2D gravity inversion of a complex interface in the presence of interfering sources

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. I13-I22 ◽  
Author(s):  
Fernando J. Silva Dias ◽  
Valeria C. Barbosa ◽  
João B. Silva
Keyword(s):  
Gravity Data ◽  
Synthetic Data ◽  
Gravity Inversion ◽  
Spectral Content ◽  
Robust Fitting ◽  
Mafic Intrusions ◽  
Fitting Procedure ◽  
Gravity Response ◽  
Geologic Setting ◽  
Gravity Interpretation

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.

A Bayesian approach to modeling 2D gravity data using polygons

Geophysics ◽  
2017 ◽  
Vol 82 (1) ◽  
pp. G1-G21 ◽  
Author(s):  
William J. Titus ◽  
Sarah J. Titus ◽  
Joshua R. Davis
Keyword(s):  
Gravity Data ◽  
Synthetic Data ◽  
Gravity Inversion ◽  
Limiting Factor ◽  
Data Sets ◽  
Data Set ◽  
Local Optima ◽  
Occupancy Probability ◽  
Compute Model ◽  
Parameter Values

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.

Gravity data as a tool for detecting faults: In-depth enhancement of subtle Almada’s basement faults, Brazil

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. B59-B68 ◽  
Author(s):  
Valeria C. Barbosa ◽  
Paulo T. Menezes ◽  
João B. Silva
Keyword(s):  
Gravity Data ◽  
Synthetic Data ◽  
Normal Fault ◽  
Northeastern Brazil ◽  
Normal Faults ◽  
Gravity Inversion ◽  
Inversion Method ◽  
Basement Faults ◽  
Depth Enhancement ◽  
Fault Displacement

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.

Utilisation of stochastic MT inversion results to constrain potential field inversion

2020 ◽  
Author(s):  
Jérémie Giraud ◽  
Hoël Seillé ◽  
Gerhard Visser ◽  
Mark Lindsay ◽  
Mark Jessell
Keyword(s):  
Prior Information ◽  
Clustering Algorithm ◽  
Gravity Data ◽  
Synthetic Data ◽  
Least Square ◽  
Gravity Inversion ◽  
Physical Parameters ◽  
Real World Data ◽  
Magnetotelluric Data ◽  
Data Inversion

<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>

Isostatic constraint for 2D nonlinear gravity inversion on rifted margins

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. G17-G34
Author(s):  
B. Marcela S. Bastos ◽  
Vanderlei C. Oliveira Jr.
Keyword(s):  
Gravity Data ◽  
A Priori ◽  
Petroleum Industry ◽  
Synthetic Data ◽  
Gravity Inversion ◽  
Rifted Margins ◽  
Isostatic Equilibrium ◽  
Priori Information ◽  
Pelotas Basin ◽  
Nonlinear Gravity

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.

Gravity inversion of 2D basement relief using entropic regularization

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. I29-I35 ◽  
Author(s):  
João B. Silva ◽  
Alexandre S. Oliveira ◽  
Valéria C. Barbosa
Keyword(s):  
A Priori ◽  
Synthetic Data ◽  
Entropy Measure ◽  
Gravity Inversion ◽  
Solution Vector ◽  
Good Definition ◽  
Northern Border ◽  
Global Smoothness ◽  
Entropic Regularization ◽  
Gravity Interpretation

We have developed a gravity interpretation method for estimating the discontinuous basement relief of a sedimentary basin. The density contrast between the basement and the sediments is assumed to be known, and it could be either constant or vary monotonically with depth. The interpretation model consists of a set of vertical, juxtaposed prisms, whose thicknesses are the parameters to be estimated. We used the entropic regularization that combines the minimization of the first-order entropy measure with the maximization of the zeroth-order entropy measure of the solution vector. We validated the method by applying it to synthetic data produced by a simulated basin bordered by high-angle step faults; we obtained a good definition of the relief, particularly of the discontinuities. We also applied the method to a profile across the Büyük Menderes Valley in West Turkey and obtained a solution exhibiting a gravity fault with large slip on the northern border of the valley. When applied to the interpretation of a discontinuous basement relief, the method has a better performance than the global smoothness method. It is comparable to the weighted smoothness method, but it does not require the a priori knowledge about the maximum basin depth.

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
Keyword(s):  
Reference Model ◽  
Mineral Exploration ◽  
Gravity Data ◽  
Synthetic Data ◽  
Density Variation ◽  
Gravity Inversion ◽  
Inversion Algorithm ◽  
Borehole Data ◽  
Text Type ◽  
The Impact

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.

scholarly journals Porosity Prediction from Gravity Inversion with Constraints from Resistivity Data

2021 ◽  
Author(s):  
Fernando A. Monteiro Santos ◽  
Patricia Represas
Keyword(s):  
Experimental Data ◽  
Random Search ◽  
Gravity Data ◽  
Synthetic Data ◽  
Gravity Inversion ◽  
Dc Resistivity ◽  
Matrix Density ◽  
Controlled Random Search ◽  
Geological Information ◽  
Resistivity Inversion

This work describes a method to carry out 2-D inversion of gravity data in terms of porosity and matrix density distribution using previous DC resistivity inversion results to constraint the fractional pore-water content in the rocks. The inversion is carried out using a controlled random search (CRS) algorithm for global optimization. The method was tested on synthetic data generated from a model representing a graben, and the results show that it can estimate accurate values of contrast-density and porosity. The method was also applied to gravity and dc experimental data collected in NE Portugal, showing results that agree quite well with the known geological information.

