Tensor Gravity Research Articles

A new method of edge detection based on the total horizontal derivative and the modulus of full tensor gravity gradient

With the rapid development of gravity gradient measurement, the full tensor gravity gradient data has been used more and more frequently in the edge detection. This article focuses on the problem that the effect of edge detection of deep geological body is not clear and false edges among positive and negative anomalies using the common edge detection method. We present a new edge detection method which is based on the total horizontal derivative and the modulus of full tensor gravity gradient. Comparing with the model experiments, it is proved that this method is clearer and more accurate in detecting the edges of geological body especially for the deep model with almost no false edge interference. Finally, the method is applied to the processing of the actual data in St. Georges Bay, Canada, and the edge results are satisfying.

Tensor Galileons and gravity

The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian p-forms. In this work we introduce an index-free formulation of these interactions in terms of two sets of Grassmannian variables. We employ this to construct Galileon interactions for mixed-symmetry tensor fields and coupled systems thereof. We argue that these tensors are the natural generalization of scalars with Galileon symmetry, similar to p-forms and scalars with a shift-symmetry. The simplest case corresponds to linearised gravity with Lovelock invariants, relating the Galileon symmetry to diffeomorphisms. Finally, we examine the coupling of a mixed-symmetry tensor to gravity, and demonstrate in an explicit example that the inclusion of appropriate counterterms retains second order field equations.

Exact scalar–tensor cosmological models

Scalar–tensor gravitational theories are important extensions of standard general relativity, which can explain both the initial inflationary evolution, as well as the late accelerating expansion of the universe. In the present paper, we investigate the cosmological solution of a scalar–tensor gravitational theory, in which the scalar field [Formula: see text] couples to the geometry via an arbitrary function [Formula: see text]. The kinetic energy of the scalar field as well as its self-interaction potential [Formula: see text] are also included in the gravitational action. By using a standard mathematical procedure, the Lie group approach, and Noether symmetry techniques, we obtain several exact solutions of the gravitational field equations describing the time evolutions of a flat Friedman–Robertson–Walker universe in the framework of the scalar–tensor gravity. The obtained solutions can describe both accelerating and decelerating phases during the cosmological expansion of the universe.

Технология определения параметров гравитационного поля Земли по градиентометрическим измерениям. 5. Вычисление производных от компонент тензора градиента геопотенциала по уточняемым гармоническим коэффициентам

Технология определения параметров гравитационного поля Земли по градиентометрическим измерениям. 5. Вычисление производных от компонент тензора градиента геопотенциала по уточняемым гармоническим коэффициентам

A new source parameters estimation method of airborne gravity gradient tensor data

One of the important tasks of potential field interpretation is source parameters estimation of the geological structures, including the horizontal position and buried depth. A new method to interpret airborne gravity tensor data is proposed in this paper based on Normalized Downward Continuation (NDC) of the tensor data directional total horizontal derivatives. The NDC method was introduced for source depth estimation, which can be applied to analytical signal modulus and potential fields themselves. And the maxima of the NDC map mainly correspond to the centre location of the geologic source. We applied the NDC method to the directional total horizontal derivatives which can be used for delineating the sources’ horizontal edges. The maximum values of the result indicate the source edges horizontal position and buried depth simultaneously. During the calculation, the iteration method of the downward continuation is used in the NDC calculation process to improve the stability. The new method was tested on synthetic models and obtained satisfactory results. Compared with previous work, this new approach has a better lateral resolution.

The 3D Resolution Power of the Full Tensor Gravity Gradient

Airborne gravity tensor (or gravity gradient) surveying is one of the newest techniques for geophysical exploration. The rise in the acquisition of this data type is partially due to the fact that these data provide much more complete, extensive and higher resolution information of rock density distribution than conventional land gravity data. This has positioned Airborne Gravity Gradient (AGG) surveys among the geophysical services requested by mining companies, alongside aeromagnetic and radiometric surveys. The use of these data has been primarily to support geological mapping given the limited access to commercial software for quantitative depth interpretation. In particular, there has been a scarce development of AGG data inversion software, which has limited our understanding of the significance of these data for resolving three-dimensional subsurface targets. In this work we hypothesize that AGG data can provide more detailed information of the multidirectional variations of subsurface density. To prove this hypothesis, we developed conjugate gradient AGG-data inversion software for three-dimensional targets. This software was applied to synthetic data generated by several test assemblages of three-dimensional bodies and used to perform a Singular Value Decomposition (SVD) sensitive analysis to explore the actual resolution power of the different tensor data components and whether they are indeed superior to the conventional vertical gravity.

On the approximation of the potential fields when using right rectangular prisms

ABSTRACTDue to its simplicity, stability, and efficiency, the use of right rectangular prisms is still widespread for potential field modelling and inversion. It is well known that modelling the subsurface with Cartesian grids has important consequences in terms of accuracy of the results. In this paper, we review the main issues that geophysicists face in day‐to‐day work when trying to use right rectangular prisms for performing gravity or full tensor gravity modelling and inversions. We demonstrate the results both theoretically and through Monte Carlo simulations, also exploiting concepts from fractal geometry. We believe that the guidelines contained in this paper may suggest a good practice for the day‐to‐day work of geophysicists dealing with gravity and full tensor gravity data.

