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.

Three‐dimensional gravity inversion using simulated annealing: Constraints on the diapiric roots of allochthonous salt structures

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1438-1449 ◽  
Author(s):  
Seiichi Nagihara ◽  
Stuart A. Hall
Keyword(s):  
Simulated Annealing ◽  
Gulf Of Mexico ◽  
Gravity Data ◽  
A Priori ◽  
Gravity Inversion ◽  
Inversion Method ◽  
A Priori Information ◽  
Final Density ◽  
Smoothing Effects ◽  
Priori Information

In the northern continental slope of the Gulf of Mexico, large oil and gas reservoirs are often found beneath sheetlike, allochthonous salt structures that are laterally extensive. Some of these salt structures retain their diapiric feeders or roots beneath them. These hidden roots are difficult to image seismically. In this study, we develop a method to locate and constrain the geometry of such roots through 3‐D inverse modeling of the gravity anomalies observed over the salt structures. This inversion method utilizes a priori information such as the upper surface topography of the salt, which can be delineated by a limited coverage of 2‐D seismic data; the sediment compaction curve in the region; and the continuity of the salt body. The inversion computation is based on the simulated annealing (SA) global optimization algorithm. The SA‐based gravity inversion has some advantages over the approach based on damped least‐squares inversion. It is computationally efficient, can solve underdetermined inverse problems, can more easily implement complex a priori information, and does not introduce smoothing effects in the final density structure model. We test this inversion method using synthetic gravity data for a type of salt geometry that is common among the allochthonous salt structures in the Gulf of Mexico and show that it is highly effective in constraining the diapiric root. We also show that carrying out multiple inversion runs helps reduce the uncertainty in the final density model.

Practical applications of uniqueness theorems in gravimetry: Part II—Pragmatic incorporation of concrete geologic information

Geophysics ◽  
2002 ◽  
Vol 67 (3) ◽  
pp. 795-800 ◽  
Author(s):  
Valéria C. F. Barbosa ◽  
João B. C. Silva ◽  
Walter E. Medeiros
Keyword(s):  
Gravity Data ◽  
A Priori ◽  
Gravity Inversion ◽  
Solution Stability ◽  
Practical Applications ◽  
Density Distributions ◽  
Alternative Method ◽  
True Source ◽  
Priori Information ◽  
Simply Connected

We illustrate the importance of establishing solution uniqueness through mathematical restrictions reflecting a source attribute. We also illustrate the validity and utility of a guideline derived in an accompanying paper for constructing sound gravity inversion methods for the class of sources presenting either homogeneous or depth‐independent density distributions. The two‐part guideline is (1) to introduce a priori information favoring uniqueness, either by assuming that a nonnull density distribution depending only on x and y is confined to the interior of a horizontal slab with known position or by limiting the class of possible solutions to homogeneous, simply connected polygons (or polyhedra) with known density, displaying no fancy shapes and no curling apophyses at their borders, and (2) to introduce information favoring solution stability by estimating only the features of the source which may be resolved by the data. Following the guideline, we apply different methods to gravity data using interpretation models consisting of a grid of cells on the x‐y and x‐z planes. In both cases the estimates are very close to the true synthetic source. The data produced by the distribution varying with x and z are also inverted using the method, which minimizes the norm of the first‐order derivative of the density. This constraint does not reflect a true source attribute but is strong enough to stabilize the solution and to guarantee its uniqueness. Because of the strong bias imposed to the solution, the estimated distribution, although unique and stable, is far from the true source, concentrating most of the anomalous mass at the surface. Finally, we present an alternative method which redistributes the estimated anomalous mass downward. To be effective, this technique requires prior knowledge about the source depth to the top. In addition, the source should not be too small and deep. Although being able to produce good results, this alternative method requires a great dose of the interpreter's art.

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.

Generalized compact gravity inversion

Geophysics ◽  
1994 ◽  
Vol 59 (1) ◽  
pp. 57-68 ◽  
Author(s):  
Valeria Cristina F. Barbosa ◽  
João B. C. Silva
Keyword(s):  
Body Shape ◽  
Sedimentary Basin ◽  
A Priori ◽  
Gravity Inversion ◽  
A Priori Information ◽  
Magnetite Ore ◽  
Inversion Technique ◽  
True Value ◽  
Ore Body ◽  
Priori Information

