Gravity inversion using open, reject, and “shape‐of‐anomaly” fill criteria

Geophysics ◽  
1986 ◽  
Vol 51 (4) ◽  
pp. 988-994 ◽  
Author(s):  
R. M. René
Keyword(s):  
Center Of Mass ◽  
Initial Density ◽  
Model Space ◽  
Constant Factor ◽  
Density Contrast ◽  
Gravity Inversion ◽  
Inversion Method ◽  
Inverse Models ◽  
Seed Method ◽  
The Given

A gravity inversion method is developed by iteratively applying open, reject, and fill (O-R-F) criteria within a model space comprising a great many rectangular prisms. Each prism is assigned a density contrast. The modeling procedure consists of filling some prisms while leaving others empty. Only one element is filled for each pass. Generally, elements are added only to the periphery of the growing model. Models can be allowed to grow in any combination of directions, or in all directions. By application of a “shape‐of‐anomaly” fill criterion, the model rapidly attains a form which yields gravity approximating the given gravity scaled down by some constant factor. As the model continues to grow, this scale factor approaches unity. The method readily yields inverse models comprising several thousand individual prisms. Examples presented here give applications to 2-D problems. The method is readily applicable to [Formula: see text] and 3-D problems as well. Overhanging elements are obtained by appropriate use of model constraints. Initial density models are not required but they are allowed. An “expanding seed” method is explained which efficiently generates sets of inverse models by using dense models to initiate development of less dense models. The method is applied to inversion of several synthetic gravity profiles from known density models. A density model is also derived from gravity across the Troodos massif in Cyprus. Using a density contrast of [Formula: see text], the resultant model extends from the surface to a depth of 20.6 km and has a center of mass distribution displaced approximately 7 km to the northeast of the anomaly peak.

scholarly journals Three‐dimensional crustal structure in central Taiwan from gravity inversion with a parallel genetic algorithm

Geophysics ◽  
2004 ◽  
Vol 69 (4) ◽  
pp. 917-924 ◽  
Author(s):  
Jian Zhang ◽  
Chi‐Yuen Wang ◽  
Yaolin Shi ◽  
Yongen Cai ◽  
Wu‐Cheng Chi ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Finite Element ◽  
Gravity Anomaly ◽  
Seismic Velocity ◽  
Empirical Relation ◽  
Initial Density ◽  
Model Space ◽  
Element Model ◽  
Gravity Inversion ◽  
Central Taiwan

The genetic algorithm method is combined with the finite‐element method for the first time as an alternative method to invert gravity anomaly data for reconstructing the 3D density structure in the subsurface. The method provides a global search in the model space for all acceptable models. The computational efficiency is significantly improved by storing the coefficient matrix and using it in all forward calculations, then by dividing the region of interest into many subregions and applying parallel processing to the subregions. Central Taiwan, a geologically complex region, is used as an example to demonstrate the utility of the method. A crustal block 120 × 150 km2 in area and 34 km in thickness is represented by a finite‐element model of 76 500 cubic elements, each 2 × 2 × 2 km3 in size. An initial density model is reconstructed from the regional 3D tomographic seismic velocity using an empirical relation between velocity and density. The difference between the calculated and the observed gravity anomaly (i.e., the residual anomaly) shows an elongated minimum of large magnitude that extends along the axis of the Taiwan mountain belt. Among the interpretive models tested, the best model shows a crustal root extending to depths of 50 to 60 km beneath the axis of the Western Central and Eastern Central Ranges with a density contrast of 400 or 500 kg/m3 across the Moho. Both predictions appear to be supported by independent seismological and laboratory evidence.

Adaptive learning 3D gravity inversion for salt-body imaging

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. I49-I57 ◽  
Author(s):  
Fernando J. S. Silva Dias ◽  
Valéria C. F. Barbosa ◽  
João B. C. Silva
Keyword(s):  
Adaptive Learning ◽  
Learning Strategy ◽  
Gravity Data ◽  
Density Contrast ◽  
Piecewise Constant Function ◽  
Gravity Inversion ◽  
Inversion Method ◽  
Outer Loop ◽  
Bottom Depth ◽  
Geometric Elements

We have developed an iterative scheme for inverting gravity data produced by salt bodies with density contrasts relative to the sediments varying from positive to negative, crossing, in this way, the nil zone. Our inversion method estimates a 3D density-contrast distribution, through a piecewise constant function defined on a user-specified grid of cells. It consists of two nested iterative loops. The outer loop uses an adaptive learning strategy that starts with a coarse grid of cells, a set of first-guess geometric elements (axes and points) and the corresponding assigned density contrasts. From the second iteration on, this strategy refines the grid and automatically creates a new set of geometric elements (points only) and associated density contrasts. Each geometric element operates as the first-guess skeletal outline of a section of the salt body to be imaged. The inner loop estimates the 3D density-contrast distribution for the grid of cells and for the set of geometric elements defined in the outer loop. The outer loop allows for easy incorporation of prior geologic information about the lithologic units and automatic evolution of the prior information. The inner loop forces the estimated density contrast of each cell to be close either to a null or to a non-null prespecified value. The iteration stops when the geometries of the estimated salt bodies are invariant along successive iterations. We apply our method to synthetic gravity data produced by a homogeneous salt body embedded in heterogeneous sediments. We tested two geologic hypotheses about the real gravity data from Galveston Island salt dome, USA. In the first, the estimated salt body attains a maximum bottom depth of 5 km, whereas in the second hypothesis, it is shallower and discloses an overhang. Both solutions fit the data and are feasible geologically, so both hypotheses are acceptable.

