Gravity inversion of a discontinuous relief stabilized by weighted smoothness constraints on depth

Geophysics ◽  
1999 ◽  
Vol 64 (5) ◽  
pp. 1429-1437 ◽  
Author(s):  
Valéria C. F. Barbosa ◽  
João B. C. Silva ◽  
Walter E. Medeiros
Keyword(s):  
A Priori ◽  
Bouguer Anomaly ◽  
Initial Solution ◽  
Maximum Depth ◽  
Normal Faults ◽  
Gravity Inversion ◽  
Inversion Method ◽  
Solution Stability ◽  
Flat Bottom ◽  
Northern Portion

We present a new stable gravity inversion method applied to the mapping of an interface separating two homogeneous media. In contrast with previous similar methods, it does not impose an overall smoothness on the estimated interface to stabilize the solution. The density contrast between the media is assumed to be known. The interpretation model for the upper medium consists of rectangular juxtaposed prisms whose thicknesses represent the depths to the interface and are the parameters to be estimated. The true interface is assumed to be flat everywhere except at faults. To incorporate this attribute into the estimated relief, we developed an iterative process in which three kinds of constraints are imposed on parameters: (1) proximity between values of adjacent parameters, (2) lower and upper bounds to parameters, and (3) proximity between the values of parameters and fixed numerical values. Starting with an initial solution which presents an overall smooth relief, the method enhances initially estimated geometric features of the interface; that is, flat areas will tend to become flatter and steep areas will tend to become steeper. This is accomplished by weighting the constraints, which requires proximity between adjacent parameters. The weights are initialized with values equal to unity and are updated automatically to enhance any discrepancy between adjacent depths that have been detected at the initial solution. Constraints 2 and 3 are used both to compensate for the decrease in solution stability caused by the introduction of small weights and to reinforce flatness at the basin bottom. Constraint 2 imposes that any depth be nonnegative and smaller than an a priori known maximum depth value, whereas constraint 3 imposes that all depths be closest to a value greater than the maximum depth. The trade‐off between these conflicting constraints is attained with a final relief presenting flat bottom and steep borders. The method was tested with a synthetic gravity anomaly produced by a simulated sedimentary cratonic extensional basin whose basement consists of steep edges and a flat bottom. The results showed an improvement in the resolution of the relief, leading to a reliable mapping both of the sharp discontinuities at the borders and of the lateral extent of the base of the basin. Additionally, the method produced excellent estimates for the average dip angles of the basin edges (presumably controlled by normal faults), indicating, in this way, its potential in interpreting data produced by this kind of basin. The method was applied to the Bouguer anomaly from the northern portion of Steptoe Valley, Nevada, delineating an isolated basin with a wider, flat base and relatively straight borders as compared with the estimate imposing overall smoothness on the relief.

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.

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.

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.

Three-dimensional gravity inversion using graph theory to delineate the skeleton of homogeneous sources

Geophysics ◽  
2015 ◽  
Vol 80 (2) ◽  
pp. G53-G66 ◽  
Author(s):  
Rodrigo Bijani ◽  
Cosme F. Ponte-Neto ◽  
Dionisio U. Carlos ◽  
Fernando J. S. Silva Dias
Keyword(s):  
Genetic Algorithm ◽  
Graph Theory ◽  
Minimum Spanning Tree ◽  
Gravity Data ◽  
A Priori ◽  
Three Dimensional ◽  
Real Data ◽  
Gravity Inversion ◽  
Inversion Method ◽  
Dimensional Gravity

We developed a new strategy, based on graph theory concepts, to invert gravity data using an ensemble of simple point masses. Our method consisted of a genetic algorithm with elitism to generate a set of possible solutions. Each estimate was associated to a graph to solve the minimum spanning tree (MST) problem. To produce unique and stable estimates, we restricted the position of the point masses by minimizing the statistical variance of the distances of an MST jointly with the data-misfit function during the iterations of the genetic algorithm. Hence, the 3D spatial distribution of the point masses identified the skeleton of homogeneous gravity sources. In addition, our method also gave an estimation of the anomalous mass of the source. So, together with the anomalous mass, the skeleton could aid other 3D methods with promising geometric a priori parameters. Several tests with different values of regularizing parameter were made to bespeak this new regularizing strategy. The inversion results applied to noise-corrupted synthetic gravity data revealed that, regardless of promising starting models, the estimated distribution of point masses and the anomalous mass offered valuable information about the homogeneous sources in the subsurface. Tests on real data from a portion of Quadrilátero Ferrífero, Minas Gerais state, Brazil, were performed for complementary analysis of the proposed inversion method.

