Three-dimensional Gravity Models Research Articles

Gravity modeling of ore gabbroids Korsun-Novomirhorod pluton

This work concerned three-dimensional gravity modeling of the Gorodishche gabbro-anorthosite massif located within the Korsun-Novomirgorod pluton of the Ukrainian Shield. A three-dimensional model of the upper crust was created using maps of the anomalous gravitational field at a scale of 1:200 000, taking into account data from seismic methods of various modifications. The differences in the structure of the intrusive complex and its gneisses were reflected in seismic wave fields, allowing us to determine the boundaries of the entire intrusive massif: rapakivi granites and basic rocks. Three-dimensional gravity was modeled to separate these complexes of different densities. This made it possible to identify gabbro-anorthosite bodies with a maximum thickness of 5 km in the upper part of the section, and to study the contacts of the intrusive complex and gneisses. In the process of solving inverse problems, various criteria for local optimization of gravitational field sources were implemented. In the iterative process, three different functionals were calculated. The mean square of the difference between the observed and theoretical fields is F1, the average sum of the moduli of the field difference is the functional F2, and the preliminary logarithm of the parameters is the functional F3. The joint use of functionals makes it possible to reduce various types of noise in the observed potential field data. In the process of research, it was found that the use of functionals of various types in the selection method algorithms is quite advisable. This makes it possible to create new algorithms that improve feasible solutions to the inverse problem, which is necessary for the implementation of additive technologies for the quantitative interpretation of gravity survey data. The constructed model, which takes into account all available a priori information about the density and geometric parameters of anome-forming objects, can be used to obtain additional reliable geological information about gabbro-anarthosite massifs.

Gravity Application to Obtain the Subsurface Structures of Mafid Region, North Nasser Lake, Egypt

This study aims to define structures below the surface of the Mafid Area by using gravity data interpretation. Estimates were made for the contact density contrast and the gravity sources' depths. The source depths and contact locations were estimated using the Euler deconvolution method. Structures with shallow and deep seats were also assessed using power spectrum analysis. The structure at a shallow depth was between 0.032 km and 0.437 km. According to the Euler deconvolution method's outcomes, the basement may be below ground in the area's southernmost portion, and it has grown to between 200 and 300 meters in the area's northernmost portion. Multiple faults affect the region that most trends in the NW-SE, NNW-SSE, E-W, NE-SW, and NNE-SSW directions, according to the structural map that has been interpreted. Three-dimensional gravity modelling shows that the upper surface depth of crystalline rocks (Basement rocks ) ranges from 170 to 374 m.

TECTONIC SCHEME FOR THE AMERASIA BASIN OF THE ARCTIC OCEAN

The tectonic scheme of the Amerasia Basin, as a result of a comprehensive analysis of geological and geophysical data, was created for the first time at 1:2 500 000 scale. The structural framework of the scheme was developed based on the results of basement mapping using reflection seismic sections and its detailing according to potential fields. The results of three-dimensional gravity modeling, presented by Moho depth and consolidated crust thickness calculations were used as basic indicators of the genesis of the crust. Tectonic elements of different ranks and kinematics were identified on seismic sections and traced according to potential fields. The created scheme is the most detailed among the published earlier, it demonstrates the features of the tectonic structure of individual geostructures, their nature and allows us to draw conclusions about the evolution of the Amerasia Basin. The listed issues are discussed in the text of the article.

A Tectonic Scheme for the Amerasia Basin of the Arctic Ocean

A tectonic scheme of the Amerasia Basin was created for the first time on a 1 : 2 500 000 scale on the basis of integrated analysis of geological and geophysical data. The structural framework of the scheme was developed according to the mapping of the basement surface using reflection seismic sections; the surface was detailed on the basis of potential fields. The results of three-dimensional gravity modeling according to calculation of the Moho depths and consolidated earth crust thickness were used as the basic indicators of the origin of the crust. Tectonic elements of different ranks and kinematics were identified on the seismic sections and traced according to the potential fields. The created scheme is the most detailed out of those published previously. It demonstrates the features of the tectonic structure of individual geostructures and their nature and allows us to draw conclusions about the evolution of the Amerasia Basin.

