gigantic quantum gravity computer known as the Hubble sphere, and we even are quantum gravity computers. The observable universe is based on this model, basically a quantum gravity computer that calculates approximately 10104 bits per second (bps).

Boundaries identification of geological structure in lunar Oceanus Procellarum region using full gravity gradient tensor methodology

Boundary recognition visually delineates the horizontal extent of subsurface anomalies, providing a foundational basis for interpreting gravity data. Compared to gravity observations, gravity gradient data offers the benefits of multiple components and the enhancement of shortwave information in graphical representations. In our study, we investigated the delineation of geological structure boundaries in the lunar Oceanus Procellarum region using gravity gradient techniques. First, based on the observations from the Gravity Recovery and Interior Laboratory (GRAIL) mission, we obtained high-precision synthetic full tensor values of the gravity gradient as our primary research data. Moreover, to reduce curvature errors during large-scale terrain forward modeling, we applied the spherical prism of tesseroid to eliminate the effects of near-surface topography. Grounded on the Bouguer anomalies of gravity gradient, four distinct boundary recognition methods have been employed to explore the geological structure of the lunar Oceanus Procellarum region. It includes the Theta map method, the directional Theta map method, the combination of total horizontal derivative and the modulus of full tensor gravity gradient, and the improved edge detection method based on the Theta map method.The common feature of these methods is the utilization of the multi-component data combination from gravity gradient tensors, which can enhance the accuracy of edge detection. From the investigation results presented in the paper, we have found the following: 1) The improved edge detection method, based on the Theta map principle, enables better identification of the center of subsurface anomaly bodies during boundary recognition, utilizing a consistent single color in graphic displays. 2) According to the results of boundary recognition, numerous strip anomalies exist in the Oceanus Procellarum area that show less correlation with topographic relief. One possible explanation for these graphical anomalies of gravity gradient is that they serve as channels for the upwelling of mantle material during lunar evolution.

Revisiting flares in Sagittarius A* based on general relativistic magnetohydrodynamic numerical simulations of black hole accretion

ABSTRACT High-resolution observations with GRAVITY-Very Large Telescope Interferometer (VLTI) instrument have provided abundant information about the flares in Sgr A*, the supermassive black hole in our Galactic centre, including the time-dependent location of the centroid (a ‘hotspot’), the light curve, and polarization. Yuan et al. (2009) proposed a ‘coronal mass ejection’ model to explain the flares and their association with the plasma ejection. The key idea is that magnetic reconnection in the accretion flow produces the flares and results in the formation and ejection of flux ropes. The dynamical process proposed in the model has been confirmed by three-dimensional general-relativistic magnetohydrodynamic simulations in a later work. Based on this scenario, in our previous works the radiation of the flux rope has been calculated analytically and compared to the observations. In the present paper, we develop the model by directly using numerical simulation data to interpret observations. We first identify flux ropes formed due to reconnection from the data. By assuming that electrons are accelerated in the reconnection current sheet and flow into the flux rope and emit their radiation there, we have calculated the time-dependent energy distribution of electrons after phenomenologically considering their injection due to reconnection acceleration, radiative and adiabatic cooling. The radiation of these electrons is calculated using the ray-tracing approach. The trajectory of the hotspot, the radiation light curve during the flare, and the polarization are calculated. These results are compared with the GRAVITY observations and good consistencies are found.

Influence of GIA Uncertainty on Climate Model Evaluation With GRACE/GRACE‐FO Satellite Gravimetry Data

AbstractGlobal coupled climate models are in continuous need for evaluation against independent observations to reveal systematic model deficits and uncertainties. Changes in terrestrial water storage (TWS) as measured by satellite gravimetry missions GRACE and GRACE‐FO provide valuable information on wetting and drying trends over the continents. Challenges arising from a comparison of observed and modelled water storage trends are related to gravity observations including non‐water related variations such as, for example, glacial isostatic adjustment (GIA). Therefore, correcting secular changes in the Earth's gravity field caused by ongoing GIA is important for the monitoring of long‐term changes in terrestrial water from GRACE in particular in former ice‐covered regions. By utilizing a new ensemble of 56 individual realizations of GIA signals based on perturbations of mantle viscosities and ice history, we find that many of those alternative GIA corrections change the direction of GRACE‐derived water storage trends, for example, from gaining mass into drying conditions, in particular in Eastern Canada. The change in the sign of the TWS trends subsequently impacts the conclusions drawn from using GRACE as observational basis for the evaluation of climate models as it influences the dis‐/agreement between observed and modelled wetting/drying trends. A modified GIA correction, a combined GRACE/GRACE‐FO data record extending over two decades, and a new generation of climate model experiments leads to substantially larger continental areas where wetting/drying trends currently observed by satellite missions coincide with long‐term predictions obtained from climate model experiments.

