Full Tensor Gravity Research Articles

Large Airborne Full Tensor Gradient Data Inversion Based on a Non-Monotone Gradient Method

Following the development of gravity gradiometer instrument technology, the full tensor gravity (FTG) data can be acquired on airborne and marine platforms. Large-scale geophysical data can be obtained using these methods, making such data sets a number of the “big data” category. Therefore, a fast and effective inversion method is developed to solve the large-scale FTG data inversion problem. Many algorithms are available to accelerate the FTG data inversion, such as conjugate gradient method. However, the conventional conjugate gradient method takes a long time to complete data processing. Thus, a fast and effective iterative algorithm is necessary to improve the utilization of FTG data. Generally, inversion processing is formulated by incorporating regularizing constraints, followed by the introduction of a non-monotone gradient-descent method to accelerate the convergence rate of FTG data inversion. Compared with the conventional gradient method, the steepest descent gradient algorithm, and the conjugate gradient algorithm, there are clear advantages of the non-monotone iterative gradient-descent algorithm. Simulated and field FTG data were applied to show the application value of this new fast inversion method.

Adaptive multinary inversion of gravity and gravity gradiometry data

We have developed a novel approach for inversion of gravity and gravity gradiometry data based on multinary transformation of the model parameters. This concept is a generalization of binary density inversion to the models described by any number of discrete model parameters. The multinary inversion makes it possible to explicitly exploit the sharp contrasts of the density between the host media and anomalous targets in the inversion of gravity and gravity gradiometry data. In the framework of the multinary inversion method, we use the given values of density and error functions to transform the density distribution into the desired step-function distribution. To accommodate a possible deviation of the densities from the fixed discrete values, we develop an adaptive technique for selecting the corresponding standard deviations, guided by the inversion process. The novel adaptive multinary inversion algorithm is demonstrated to be effective in determining the shape, location, and densities of the anomalous targets. We find that this method can be effectively applied for the inversion of the full tensor gravity gradiometry (FTG) data computer simulated for the SEG salt density model and for the field FTG data collected in the Nordkapp Basin, Barents Sea.

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.

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.

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.

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.

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.

Full tensor gravity gradiometry data inversion: Performance analysis of parallel computing algorithms

We apply reweighted inversion focusing to full tensor gravity gradiometry data using message-passing interface (MPI) and compute unified device architecture (CUDA) parallel computing algorithms, and then combine MPI with CUDA to formulate a hybrid algorithm. Parallel computing performance metrics are introduced to analyze and compare the performance of the algorithms. We summarize the rules for the performance evaluation of parallel algorithms. We use model and real data from the Vinton salt dome to test the algorithms. We find good match between model and real density data, and verify the high efficiency and feasibility of parallel computing algorithms in the inversion of full tensor gravity gradiometry data.

Fast Density Inversion Solution for Full Tensor Gravity Gradiometry Data

We modify the classical preconditioned conjugate gradient method for full tensor gravity gradiometry data. The resulting parallelized algorithm is implemented on a cluster to achieve rapid density inversions for various scenarios, overcoming the problems of computation time and memory requirements caused by too many iterations. The proposed approach is mainly based on parallel programming using the Message Passing Interface, supplemented by Open Multi-Processing. Our implementation is efficient and scalable, enabling its use with large-scale data. We consider two synthetic models and real survey data from Vinton Dome, US, and demonstrate that our solutions are reliable and feasible.

Depth Estimation Method Based on the Ratio of Gravity and Full Tensor Gradient Invariant

In this paper, I present a new depth estimation method based on the ratio of gravity and full tensor gradient invariant. The new approach is designed to be stably and quickly interpret the gravity data and full tensor gravity data. First, we deduce two simple calculation equations using the particular models (sphere and horizontal cylinder model). The depths of the particular sources can be directly calculated using the simple equations. However, a shape factor similar to the structural index of Euler deconvolution is contained in the simple calculation equations. It directly relates to the accuracy of calculation depth. To calculate the depth of source accurately, the shape factor must be determined first. Thus, the application of the simple equations is very circumscribed. To overcome the limitation, I calculate the ratio of the simple equations of different altitudes to improve the original algorithm. It effectively eliminates the influence of the shape factor. I use different model to test the method and apply the method on real gravity data. It demonstrates that the new approach is stable, simple and effective depth estimation method. The new improved approach not only can be used to calculate the sphere and cylinder model depth, but also can be used to calculate other general models. It is a very useful tool to calculate the depth of gravity bodies.