Geophysical data interpretation technologies in the study and exploration of oil-and-gas deposits

The article presents the results of scientific research on the creation of computer technology for the interpretation of geophysical field data in the exploration of oil-and-gas deposits of Ukraine. The theoretical, informational, technological and methodical foundations for increasing the efficiency of geological exploration work due to the in-depth extraction of information from geological and geophysical data based on their complex interpretation within the framework of new mathematical models have been developed. Three-dimensional gravity and magnetometric modeling can be directed to the detection of densification zones and the tracing of tectonic disturbances in the consolidated crust, without which the existence of hydrocarbon transportation channels is impossible. The practical application of examples of quantitative interpretation of three-component magnetic survey data is given, which will significantly help in the detection and localization of hydrocarbon deposits. Development and expansion of the software complex for the interpretation of magnetotelluric data based on the use of impedance-type boundary conditions. The technique is intended for visualization of MTS data at the stage of qualitative interpretation in parallel with the method of the impedance tensor and Wiese vectors. The absolute advantage of this approach is its independence from the condition of a plane incident wave and the use of all six components of the electromagnetic field (including the Z component of the electric component of the MT field). The integration of statistical and deterministic methods during the inversion of geophysical data will increase the re-liability of the obtained geological results. The relevance and importance of the results presented in the work is determined by the conceptual novelty of methods and tools for forecasting new promising areas, as well as the reassessment of reserves of known deposits.

The density of sedimentary complexes of the Carpathian-Pannonian region (generalization)

An extensive analysis of the available information on the density of themain tectonic elements of the Ukrainian Carpathians is given in connection with the need for further construction of a three-dimensional gravity model. The density was studied both from cores of reference, exploration, crelius and deep exploration wells, and from samples taken from numerous outcrops. In the Ukrainian Carpathians, there is a change in the density of rocks depending on the age, lithological composition and depth of occurrence. Local metamorphism plays a significant role in the increase in density. It is shown that in the Bilche-Volitsky Nappe of the Precarpathian Trough, a discontinuous change in the density of clays with increasing depth is more often observed, which is caused not by a static load, but by the geological conditions of the formation of the region: by tectonic processes and a change in sedimentation and denudation processes, which cause residual compaction. According to the analysis of available data, the density of molasse and flysch strata within the Borislav-Pokutsky and Sambir Nappes at depths of 1000 m and more practically does not change, and an increase in the density of Pokuttya rocks is associated with a decrease in the porosity of rocks by 2—5 % and is due to the degree of their metamorphism. Analysis of a large amount of data showed a very complex nature of the density distribution in the Folded Carpathians and its dependence, mainly, on porosity. For different stratigraphic subdivisions of the Skiba Nappe, there is a general tendency to an increase in density with depth (in most cases, unevenly), which is most clearly manifested in the Stryi series of deposits.In the Transcarpathian Trough, the change in density with depth depends on the ratio of clay, tuffogenic and sandy material in the rock. Sedimentary and igneous rocks in the upper part of the section of the Vygurlat-Gutinskaya volcanic ridge are not differentiated in density, which can be explained by the high densities of sedimentary rocks, on the one hand, and a decrease in the density of igneous rocks due to their decompaction, on the other. In the stratigraphic complexes of the Solotvino and Mukachevo Depressions, the density varies over the area. For the first time, based on generalized data on the density of rocks of different age groups of the sedimentary complex for the folded region of the Ukrainian Carpathians, a diagram of the distribution of the average density for each structural-facial zone has been drawn up. An increase in density from north-east to south-west is shown. It is concluded that the density of the Precarpathian and TranscarpathianTroughsis much lower than the density of the rocks of the Folded Carpathians.