Kerr binary dynamics from minimal coupling and double copy

We construct a new Yang-Mills Lagrangian based on a notion of minimal coupling that incorporates classical spin effects. The construction relies on the introduction of a new covariant derivative, which we name “classical spin covariant derivative”, that is compatible with the three-point interaction of the Kerr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{\ extrm{Kerr}} $$\\end{document} solution with the gauge field. The resulting Lagrangian, besides the correct three-point coupling, predicts a unique choice for contact terms and therefore it can be used to compute higher-point amplitudes such as the Compton, unaffected by spurious poles. Using double copy techniques we use this theory to extract gravity amplitudes and observables that are relevant to describe Kerr binary dynamics to all orders in the spin. In particular, we compute the 2PM (O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(GN2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {G}_N^2 $$\\end{document})) 2 → 2 elastic scattering amplitude between two classically spinning objects to all orders in the spin and use it to extract the 2PM scattering angle.

Improved Approaches for 3D Gravity and Gradient Imaging Based on Potential Field Separation: Application to the Magma Chamber in Wudalianchi Volcanic Field, Northeastern China

The gravity and gradient anomalies contain valuable information about the underground geological structures at various depths. Deep and shallow buried source bodies are able to be identified through multi-scale field separation processes, and visual comprehensions of geological structures can be obtained via 3D density inversion techniques. In this study, we propose an improved 3D imaging strategy based on gravitational field separation using the preferential continuation filter. This strategy incorporates the relationship between spectral features and buried depths of source bodies, allowing for a one-step transformation from planar gravity and full-tensor gradient field observations to a 3D density structure in the wave-number domain. Synthetic tests validate the effectiveness and robustness of the gravity and gradient imaging approaches, highlighting their advantages in high vertical resolution and low computational requirements. Nonetheless, it should be noted that the imaging effects of horizontal gradients Γxx and Γyy are unsatisfactory due to their weak noise resistance. Thus, they are not suitable for real data applications. The other imaging approaches are further applied to recover the subsurface 3D density structure beneath the Weishan cone in Wudalianchi Volcanic Field, Northeastern China. Our results provide insights into the possible location and shape of the low-density magma chamber. Also, the potential presence of partial melts is inferred and supported from a gravity perspective. The primary advantage of these approaches is their ability to generate a reasonable geological model in scenarios with limited prior information and physical property constraints. As a result, they have significant practical value in the field of applied geophysics, including mineral exploration and volcanology studies.

GeoMed2,the geoid of the Mediterranean: work in progress

Geodesy can provide valuable information on marine current estimation based on the combination of gravity and altimetry. Gravity is standardly used to estimate the geoid undulation, i.e. the height of the geoid over a given reference ellipsoid. As it is well known, the geoid undulation over the oceans is closely related to the Mean Sea Surface (MSS) with discrepancies that can reach 1–2 m at global scale. By satellite altimetry, one can get the MSS and then estimate the Mean Dynamic Topography (MDT) as the difference between the MSS and the geoid undulation. As the MDT is related to the ocean circulation, information on the ocean circulation to be compared with oceanographic estimates can be provided using these geodetic measurements. In this context, the GeoMed2 project aims at estimating a high-accuracy and high-resolution geoid model for the Mediterranean Sea based on land and marine gravity data and on recent Global Geopotential Models. In this paper, the processing methodology based on the well-known remove–compute–restore approach for the determination of the geoid in the Mediterranean area is presented. In a pre-processing step, all available gravity observations for the wider Mediterranean basin have been collected, validated, homogenized, and unified in terms of their horizontal and gravity system. In this way, a reliable gravity database to be used for the determination of the geoid has been prepared. This data set has been used in computing a gravimetric geoid estimate based on which the MDT over the Mediterranean Sea was obtained. The results of this computation were then revised, commented and compared with other existing MDT solutions. By these comparisons, it can be concluded that the geodetic computed MDT is not yet satisfactory since it is too noisy. This is possibly due to some inconsistencies still present in the gravity data used for estimating the geoid undulation and to the adopted MSS which seems to be too smooth over the Mediterranean area.