Normalized full gradient of full tensor gravity gradient based on adaptive iterative Tikhonov regularization downward continuation

Normalized full gradient (NFG) method depends on the downward continuation of NFG values of gravity data. In this paper, I deduce an improved NFG method of full tensor gravity gradient (FTG) data by using x-, y- and z-directional analytic signals of FTG data. During the calculation, I introduce the adaptive iterative Tikhonov regularization downward continuation method in the calculation process to improve the stability of the NFG method. The new approach is tested on various model data with and without noise, and satisfactory results are obtained. It demonstrates that the new NFG method of FTG can improve the lateral resolution and describe the gravity bodies in more detail. In addition, the method is applied to a real field FTG data acquired over the Vinton Salt Dome, Louisiana, USA. All results demonstrate that the new method can accurately detect the depth of the geologic sources while providing enhanced information of the sources simultaneously.

The role of pre-existing Precambrian structures in rift evolution: The Albertine and Rhino grabens, Uganda

We integrated Shuttle Radar Topography Mission (SRTM) Digital Elevation Models (DEM), airborne magnetic, radiometric and three-dimensional Full Tensor Gravity Gradiometry (3D-FTG) data to investigate the role of Precambrian structures in the evolution of the largely amagmatic Miocene–Recent aged Albertine and Rhino grabens in Uganda. These grabens represent the northern segment of the Western Branch of the East African Rift System (EARS). The two NE-trending grabens are connected by a right-stepping transfer zone and they extend within the Archean–Paleoproterozoic Northeast Congo block which represents the northeastern extension of the Congo craton. Our results show the following and highlight the importance of pre-existing structures in the evolution of continental rift systems: (1) The NE-extent of the Albertine full-graben is controlled by NE-trending Precambrian fabric and the graben terminates at its northeastern end when it encounters a multiply folded Precambrian basement terrain with poorly-developed NW-trending structural grain. Additionally, the northeastern termination of the Albertine graben coincides with the presence of NW-trending right-stepping high-density bodies within the Precambrian terrain. (2) The transfer zone between the Albertine and Rhino grabens is controlled by NE-trending Precambrian structures which might have facilitated the development of relay ramp faults. (3) Strain localization within the better-developed southeastern border fault of the Rhino half-graben is facilitated by the presence of Precambrian structures better aligned in a NE-direction in the southeastern part of the basin compared to its northwestern part. (4) Further to the northeast, the Rhino graben is segmented and transitions into a narrower ENE-trending half-graben with a better-developed border fault on its northwestern side. This segmentation coincides with the presence of N-trending Precambrian structures. (5) The Rhino graben terminates farther northeast against the NW-trending Precambrian Aswa shear zone; a prominent structure with complex, but generally NW-trending fabric.

Lithological variations of sedimentary succession within a meteorite impact crater - Jwaneng South Structure, Botswana

The Jwaneng South Structure is a meteorite impact crater located in the Kalahari region of Botswana. The structure has the shape of a bowl 1.3 km in diameter and a maximum depth of 275 m in the centre. It was discovered by an airship-mounted full tensor gravity gradiometer and penetrated by nine vertical diamond drill-holes. The crater is underlain by the Gaborone Granite (2785 Ma) and basalts of the Karoo Supergroup (182 Ma). The covering aeolian sediments of the Kalahari Group (Late Cretaceous-Recent) completely obscure the structure. A succession of the following lithofacies overlying authigenic in situ brecciated granite was intersected in the boreholes (from base to top): (i) allogenic heterolithic/oligomictic “fallback” and resedimented breccia (ii) sedimentary breccia and conglomerate with sand matrix; (iii) six intervals of carbonate sediments, with traces of evaporites and mudstone interbeds, which are interlayered with (iv) five intervals of sandstone and sedimentary breccia composed of granules, pebbles and cobbles, mostly of granite, embedded in a matrix of well-sorted medium-grained sand; (v) bioturbated, mostly massive sandstone rich in mud matrix (wacke), with locally preserved interbeds of mudstone and cross-bedded sandstone, and abundant root traces; (v) silcrete and calcrete that occur at the top of the succession. This lithological association suggests that deposition within the Jwaneng South meteorite impact crater took place in a playa lake surrounded by steeply-dipping talus piedmont fans. The depositional cycles were controlled by pronounced climatic oscillations. Wet periods are recorded by lithofacies (iii), which reflects intense supply of sand eroded from the Kalahari dune field surrounding the crater and coarse detritus derived from its rim and steep talus below. Dry intervals of high evaporation and fall of the lake level are reflected by lithofacies (iv). During the youngest wet period (v) the lake filled up with alluvia sands interbedded with muds, abundantly vegetated and homogenised by bioturbation. The silcrete and calcrete layer at the top of the succession is the product of pedogenic processes that affected the Kalahari Desert environment. An asymmetry of lateral distribution of the lithofacies (ii) – (iv) and the presence of sedimentary breccia redeposited into the marginal E (and NE) parts of the crater suggest an asymmetry of the crater depression and its coarse clastic rim, which may imply an oblique trajectory of the impactor approaching from the SW.