Three-dimensional gravity modelling of a Quaternary overdeepening fill in the Bern area of Switzerland discloses two stages of glacial carving

The geometry of glacial overdeepenings on the Swiss Plateau close to Bern was inferred through a combination of gravity data with a 3D gravity modelling software. The target overdeepenings have depths between 155 and > 270 m and widths between 860 and 2400 m. The models show incisions characterized by U-shaped cross-sectional geometries and steep to over-steepened lateral flanks. Existing stratigraphic data reveals that the overdeepenings were formed and then filled during at least two glacial stages, which occurred during the Last Glacial Maximum (LGM) within the Marine Isotope Stage (MIS) 2, and possibly MIS 6 or before. The U-shaped cross-sectional geometries point towards glacial erosion as the main driver for the shaping of the overdeepenings. The combination of the geometries with stratigraphic data suggests that the MIS 6 (or older) glaciers deeply carved the bedrock, whereas the LGM ice sheet only widened the existing valleys but did not further deepen them. We relate this pattern to the different ice thicknesses, where a thicker MIS 6 ice was likely more powerful for wearing down the bedrock than a thinner LGM glacier. Gravity data in combination with forward modelling thus offers robust information on the development of a landscape formed through glaciers.

Density heterogeneity of the Earth’s crust of Ukraine and adjacent territories from three-dimensional gravity modelling

The work was performed to study the density heterogeneity of the crust of Ukraine and adjacent regions analyzing detailed 3D gravity models of the following tectonic regions and separate structures: Dnieper-Donets Basin and Donbas, Ingulsky megablock, Golovanivska suture zone, latitudinal zones of fractures of the Ukrainian Shield, Black Sea megadepression and surrounding areas. The models are constructed on the basis of geological, petrophysical and seismic data along geotravers, DSS profiles, the modern WARR methodsand are calculated using the automated software complex for interpretation of potential fields GMT-Auto. As a result, new information was obtained for the density distribution in the whole Earth’s crust.The density distributions construct for the entire crust of Ukraine and adjacent regions at certain depths (surface of the basement, 10, 20, 30 km, Moho discontinuity). The thickness was determined for conditionally distinguished «granite», «diorite», «basalt» layers of the Earth’s crust and crust-mantle mixture within the whole region of the study. Its values are graphically represented by isolines on the respective schematical maps. The resulting density inhomogeneity became the basis for constructing, for the first time in a three-dimensional version, a scheme for the predictive composition of the Earth’s crust with typification according to the power ratios of its constituent layers. The heterogeneity of the present-day consolidated crust of the whole study area is characterized by granitic, granitic-dioritic, dioritic and basaltoid types. To clearly identify the dismemberment of the lower layer of the crust which is considered inseparable by the classification of the DSS method the basaltoid type is divided into 3 subtypes. The subtype 1 with a content of 40—70 % of basalt, subtype 2, where concent-ration of basalt increases to 70—90 % and subtype 3, which is composed only of basalt.It has been established that the basicity of the Earth’s crust of the USh changes from west to east, respectively, from basalt to diorite type. Decrease in crustal basicity is also observed in suture zones, namely from diorite and basaltoid typein Golovanivskii suture to basaltoid and diorite type in the Inguletsko-Kryvorizckii suture and diorite type in the Orikhivsko-Pavlogradskii suture. In the DDB the crustal basicity increases from northwest to southeast in accordance with the segmentation of this feature. The basaltoid type of the crust is predominant in the Black Sea megadepression and adjacent territories. For the first time, a type of crust was identified that does not coincide with the known ones and is characterized by the presence in the section of the «basalt» and «granite» layers (with a zero or very low «diorite» thickness). A similar type of bark is present in the Ingul megablock of the USh, in the northern side zone of the DDB, as well as in the Black Sea megadepression.

Structure, Rheology, Petrology, and Geodynamics of the Tectonosphere of the Sea of Japan

The geological-structural, magmatic, seismic, and thermometric models of the Earth’s crust and upper mantle of the Sea of Japan region are considered in relation to three-dimensional rheological gravity models reflected in horizontal and vertical sections of density contrast of the tectonosphere. In the crust and the upper mantle, formal manifestations of a right-lateral strike-slip duplex were found, in association with rift-related extension zones and central vortex structures. In the central regions of the Sea of Japan, a mushroomlike low-viscosity zone of typical of plumes is mapped in the depth interval of 60–200 km. The gravity models show signs of Late Cretaceous subduction of the Pacific Plate under the continental margin and Eocene–Oligocene subduction of this plate under the Japanese island arc. The Pacific lithosphere is split into crustal and lower lithospheric plates. The depth and thickness of rigid crustal and lithospheric plates have been estimated, faults of which are observed in rift-related extension zones. Petrochemical analysis of volcanic rocks dredged from the floor of the Sea of Japan confirms the existence of two extension stages, accompanied by volcanism of an initially postsubduction (ACMB), then spreading (N-MORB) and postspreading plume (OIB) nature.

