Gravity Gradiometry Data Research Articles

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.

Evaluation of gravity field model EIGEN-6C4 by means of various functions of gravity potential, and by GNSS/levelling

<p>The combined gravity field model EIGEN-6C4 (Förste et al., 2014) is the latest combined global gravity field model of GFZ Potsdam and GRGS Toulouse. EIGEN-6C4 has been generated including the satellite gravity gradiometry data of the entire GOCE mission (November 2009 till October 2013) and is of maximum spherical degree and order 2190. In this study EIGEN-6C4 has been compared with EGM2008 to its maximum degree and order via gravity disturbances and T<sub>zz</sub> part of the Marussi tensor of the second derivatives of the disturbing potential. The emphasis is put on such areas where GOCE data (complete set of gradiometry measurements after reductions) in EIGEN-6C4 obviously contributes to an improvement of the gravity field description. </p><p>GNSS/levelling geoid heights are independent data source for the evaluation of gravity field models. Therefore, we use the GNSS/levelling data sets over the territories of Europe, Czech Republic and Slovakia for the evaluation of EIGEN-6C4 w.r.t. EGM2008.</p>

Lithologic characterization using airborne gravity gradient and aeromagnetic data for mineral exploration: A case study in the Quadrilátero Ferrífero, Brazil

We present a study on utilizing airborne gravity gradient and magnetic data to characterize an iron ore formation in Minas Gerais, Brazil. The target iron ore bodies have a distinctly high density contrast and produce well-defined anomalies in airborne gravity gradiometry data. The high-grade hematite iron ores are associated with low and moderate susceptibility, making magnetic data useful in distinguishing potential ore bodies from the host iron formation. The airborne gravity gradient and magnetic data over part of the Gandarela Syncline iron formation in the Quadrilátero Ferrífero are independently inverted to obtain a 3D susceptibility and density contrast model. These detailed 3D physical property distributions of subsurface features are then used for geologic characterization and interpretation purposes through lithologic associations. We outline two approaches to link the two physical property distributions and identify representative geologic units in the study area. The geologic units are then organized into a 3D lithology model to help characterize subsurface geologic structure and ore distribution. The lithologic models provide an intuitive representation of the geology and can assist in future exploration plans or in assessment of resource distribution and quality. Our study demonstrates that such approaches are feasible on the deposit scale.

Feasibility of time-lapse gravity and gravity gradiometry monitoring for steam-assisted gravity drainage reservoirs

There is presently an increased need to monitor production efficiency as heavy oil reservoirs become more economically viable. We present a feasibility study of monitoring steam-assisted gravity drainage (SAGD) reservoirs using time-lapse gravimetry and gravity gradiometry. Even though time-lapse seismic has historically shown great success for SAGD monitoring, the gravimetry and gravity gradiometry methods offer a low-cost interseismic alternative that can complement the seismic method, increase the survey frequency, and decrease the cost of monitoring. In addition, both gravity-based methods are directly sensitive to the density changes that occur as a result of the replacement of heavy oil by steam. Advances in technologies have made both methods viable candidates for consideration in time-lapse reservoir monitoring, and we have numerically evaluated their potential application in monitoring SAGD production. The results indicate that SAGD production should produce a strong anomaly for both methods at typical SAGD reservoir depths. However, the level of detail for steam-chamber geometries and separations that can be recovered from the gravimetry and gravity gradiometry data is site dependent. Gravity gradiometry shows improved monitoring ability, such as better recovery of nonuniform steam movement due to reservoir heterogeneity, at shallower production reservoirs. Gravimetry has the ability to detect SAGD steam-chamber growth to greater depths than does gravity gradiometry, although with decreasing resolution of the expanding steam chambers.