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.

The Congo basin: an example of failed rift

2021 ◽  
Author(s):  
Francesca Maddaloni ◽  
Damien Delvaux ◽  
Magdala Tesauro ◽  
Taras Gerya ◽  
Carla Braitenberg
Keyword(s):  
Congo Basin ◽  
Gravity Inversion ◽  
Inversion Method ◽  
Formation Mechanisms ◽  
Equatorial Position ◽  
The South ◽  
Weak Zone ◽  
Lithospheric Thickness ◽  
Numerical Tests ◽  
History Of

<p>The Congo basin (CB), considered as a typical intracratonic basin, due its slow and long-lived subsidence history and the largely unknown formation mechanisms, occupies a large part of the Congo craton, derived from the amalgamation of different cratonic pieces. It recorded the history of deposition of up to one billion years of sediments, one of the longest geological records on Earth above a metamorphic basement. The CB initiated very probably as a failed rift in late Mesoproterozoic and evolved during the Neoproterozoic and Phanerozoic under the influence of far-field compressional tectonic events, global climate fluctuation between icehouse and greenhouse conditions and drifting of Central Africa through the South Pole then towards its present-day equatorial position. Since Cretaceous, the CB has been subjected to an intraplate compressional setting due to ridge-push forces related to the spreading of the South Atlantic Ocean, where most of sediments are being eroded and accumulated only in the center of the basin.</p><p>In this study, we first reconstructed the stratigraphy, the depths of the main seismic horizons, and the tectonic history of the CB, using geological and exploration geophysical data. In particular, we interpreted about 2600 km of seismic reflection profiles and well log data located inside the central area of the CB (Cuvette Centrale). We used the obtained results to constrain the gravity field data that we analyzed, in order to reconstruct the depth of the basement and investigate the shallow crustal structure of the basin. To this purpose, we used a gravity inversion method with two different density contrasts between the surface sediments and crystalline rocks.</p><p>The results evidence NW-SE trending structures, also revealed by magnetic and seismic data, corresponding to the alternation of highs and sediments filled topographic depressions, related to rift structures, characterizing the first stage of evolution of the CB. They also show a general good consistency between the seismic and gravity basement along the seismic profiles and evidence the presence of possible high-density bodies in the shallow to deep crust. The identified structures are prevalently the product of an extensional tectonics, which likely acted in more than one direction.</p><p>Therefore, we performed 3D numerical simulations to test the hypothesis of the formation of the CB as multi-extensional rift in a cratonic area, using the thermomechanical I3ELVIS code, based on a combination of a finite difference method applied on a uniformly spaced Eulerian staggered grid with the marker-in-cell technique. To this purpose, the numerical tests have been conducted considering a sub-circular weak zone in the central part of the cratonic lithosphere and applying a velocity of 2.5 cm/yr in two orthogonal directions (N-S and E-W). We repeated these numerical tests by increasing the size of the weak zone and varying its lithospheric thickness. The results show the formation of a circular basin in the central part of the cratonic lithosphere, characterized by a series of highs and depressions, consistent with those obtained from geophysical/geological reconstructions.</p>

Source-independent extended waveform inversion based on space-time source extension: Frequency-domain implementation

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. R449-R461 ◽  
Author(s):  
Guanghui Huang ◽  
Rami Nammour ◽  
William W. Symes
Keyword(s):  
Source Function ◽  
Random Noise ◽  
A Priori ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Inversion Method ◽  
Target Velocity ◽  
Extended Source ◽  
Full Waveform ◽  
Time Variables