A tutorial and open source software for the efficient evaluation of gravity and magnetic kernels

Fast computation of three-dimensional gravity and magnetic forward models is considered. When the measurement data is assumed to be obtained on a uniform grid which is staggered with respect to the discretization of the parameter volume, the resulting kernel sensitivity matrices exhibit block-Toeplitz–Toeplitz-block (BTTB) structure. These matrices are symmetric for the gravity problem but unsymmetric for the magnetic problem. In each case, the structure facilitates fast forward computation using two-dimensional fast Fourier transforms. The construction of the kernel matrices and the application of the transform for fast forward multiplication, for each problem, is carefully described. But, for purposes of comparison with the non-transform approach, the generation of the unique entries that define a given kernel matrix is also explained. It is also demonstrated how the matrices, and hence transforms, are adjusted when padding around the volume domain is introduced. The transform algorithms for fast forward matrix multiplication with the sensitivity matrix and its transpose, without the direct construction of the relevant matrices, are presented. Numerical experiments demonstrate the significant reduction in computation time and memory requirements that are achieved using the transform implementation. Thus, it becomes feasible, both in terms of reduced memory requirements and computational time, to implement the transform algorithms for large three-dimensional volumes. All presented algorithms, including with variable padding, are coded for optimal memory, storage and computation as an open source Matlab code which can be adapted for any convolution kernel which generates a BTTB matrix, whether or not it is symmetric. This work, therefore, provides a general tool for the efficient simulation of gravity and magnetic field data, as well as any formulation which admits a sensitivity matrix with the required structure.

Density inhomogeneity of the Earth’s crust of the Black Sea and adjacent territories from three dimensional gravity modelling. Part II. Density sections

To obtain a more complete picture of the deep structure and density heterogeneity of the main tectonic structures of the Black Sea megadepression and adjacent territories, density sections were constructed that intersect structures along geotraverses, DPS profiles and illustration profiles. Based on the results of three-dimensional gravity modelling, the Scythian plate has a block structure, more complex than the East European platform. It is also characterized by a thick layer of deformed sediments, with the largest compaction of the crust is being in its western and southern parts. The pre-Dobrudzha Trough consists of two parts: the denser one, which adjoins the Serpentine Rise, and the less dense one, adjacent to Zmeiny Uplift. The Karkinitsky Trough is characterized by compaction of the middle and lower parts of the Earth's crust in the south and west, that is associated with tectonic processes during riftogenesis, namely, the introduction of mantle matter into the lower and middle parts of the Earth's crust. There is no «granite» layer under the Black Sea-Kalamitsky Swell, the «basalt» layer is represented by a crust-mantle mixture. The deep domain of the Indolo-Kuban Trough is divided into two blocks along the axis: denser (south, west and southwest) and less dense (northeast, east and north). In Crimea, in all density sections a thick layer of dislocated sediments is observed, the crystalline crust is characterized by significant compaction (especially the southern part), the absence of a «granite» layer, the occurrence of the subsurface «basalt» layer and the presence of the thick crust-mantle mixture. The West Black Sea Depression is characterized by the absence of a granite layer in the central part, the occurrence of sediments on the «basalt» (and sometimes on the «diorite») layer. In this case, the crust is of the oceanic type. In the East Black Sea basin there is a thin layer of dislocated deposits with a density close to the density of crystalline rocks. According to the density value, this layer can be attributed to very compact dislocated deposits that suggests the oceanic or rifted continental crust. The crystalline crust of the Central Black Sea Rise is heterogeneous in composition and structure. The Andrusov and Arkhangelsk Ridges, which echelonedly displaced to each other, have different density characteristics of the crystalline crust, the depth of its bottom and density on it. Collectively, these features give evidence of the heterogeneous history of the formation and development of these structures. The Sinop Depression is a large Neogene graben which is underlain by a crust-mantle mixture of different thickness. The Sorokin Basin is characterized by an increased thickness of the sedimentary cover, the absence of a «granite» layer and a rise in the roof of the «diorite» layer to a depth of 2―3 km in the eastern part, as well as the presence of a «granite» layer with a thickness of over 10 km in the western. The northwestern part of the Shatsky Uplift is characterized by decompression of the entire Earth's crust, and in the southeastern part, decompression is observed only in the middle part of the section.

