3D Gravity Research Articles

Multiboundary wormholes and OPE statistics

We derive higher moments in the statistical distribution of OPE coefficients in holographic 2D CFTs, and show that such moments correspond to multiboundary Euclidean wormholes in pure 3D gravity. The nth cyclic non-Gaussian contraction of heavy-heavy-light OPE coefficients follows from crossing symmetry of the thermal n-point function. We derive universal expressions for the cubic and quartic moments and demonstrate that their scaling with the microcanonical entropy agrees with a generalization of the Eigenstate Thermalization Hypothesis. Motivated by this result, we conjecture that the full statistical ensemble of OPE data is fixed by three premises: typicality, crossing symmetry and modular invariance. Together, these properties give predictions for non-factorizing observables, such as the generalized spectral form factor. Using the Virasoro TQFT, we match these connected averages to new on-shell wormhole topologies with multiple boundary components. Lastly, we study and clarify examples where the statistics of heavy operators are not universal and depend on the light operator spectrum. We give a gravitational interpretation to these corrections in terms of Wilson loops winding around non-trivial cycles in the bulk.

Do gravity data justify a rifted “Liguro-Provençal Basin”?

The geodynamic evolution of the Liguro-Provençal Basin and its crust and upper mantle structure remain debated, especially regarding the role of rifting in continental break-up and seafloor spreading. Our study incorporates updated datasets, including new gravity maps from the AlpArray Gravity Working Group (complete Bouguer, free air, and isostatic anomalies) for 3D modeling and gravity field analysis, seismic data from Lobster offshore campaigns for direct comparison, and geodynamic models, supplemented by seismic profiles from previous French and Italian campaigns to constrain the interpretation. We used GFZ’s IGMAS + software for interactive 3D modeling, creating a density model extending to 300 km depth that includes crustal and upper mantle inhomogeneities based on prior geodynamic models. This hybrid approach, with polygonal structures for the crust and voxels for the upper mantle, clarifies individual contributions to the gravity field. Extending initial gravity modeling from the SPP MB4D project INTEGRATE, our work provides a consistent 3D density model for the Alps and Ligurian Basin. The constrained 3D modeling and numerical analyses (terracing, clustering, filtering, curvature), along with vertical stress and gravitational potential energy calculations, suggest that rifting has significantly influenced the basin’s geological evolution.

Topological 4D gravity and gravitational defects

Using the Chern-Simons formulation of AdS3 gravity as well as the Costello-Witten-Yamazaki (CWY) theory for quantum integrability, we construct a novel topological 4D gravity given by equation (5.1) with observables based on gravitational gauge field holonomies. The field action S4Dgrav of this gravity has a gauge symmetry SL(2,C) and reads also as the difference S4DCWYL−S4DCWYR with 4D Chern-Simons field actions S4DCWYL/R given by left/right CWY theory equation (3.9). We also use this 4D gravity derivation to build observables describing gravitational topological defects and their interactions. We conclude our study with few comments regarding quantum integrability and the extension of AdS3/CFT2 correspondence with regard to the obtained topological 4D gravity.

Architecture of the post-obductional Sunub Structure, northeastern Sultanate of Oman: Based on mapping, 3D gravity inversion and shale migration

We examined the structural evolution of the poorly understood Sunub Structure, which is associated with the northern margin of the Saih Hatat Dome and the extensional Frontal Range Fault (northeastern Oman). The Sunub Structure is located at a dextral transtensional segment and on the hanging wall of the NNE-striking Frontal Range Fault. The fault was active during the Campanian(?)/Maastrichtian to early Eocene (Interval I) and mid-/late Eocene to early Miocene (Interval II). Gravitational inversion using 175 stations and mapping shows: (1) The Sunub Structure is possibly >1200–1350 m deep and filled mostly with the >900-m-thick Campanian(?)/Maastrichtian siliciclastic Al-Khod Formation, including shale, and some overlying Paleogene limestones. (2) The bottom of the basin cannot be depicted. (3) The lower part of the structure is a basin (Sunub Sedimentary Basin), bounded by sub-vertical to steep contacts. (4) The upper part of the Sunub Structure is a basin fold displaying a bowl-shape down to ∼300 m below the surface, referred to as the Sunub Bowl. (5) The bowl is cut by radial faults and five ∼E/W-striking transverse faults. The Sunub Structure formed during Interval I as a deep transtensional, syn-depositional basin. Gentle post-depositional tectonics during Interval II and visco-plastic shale movements produced the present-day bowl-shape that is visible at the surface. Gravitational inversion depict possible evidence for shale migration within the Al-Khod Formation. Although no hydrocarbons are present, the Sunub Structure can serve as an analogue for hydrocarbon migration and storage in similar structures.