Defining a deep fault network for Australia, using 3D “worming”

Defining a deep fault network for Australia, using 3D 'worming'. The original work on multi-scale edge detection ('worming') done by Hornby et al. in 1999 has become increasingly popular as a starting point for rapid interpretation using potential field data. Both gravity and magnetic grids are used. Several improvements have been made in the following years such that it is routine to capture points, 'worms' and linear features in a form suitable for overlay in GIS packages. There are important extensions which have recently been completed: (a). support for gravity gradiometry using the measured gradients directly (b). creation of interface and foliation data implying 3D surfaces that are geolocated. (c). adaption of Euler deconvolution techniques to both full tensor gravity gradiometry (FTG) and a best located method for scalar measures. This paper reports on these new extensions applied to the Australian gravity grid and on issues arising from these efforts to improve/generalise the worming technology and get 3D contacts that can be interpreted. This large scale gravity dataset, with a high density of near surface features, contains far too many gradients interpreted as faults, so a thinning strategy is required to find the significant deep crustal faults. These deep crustal faults require proper attribution of depth, dip direction and dip, and also extent constraints. For the FTG case, the largest 3-survey merge attempted to date has occurred with data acquired in Kenya. The new and improved 3D worming has been applied in the context of rapidly defining the horst/graben layouts in an active rift zone. Some discussion and illustration of the present problems of how to build, merge and manage a 3D fault network, where the issues of faults terminating on other faults and which fault cuts which, will be shown and discussed.

Multinary Inversion for Tunnel Detection

We introduce multinary inversion to explicitly exploit the physical property contrasts between different objects and their host medium, e.g., between air-filled tunnels and their surrounding earth. Conceptually, multinary inversion is a generalization of binary inversion to multiple physical properties. However, unlike existing realizations of binary inversion which are solved using stochastic optimization methods, our realization of multinary inversion can be solved using deterministic optimization methods. This is significant as the method can be applied to both linear and nonlinear operators and easily extends to joint inversion of multimodal geophysical data. Using synthetic models of full-tensor gravity gradiometry data, multinary inversion is demonstrated to be robust for tunnel detection relative to the presence of significant geological noise.

Full tensor CSEM and MT for subsalt structural imaging in the Red Sea: Implications for seismic and electromagnetic integration

The mapping of complex salt, subsalt sediments, and basement structures in the Red Sea was addressed through the integration of coincident high-resolution wide-azimuth (WAZ) 3D seismic data, full tensor gravity gradiometry (FTG), and MT/CSEM techniques. The data acquisition was designed to enable advanced multi-geophysical integration schemes to image the subsalt geologic structures. Multi-offset, multicomponent electromagnetic measurements were recorded for both MT and CSEM with overlapping frequency bands. The analysis of the data and the preliminary 3D inversion results indicate that the two methods provide coherent information for the evaporitic overburden and the subsalt sediment sections. In addition, the MT data also show sensitivity to the deep basement structures. The obtained resistivity distributions strongly correlate with imaged seismic events from the 3D migrated seismic volumes and with the lateral- and vertical-velocity variations in the salt and presalt sections. These data suggest that the acquired electromagnetic data set can support the interval velocity-depth model building in areas of low seismic sensitivity such as the intrasalt and subsalt sections.