Application of Cauchy-type integrals in developing effective methods for depth-to-basement inversion of gravity and gravity gradiometry data

One of the most important applications of gravity surveys in regional geophysical studies is determining the depth to basement. Conventional methods of solving this problem are based on the spectrum and/or Euler deconvolution analysis of the gravity field and on parameterization of the earth’s subsurface into prismatic cells. We have developed a new method of solving this problem based on 3D Cauchy-type integral representation of the potential fields. Traditionally, potential fields have been calculated using volume integrals over the domains occupied by anomalous masses subdivided into prismatic cells. This discretization can be computationally expensive, especially in a 3D case. The technique of Cauchy-type integrals made it possible to represent the gravity field and its gradients as surface integrals. In this approach, only the density contrast surface between sediment and basement needed to be discretized for the calculation of gravity field. This was especially significant in the modeling and inversion of gravity data for determining the depth to the basement. Another important result was developing a novel method of inversion of gravity data to recover the depth to basement, based on the 3D Cauchy-type integral representation. Our numerical studies determined that the new method is much faster than conventional volume discretization method to compute the gravity response. Our synthetic model studies also showed that the developed inversion algorithm based on Cauchy-type integral is capable of recovering the geometry and depth of the sedimentary basin effectively with a complex density profile in the vertical direction.

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.

Gravity gradient distribution in mainland China from GOCE satellite gravity gradiometry data

At present, gravity field and steady-state ocean circulation explorer (GOCE) gravity data are always used to compute regional gravity anomaly and geoid height. In this study, the latest GOCE gravity field model data (from Oct. 2009 to Jul. 2010) are used to compute the gravity gradient of mainland China according to a rigorous recursion formula (in all the six directions). The results show that the numerical values of the gravity gradients are larger in the Trr direction than those in the other directions. They reflect the terrain characteristics in detail and correlate with the regional tectonics; however, in the Tθλ and Trλ directions, the numerical values are relatively smaller and the gravity gradients in the Trλ direction do not reflect the terrain characteristics in detail.

Regional quasigeoid from GOCE and terrestrial measurements

Results obtained as a solution to the geodetic boundary-value problem, where two different sources of input boundary data are combined together, are presented. On the upper part of the boundary defined by the Earth surface and separated from the Earth masses, the gravity anomalies are derived from GOCE gravity gradiometry data using a transformation and downward continuation procedure. On the bottom part of the boundary, the gravity anomalies derived from the terrestrial or marine gravity measurements are used. The boundary-value problem is then solved numerically by the finite element method. In some cases an independency of our solution from the highdegree global gravity models (e.g. EGM2008) can be considered as the advantage. The standard deviation of our model tested by GNSS/leveling method in Auvergne area is 10 cm.

3D inversion of airborne gravity-gradiometry data using cokriging

We developed a new method for interpretation of airborne gravity gradiometry data, based on cokriging inversion. The cokriging method that we evaluated minimized the theoretical estimation error variance by using auto- and crosscorrelations of several variables. It does not require iterations and can easily include complex a priori information. Moreover, the smoothing effects in the inverted density structure model can be reduced to a certain extent due to the anisotropy constrain in the covariance model. We compared the recovered models obtained by inverting the different combinations of gravity-gradient components to understand how different component combinations contributed to the resolution of the recovered model. The results indicated that including multiple components for inversion increased the resolution of the recovered density model and improved the structure delineation. Moreover, in the case in which the parameters of the variogram model are not well chosen, cokriging with multicomponent combinations can still correctly recover the geometry of the targeted sources. The survey data of the Vinton dome were considered as a case study. The results of the inversion were in good agreement with the known formation in the region. This supports the validity of our method.

From Tensor to Vector of Gravitation

ABSTRACT Different gravitational force models are used for determining the satellites’ orbits. The satellite gravity gradiometry (SGG) data contain this gravitational information and the satellite accelerations can be determined from them. In this study, we present that amongst the elements of the gravitational tensor in the local north-oriented frame, all of the elements are suitable for this purpose except Txy. Three integral formulae with the same kernel function are presented for recovering the accelerations from the SGG data. The kernel of these integrals is well-behaving which means that the contribution of the far-zone data is not very significant to their integration results; but this contribution is also dependent on the type of the data being integrated. Our numerical studies show that the standard deviations of the differences between the accelerations recovered from Tzz, Txz and Tzy and those computed by an existing Earth´s gravity model reduce by increasing the cap size of integration. However, their root mean squared errors increase for recovering Ty from Tyz. Larger cap sizes than 5 on is recommended for recovering Tx and Tz but smaller ones for Ty.

