Minimum-structure borehole gravity inversion for mineral exploration: A synthetic modeling study

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. G25-G39 ◽  
Author(s):  
Craig R. W. Mosher ◽  
Colin G. Farquharson

A borehole gravimeter for the diameters of holes typically used in mineral exploration has recently been developed. Investigating how the data from such instruments can contribute to the gravity interpretation procedures used in mineral exploration is therefore appropriate. Here, results are presented from a study in which synthetic data for 3D exploration-relevant earth models were inverted and the impact of borehole data assessed. The inversions were carried out using a minimum-structure procedure that is typical of those commonly used to invert surface gravity data. Examples involving data from a single borehole, from multiple boreholes, and combinations of borehole and surface data, are considered. Also, a range of options for the particulars of the inversion algorithm are investigated, including using a reference model and cell weights to incorporate along-borehole density information, and an [Formula: see text]-type measure of model structure. The selection of examples presented demonstrates what one can and cannot expect to determine about the density variation around and between boreholes when borehole gravity data are inverted using a minimum-structure approach. Specifically, the density variation along a borehole can be accurately determined, even without constraints in the inversion, but this capability decreases dramatically a few tens of meters from a borehole.

Geophysics ◽  
2017 ◽  
Vol 82 (1) ◽  
pp. G1-G21 ◽  
Author(s):  
William J. Titus ◽  
Sarah J. Titus ◽  
Joshua R. Davis

We apply a Bayesian Markov chain Monte Carlo formalism to the gravity inversion of a single localized 2D subsurface object. The object is modeled as a polygon described by five parameters: the number of vertices, a density contrast, a shape-limiting factor, and the width and depth of an encompassing container. We first constrain these parameters with an interactive forward model and explicit geologic information. Then, we generate an approximate probability distribution of polygons for a given set of parameter values. From these, we determine statistical distributions such as the variance between the observed and model fields, the area, the center of area, and the occupancy probability (the probability that a spatial point lies within the subsurface object). We introduce replica exchange to mitigate trapping in local optima and to compute model probabilities and their uncertainties. We apply our techniques to synthetic data sets and a natural data set collected across the Rio Grande Gorge Bridge in New Mexico. On the basis of our examples, we find that the occupancy probability is useful in visualizing the results, giving a “hazy” cross section of the object. We also find that the role of the container is important in making predictions about the subsurface object.


Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. I13-I22 ◽  
Author(s):  
Fernando J. Silva Dias ◽  
Valeria C. Barbosa ◽  
João B. Silva

We present a new semiautomatic gravity interpretation method for estimating a complex interface between two media containing density heterogeneities (referred to as interfering sources) that give rise to a complex and interfering gravity field. The method combines a robust fitting procedure and the constraint that the interface is very smooth near the interfering sources, whose approximate horizontal coordinates are defined by the user. The proposed method differs from the regional-residual separation techniques by using no spectral content assumption about the anomaly produced by the interface to be estimated, i.e., the interface can produce a gravity response containing both low- and high-wavenumber features. As a result, it may be applied to map the relief of a complex interface in a geologic setting containing either shallow or deep-seated interfering sources. Tests conducted with synthetic data show that the method can be of utility in estimating the basement relief of a sedimentary basin in the presence of salt layers and domes or in the presence of mafic intrusions in the basement or in both basement and the sedimentary section. The method was applied to real gravity data from two geologic settings having different kinds of interfering sources and interfaces to be interpreted: (1) the interface between the upper and lower crusts over the Bavali shear zone of southern India and (2) the anorthosite-tonalite interface over the East Bull Lake gabbro-anorthosite complex outcrop in Ontario, Canada.


2003 ◽  
Vol 40 (10) ◽  
pp. 1307-1320 ◽  
Author(s):  
B Nitescu ◽  
A R Cruden ◽  
R C Bailey

The Moho undulations beneath the western part of the Archean Superior Province have been investigated with a three-dimensional gravity inversion algorithm for a single interface of constant density contrast. Inversion of the complete gravity data set produces unreal effects in the solution due to the ambiguity in the possible sources of some crustal gravity anomalies. To avoid these effects a censored gravity data set was used instead. The inversion results are consistent with reflection and refraction seismic data from the region and, therefore, provide a basis for the lateral correlation of the Moho topography between parallel seismic lines. The results indicate the existence of a major linear east–west-trending rise of the Moho below the metasedimentary English River subprovince, which is paralleled by crustal roots below the granite–greenstone Uchi and Wabigoon subprovinces. This correlation between the subprovincial structure at the surface and deep Moho undulations suggests that the topography of the crust–mantle boundary is related to the tectonic evolution of the Western Superior belts. Although certain features of the crust–mantle boundary are likely inherited from the accretionary and collisional stages of the Western Superior craton, gravity-driven processes triggered by subsequent magmatism and crustal softening may have played a role in both the preservation of those features, as well as in the development of new ones.


Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. B59-B68 ◽  
Author(s):  
Valeria C. Barbosa ◽  
Paulo T. Menezes ◽  
João B. Silva

We demonstrate the potential of gravity data to detect and to locate in-depth subtle normal faults in the basement relief of a sedimentary basin. This demonstration is accomplished by inverting the gravity data with the constraint that the estimated basement relief presents local abrupt faults and is smooth elsewhere. We inverted the gravity data from the onshore Almada Basin in northeastern Brazil, and we mapped several normal faults whose locations and plane geometries were already known from seismic imaging. The inversion method delineated well both the discontinuities with small or large slips and a sequence of step faults. Using synthetic data, we performed a systematic search of normal fault slips versus fault displacement depths to map the fault-detectable region in this space. This mapping helps to assess the ability of gravity inversion to detect normal faults. Mapping shows that normal faults with small [Formula: see text], medium (about [Formula: see text]), and large (about [Formula: see text]) vertical slips can be detected if the maximum midpoint depths of the fault planes are smaller than 1.8, 3.8, and [Formula: see text], respectively.


2020 ◽  
Author(s):  
Jérémie Giraud ◽  
Hoël Seillé ◽  
Gerhard Visser ◽  
Mark Lindsay ◽  
Mark Jessell

<p>We introduce a methodology for the integration of results from 1D stochastic magnetotelluric (MT) data inversion into deterministic least-square inversions of gravity measurements. The goal of this study is to provide a technique capable of exploiting complementary information between 1D magnetotelluric data and gravity data to reduce the effect of non-uniqueness existing in both methodologies. Complementarity exists in terms of resolution, the 1D MT being mostly sensitive to vertical changes and gravity data sensitive to lateral property variations, but also in terms of the related petrophysics, where the sensitivity to different physical parameters (electrical conductivity and density) allows to distinguish between different contrasts in lithologies.  To this end, we perform a three-step workflow. Stochastic 1D MT inversions are performed first. The results are then fused to create 2D model ensembles. Thirdly, these ensembles are utilised as a source of prior information for gravity inversion. This is achieved by extracting geological information from the ensemble of resistivity model realisations honouring MT data (typically, ensemble comprising several thousands of models) to constrain gravity data inversion. <br><br>In our investigations, we generate synthetic data using the 3D geological structural framework of the Mansfield area  (Victoria, Australia) and subsequently perform stochastic MT inversions using a 1D trans-dimensional Markov chain Monte Carlo sampler. These inversions are designed to account for the uncertainty introduced by the presence of non-1D structures.  Following this, the 1D probabilistic ensembles for each site are fused into an ensemble of 2D models which can then be used for further modelling. The fusion method incorporates prior knowledge in terms of spatial lateral continuity and lithological sequencing, to create an image that reflects different scenarios from the ensemble of models from 1D MT inversion. It identifies several domains across the considered area where it is plausible for the different lithologies to occur. This information is then used to constrain gravity inversion using a clustering algorithm by varying the weights assigned to the different lithologies spatially accordingly with the domains defined from MT inversions. <br><br>Our results reveal that gravity inversion constrained by MT modelling results in this fashion provide models that present a lower model misfit and are geologically closer to the causative model than without MT-derived prior information. This is particularly true in areas poorly constrained by gravity data such as the basement. Importantly, in this example, the basement is better imaged by the combination of both gravity and MT data than by the separate techniques. The same applies, to a lesser extent, to dipping geological structures closer to surface. In the case of the Mansfield area, the synthetic modelling investigation we performed shows the potential of the workflow introduced here and that it can be confidently applied to real world data.</p>


Geophysics ◽  
1991 ◽  
Vol 56 (1) ◽  
pp. 68-79 ◽  
Author(s):  
P. T. C. Hammer ◽  
J. A. Hildebrand ◽  
R. L. Parker