Integration of 2D and 3D electrical resistivity tomography and 2D gravity modeling to evaluate groundwater investigations in the Burka Uke catchment area, western Ethiopia

The increasing demand for water resources due to the expanding infrastructure and growing population of Uke town, West Ethiopia, necessitates a comprehensive understanding of groundwater potential within the Burka Uke catchment. The aims and objectives of this study are to identify a map of the aquifer by characterizing the subsurface earth, basement rock depth, resistivity and density of geological layers, their thicknesses, and structural features. The investigation integrates electrical resistivity tomography and gravity modeling to delineate potential groundwater zones and their structural controls. Electrical resistivity tomography profiles (1, 4, and 6) revealed low resistivity zones indicative of potential aquifers. The significant resistivity contrast (378 to 1412 Ω.m) suggests a high fracture density, potentially enhancing groundwater storage. The Bouguer gravity anomaly map, separated into regional and residual components, displayed values ranging from 51.79 to 41.59 mGal, highlighting density variations in the subsurface. As a result, analysis of the residual gravity anomaly map identifies north–south striking fault elements, indicating their influence on groundwater flow.The combined 2D and 3D ERT data also revealed a 2D gravity model of the aquifer from which the concentration extended throughout the study area. Data validation with previously drilled wells has confirmed the effectiveness of the geophysical methods used in identifying potential groundwater zones. This study provided critical information for the sustainable management of existing groundwater and demonstrated the effectiveness of integrating geophysical techniques to delineate and characterize aquifers in water-stressed areas.

CFT Correlators and Mapping Class Group Averages

Mapping class group averages appear in the study of 3D gravity partition functions. In this paper, we work with 3D topological field theories to establish a bulk-boundary correspondence between such averages and correlators of 2D rational CFTs whose chiral mapping class group representations are irreducible and satisfy a finiteness property. We show that Ising-type modular fusion categories satisfy these properties on surfaces with or without field insertions, extending results in [1], and we comment on the absence of invertible global symmetries in the examples we consider.

Self-gravitating solutions in Yang–Mills–Chern–Simons theory coupled to 3D massive gravity

We study self-gravitating solutions of three-dimensional massive gravity coupled to the Yang–Mills–Chern–Simons gauge theory. Among these, there is a family of asymptotically Warped-Anti de Sitter black holes that come to generalize previous solutions found in the literature and studied in the context of WAdS3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_3$$\\end{document}/CFT2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}. We also present self-gravitating solutions to three-dimensional Einstein–Yang–Mills theory, as well other self-gravitating solutions in the presence of higher-curvature terms.

Benefits of Integrating Seismic and Gravity Data in a Subsalt Environment. A Case Study at Block BM-C-33, Deepwater Campos Basin, offshore Brazil

Imaging subsalt layers is challenging in the BM-C-33 block in the Campos Basin's ultradeep waters. This block is important as it has three significant gas and condensate discoveries in the pre-salt carbonate and volcanic reservoirs -- Seat, G൥a, and P⭠de A洣ar. Understanding basement morphology is essential to better define the petroleum system in the area. To that end, we performed a 2D gravity modeling exercise along a northwest-southeast section, using seismic interpretation as input to reduce the ambiguity of the modeling exercise. To achieve this, we fixed the main sedimentary horizons and their densities (calculated via well-log information) to better estimate the top of the basement morphology. This interpretation strategy better delineated the pre-salt sedimentary section and the complex structural framework with two asymmetric grabens bounded by a prominent horst, interpreted as a migration focusing high in the BM-C-33 area. In addition, our findings show that obtaining clear images remains challenging even after extensive processing of the seismic data set. We suggest that seismic node acquisition with ultra-long offsets and multi-azimuthal illumination and then carefully processing the data is required to accurately reveal the area's pre-rift section and basement morphology under study.

Classical Dynamical r-matrices for the Chern–Simons Formulation of Generalized 3d Gravity

AbstractClassical dynamical r-matrices arise naturally in the combinatorial description of the phase space of Chern–Simons theories, either through the inclusion of dynamical sources or through a gauge fixing procedure involving two punctures. Here we consider classical dynamical r-matrices for the family of Lie algebras which arise in the Chern–Simons formulation of 3d gravity, for any value of the cosmological constant. We derive differential equations for classical dynamical r-matrices in this case and show that they can be viewed as generalized complexifications, in a sense which we define, of the equations governing dynamical r-matrices for $$\mathfrak {su}(2)$$ su ( 2 ) and $$\mathfrak {sl}(2,{\mathbb {R}})$$ sl ( 2 , R ) . We obtain explicit families of solutions and relate them, via Weierstrass factorization, to solutions found by Feher, Gabor, Marshall, Palla and Pusztai in the context of chiral WZWN models.

