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.

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.

Total variation regularization for depth-to-basement estimate: Part 2 — Physicogeologic meaning and comparisons with previous inversion methods

Geophysics ◽  
2011 ◽  
Vol 76 (1) ◽  
pp. I13-I20 ◽  
Author(s):  
Williams A. Lima ◽  
Cristiano M. Martins ◽  
João B. Silva ◽  
Valeria C. Barbosa
Keyword(s):  
Total Variation ◽  
Regularization Parameter ◽  
Synthetic Data ◽  
Gravity Inversion ◽  
Total Variation Regularization ◽  
Discontinuous Solutions ◽  
Mathematical Basis ◽  
Inversion Methods ◽  
Tv Regularization ◽  
Entropic Regularization

We applied the mathematical basis of the total variation (TV) regularization to analyze the physicogeologic meaning of the TV method and compared it with previous gravity inversion methods (weighted smoothness and entropic Regularization) to estimate discontinuous basements. In the second part, we analyze the physicogeologic meaning of the TV method and compare it with previous gravity inversion methods (weighted smoothness and entropic regularization) to estimate discontinuous basements. Presenting a mathematical review of these methods, we show that minimizing the TV stabilizing function favors discontinuous solutions because a smooth solution, to honor the data, must oscillate, and the presence of these oscillations increases the value of the TV stabilizing function. These three methods are applied to synthetic data produced by a simulated 2D graben bordered by step faults. TV regularization and weighted smoothness are also applied to the real anomaly of Steptoe Valley, Nevada, U.S.A. In all applications, the three methods perform similarly. TV regularization, however, has the advantage, compared with weighted smoothness, of requiring no a priori information about the maximum depth of the basin. As compared with entropic regularization, TV regularization is much simpler to use because it requires, in general, the tuning of just one regularization parameter.

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.

Apparent-density mapping using entropic regularization

Geophysics ◽  
2007 ◽  
Vol 72 (4) ◽  
pp. I51-I60 ◽  
Author(s):  
João B. C. Silva ◽  
Francisco S. Oliveira ◽  
Valéria C. F. Barbosa ◽  
Haroldo F. Campos Velho
Keyword(s):  
Apparent Density ◽  
Synthetic Data ◽  
Eastern Alps ◽  
Mapping Method ◽  
Zeroth Order ◽  
First Order ◽  
Density Mapping ◽  
First Case ◽  
Global Smoothness ◽  
Entropic Regularization

We present a new apparent-density mapping method on the horizontal plane that combines the minimization of the first-order entropy with the maximization of the zeroth-order entropy of the estimated density contrasts. The interpretation model consists of a grid of vertical, juxtaposed prisms in both horizontal directions. We assume that the top and the bottom of the gravity sources are flat and horizontal and estimate the prisms’ density contrasts. The minimization of the first-order entropy favors solutions presenting sharp borders, and the maximization of the zeroth-order entropy prevents the tendency of the source estimate to become a single prism. Thus, a judicious combination of both constraints may lead to solutions characterized by regions with virtually constant estimated density contrasts separated by sharp discontinuities. We apply our method to synthetic data from simulated intrusive bodies in sediments that present flat and horizontal tops. By comparing our results with those obtained with the smoothness constraint, we show that both methods produce good and equivalent locations of the sources’ central positions. However, the entropic regularization delineates the boundaries of the bodies with greater resolution, even in the case of 100-m-wide bodies separated by a distance as small as [Formula: see text]. Both the proposed and the global smoothness constraints are applied to real anomalies from the eastern Alps and from the Matsitama intrusive complex, northeastern Botswana. In the first case, the entropic regularization delineates two sources, with a horizontal and nearly flat top being consistent with the known geologic information. In the second case, both constraints produce virtually the same estimate, indicating, in agreement with results of synthetic tests, that the tops of the sources are neither flat nor horizontal.