A gravity inversion algorithm for modeling discrete bodies with nonuniform density distributions is presented. The algorithm selects the maximally uniform model from the family of models which fit the data, ensuring a conservative and unprejudiced estimate of the density variation within the body. The only inputs required by the inversion are the gravity anomaly field and the body shape. Tests using gravity anomalies generated from synthetic bodies confirm that seminorm minimizing inversions successfully represent mass distribution trends but do not reconstruct sharp discontinuities. We apply the algorithm to model the density structure of seamounts. Inversion of the seasurface gravity field observed over Jasper Seamount suggests the edifice has a low average density of [Formula: see text] and contains a dense body within its western flank. These results are consistent with seismic, magnetic, and petrologic studies of Jasper Seamount.


2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Huan Ma ◽  
Handong Tan ◽  
Yue Guo

Four kinds of array of induced polarization (IP) methods (surface, borehole-surface, surface-borehole, and borehole-borehole) are widely used in resource exploration. However, due to the presence of large amounts of the sources, it will take much time to complete the inversion. In the paper, a new parallel algorithm is described which uses message passing interface (MPI) and graphics processing unit (GPU) to accelerate 3D inversion of these four methods. The forward finite differential equation is solved by ILU0 preconditioner and the conjugate gradient (CG) solver. The inverse problem is solved by nonlinear conjugate gradients (NLCG) iteration which is used to calculate one forward and two “pseudo-forward” modelings and update the direction, space, and model in turn. Because each source is independent in forward and “pseudo-forward” modelings, multiprocess modes are opened by calling MPI library. The iterative matrix solver within CULA is called in each process. Some tables and synthetic data examples illustrate that this parallel inversion algorithm is effective. Furthermore, we demonstrate that the joint inversion of surface and borehole data produces resistivity and chargeability results are superior to those obtained from inversions of individual surface data.


Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. G17-G34
Author(s):  
B. Marcela S. Bastos ◽  
Vanderlei C. Oliveira Jr.

We have developed a nonlinear gravity inversion for simultaneously estimating the basement and Moho geometries, as well as the depth of the reference Moho along a profile crossing a passive rifted margin. To obtain stable solutions, we impose smoothness on basement and Moho, force them to be close to previously estimated depths along the profile and also impose local isostatic equilibrium. Different from previous methods, we evaluate the information of local isostatic equilibrium by imposing smoothness on the lithostatic stress exerted at depth. Our method delimits regions that deviate and those that can be considered in local isostatic equilibrium by varying the weight of the isostatic constraint along the profile. It also allows controlling the degree of equilibrium along the profile, so that the interpreter can obtain a set of candidate models that fit the observed data and exhibit different degrees of isostatic equilibrium. Our method also differs from earlier studies because it attempts to use isostasy for exploring (but not necessarily reducing) the inherent ambiguity of gravity methods. Tests with synthetic data illustrate the effect of our isostatic constraint on the estimated basement and Moho reliefs, especially at regions with pronounced crustal thinning, which are typical of passive volcanic margins. Results obtained by inverting satellite data over the Pelotas Basin, a passive volcanic margin in southern Brazil, agree with previous interpretations obtained independently by combining gravity, magnetic, and seismic data available to the petroleum industry. These results indicate that combined with a priori information, simple isostatic assumptions can be very useful for interpreting gravity data on passive rifted margins.


2013 ◽  
Vol 31 (4) ◽  
pp. 661 ◽  
Author(s):  
Marina B. Gaino ◽  
Julio Cesar S.O. Lyrio ◽  
Walter E. Medeiros