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.

3D gravity inversion through an adaptive-learning procedure

Geophysics ◽  
2009 ◽  
Vol 74 (3) ◽  
pp. I9-I21 ◽  
Author(s):  
Fernando J. Silva Dias ◽  
Valéria C. Barbosa ◽  
João B. Silva
Keyword(s):  
Adaptive Learning ◽  
Measurement Errors ◽  
Gravity Anomalies ◽  
Density Contrast ◽  
Gravity Inversion ◽  
Inversion Method ◽  
Target Density ◽  
Geometric Element ◽  
Geometric Elements ◽  
Interpretation Model

We have developed a gravity inversion method to estimate a 3D density-contrast distribution producing strongly interfering gravity anomalies. The interpretation model consists of a grid of 3D vertical, juxtaposed prisms in the horizontal and vertical directions. Iteratively, our approach estimates the 3D density-contrast distribution that fits the observed anomaly within the measurement errors and favors compact gravity sources closest to prespecified geometric elements such as axes and points. This method retrieves the geometry of multiple gravity sources whose density contrasts (positive and negative values) are prescribed by the interpreter through the geometric element. At the first iteration, we set an initial interpretation model and specify the first-guess geometric elements and their target density contrasts. Each geometric element operates as the first-guess skeletal outline of the entire homogeneous gravity source or any of its homogeneous parts to be reconstructed. From the second iteration on, our method automatically redefines a new set of geometric elements, the associated target density contrasts, and a new interpretation model whose number of prisms increases with the iteration. The iteration stops when the geometries of the estimated sources are invariant along successive iterations. Tests on synthetic data from geometrically complex bodies and on field data collected over a mafic-ultramafic body and a volcanogenic sedimentary sequence located in the Tocantins Province, Brazil, confirmed the potential of our method in producing a sharp image of multiple and adjacent bodies.

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>

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.

THE CLASSICAL LIMIT OF A SELF-CONSISTENT QUANTUM-VLASOV EQUATION IN 3D

1993 ◽  
Vol 03 (01) ◽  
pp. 109-124 ◽  
Author(s):  
PETER A. MARKOWICH ◽  
NORBERT J. MAUSER
Keyword(s):  
Kinetic Energy ◽  
Initial Density ◽  
Poisson System ◽  
Planck Constant ◽  
Density Matrices ◽  
Accumulation Points ◽  
Schmidt Norm ◽  
Bounded Trace ◽  
The Given ◽  
Uniformly Bounded

Under natural assumptions on the initial density matrix of a mixed quantum state (Hermitian, non-negative definite, uniformly bounded trace, Hilbert-Schmidt norm and kinetic energy) we prove that accumulation points (as the scaled Planck constant tends to zero) of solutions of a corresponding slightly regularized Wigner-Poisson system are distributional solutions of the classical Vlasov-Poisson system. The result holds for the gravitational and repulsive cases. Also, for every phase-space density in [Formula: see text] (with bounded kinetic energy) we prepare a sequence of density matrices satisfying the above assumptions, such that the given density is the limit of the Wigner transforms of these density matrices.

scholarly journals Angle Bisector Algorithm and Modified Dynamic Programming Algorithm for Dubins Traveling Salesman Problem

2021 ◽  
Author(s):  
Eswara Venkata Kumar Dhulipala
Keyword(s):  
Euclidean Distance ◽  
Travelling Salesman Problem ◽  
Dynamic Programming Algorithm ◽  
Constant Factor ◽  
Programming Algorithm ◽  
Worst Case ◽  
Angle Bisector ◽  
Set Of Points ◽  
The Given ◽  
Tour Length

A Dubin's Travelling Salesman Problem (DTSP) of finding a minimum length tour through a given set of points is considered. DTSP has a Dubins vehicle, which is capable of moving only forward with constant speed. In this paper, first, a worst case upper bound is obtained on DTSP tour length by assuming DTSP tour sequence same as Euclidean Travelling Salesman Problem (ETSP) tour sequence. It is noted that, in the worst case, \emph{any algorithm that uses of ETSP tour sequence} is a constant factor approximation algorithm for DTSP. Next, two new algorithms are introduced, viz., Angle Bisector Algorithm (ABA) and Modified Dynamic Programming Algorithm (MDPA). In ABA, ETSP tour sequence is used as DTSP tour sequence and orientation angle at each point $i_k$ are calculated by using angle bisector of the relative angle formed between the rays $i_{k}i_{k-1}$ and $i_ki_{k+1}$. In MDPA, tour sequence and orientation angles are computed in an integrated manner. It is shown that the ABA and MDPA are constant factor approximation algorithms and ABA provides an improved upper bound as compared to Alternating Algorithm (AA) \cite{savla2008traveling}. Through numerical simulations, we show that ABA provides an improved tour length compared to AA, Single Vehicle Algorithm (SVA) \cite{rathinam2007resource} and Optimized Heading Algorithm (OHA) \cite{babel2020new,manyam2018tightly} when the Euclidean distance between any two points in the given set of points is at least $4\rho$ where $\rho$ is the minimum turning radius. The time complexity of ABA is comparable with AA and SVA and is better than OHA. Also we show that MDPA provides an improved tour length compared to AA and SVA and is comparable with OHA when there is no constraint on Euclidean distance between the points. In particular, ABA gives a tour length which is at most $4\%$ more than the ETSP tour length when the Euclidean distance between any two points in the given set of points is at least $4\rho$.

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