Analysis of tourism demand using a multi-dimensional panel gravity model

PurposeThis study aims to estimate the determinants of international tourist flows between destinations by using the panel gravity model.Design/methodology/approachThe multi-dimensional panel gravity model was used to analyse tourism originating from 30 different countries to the 14 most-visited countries in the world between 2008 and 2016. Income (i.e. per capita gross domestic product for both the origin and destination countries), distance between countries, various economic indicators and six dummy variables were added to the gravity model as control variables.FindingsThe results indicated that tourist arrivals depended mainly on economic factors, i.e. income and trade variables were significant determinants of tourist arrivals. The results also suggested that estimated international tourist flows are a negative function of distance, as is postulated in economic theory.Originality/valueIn recent years, gravity models have been used frequently to analyse international tourism demand and have demonstrated their ability to evaluate the effects of various determinants of international tourism for many countries. The literature includes studies that used a two-dimensional panel gravity model to analyse the determinants of tourism demand to a single country from many different countries. This study differs in terms of specificity; in that, it relied on a three-dimensional panel gravity model that allowed for modelling of multiple destination countries. As a result, more comprehensive and general results relative to the determinants of tourism demand were obtained. In addition, the application of a non-nested three-dimensional panel data model, which has limited use, contributes a new perspective to the econometric literature.

Density heterogeneity of the Earth’s crust of the Black Sea megadepression and adjacent territories from three-dimensional gravity modelling. 1. Regional density distribution at different depths.

This paper presents a comprehensive analytical review of the various approaches to the gravity modelling of the Earth’s crust of the Black Sea and adjacent territories. It is shown that even in using the same thickness of sedimentary layers whose total gravitational effect makes a considerable contribution to the observed field the results of different authors do not coincide and in some cases contradict each other. The reason is that every researcher uses ad hoc reference density and a method of reducing the calculated curves. Therefore, an unified three-dimensional density model of this region was first developed that significantly increased the reliability of the geological interpretation of the modelling results. In additional the spatial distribution of density was first used for the Maykop Series, the Eocene- Pliocene, and Cretaceous deposits that allowed us to obtain principally new data on the heterogeneous structure of the main horizons of the sedimentary cover. An analysis of the density distribution of the consolidated crust revealed anomalously weakened and compacted areas in the shelf zones. A pattern was constructed for the distribution and depth to the basement of dislocated sediments. The density of rocks was also calculated on this surface. The granitic, granitic-diorite, dioritic and basaltoid types of the crust were identified that for the first time made it possible to delineate the areas of different composition in the present - day consolidated crust of the entire study region. A decrease in crustal basicity was unveiled in the direction from the deep-water basins to the northwestern, western, and southern offshore zones. On the shelf local density inhomogeneities were at the base of the basalt layer, which are indicators for penetration of basic and ultrabasic intrusions into the crust.

Co-seismic grace gravity-based 11-layered 3-D thrust fault model for the Sumatra earthquake 2004

Our co-seismic Gravity Recovery and Climate Experiment gravity data (level 2 ‘RL_05’ data product ‘GX-OG-_2-GSM) for the Sumatra earthquake 2004 is obtained by differencing monthly gravity field average for November 2004 from that of January 2005 and band-pass filtering (\(17{-}30^{\circ }\) and orders) in the spectral domain. Here, we propose a 11-layered three-dimensional (3-D) thrust fault gravity model based on different co-seismic rupture models in the literature. It honours co-seismic deformation of the ocean surface, ocean bottom and subsurface earth medium, different earthquake parameters and hypocentre information (\({\sim }35\) km below mean sea level). Our forward gravity response matches well with the observed gravity (RMS error of \(0.06257\,\upmu \hbox {gal}\) (6.26%)) data and our model allowed an independent computation of rupture length, instantaneous velocity, average seismic moment and momentum, which are, respectively, 1560 km, 2.9 km/s, \(4.53\times 10^{22 }\,\hbox {N}\,\hbox {m}\) and \( 9.7\times 10^{17}\,\hbox {kg}\,\hbox {m/s}\). These parameters fairly agree with those in the literature. The computed momentum indeed corresponds to an area pulse (\(9.7\times 10^{17}\,\hbox {kg}\,\hbox {m/s}\)) at ocean bottom that led to a tsunami generation. Thus, the proposed multi-layered 3-D gravity model in traditional fashion fully accounts for co-seismic gravity signal of the Sumatra earthquake 2004.