Three-Dimensional Gravity Inversion Based on Attention Feature Fusion.

Three-dimensional gravity inversion is a process of obtaining the location, shape, and physical property parameters of underground anomaly sources using gravity anomaly data observed on the surface. In recent years, with the rapid development of data-driven methods, the application of deep learning (DL) to 3D gravity inversion has also attracted wide attention and achieved certain results. In this paper, based on the U-Net network, a three-dimensional gravity inversion method using an attention feature fusion mechanism is proposed. Using U-Net as the basic framework, the coarse-grained semantic features and fine-grained semantic features in the encoder and decoder are connected by long hops, and the global and local semantic features are aggregated through the attention feature fusion module, which avoids feature loss in the network training process. Compared with the inversion results of the U-Net network, the proposed method has a higher vertical resolution and effectively alleviates the influence of the skin effect on three-dimensional gravity inversion. Ablation experiments show that the attention feature fusion module is the key to improving the vertical resolution and prediction accuracy of inversion results. Noise experiments show that the inversion network in this study has a strong anti-noise ability and good generalization performance. The experimental results of the inversion network used in the prediction of the SAN Nicolas deposit in Mexico show that the inversion network can clearly predict the basic location and general shape of the sulfur deposit, and the results are in good agreement with the known geological data.

Efficient large-scale 3D gravity modeling using a fast evaluate kernel matrix combined with compressed matrix techniques

A fast calculated kernel matrix method is coupled with a compressed matrix technique to solve the large-scale gravity forward-modeling problem. This method accelerates the coefficient matrix computation by reducing the arctangent, logarithm, and multiplication functions in the prismatic gravity analytical expression. In addition, the use of the compressed matrix technique presents a significant advantage in that it does not require the storage of redundant kernel matrices, further reducing the memory requirements and computation time. Moreover, the discrete convolution of the compressed matrix with density is executed through the 2D fast Fourier transform (FFT). Two typical synthetic models are used to test the performance of the novel algorithm. The results demonstrate that the developed algorithm is approximately 15 times faster than the traditional algorithm. Concurrently, it demands almost 1/7th of the memory while ensuring equivalent computational accuracy. To further illustrate the capability of the algorithm, we apply our method to the terrain correction of an airborne gravity data set using a real digital elevation model. Our approach efficiently calculates 250,000 observation points across 25 million cells in only 5.42 s, compared with 234.81 s for the latest 2D Gauss-FFT method.

Implementation of the Gauss-Kronrod Quadrature Method (G7, K15) on 2D Gravity Anomaly Modeling in Basins with a Polynomial Variation of Density Distribution with Depth

Forward modeling of 2D gravity anomalies, considering density contrasts that vary polynomially with depth, was performed to examine basin structures. This process involved two main stages: deriving analytical formulas and executing numerical integration. The Gauss-Kronrod Quadrature Method, utilizing 7 Gauss points and 15 Kronrod points, was employed to precisely compute these integrals. Initial modeling applied to theoretical basement scenarios with fixed density contrasts showed gravity anomalies that accurately reflected the curvature of the basement. To validate the approach, it was then applied to real-world cases including the Sebastian Vizcaino Basin, San Jacinto Graben, and Sayula Basin. By incorporating suitable density contrasts, modeling lengths, and basement curvature shapes, the results revealed that both fixed-density and depth-variable density models produced gravity anomalies with patterns consistent with the actual basement curvature. These findings validate the modeling technique’s effectiveness in representing real geological features accurately. The study confirms that the Gauss-Kronrod Quadrature Method (G7, K15) is robust for analyzing 2D gravity anomalies, providing a reliable tool for understanding the influence of varying density contrasts on gravity responses.

The near horizon dynamics in three-dimensional Einstein gravity

We study the asymptotic dynamics of 3D gravity with Rindler boundary conditions both in flat and AdS spacetimes. We do this by using the angular quantization and Hamiltonian reduction of the action to the Wess-Zumino-Witten theory on the boundary. We then rewrite the boundary action as a functional of elements of the asymptotic symmetry group.