Accuracy assessment of GOCE-based geopotential models and their use for modelling the gravimetric quasigeoid - A case study for Poland

Abstract The GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) has significantly upgraded the knowledge on the Earth gravity field. In this contribution the accuracy of height anomalies determined from Global Geopotential Models (GGMs) based on approximately 27 months GOCE satellite gravity gradiometry (SGG) data have been assessed over Poland using three sets of precise GNSS/levelling data. The fits of height anomalies obtained from 4th release GOCE-based GGMs to GNSS/levelling data were discussed and compared with the respective ones of 3rd release GOCE-based GGMs and the EGM08. Furthermore, two highly accurate gravimetric quasigeoid models were developed over the area of Poland using high resolution Faye gravity anomalies. In the first, the GOCE-based GGM was used as a reference geopotential model, and in the second - the EGM08. They were evaluated with GNSS/levelling data and their accuracy performance was assessed. The use of GOCE-based GGMs for recovering the long-wavelength gravity signal in gravimetric quasigeoid modelling was discussed.

Interpretation of magnetic and gravity gradient tensor data using normalized source strength – A case study from McFaulds Lake, Northern Ontario, Canada

ABSTRACTIn this paper, we present a case study on the use of the normalized source strength (NSS) for interpretation of magnetic and gravity gradient tensors data. This application arises in exploration of nickel, copper and platinum group element (Ni‐Cu‐PGE) deposits in the McFaulds Lake area, Northern Ontario, Canada. In this study, we have used the normalized source strength function derived from recent high resolution aeromagnetic and gravity gradiometry data for locating geological bodies.In our algorithm, we use maxima of the normalized source strength for estimating the horizontal location of the causative body. Then we estimate depth to the source and structural index at that point using the ratio between the normalized source strength and its vertical derivative calculated at two levels; the measurement level and a height h above the measurement level. To discriminate more reliable solutions from spurious ones, we reject solutions with unreasonable estimated structural indices.This method uses an upward continuation filter which reduces the effect of high frequency noise. In the magnetic case, the advantage is that, in general, the normalized magnetic source strength is relatively insensitive to magnetization direction, thus it provides more reliable information than standard techniques when geologic bodies carry remanent magnetization. For dipping gravity sources, the calculated normalized source strength yields a reliable estimate of the source location by peaking right above the top surface.Application of the method on aeromagnetic and gravity gradient tensor data sets from McFaulds Lake area indicates that most of the gravity and magnetic sources are located just beneath a 20 m thick (on average) overburden and delineated magnetic and gravity sources which can be probably approximated by geological contacts and thin dikes, come up to the overburden.

Comparison of GGMs based on one year GOCE observations with the EGM08 and terrestrial data over the area of Sudan

Since 2010, a series of Global Geopotential Models (GGMs) based on Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite gravimetry mission have been released. In this study, the GGMs based on approximately 12 months of GOCE satellite gravity gradiometry (SGG) data have been compared over the area of Sudan with the EGM08 and terrestrial data. Geoid heights and free-air gravity anomalies from four GOCE/GRACE satellite-only GGMs, and one GOCE/GRACE GGM combined with terrestrial/altimetric gravity data were compared with the corresponding ones obtained from the EGM08, terrestrial free-air gravity anomalies and GNSS/levelling data.The results reveal that geoid heights and free-air gravity anomalies obtained from the GOCE-based GGMs agree with the corresponding ones from the EGM08 truncated to d/o 200 with standard deviation of 18–20cm, and 3.4–4.2mGal, respectively. Their agreement with the terrestrial free-air gravity anomalies and the GNSS/levelling geoid heights, in terms of standard deviation is about 5.5mGal, and about 50cm, respectively.