Defining potentials and barriers to trade in the Malaysia–Chile partnership

PurposeThe purpose of this paper is to investigate the potentials and barriers to trade in the Malaysia–Chile partnership.Design/methodology/approachThis paper estimates two-way export potentials from an augmented three-dimensional panel gravity model of bilateral trade between Malaysia and the Latin America and the Caribbean (LAC) region, spanning the 1990–2014 period. Utilizing interviews with government officials and industry experts in Malaysia and Chile, this paper also provides insights into market access issues.FindingsThe empirical findings of this study suggest that Malaysia has trade potential in Chile, but Chile is “overtrading” with Malaysia. By major products traded, both countries are found to be “overtrading,” as the export basket remains concentrated in this partnership. Through the interviews, fewer restrictions are reported by the various stakeholders, as the extent of trade engagement remains somewhat low. The main challenge identified within specific sectors in both the countries relates mainly to procedures established to secure compliance with labeling regulations for food products.Research limitations/implicationsThe sectoral findings reveal that there is indeed scope for expanding exports beyond the current major products traded, particularly in base metal and scientific and measuring equipment from the Malaysia and Chile perspectives, respectively. Thus, product diversification matters to intensify trade cooperation between the two countries. Non-tariff measures need to be streamlined by both parties to ensure further product diversification to food trade, particularly for Chile.Originality/valueThe limited literature on cross-regional trade within the broader framework of Southeast Asia and LAC only support the fact that potentials do exist but do not appear to provide much research evidence. Empirically, this paper will add to the existing literature on the potentials that hold in the Malaysia–Chile partnership. Further, a lack of adequate information remains on market access and other barriers in both the nations to facilitate decisions on trade opportunities. The findings of the study fill that vacuum of information pertaining to market access and trade facilitation through interviews with various stakeholders in Malaysia and Chile.

Gravity contribution to the geological study of grabens in the northwest region of Tunisia including the Kef Basin region

The northern Atlas region of Tunisia is characterized by northeast-trending compressional structures that affected the extensionally formed Late Permian to Mid Cretaceous Tunisian Trough. More recently, Late Cenozoic extensional forces have formed a series of northwest-trending grabens whose origins are partially controlled by geologic structures formed since the Late Permian. In order to aid in determining how these grabens were formed, a detailed gravity analysis was conducted in the western region of the Tunisian Trough. The gravity analysis included the construction of a residual gravity field using wavelength filtering which was further analyzed using derivatives, Euler deconvolution and three-dimensional modeling. The resulting residual gravity anomaly field consists of a series of short wavelength maxima that are mainly related to anticlinal structures and minima related to sediment-filled grabens. To better define the structure of the basins, three-dimensional (3D) gravity models were constructed, where the grabens were found to be approximately 3–5 km in thickness and mainly bounded by normal faults and underlain by low density Triassic evaporites. This evaporitic layer was not underlying the entire study area but only in the vicinity of the grabens. In particular, the Kef Basin region was found to be two separate grabens, the Kef and the Ksour located southeast of the Kef graben. The Kef graben has a maximum thickness of 3–4 km while the wider Ksour graben is between 4 and 5 km thick. The gravity analysis cannot determine exact origin of the grabens but extension is the most plausible cause of the grabens with strike-slip motion may have played a role in the formation of the Ksour graben if not the other grabens. The location of the grabens was controlled by the lateral extent of the Triassic evaporates which provided the rheological weakness to initiate the grabens.