Heavy states in 3d gravity and 2d CFT

We discuss correlators of light fields in heavy states in AdS3 gravity and holographic 2d CFTs. In the bulk, the propagator of free fields in AdS backgrounds containing a conical defect or a BTZ black hole can be obtained by solving a wave equation, as well as by the method of images. On the boundary, these geometries are sourced by heavy operator insertions, and the propagator is dual to a heavy-light (HHLL) correlator. By matching its expansion in Virasoro blocks to our bulk results, we determine the OPE coefficients of all contributing states in both the s and t channels. In the s channel, these states are excitations of the light field on top of the heavy state, and their OPE coefficients are the amplitudes to create them. The t-channel OPE is dominated by the Virasoro vacuum block, but there is also an infinite family of light two-particle states that contribute to the correlator. The OPE coefficients that couple these states to heavy operators represent their expectation values in heavy backgrounds. We determine them exactly, derive their asymptotic form at large twist, and discuss their behavior near and above the BTZ threshold, where they become thermal one-point functions.

3D Gravity and magnetic inversion modelling for geothermal assessment and temperature modelling in the central eastern desert and Red Sea, Egypt

The Central Eastern Desert and Red Sea region have emerged as a significant area of interest for geothermal energy exploration, owing to their unique geological characteristics and active tectonic activity. This research aims to enhance our understanding of the region's geothermal potential through a comprehensive analysis of gravity and magnetic data. By utilizing a 3D gravity inversion model, a detailed examination of subsurface structures and density variations was conducted. Similarly, a 3D magnetic inversion model was employed to investigate subsurface magnetic properties. Integration result from the Pygimli library ensured robustness and accuracy in the inversion results. Furthermore, a temperature model was developed using the WINTERC-G model and inversion techniques, shedding light on the thermal structure and potential anomalies in the study area. The analysis of the Bouguer gravity map, 3D gravity inversion model, and magnetic data inversion yielded significant findings. The Red Sea exhibited higher gravity values compared to the onshore Eastern Desert, attributed to the presence of a thinner and denser oceanic crust as opposed to the less dense continental crust in the Eastern Desert. The 3D gravity inversion model revealed distinct variations in density, particularly high-density zones near the surface of the Red Sea, indicating underlying geological structures and processes. Conversely, density gradually decreased with depth along the onshore line, potentially influenced by a higher concentration of crustal fractures. The magnetic data inversion technique provided additional insights, highlighting areas with demagnetized materials, indicative of elevated temperatures. These findings were consistent with the correlation between high-density areas and low magnetic susceptibility values, reinforcing the proposition of increased heat transfer from the Red Sea. Comparative analysis of temperature profiles further confirmed the presence of elevated temperatures in promising zones, emphasizing the geothermal potential associated with heat transfer from the Red Sea.This research contributes to the understanding of the geothermal resources in the Central Eastern Desert and Red Sea region. The results from gravity and magnetic data inversions, combined with temperature profiles, provide valuable information for future geothermal exploration and utilization efforts. The findings underscore the importance of geothermal energy in achieving sustainability and contribute to the global discourse on renewable energy sources.

Turunan Radial dari Anomali Gravitasi untuk Identifikasi Injeksi Air pada Reservoir

Time Lapse micro-gravity or 4D microgravity has been developed and applied for various purposes related to the dynamics change beneath the earth's surface. The principle is a repeated and periodic measurement to determine the change in gravity value at time interval as a yield of the dynamics changes in the density change of the subsurface. This method can be used for monitoring and identify water or gas injections in reservoirs. Mass density taht changes due to gas injection provide changes in the values of gravity over time. This change allows us to identify the dynamics of gas movement in reservoir. A reservoir model has been made in this research with gas injected in reservoir bulk. The time lapse gravity respons value is calculated numerically. Oil-gas contact is an edge between gas injection front with oil which move direction away from injection point. The first and second radial derivatives of 4D gravity can provide as a front of the gas movement in the reservoir. A radial derivatives is a horizontal derivative of gravity anomaly along radial direction from a point which selected as a entre of the anomaly. The second radial derivative is derivative of radial deriative. Radial derivatives value of this model response have range of 20 microGals/m and second radial derivative has a values of 0.05 microGals/m2. Graphics of absolute value of radial derivative and second radial derivative of 4D gravity anomaly seemingly correlated with the oil-gas contact of reservoir models. Radial derivative and second radial derivative has been proven as new available method wich has ability to shows a boundary of a horizontal layer with vertical density contrast. Keywords: Radial derivatives, reservoir, gas injection.