A Deep Learning Gravity Inversion Method Based on a Self-Constrained Network and Its Application

Gravity inversion can be used to obtain the spatial structure and physical properties of subsurface anomalies through gravity observation data. With the continuous development of machine learning, geophysical inversion methods based on deep learning have achieved good results. Geophysical inversion methods based on deep learning often employ large-scale data sets to obtain inversion networks with strong generalization. They are widely used but face a problem of lacking information constraints. Therefore, a self-constrained network is proposed to optimize the inversion results, composed of two networks with similar structures but different functions. At the same time, a fine-tuning strategy is also introduced. On the basis of data-driven deep learning, we further optimized the results by controlling the self-constrained network and optimizing fine-tuning strategy. The results of model testing show that the method proposed in this study can effectively improve inversion precision and obtain more reliable and accurate inversion results. Finally, the method is applied to the field data of Gonghe Basin, Qinghai Province, and the 3D inversion results are used to effectively delineate the geothermal storage area.

InSAR, Gravity, and Geomagnetic Observations Suggest the 2020 Mw 6.5 Stanley Earthquake Occurred on a Blind Strike-Slip and a Normal Fault

ABSTRACT The 2020 Mw 6.5 Stanley earthquake occurred in western North America and is the largest earthquake in Idaho state in the past ∼40 yr. The hypocenter is located at the western margin of the Centennial Tectonic Belt (CTB), which is a subprovince of the Basin and Range and characterized by a series of normal faults. In this study, the coseismic Interferometric Synthetic Aperture Radar observations, geophysical data, and aftershocks are jointly collected to estimate the seismogenic fault of the 2020 Stanley earthquake. The best-fitting fault models suggest the earthquake occurred on two blind faults. Slip on the main, west-dipping, seismogenic fault was sinistral and on the second fault predominantly normal slip with a minor component of right-lateral strike slip. Geophysical observations including gravity and geomagnetic data are consistent with the fault interpretations. The Coulomb failure stress (CFS) change indicates that the rupture of the main seismogenic fault had a positive triggering effect on the slip of the second fault and may have increased the rupture risk of the Sawtooth fault. Moreover, a potential seismic hazard risk zone with a notably low occurrence of aftershocks is found in the west of the central segment of the main seismogenic fault.

Crustal Apparent Density Variations in the Middle Segment of the North Tianshan Mountains and Their Tectonic Significance

In this study, we collected mobile gravity observations in the middle segment of the North Tianshan Mountains from August 2016 to July 2022 and carried out classical adjustment calculations under the constraint of the absolute gravity datum to obtain the spatiotemporal variation pattern of the local gravity field. We used equivalent source inversion to obtain the spatiotemporal variation characteristics of crustal apparent density. We also extracted the coseismic deformation field from SAR data, using the 2016 Hutubi earthquake as an example, and constructed a model of the seismogenic fault. The gravity monitoring network in the study area performed well in resolving the earthquake source parameters. Both the time-varying gravity field and equivalent apparent density variation pattern show prominent zoning characteristics with a smoothly evolving spatial distribution over time. The variation trends of the gravity field and equivalent apparent density are in line with the orientation of tectonic structures, and their anomalous signals can be detected before and after an earthquake. The constructed seismogenic structure of the 2016 Hutubi earthquake indicates a typical thrust earthquake, probably occurring on a north-dipping blind fault beneath a region with intense crustal deformation. The subsurface tectonic system reflected by this earthquake can be informatively extended to the entire middle segment of the North Tianshan Mountains by subsurface configuration. Our findings can serve as a reference for analyzing the source characteristics of the time-varying gravity field and interpreting anomalous pre-seismic signals, and aid in understanding earthquake preparation zones and the mode of crustal tectonic movements.

Equivariant localization for AdS/CFT

We explain how equivariant localization may be applied to AdS/CFT to compute various BPS observables in gravity, such as central charges and conformal dimensions of chiral primary operators, without solving the supergravity equations. The key ingredient is that supersymmetric AdS solutions with an R-symmetry are equipped with a set of equivariantly closed forms. These may in turn be used to impose flux quantization and compute observables for supergravity solutions, using only topological information and the Berline-Vergne-Atiyah-Bott fixed point formula. We illustrate the formalism by considering AdS5 × M6 and AdS3 × M8 solutions of D = 11 supergravity. As well as recovering results for many classes of well-known supergravity solutions, without using any knowledge of their explicit form, we also compute central charges for which explicit supergravity solutions have not been constructed.