Quasi-local holographic dualities in non-perturbative 3d quantum gravity II – From coherent quantum boundaries to BMS3 characters

We analyze the partition function of three-dimensional quantum gravity on the twisted solid torus and the ensuing dual field theory. The setting is that of a non-perturbative model of three-dimensional quantum gravity, the Ponzano–Regge model, which is here reviewed in a self-contained manner and then used to compute quasi-local amplitudes for its boundary states. In this second paper of the series, we choose a particular class of boundary spin network states which impose Gibbons–Hawking–York boundary conditions to the partition function. The peculiarity of these states is to encode a two-dimensional quantum geometry peaked around a classical quadrangulation of the finite toroidal boundary. Thanks to the topological properties of three-dimensional gravity, the theory easily projects onto the boundary while crucially still keeping track of the topological properties of the bulk. This produces, at the non-perturbative level, a specific non-linear sigma-model on the boundary, akin to a Wess–Zumino–Novikov–Witten model, whose classical equations of motion can be used to reconstruct different bulk geometries: the expected classical one is accompanied by other “quantum” solutions. The classical regime of the sigma-model becomes reliable in the limit of large boundary spins, which coincides with the semi-classical limit of the boundary geometry. In a 1-loop approximation around the solutions to the classical equations of motion, we recover (with corrections due to the non-classical bulk geometries) results obtained in the past via perturbative quantum General Relativity and through the study of characters of the BMS3 group. The exposition is meant to be completely self-contained.

Non-geometric Kaluza-Klein monopoles and magnetic duals of M-theory R-flux backgrounds

We introduce a magnetic analogue of the seven-dimensional nonassociative octonionic R-flux algebra that describes the phase space of M2-branes in four-dimensional locally non-geometric M-theory backgrounds. We show that these two algebras are related by a Spin(7) automorphism of the 3-algebra that provides a covariant description of the eight-dimensional M-theory phase space. We argue that this algebra also underlies the phase space of electrons probing a smeared magnetic monopole in quantum gravity by showing that upon appropriate contractions, the algebra reduces to the noncommutative algebra of a spin foam model of three-dimensional quantum gravity, or to the nonassociative algebra of electrons in a background of uniform magnetic charge. We realise this set-up in M-theory as M-waves probing a delocalised Kaluza-Klein monopole, and show that this system also has a seven-dimensional phase space. We suggest that the smeared Kaluza-Klein monopole is non-geometric because it cannot be described by a local metric. This is the magnetic analogue of the local non-geometry of the R-flux background and arises because the smeared Kaluza-Klein monopole is described by a U(1)-gerbe rather than a U(1)-fibration.

Density heterogeneity of the Earth’s crust of the Ingul megablock of the Ukrainian Shield according to the data of three-dimensional gravity modeling

Density heterogeneity of the Earth’s crust of the Ingul megablock of the Ukrainian Shield according to the data of three-dimensional gravity modeling

Three-dimensional gravity modelling applied to the exploration of uranium unconformity-related basement-hosted deposits: the Contact prospect case study, Kiggavik, northeast Thelon region (Nunavut, Canada)

In unconformity-related uranium deposits, mineralization is associated with hydrothermal clay-rich alteration haloes that decrease the density of the host rock. In the Kiggavik uranium project, located in the eastern Thelon Basin, Nunavut (Canada), basement-hosted shallow deposits were discovered by drilling geophysical anomalies in the 1970s. In 2014, gravity data were inverted for the first time using the Geosoft VOXI Earth ModellingTM system to generate three-dimensional (3D) models to assist exploration in the Contact prospect, the most recent discovery at Kiggavik. A 3D unconstrained inversion model was calculated before drilling, and a model constrained by petrophysical data was computed after drilling. The unconstrained inversion provided a first approximation of the geometry and depth of a low-density body and helped to collar the discovery holes of the Contact mineralization. The constrained inversion was computed using density values measured on 315 core samples collected from 21 drill holes completed between 2014 and 2015. The constrained modelling highlights three shallower and smaller low-density bodies that match the geological interpretation and refines the footprint of the gravity anomalies in relation to the current understanding of the deposit. The 3D inversion of gravity data is a valuable tool to guide geologists in exploration of shallow basement-hosted uranium deposits associated with alteration haloes and to assess the deposit gravity geometry.