USING THE ANALYTIC SIGNAL METHOD OF GRAVITY GRADIENT TENSOR (GGT) TO DETERMINE THE LOCATION AND DEPTH OF THE FAULTS IN THE PRE-CENOZOIC BASEMENT ROCKS OF THE RED RIVER TROUGH

USING THE ANALYTIC SIGNAL METHOD OF GRAVITY GRADIENT TENSOR (GGT) TO DETERMINE THE LOCATION AND DEPTH OF THE FAULTS IN THE PRE-CENOZOIC BASEMENT ROCKS OF THE RED RIVER TROUGH

Numerical relativity and high energy physics: Recent developments

We review recent progress in the application of numerical relativity techniques to astrophysics and high-energy physics. We focus on recent developments regarding the spin evolution in black hole binaries, high-energy black hole collisions, compact object solutions in scalar–tensor gravity, superradiant instabilities, hairy black hole solutions in Einstein’s gravity coupled to fundamental fields, and the possibility to gain insight into these phenomena using analog gravity models.

Joint inversion of gravity and multiple components of tensor gravity data

Geological structures often exhibit smooth characteristics away from sharp discontinuities. One aim of geophysical inversion is to recover information about the smooth structures as well as about the sharp discontinuities. Because no specific operator can provide a perfect sparse representation of complicated geological models, hyper-parameter regularization inversion based on the iterative split Bregman method was used to recover the features of both smooth and sharp geological structures. A novel preconditioned matrix was proposed, which counteracted the natural decay of the sensitivity matrix and its inverse matrix was calculated easily. Application of the algorithm to synthetic data produces density models that are good representations of the designed models. The results show that the algorithm proposed is feasible and effective.

Advantages of horizontal directional Theta method to detect the edges of full tensor gravity gradient data

Full tensor gravity gradient data contain nine signal components. They include higher frequency signals than traditional gravity data, which can extract the small-scale features of the sources. Edge detection has played an important role in the interpretation of potential-field data. There are many methods that have been proposed to detect and enhance the edges of geological bodies based on horizontal and vertical derivatives of potential-field data. In order to make full use of all the measured gradient components, we need to develop a new edge detector to process the full tensor gravity gradient data. We first define the directional Theta and use the horizontal directional Theta to define a new edge detector. This method was tested on synthetic and real full tensor gravity gradient data to validate its feasibility. Compared the results with other balanced detectors, the new detector can effectively delineate the edges and does not produce any additional false edges.

Stress tensor correlators in three dimensional gravity

We calculate holographically arbitrary n-point correlators of the boundary stress tensor in three-dimensional Einstein gravity with negative or vanishing cosmological constant. We provide explicit expressions up to 5-point (connected) correlators and show consistency with the Galilean conformal field theory Ward identities and recursion relations of correlators, which we derive. This provides a novel check of flat space holography in three dimensions.

3D inversion of full gravity gradient tensor data using SL0 sparse recovery

We present a new method dedicated to the interpretation of full gravity gradient tensor data, based on SL0 sparse recovery inversion. The SL0 sparse recovery method aims to find out the minimum value of the objective function to fit the data function and to solve the non-zero solution to the objective function. Based on continuous iteration, we can easily obtain the final global minimum (namely the property and space attribute of the inversion target). We consider which type of tensor data combination produces the best inversion results based on the inversion results of different full gravity gradient tensor data combinations (separate tensor data and combined tensor data). We compare the recovered models obtained by inverting the different combinations of different gravity gradient tensor components to understand how different component combinations contribute to the resolution of the recovered model. Based on the comparison between the SL0 sparse recovery inversion results and the smoothest and focusing inversion results of the full gravity gradient tensor data, we show that SL0 sparse recovery inversion can obtain more stable and efficient inversion results with relatively sharp edge information, and that this method can also produce a stable solution of the inverse problem for complex geological structures. This new method to resolve very large full gravity gradient tensor datasets has the considerable advantage of being highly efficient; the full gravity gradient tensor inversion requires very little time. This new method is very effective in explaining the full gravity tensor which is very sensitive to small changes in local anomaly. The numerical simulation and inversion results of the compositional model indicates that including multiple components for inversion increases the resolution of the recovered density model and improves the structure delineation. We apply our inversion method to invert the gravity gradient tensor survey data from the Vinton salt dome, Louisiana. The results of inversion are in good agreement with the known formation in the region, which supports the validity of our method.