Source signature estimation from seismic data is a crucial ingredient for successful application of seismic migration and full-waveform inversion (FWI). If the starting velocity deviates from the target velocity, FWI method with on-the-fly source estimation may fail due to the cycle-skipping problem. We have developed a source-based extended waveform inversion method, by introducing additional parameters in the source function, to solve the FWI problem without the source signature as a priori. Specifically, we allow the point source function to be dependent on spatial and time variables. In this way, we can easily construct an extended source function to fit the recorded data by solving a source matching subproblem; hence, it is less prone to cycle skipping. A novel source focusing annihilator, defined as the distance function from the real source position, is used for penalizing the defocused energy in the extended source function. A close data fit avoiding the cycle-skipping problem effectively makes the new method less likely to suffer from local minima, which does not require extreme low-frequency signals in the data. Numerical experiments confirm that our method can mitigate cycle skipping in FWI and is robust against random noise.

scholarly journals A new lidar inversion method using a surface reference target applied to the backscattering coefficient and lidar ratio retrievals of a fog-oil plume at short range

2020 ◽  
Vol 13 (4) ◽  
pp. 1921-1935
Author(s):  
Florian Gaudfrin ◽  
Olivier Pujol ◽  
Romain Ceolato ◽  
Guillaume Huss ◽  
Nicolas Riviere
Keyword(s):  
Short Range ◽  
A Priori ◽  
Inversion Method ◽  
Backscattering Coefficient ◽  
Reference Target ◽  
Lidar Measurements ◽  
Lidar Ratio ◽  
Aerosol Plume ◽  
Good Agreement

Abstract. In this paper, a new elastic lidar inversion equation is presented. It is based on the backscattering signal from a surface reference target (SRT) rather than that from a volumetric layer of reference (Rayleigh molecular scatterer) as is usually done. The method presented can be used when the optical properties of such a layer are not available, e.g., in the case of airborne elastic lidar measurements or when the lidar–target line is horizontal Also, a new algorithm is described to retrieve the lidar ratio and the backscattering coefficient of an aerosol plume without any a priori assumptions about the plume. In addition, our algorithm allows a determination of the instrumental constant. This algorithm is theoretically tested, viz. by means of simulated lidar profiles and then using real measurements. Good agreement with available data in the literature has been found.

X.—A Gravity Survey in Ayrshire and its Geological Interpretation

1966 ◽  
Vol 66 (10) ◽  
pp. 239-265 ◽  
Author(s):  
Adam C. McLean
Keyword(s):  
Gravity Field ◽  
Bouguer Anomaly ◽  
Gravity Survey ◽  
Normal Faults ◽  
Red Sandstone ◽  
Geological Interpretation ◽  
The North ◽  
Close Relationship ◽  
Lower Palaeozoic ◽  
Western Limb

SynopsisBouguer anomaly maps covering most of Ayrshire at a density of about one station per sq. km., show a close relationship between anomalies and the distribution of the Upper Palæozoic rocks in the area south of the Inch-gotrick Fault, but are less clearly interpreted to the north, where thick dense igneous masses are present.In central and south Ayrshire the gravity field may be largely interpreted in terms of the known density-contrasts at the interfaces separating Upper and Lower Old Red Sandstone, and Lower Old Red Sandstone and Lower Palæozoic rocks. The major structure, the Mauchline Basin, is reflected clearly in the largest anomaly, and there is evidence of a culmination of its south-western limb near Kirkoswald. The important N.E.–S.W. faults also give rise to large anomalies, which may be connected with the known geology. It is inferred that they moved as normal faults in Carboniferous times, and that the adjacent synclines are essentially sags associated with the fault displacements. There is geophysical evidence that both the Southern Upland and Kerse Loch Faults existed in Middle O.R.S. (proto-Armorican) times. It is concluded that a hypothesis of N.–S. Armorican stress is not valid in south Ayrshire.In north Ayrshire, many of the anomalies are best explained by changes of thickness of the Millstone Grit lavas and of the Clyde Plateau lavas, and by the presence of thick dolerite intrusions. Additional evidence is needed, however, before final conclusions may be drawn.

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.

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