Depth estimating Full Tensor Gravity data with the Adaptive Tilt Angle method

Depth estimation procedures for potential field data are well recognised techniques. Both Euler and Werner methodologies are typically used as a series of automated steps and applied to both gridded and profile data. The Tilt Derivative Depth method works on gridded data and has been used extensively on magnetic data. Its advantage is its ability to produce a focused set of solutions and is now being commonly adopted for potential field data. This paper describes an Adaptive Tilt Angle method for depth estimating Full Tensor Gravity data. The method is an adaptation of the Tilt Derivative depth estimation procedure adopted for magnetic data. The procedure works on 4 of the independently measured Tensor components and produces sets of solutions that are more easily interpreted. The tilt angle method is defined as a ratio of the Tensor components in each of the X, Y and Z directions and assumes a vertical contact geological setting. The implementation of a scaling factor allows the technique to work on horizontal contacts. The scaling factor is essentially similar to the concept of a Structural Index as used with Euler depth estimation methods. The technique was tested successfully on an Air-FTG® survey data set over a shallow salt feature onshore USA and is now being routinely deployed. The benefits of the direct depth estimation technique are immense in that it not only provides constraint on other interpretative processing techniques, but quickly establishes a starting depth model for any detailed forward / inverse modelling exercises.

Hybrid modelling of gravity, gravity gradients and magnetic fields

ABSTRACTModern geophysical interpretation requires an interdisciplinary approach and software capable of handling multiple geophysical data types such as seismic, full tensor gravity gradiometry, magnetics and magnetotellurics. We use the IGMAS+ (Interactive Gravity and Magnetic Application System) geo‐modelling software that is designed for 3D gravity, gravity gradient and magnetic modelling. This paper deals with a special aspect of potential field modelling, combining conventional triangulated model geometries (building polyhedrons) with voxel cubes.The hybrid modelling combines the advantages of both the vector and raster modelling system: both may be used alone (polyhedrons without voxels, voxels without polyhedrons) or simultaneously by superposition of both effects, which provides flexibility towards full interoperability. The key idea of our approach is, on the one hand to use two different, completely independent geometries (vector and raster) and give on the other hand the possibility to link both on demand for either editing the voxel model or to combine a large number of voxel cells under a common physical parameter function – which results in more reliable parameter inversion results.

Processing gravity gradient data

As the demand for high-resolution gravity gradient data increases and surveys are undertaken over larger areas, new challenges for data processing have emerged. In the case of full-tensor gradiometry, the processor is faced with multiple derivative measurements of the gravity field with useful signal content down to a few hundred meters’ wavelength. Ideally, all measurement data should be processed together in a joint scheme to exploit the fact that all components derive from a common source. We have investigated two methods used in commercial practice to process airborne full-tensor gravity gradient data; the methods result in enhanced, noise-reduced estimates of the tensor. The first is based around Fourier operators that perform integration and differentiation in the spatial frequency domain. By transforming the tensor measurements to a common component, the data can be combined in a way that reduces noise. The second method is based on the equivalent-source technique, where all measurements are inverted into a single density distribution. This technique incorporates a model that accommodates low-order drift in the measurements, thereby making the inversion less susceptible to correlated time-domain noise. A leveling stage is therefore not required in processing. In our work, using data generated from a geologic model along with noise and survey patterns taken from a real survey, we have analyzed the difference between the processed data and the known signal to show that, when considering the Gzz component, the modified equivalent-source processing method can reduce the noise level by a factor of 2.4. The technique has proven useful for processing data from airborne gradiometer surveys over mountainous terrain where the flight lines tend to be flown at vastly differing heights.

Comparing gravity and gravity gradient surveys

Noise levels in marine and airborne full tensor gravity gradiometer surveys together with conventional land, marine and airborne gravity surveys are estimated and analysed in gridded form, resulting in relations that detail how these different survey systems can be compared analytically. After defining survey parameters including line spacing, speed and instrument bandwidth, the relations estimate the noise levels that result on either grids of gravity (gz) or gravity gradient (Gzz) as a function of the spatial filtering often applied during geological interpretation. Such comparisons are believed to be a useful preliminary guide for survey selection and planning.