Feasibility and Limitations of Void Detection Using Gravity Gradiometry

Detecting and characterizing near-surface voids is a long-standing problem in near-surface geophysics primarily because of the low signal-to-noise ratio due to the typically small sizes of these targets. Anticipated advances in gravity gradiometry instrumentation and data acquisition may provide the improved resolution required to address these targets. In this paper, we investigate void detection using simulated full tensor gravity gradiometry data. We show through numerical simulations that low-altitude gravity gradiometry can observe signals from voids well above the modern instrument noise level. We develop a practical detection algorithm to determine the tunnel orientation and its location in the subsurface. The algorithm first finds the tunnel orientation through a tensor rotation and then solves for the tunnel location in the subsurface based on the directional vectors obtained from the rotated tensor data. We use this algorithm to study the feasibility and limitations of the gravity gradiometry technique in void detection. We conclude that the method can be effective in many practical scenarios.

Conformal gravity and “gravitational bubbles”

We describe the general structure of the spherically symmetric solutions in the Weyl conformal gravity. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions, consisting of two classes, is found. The first one contains the solutions with constant two-dimensional curvature scalar, and the representatives are the famous Robertson–Walker metrics. We called one of them the “gravitational bubbles”, which is compact and with zero Weyl tensor. These “gravitational bubbles” are the pure vacuum curved space-times (without any material sources, including the cosmological constant), which are absolutely impossible in General Relativity. This phenomenon makes it easier to create the universe from “nothing”. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family, which can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We describe the general structure of the energy-momentum tensor in the spherical conformal gravity and construct the vectorial equation that reveals clearly some features of non-vacuum solutions.

Fourier forward modeling of vector and tensor gravity fields due to prismatic bodies with variable density contrast

Prismatic bodies with variable density contrasts are very useful in modeling and inversion of gravity anomalies for sedimentary basins, in which some simple mathematical functions offer better approximations for the density-depth relationship of the basin fill than a constant density model. We have explored Fourier-domain modeling of vector and tensor gravity anomalies due to 2D and 3D prismatic bodies following a wide class of variable density functions. We placed the emphasis on general polynomial models because they provided a flexible way to approximate arbitrary density functions. The recently proposed Gauss-fast Fourier transform method was applied to improve the accuracy of inverse Fourier transform. The numerical performance of the presented method was examined by comparing with space-domain analytical, seminumerical, or completely numerical solutions. Singularity and numerical stability of the algorithm were also analyzed with ranges of numerical stability for polynomial density models of different orders specified. Truncation errors of Fourier forward methods were estimated quantitatively using relevant model parameters, and the behavior was observed through theoretical analysis and model tests. Synthetic models, of 2D and 3D prisms with variable density contrasts, found the accuracy, efficiency, and flexibility of the method. We also interpreted a real data example of the gravity profile across the San Jacinto graben.

Spherically symmetric conformal gravity and ``gravitational bubbles''

The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson-Walker metrics. One of them we called the ``gravitational bubbles'', which is compact and with zero Weyl tensor. Thus, we obtained the pure vacuum curved space-times (without any material sources, including the cosmological constant) what is absolutely impossible in General Relativity. Such a phenomenon makes it easier to create the universe from ``nothing''. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly some features of non-vacuum solutions. Two of them are explicitly written, namely, the metrics à la Vaidya, and the electrovacuum space-time metrics.

Quasilocal energy in modified gravity

A new generalization of the Hawking–Hayward quasilocal energy to scalar–tensor gravity is proposed without assuming symmetries, asymptotic flatness, or special spacetime metrics. The procedure followed is simple but powerful and consists of writing the scalar–tensor field equations as effective Einstein equations and then applying the standard definition of quasilocal mass. An alternative procedure using the Einstein frame representation leads to the same result in vacuo.

Three-dimensional geology from potential field geophysics: Applications to Bathurst Mining Camp, Eastern Canada

SUMMARY Interpretation methods and tools for geophysics datasets continue to evolve. Advances in clustering algorithms, the use of implicit functions to create 3D surfaces, new algorithms to estimate source depths and dips, and the availability of clever computational geometry libraries, contribute to the discipline of potential field interpretation techniques, allowing for a much more explicit statement of implied 3D description. While traditional scalar measures of potential fields have benefited from applying new ideas, perhaps more exciting is the reduction in ambiguity imposed from gradient measurement when used as the basis for field interpretation. Full tensor gravity gradiometry in particular, allows for 2D fault dip and throw calculations. Direct detection of high density bodies and faults via state-of-the-art gravity gradiometry is now a reality. Bodies greater than 200m in lateral extent are detectable. Implicit 3D structural geology modelling techniques derived from gravity curvature attributes of the observed gravity field present a leading edge technique for defining structurally controlled near surface geology geometry. A demonstration from the Bathurst camp dataset is given.

Kaluza–Klein reduction and Bergmann–Wagoner bi-scalar general action of scalar–tensor gravity

We examine the Kaluza–Klein (KK) dimensional reduction from higher dimensional space-time and the properties of the resultant Bergmann–Wagoner general action of scalar–tensor theories. With the analysis of the perturbations, we also investigate the stability of the anti-de Sitter (AdS) space-time in the (D ∈ 𝒩)-dimensional Einstein gravity with the negative cosmological constant. Furthermore, we derive the conditions for the dimensional reduction to successfully be executed and present the KK compactification mechanism.