ABSTRACT. Gravity inversion results aiming to estimate the crystalline basement relief of the onshore Potiguar Basin are presented. It is assumed that the density contrast between the sediments and the crystalline basement is constant and known. The sediments are approximated with vertical rectangular prisms whose thicknesses, representing the depths to crystalline basement, are the parameters to be estimated from the gravity inversion. In all cases, the inversion process was stabilized with smoothness constraint on the spatial variation of the basement relief. Besides the gravity data, we used information about the basement relief obtained from boreholes and from seismic interpretation. These data were combined in order to compose three different scenarios simulating different phases during the exploratory development of the basin. In the first scenario we used the gravity data only. In the second scenario we worked with two combinations, first we combined the gravity data with information from boreholes, and second, with the basement relief reference model that resulted from the seismic interpretation. Finally, in the third scenario, we used the gravity data, the information from the boreholes and the reference model obtained from the seismic interpretation. In all scenarios, we obtained reliable estimates for the basement relief. Concerning the discrepancies among the results, the estimates obtained with additional constraints (from boreholes and/or seismic interpretation) increased the overall resolution of the basement relief and the reliability of the absolute depth values. However, it is important to stress that the first scenario already yielded a reliable estimate to the basin relief. If one takes into account the huge difference both in financial cost and environmental impact associated with gravity and seismic surveys, respectively, as well as with borehole drilling, this result highlights the great importance of properly using the gravity data in the initial exploratory phase of the basin.Keywords: gravity inversion, basement relief, Potiguar Basin, constrained inversion. RESUMO. Este trabalho apresenta aplicações de inversão gravimétrica para a estimativa do relevo do embasamento cristalino da Bacia Potiguar emersa. Admite-se que o contraste de densidade entre os sedimentos e o embasamento da bacia é constante e conhecido. O pacote sedimentar é aproximado por um conjunto de prismas lateralmente justapostos cujas espessuras, ou profundidades até o embasamento, são os parâmetros a serem estimados na inversão. Em todos os casos, o processo de inversão foi estabilizado com o uso do vínculo de suavidade na variação espacial do relevo do embasamento. Além das medidas gravimétricas, foram utilizados dados de poços e/ou oriundos da interpretação sísmica, em diferentes combinações, de modo a simular diferentes etapas, ou cenários, de exploração da bacia ao longo do tempo. No primeiro cenário foram utilizados somente dados gravimétricos. No segundo cenário, simulamos duas situações, em ambas adicionando outras informações aos dados gravimétricos: na primeira delas, adicionamos somente vínculos de poços e, na segunda, apenas um modelo sísmico de referencia para o embasamento. Por fim, no último cenário foram agregados aos dados gravimétricos os dados de poços e o modelo sísmico. As estimativas obtidas para o relevo do embasamento revelaram nitidamente o arcabouço da bacia em todos os cenários. Em relação às variações das profundidades entre os cenários, as inclusões dos vínculos dos poços e do modelo sísmico aprimoraram a resolução global dos resultados, como esperado. Contudo, é relevante destacar que a inversão no primeiro cenário já forneceu um relevo bastante aproximado do arcabouço conhecido da bacia. Se levarmos em conta as grandes diferenças de custo financeiro e de impacto ambiental, respectivamente associados com os levantamentos gravimétrico e sísmico, bem como com a perfuração de poços, esse resultado evidencia a grande importância de uma adequada utilização dos dados gravimétricos nas fases exploratórias iniciais de uma bacia.Palavras-chave: inversão gravimétrica, relevo do embasamento, Bacia Potiguar, inversão vinculada.


Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. C25-C35 ◽  
Author(s):  
Ulrich Theune ◽  
Ingrid Østgård Jensås ◽  
Jo Eidsvik

Resolving thinner layers and focusing layer boundaries better in inverted seismic sections are important challenges in exploration and production seismology to better identify a potential drilling target. Many seismic inversion methods are based on a least-squares optimization approach that can intrinsically lead to unfocused transitions between adjacent layers. A Bayesian seismic amplitude variation with angle (AVA) inversion algorithm forms sharper boundaries between layers when enforcing sparseness in the vertical gradients of the inversion results. The underlying principle is similar to high-resolution processing algorithms and has been adapted from digital-image-sharpening algorithms. We have investigated the Cauchy and Laplace statistical distributions for their potential to improve contrasts betweenlayers. An inversion algorithm is derived statistically from Bayes’ theorem and results in a nonlinear problem that requires an iterative solution approach. Bayesian inversions require knowledge of certain statistical properties of the model we want to invert for. The blocky inversion method requires an additional parameter besides the usual properties for a multivariate covariance matrix, which we can estimate from borehole data. Tests on synthetic and field data show that the blocky inversion algorithm can detect and enhance layer boundaries in seismic inversions by effectively suppressing side lobes. The analysis of the synthetic data suggests that the Laplace constraint performs more reliably, whereas the Cauchy constraint may not find the optimum solution by converging to a local minimum of the cost function and thereby introducing some numerical artifacts.


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