Getting the best value from gravity gradiometry

The critically important steps to get best value from your gravity gradiometry data, assuming your contractor has done his job well in designing and acquiring the data, is the preparation of the representation of the potential field gradients. The ~200 m resolving power of existing gradiometer systems approaches what is necessary for minerals applications. In particular, beyond the aircraft, the topographic surface represents the largest and most proximal density contrast encountered in an airborne survey. Hence terrain effects can have significant impact on AGG data. The critical steps are: Terrain correction and determining ‘best’ terrain densityGridding, using all the measured gradients to constrain the interpolationSmoothing/de-noising by using the 3 rd order tensor constraintsAnti-alias filtering of the gradient signals so that wave lengths are properly represented in all directionsTransformation of the gradients by integration to estimate the gravity or magnetic fieldTerrain corrections are a necessary step in the processing of observed AGG data in rugged terrain, in order to highlight subsurface density variations with a minimal overprint from the terrain. We propose a simple and rapid AGG tensor-based method to estimate an optimum bulk terrain density for subsequent terrain-correction. Each of the currently deployed systems for acquiring gradiometry is evolving driven by competition and the users’ needs. Mining applications of the technology to directly detect ore-bodies that show up as anomalies can now be successful provided the dimensions are of the order of 200 m or more. High resolution 3D geology models of operating mines can be used to calibrate gradiometry surveys

Geometric shapes derived from airborne gravity gradiometry data: New tools for the explorationist

We display airborne gravity gradient data using curvature attributes of the equipotential surface to derive geometric shapes that can be associated with structural and geologic features. Concepts used in differential geometry that describe all geometric aspects of a surface are applied to airborne gravity gradiometry data. Gravity gradient components are ideal for this application because they are related to curvature of the gravitational potential. We also emphasize that with gravity methods, the surfaces for which the curvature attributes are derived represent the succession of equipotential surfaces, which, under favorable circumstances, correspond to one or more geologic surfaces that dominate the signature of the airborne gravity gradiometry data.

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.

Introduction to this special section: Gravity and potential fields

Tien Grauch and her coauthors describe an integrated study of high-resolution aeromagnetics, ground gravity, airborne gravity gradiometry, TEM, and 2D seismic data for imaging not only basement faulting and relief, but also shallow faulting within the sedimentary section. Rather than invoking magnetic mineralization along fault zones (or other geochemical explanations) as an explanation for the observed sedimentary magnetic anomalies, they show that the anomalies can be completely explained by tectonic juxtaposition of strata of differing magnetic properties across the fault zones. They document, through 2D forward magnetic modeling, a faulted geologic column of juxtaposed magnetite-enriched clastics with magnetite-depleted clastics. These laterally varying magnetite-bearing horizons stack to produce super-positioned magnetic anomalies of relatively low amplitude and short wavelength which are superimposed on the longer wavelength, higher-amplitude magnetic anom-alies sourced by basement composition heterogeneities and structural relief.

Interpretation of tensor gravity data using an adaptive tilt angle method

ABSTRACTFull Tensor Gravity Gradiometry (FTG) data are routinely used in exploration programmes to evaluate and explore geological complexities hosting hydrocarbon and mineral resources. FTG data are typically used to map a host structure and locate target responses of interest using a myriad of imaging techniques. Identified anomalies of interest are then examined using 2D and 3D forward and inverse modelling methods for depth estimation. However, such methods tend to be time consuming and reliant on an independent constraint for clarification. This paper presents a semi‐automatic method to interpret FTG data using an adaptive tilt angle approach. The present method uses only the three vertical tensor components of the FTG data (Tzx, Tzy and Tzz) with a scale value that is related to the nature of the source (point anomaly or linear anomaly). With this adaptation, it is possible to estimate the location and depth of simple buried gravity sources such as point masses, line masses and vertical and horizontal thin sheets, provided that these sources exist in isolation and that the FTG data have been sufficiently filtered to minimize the influence of noise. Computation times are fast, producing plausible results of single solution depth estimates that relate directly to anomalies. For thick sheets, the method can resolve the thickness of these layers assuming the depth to the top is known from drilling or other independent geophysical data. We demonstrate the practical utility of the method using examples of FTG data acquired over the Vinton Salt Dome, Louisiana, USA and basalt flows in the Faeroe‐Shetland Basin, UK. A major benefit of the method is the ability to quickly construct depth maps. Such results are used to produce best estimate initial depth to source maps that can act as initial models for any detailed quantitative modelling exercises using 2D/3D forward/inverse modelling techniques.