Deformation under a Young Volcanic Covered Area in Southern Garut, Indonesia: Insight from 3D Gravity Modelling

Destructive earthquakes are frequently related to inland active faults. In recent years, a significant number of shallow earthquakes with low magnitude have occurred in southern Garut, West Java, Indonesia. Two earthquakes, with magnitudes of M4.2 and M3.9 in 2016 and 2017, respectively, have caused significant damage and were interpreted as indications of an active fault. We used publicly available gravity data to infer the subsurface structure that may be related to recent seismic activity. We used spectral analysis and filtering techniques for the regional-residual anomaly separation and anomaly enhancement to show the basin structure in the study area. 3D gravity inversion modelling was performed to obtain the subsurface density distribution. The result indicates the sedimentary layers with a density of 2.4 to 2.5 gr/cm3 with an underlying basement with a density of 2.65 gr/cm3. An intra-basin basement high with an NE-SW trend divides the basin into two sub-basins. This local basement high can be associated with a magmatic intrusion body and a series of young volcanic bodies located at the northeastern end of the basin. Our results emphasize a possible strong interaction between the tectonic and magmatic activities in this region.

Superspace worldline formalism approach to quantum gravity: dimensional reduction and holography

Using the ADM formalism, we demonstrate that the Hamiltonian formulation of Quantum Gravity is exactly in the form of a worldline formalism in the superspace. We then show that the Keldysh partition function reduces to the partition function of Euclidean 3D gravity. After discussing the meaning of the time parameter, we show that in the gauge fields formalism, our Keldysh partition function reduces to a generating functional of a 2D conformal field theory. This functional exhibits a minimal time-lapse proportional to the square root of the cosmological constant. From the viewpoint of the Chern–Simons/Liouville correspondence, we calculate the exchange of virtual gravitons between two massive probes from the cosmological boundary.

Asymptotic Weak Gravity Conjecture in M-theory on K3× K3

Abstract The Asymptotic Weak Gravity Conjecture (WGC) has been proposed as a special case of the Tower WGC that probes infinite distances in the moduli space corresponding to weakly coupled gauge regimes. The conjecture has been studied in M-theory on a Calabi–Yau threefold (CY3) with finite volume inducing a 5D effective quantum field theory. In this paper, we extend the scope of the previous study to encompass lower dimensions, particularly we generalize the obtained 5D Asymptotic WGC to the effective field theory (EFT$_{3D}$) coupled to 3D gravity that descends from M-theory compactified on a Calabi–Yau fourfold with an emphasis on $K3\times K3$. We find that the CY4 has three fibration structures labeled as line Type-$\mathbb {T}^{2}$, surface Type-$\mathbb {S}$, and bulk Type-$\mathbb {V}$. The emergent EFT$_{3D}$ is shown to have 2+2 towers of particle states termed as the BPS $\mathcal {T}_{M_{\mathrm{k}}\rightarrow 0}^{\rm{{\small BPS}}}$ and $\mathcal {T}_{M_{\mathrm{k}}\rightarrow \infty }^{\rm{{\small BPS}}}$ as well as the non-BPS $\mathcal {T}_{M_{\mathrm{k}}\rightarrow 0}^{\rm{{\small N-BPS}}}$ and $\mathcal {T}_{M_{\mathrm{k}}\rightarrow \infty }^{\rm{{\small N-BPS}}}$. To ensure the viability of the 3D Asymptotic WGC, we give explicit calculations to thoroughly test the Swampland constraint for both the weakly and strongly gauge coupled regimes. Additional aspects, including the gauge symmetry breaking and duality symmetry, are also investigated.

Rapid mapping of global flood precursors and impacts using novel five-day GRACE solutions

Floods affect communities and ecosystems worldwide, emphasizing the importance of identifying their precursors and enhancing resilience to these events. Here, we calculated Antecedent Total Water Storage (ATWS) anomalies from the new 5-day (5D) Gravity Recovery and Climate Experiment (GRACE) and its Follow-On (GRACE-FO) satellite solutions to enhance the detection of pre-flood and active flood conditions and to map post-flood storage anomalies. The GRACE data were compared with ~ 3300 flood events reported by the Dartmouth Flood Observatory (2002–2021), revealing distinct ATWS precursor signals in 5D solutions, in contrast to the monthly solutions. Specifically, floods caused by saturation-excess runoff—triggered by persistent rainfall, monsoonal patterns, snowmelt, or rain-on-snow events—show detectable ATWS increases 15 to 50 days before and during floods, providing a valuable opportunity to improve flood monitoring. These 5D solutions also facilitate a more rapid mapping of post-flood storage changes to assess flood recovery from tropical cyclones and sub-monthly weather extremes. Our findings show the promising potential of 5D GRACE solutions, which are still in the development phase, for future integration into operational frameworks to enhance flood detection and recovery, facilitating the rapid analysis of storage changes relative to monthly solutions.