Gravity inversion of basement relief constrained by the knowledge of depth at isolated points

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1702-1714 ◽  
Author(s):  
Jorge W. D. Leão ◽  
Paulo T. L. Menezes ◽  
Jacira F. Beltrão ◽  
João B. C. Silva
Keyword(s):  
Linear Trend ◽  
Gravity Data ◽  
Synthetic Data ◽  
Effective Density ◽  
Density Contrast ◽  
Gravity Inversion ◽  
True Value ◽  
Isolated Points ◽  
The Media ◽  
Homogeneous Media

We present an interpretation method for the gravity anomaly of an arbitrary interface separating two homogeneous media. It consists essentially of a downward continuation of the observed anomaly and the division of the continued anomaly by a scale factor involving the density contrast between the media. The knowledge of the interface depth at isolated points is used to estimate the depth [Formula: see text] of the shallowest point of the interface, the density contrast Δρ between the two media, and the coefficients [Formula: see text] and [Formula: see text] of a first‐order polynomial representing a linear trend to be removed from data. The solutions are stabilized by introducing a damping parameter in the computation of the downward‐continued anomaly by the equivalent layer method. Different from other interface mapping methods using gravity data, the proposed method: (1) takes into account the presence of an undesirable linear trend in data; (2) requires just intervals for both Δρ (rather than the knowledge of its true value) and coefficients [Formula: see text] and [Formula: see text]; and (3) does not require the knowledge of the average interface depth [Formula: see text]. As a result of (3), the proposed method does not call for extensive knowledge of the interface depth to obtain a statistically significant estimate of [Formula: see text]; rather, it is able to use the knowledge of the interface depth at just a few isolated points to estimate [Formula: see text], Δρ, [Formula: see text], and [Formula: see text]. Tests using synthetic data confirm that the method produces good and stable estimates as far as the established premises (smooth interface separating two homogeneous media and, at most, the presence of an unremoved linear trend in data) are not violated. If the density contrast is not uniform, the method may still be applied using Litinsky’s concept of effective density. The method was applied to gravity data from Recôncavo Basin, Brazil, producing good correlations of estimated lows and terraces in the basement with corresponding known geological features.

Simultaneous 3D depth-to-basement and density-contrast estimates using gravity data and depth control at few points

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. I21-I28 ◽  
Author(s):  
Cristiano M. Martins ◽  
Valeria C. Barbosa ◽  
João B. Silva
Keyword(s):  
Gravity Data ◽  
Synthetic Data ◽  
Structural Features ◽  
Density Contrast ◽  
Gravity Inversion ◽  
Inversion Method ◽  
Contrast Variation ◽  
Parabolic Law ◽  
Depth Control ◽  
Basement Depth

We have developed a gravity-inversion method for simultaneously estimating the 3D basement relief of a sedimentary basin and the parameters defining a presumed parabolic decay of the density contrast with depth in a sedimentary pack, assuming prior knowledge about the basement depth at a few points. The sedimentary pack is approximated by a grid of 3D vertical prisms juxtaposed in both horizontal directions of a right-handed coordinate system. The prisms’ thicknesses represent the depths to the basement and are the parameters to be estimated from the gravity data. To estimate the parameters defining the parabolic decay of the density contrast with depth and to produce stable depth-to-basement estimates, we imposed smoothness on the basement depths and proximity between estimated and known depths at boreholes. We applied our method to synthetic data from a simulated complex 3D basement relief with two sedimentary sections having distinct parabolic laws describing the density-contrast variation with depth. The results provide good estimates of the true parameters of the parabolic law of density-contrast decay with depth and of the basement relief. Inverting the gravity data from the onshore and part of the shallow offshore Almada Basin on Brazil’s northeastern coast shows good correlation with known structural features.

Assessing Model Uncertainty for the Scaling Function Inversion of Potential Fields

Geophysics ◽  
2021 ◽  
pp. 1-39
Author(s):  
Mahak Singh Chauhan ◽  
Ivano Pierri ◽  
Mrinal K. Sen ◽  
Maurizio FEDI
Keyword(s):  
Simulated Annealing Algorithm ◽  
Scaling Function ◽  
Vertical Section ◽  
Gravity Data ◽  
Geometric Model ◽  
Salt Dome ◽  
The Body ◽  
Gravity Inversion ◽  
Geometrical Parameters ◽  
The Scaling Function

We use the very fast simulated annealing algorithm to invert the scaling function along selected ridges, lying in a vertical section formed by upward continuing gravity data to a set of altitudes. The scaling function is formed by the ratio of the field derivative by the field itself and it is evaluated along the lines formed by the zeroes of the horizontal field derivative at a set of altitudes. We also use the same algorithm to invert gravity anomalies only at the measurement altitude. Our goal is analyzing the different models obtained through the two different inversions and evaluating the relative uncertainties. One main difference is that the scaling function inversion is independent on density and the unknowns are the geometrical parameters of the source. The gravity data are instead inverted for the source geometry and the density simultaneously. A priori information used for both the inversions is that the source has a known depth to the top. We examine the results over the synthetic examples of a salt dome structure generated by Talwani’s approach and real gravity datasets over the Mors salt dome and the Decorah (USA) basin. For all these cases, the scaling function inversion yielded models with a better sensitivity to specific features of the sources, such as the tilt of the body, and reduced uncertainty. We finally analyzed the density, which is one of the unknowns for the gravity inversion and it is estimated from the geometric model for the scaling function inversion. The histograms over the density estimated at many iterations show a very concentrated distribution for the scaling function, while the density contrast retrieved by the gravity inversion, according to the fundamental ambiguity density/volume, is widely dispersed, this making difficult to assess its best estimate.

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