Structure-guided gravity inversion for layered density modeling with an application in the Chezhen Depression, Bohai Bay Basin

Geophysics ◽  
2021 ◽  
pp. 1-54
Author(s):  
Jie Liu ◽  
Jianzhong Zhang
Keyword(s):  
Spline Interpolation ◽  
A Priori ◽  
Structural Similarity ◽  
Gravity Inversion ◽  
Inversion Method ◽  
Bohai Bay ◽  
Bohai Bay Basin ◽  
Lower Paleozoic ◽  
Gas Targets ◽  
Density Modeling

Gravity inversion, as a static potential field inversion, has inherent ambiguity with low vertical resolution. In order to reduce the nonuniqueness of inversion, it is necessary to impose the apriori constraints derived by other geophysical inversion, drilling or geological modeling. Based on the a priori normalized gradients derived from seismic imaging or reference models, a structure-guided gravity inversion method with a few known point constraints is developed for mapping density with multiple layers. The cubic B-spline interpolation is used to parameterize the forward modeling calculation of the gravity response to smooth density fields. A recently proposed summative gradient is used to maximize the structural similarity between the a priori and inverted models. We first demonstrate the methodology, followed by a synthetic fault model example to confirm its validity. Monte Carlo tests and uncertainty tests further illustrate the stability and practicality of the method. This method is easy to implement, and consequently produces an interpretable density model with geological consistency. Finally, we apply this method to the density modeling of the Chezhen Depression in the Bohai Bay Basin. Our work determines the distribution of deep Lower Paleozoic carbonate rocks and Archean buried hills with high-density characteristics. Our results are consistent with the existing formation mechanism of the “upper source-lower reservoir” type oil-gas targets.

On the reconstruction of the shape of a seismic streamer

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. H1-H6
Author(s):  
Bruno Goutorbe ◽  
Violaine Combier
Keyword(s):  
A Priori ◽  
Synthetic Data ◽  
Seismic Survey ◽  
Random Errors ◽  
Generalized Inversion ◽  
Reconstruction Methods ◽  
Seismic Acquisition ◽  
Marine Seismic ◽  
Gps Devices ◽  
Vessel Reconstruction

In the frame of 3D seismic acquisition, reconstructing the shape of the streamer(s) for each shot is an essential step prior to data processing. Depending on the survey, several kinds of constraints help achieve this purpose: local azimuths given by compasses, absolute positions recorded by global positioning system (GPS) devices, and distances calculated between pairs of acoustic ranging devices. Most reconstruction methods are restricted to work on a particular type of constraint and do not estimate the final uncertainties. The generalized inversion formalism using the least-squares criterion can provide a robust framework to solve such a problem — handling several kinds of constraints together, not requiring an a priori parameterization of the streamer shape, naturally extending to any configuration of streamer(s), and giving rigorous uncertainties. We explicitly derive the equations governing the algorithm corresponding to a marine seismic survey using a single streamer with compasses distributed all along it and GPS devices located on the tail buoy and on the vessel. Reconstruction tests conducted on several synthetic examples show that the algorithm performs well, with a mean error of a few meters in realistic cases. The accuracy logically degrades if higher random errors are added to the synthetic data or if deformations of the streamer occur at a short length scale.

Explaining monotonic ranking functions

2020 ◽  
Vol 14 (4) ◽  
pp. 640-652
Author(s):  
Abraham Gale ◽  
Amélie Marian
Keyword(s):  
Decision Making ◽  
Selection Process ◽  
A Priori ◽  
Data Distribution ◽  
Synthetic Data ◽  
Decision Processes ◽  
Decision Makers ◽  
Ranking Functions ◽  
High School Admissions ◽  
Parameter Values