Validation of static gravity field models using GRACE K-band ranging and GOCE gradiometry data

The ability of satellite gravimetry data to validate global static models of the Earth’s gravity field is studied. Two types of data are considered: K-band ranging (KBR) data from the Gravity Recovery and Climate Experiment (GRACE) mission and Satellite Gravity Gradiometry (SGG) data from the GOCE (Gravity field and steady-state Ocean Circulation Explorer) mission. The validation is based on analysis of misfits obtained as the differences between the data observed and those computed with a force model that includes, in particular, a static gravity field model to be assessed. To facilitate the model assessment on a region-by-region basis, we convert KBR data into so-called range combinations, which are approximately equivalent to the intersatellite accelerations.We only use the accurately measured components of SGG data, that is, xx, yy, zz and xz components with x, y and z being along-track, cross-track and radial axes.We perform the validation in spectral and spatial domain. The latter requires elimination of low-frequency noise in the misfit data with a subsequent averaging over pre-defined blocks. Only ‘independent’ data are used, that is, those that have not been used in the production of the models under consideration. The proposed methodology is applied to eight models: EGM2008 (truncated at degree 250), EIGEN-6C (truncated at degree 250), two GRACE-only models (ITG-Grace03 and ITGGrace2010s) and four (satellite-only) combined GRACE/GOCE models (GOCO01S, EIGEN- 6S, GOCO02S and DGM-1S). The latter is a novel model developed at Delft University of Technology in collaboration with GNSS Research Centre of Wuhan University. The GRACE KBR and GOCE SGG data demonstrate a pronounced sensitivity to inaccuracies of EGM2008 in 5–22 mHz (27–120 cycles-per-revolution, cpr) and 10–28 mHz (54–150 cpr) frequency ranges, respectively. The latter data also show a high sensitivity to inaccuracies of ITGGrace2010s in 25–37 mHz (135–200 cpr) frequency range. From the validation in the spatial domain, it is confirmed that independent data of both types allow a difference in performance of the models to be observed, despite the fact that the duration of these data is much shorter than that of data used to produce those models. It is shown that EGM2008 performs weaker than the combined GRACE/GOCE models (up to the highest spectral sensitivity of the validation data). Considering the root mean square misfits related to the zz gravity gradient component, the differences in performance are: 76–83 per cent in the continental areas poorly covered by terrestrial gravimetry measurements (Himalayas, South America and Equatorial Africa); 4–16 per cent in the continental areas well covered by these measurements (Australia, North Eurasia and North America); and 11 per cent in theworld’s oceans (65?S–65?N). The identified differences in the regions of the latter two categories are related to the added value of the GOCE mission. It is shown that ITG-Grace03 and ITG-Grace2010s are of a much lower accuracy than EGM2008 in the gravimetrically well-surveyed continental areas: by 62–70 and 19–35 per cent and in the world’s oceans: by 54 and 18 per cent, respectively. Nevertheless, the former models show a higher accuracy in the gravimetrically poorly surveyed continental areas: by 62–69 and 69–75 per cent, respectively. This difference is explained mostly by a loss of information content of ITG-Grace03 when it was combined with terrestrial gravimetry data to produce EGM2008. The KBR and SGG test data identify this loss of information content in 4–23 mHz (22–124 cpr) and 9–26 mHz (50–140 cpr) frequency ranges, respectively. It is shown that EIGEN-6C also suffers from a similar problem but in a much less pronounced manner. In South America, for instance, this model is found to perform somewhat poorer than its satellite-only counterpart, that is, EIGEN-6S, by about 12 per cent. The combined GRACE/GOCE models show in the poorly surveyed continental areas a higher accuracy than ITG-Grace2010s: by 23–36 per cent, which is attributed to the added value of the GOCE mission data. GOCO02S outperforms GOCO01S by not more than 2–5 per cent. DGM-1S and GOCO02S show an almost similar performance against SGG test data. However, the former model shows a slightly better agreement with KBR test data. Both models agree with test data better than EIGEN-6S.