Extending the compact gravity inversion technique by incorporating a priori information about the maximum compactness of the anomalous sources along several axes provides versatility. Thus, the method may also incorporate information about limits in the axes lengths or greater concentration of mass along one or more directions. The judicious combination of different constraints on the anomalous mass distribution allows the introduction of several kinds of a priori information about the (arbitrary) shape of the sources. This method is particularly applicable to constant, linear density sources such as mineralizations along faults and intruded sills, dikes, and laccoliths in a sedimentary basin. The correct source density must be known with a maximum uncertainty of 40 percent; otherwise, the inversion produces thicker bodies for densities smaller than the true value and vice‐versa. Because of the limitations of the inverse gravity problem, the proposed technique requires an empirical technique to analyze the sensitivity of solutions to uncertainties in the a priori information. The proposed technique is based on a finite number of acceptable solutions, presumably representative of the ambiguity region. By using standard statistical techniques, each parameter is assigned a coefficient measuring its uncertainty. The known hematite and magnetite ore body shape, in the vicinity of Iron Mountain, MO, was reproduced quite well using this inversion technique.

An attempt to formulate well‐posed questions in gravity: Application of linear inverse techniques to mining exploration

Geophysics ◽  
1984 ◽  
Vol 49 (10) ◽  
pp. 1781-1793 ◽  
Author(s):  
Vincent Richard ◽  
Roger Bayer ◽  
Michel Cuer
Keyword(s):  
Linear Programming ◽  
Gravity Data ◽  
A Priori ◽  
Massive Sulfide ◽  
Sulfide Deposit ◽  
Exploration Process ◽  
Programming Techniques ◽  
Priori Information ◽  
Mining Exploration ◽  
Well Posed

The aim of this paper is to use linear inverse theory to interpret gravity surveys in mining exploration by incorporating a priori information on the densities and data in terms of Gaussian or uniform probability laws. The Bayesian approach and linear programming techniques lead to the solution of well‐posed questions resulting from the exploration process. In particular, we develop a method of measuring the possible heterogeneity within a given domain by using linear programming. These techniques are applied to gravity data taken over the massive sulfide deposit of Neves Corvo (Portugal). We show how crude constraints on the densities lead to a first estimation of the location of sources, while further geologic constraints allow us to estimate the heterogeneity and to put definite bounds on the ore masses.

1D single-site and laterally constrained inversion of multifrequency and multicomponent ground-based electromagnetic induction data — Application to the investigation of a near-surface clayey overburden

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. WB19-WB35 ◽  
Author(s):  
Cyril Schamper ◽  
Fayçal Rejiba ◽  
Roger Guérin
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Induction ◽  
Search Algorithm ◽  
Random Search ◽  
A Priori ◽  
Synthetic Data ◽  
Conductive Layer ◽  
Near Surface ◽  
Priori Information ◽  
Definition Of

Electromagnetic induction (EMI) methods are widely used to determine the distribution of the electrical conductivity and are well adapted to the delimitation of aquifers and clayey layers because the electromagnetic field is strongly perturbed by conductive media. The multicomponent EMI device that was used allowed the three components of the secondary magnetic field (the radial [Formula: see text], the tangential [Formula: see text], and the vertical [Formula: see text]) to be measured at 10 frequencies ranging from 110 to 56 kHz in one single sounding with offsets ranging from 20 to 400 m. In a continuing endeavor to improve the reliability with which the thickness and conductivity are inverted, we focused our research on the use of components other than the vertical magnetic field Hz. Because a separate sensitivity analysis of [Formula: see text] and [Formula: see text] suggests that [Formula: see text] is more sensitive to variations in the thickness of a near-surface conductive layer, we developed an inversion tool able to make single-sounding and laterally constrained 1D interpretation of both components jointly, associated with an adapted random search algorithm for single-sounding processing for which almost no a priori information is available. Considering the complementarity of [Formula: see text] and [Formula: see text] components, inversion tests of clean and noisy synthetic data showed an improvement in the definition of the thickness of a near-surface conductive layer. This inversion code was applied to the karst site of the basin of Fontaine-Sous-Préaux, near Rouen (northwest of France). Comparison with an electrical resistivity tomography tends to confirm the reliability of the interpretation from the EMI data with the developed inversion tool.

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.

scholarly journals Seismic Constrained Gravity Inversion: A Reliable Tool to Improve Geophysical Models Away from Seismic Information

Geosciences ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 467
Author(s):  
Daniele Sampietro ◽  
Martina Capponi
Keyword(s):  
High Resolution ◽  
Gravity Field ◽  
A Priori ◽  
Geophysical Methods ◽  
Real Life ◽  
Gravity Inversion ◽  
Seismic Surveys ◽  
Real Model ◽  
Gravity Fields ◽  
Priori Information