Ranking functions are commonly used to assist in decision-making in a wide variety of applications. As the general public realizes the significant societal impacts of the widespread use of algorithms in decision-making, there has been a push towards explainability and transparency in decision processes and results, as well as demands to justify the fairness of the processes. In this paper, we focus on providing metrics towards explainability and transparency of ranking functions, with a focus towards making the ranking process understandable, a priori , so that decision-makers can make informed choices when designing their ranking selection process. We propose transparent participation metrics to clarify the ranking process, by assessing the contribution of each parameter used in the ranking function in the creation of the final ranked outcome, using information about the ranking functions themselves, as well as observations of the underlying distributions of the parameter values involved in the ranking. To evaluate the outcome of the ranking process, we propose diversity and disparity metrics to measure how similar the selected objects are to each other, and to the underlying data distribution. We evaluate the behavior of our metrics on synthetic data, as well as on data and ranking functions on two real-world scenarios: high school admissions and decathlon scoring.

Marlim R3D: A realistic model for controlled-source electromagnetic simulations — Phase 2: The controlled-source electromagnetic data set

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. E293-E299
Author(s):  
Jorlivan L. Correa ◽  
Paulo T. L. Menezes
Keyword(s):  
A Priori ◽  
Synthetic Data ◽  
Realistic Model ◽  
Earth Model ◽  
Data Sets ◽  
Data Set ◽  
Geoelectric Model ◽  
Controlled Source ◽  
The North ◽  
Electromagnetic Simulations

Synthetic data provided by geoelectric earth models are a powerful tool to evaluate a priori a controlled-source electromagnetic (CSEM) workflow effectiveness. Marlim R3D (MR3D) is an open-source complex and realistic geoelectric model for CSEM simulations of the postsalt turbiditic reservoirs at the Brazilian offshore margin. We have developed a 3D CSEM finite-difference time-domain forward study to generate the full-azimuth CSEM data set for the MR3D earth model. To that end, we fabricated a full-azimuth survey with 45 towlines striking the north–south and east–west directions over a total of 500 receivers evenly spaced at 1 km intervals along the rugged seafloor of the MR3D model. To correctly represent the thin, disconnected, and complex geometries of the studied reservoirs, we have built a finely discretized mesh of [Formula: see text] cells leading to a large mesh with a total of approximately 90 million cells. We computed the six electromagnetic field components (Ex, Ey, Ez, Hx, Hy, and Hz) at six frequencies in the range of 0.125–1.25 Hz. In our efforts to mimic noise in real CSEM data, we summed to the data a multiplicative noise with a 1% standard deviation. Both CSEM data sets (noise free and noise added), with inline and broadside geometries, are distributed for research or commercial use, under the Creative Common License, at the Zenodo platform.

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.

Migration moveout analysis and depth focusing

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 91-100 ◽  
Author(s):  
Claude F. Lafond ◽  
Alan R. Levander
Keyword(s):  
Heterogeneous Media ◽  
A Priori ◽  
Complex Structure ◽  
Tomographic Reconstruction ◽  
Synthetic Data ◽  
Real Data ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Data Set ◽  
Velocity Models

Prestack depth migration still suffers from the problems associated with building appropriate velocity models. The two main after‐migration, before‐stack velocity analysis techniques currently used, depth focusing and residual moveout correction, have found good use in many applications but have also shown their limitations in the case of very complex structures. To address this issue, we have extended the residual moveout analysis technique to the general case of heterogeneous velocity fields and steep dips, while keeping the algorithm robust enough to be of practical use on real data. Our method is not based on analytic expressions for the moveouts and requires no a priori knowledge of the model, but instead uses geometrical ray tracing in heterogeneous media, layer‐stripping migration, and local wavefront analysis to compute residual velocity corrections. These corrections are back projected into the velocity model along raypaths in a way that is similar to tomographic reconstruction. While this approach is more general than existing migration velocity analysis implementations, it is also much more computer intensive and is best used locally around a particularly complex structure. We demonstrate the technique using synthetic data from a model with strong velocity gradients and then apply it to a marine data set to improve the positioning of a major fault.

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