The exploitation of gravity fields in order to retrieve information about subsurface geological structures is sometimes considered a second rank method, in favour of other geophysical methods, such as seismic, able to provide a high resolution detailed picture of the main geological horizons. Within the current work we prove, through a realistic synthetic case study, that the gravity field, thanks to the availability of freely of charge high resolution global models and to the improvements in the gravity inversion methods, can represent a valid and cheap tool to complete and enhance geophysical modelling of the Earth’s crust. Three tests were carried out: In the first one a simple two-layer problem was considered, while in tests two and three we considered two more realistic scenarios in which the availability on the study area of constraints derived from 3D or 2D seismic surveys were simulated. In all the considered test cases, in which we try to simulate real-life scenarios, the gravity field, inverted by means of an advanced Bayesian technique, was able to obtain a final solution closer to the (simulated) real model than the assumed a priori information, typically halving the uncertainties in the geometries of the main geological horizons with respect to the initial model.

scholarly journals SIMULATION MODELLING IN THE STRUCTURAL GRAVITY PROSPECTING

2019 ◽  
pp. 38-48
Author(s):  
S. H. Anikeyev ◽  
S. M. Bahriy ◽  
B. B. Hablovskiy
Keyword(s):  
Cross Sections ◽  
Gravity Data ◽  
A Priori ◽  
Structural Type ◽  
Simulation Modelling ◽  
Gravity Modeling ◽  
Gravity Inversion ◽  
Density Structure ◽  
Data Modelling ◽  
Computer Technologies

In accordance with the purpose of geophysical exploration, the gravity data interpretation is aimed at prospecting mineral resources which is based on the study of the geological cross-section structure. The task of quantitative interpretation, which uses methods of gravity modeling and gravity inversion, is the modelling of a gravity field (gravity modeling) and of a density structure of geological environments (gravity inversion). The article presents the definition and steps of the gravity data modelling technique. This technique is based on the construction of an informal sequence of equivalent solutions. The technological and geological features of methods for modelling the density structure of complex geological environments are given; among them geological content, consistency with a priori data and the subordination of modelling to geological hypotheses are important. The topicality and methods of simulation modelling are outlined. The purpose of simulation modelling is to study the properties of gravity inversion in the general formulation, as well as to evaluate the degree of detail and reliability of the methods and technologies of gravity modelling, which claim to be an effective solution to geological problems. The example of structural simulation testing of the methods of informal sequence of equivalent solutions and its computer technologies shows that a complex interpretation of seismic and gravity measurements data enables the creation of detailed density models of structural cross-sections. The ways of increasing the veracity of gravity data modelling of structural cross-sections have been studied. It is revealed that the best approximation of the regional background is an inclined plane which approximates the observed field of gravity according to characteristic pickets over the research areas that are better studied. The increase in the veracity of modeling can also be achieved by rebuilding the near side zones in the structural type models in an interactive process of solving structural gravity inversion problems. Substantive modeling depends primarily on the experience of the interpreter since computer technologies for gravity modeling and gravity inversion are merely an interpretation tool.

Generalized positivity constraint on magnetic equivalent layers

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. J99-J110
Author(s):  
André L. A. Reis ◽  
Vanderlei C. Oliveira Jr. ◽  
Valéria C. F. Barbosa
Keyword(s):  
Inverse Problem ◽  
Magnetic Moment ◽  
A Priori ◽  
Synthetic Data ◽  
Total Field ◽  
Magnetization Direction ◽  
Moment Distribution ◽  
Equivalent Sources ◽  
Priori Information ◽  
Equivalent Layer

It is known from the potential theory that a continuous and planar layer of dipoles can exactly reproduce the total-field anomaly produced by arbitrary 3D sources. We have proven the existence of an equivalent layer having an all-positive magnetic-moment distribution for the case in which the magnetization direction of this layer is the same as that of the true sources, regardless of whether the magnetization of the true sources is purely induced or not. By using this generalized positivity constraint, we have developed a new iterative method for estimating the total magnetization direction of 3D magnetic sources based on the equivalent-layer technique. Our method does not impose a priori information about the shape or the depth of the sources, does not require regularly spaced data, and presumes that the sources have a uniform magnetization direction. At each iteration, our method performs two steps. The first step solves a constrained linear inverse problem to estimate a positive magnetic-moment distribution over a discrete equivalent layer of dipoles. We consider that the equivalent sources are located on a plane and have a uniform and fixed magnetization direction. In the second step, we use the estimated magnetic-moment distribution and solve a nonlinear inverse problem for estimating a new magnetization direction for the dipoles. The algorithm stops when the equivalent layer yields a total-field anomaly that fits the observed data. Tests with synthetic data simulating different geologic scenarios show that the final estimated magnetization direction is close to the true one. We apply our method to field data from the Goiás alkaline province, over the Montes Claros complex, in the center of Brazil. The results suggest the presence of intrusions with remarkable remanent magnetization, in agreement with the current literature for this region.

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