scholarly journals A Fast Interpretation Method for Inverse Modeling of Residual Gravity Anomalies Caused by Simple Geometry

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Khalid S. Essa
Keyword(s):  
Gravity Anomaly ◽  
Shape Factor ◽  
Vertical Cylinder ◽  
Gravity Anomalies ◽  
Depth Estimation ◽  
Model Parameters ◽  
Fast Method ◽  
Random Errors ◽  
Residual Gravity ◽  
Amplitude Coefficient

An inversion technique using a fast method is developed to estimate, successively, the depth, the shape factor, and the amplitude coefficient of a buried structure using residual gravity anomalies. By defining the anomaly value at the origin and the anomaly value at different points on the profile, the problem of depth estimation is transformed into a problem of solving a nonlinear equation of the form . Knowing the depth, the shape factor can be estimated and finally the amplitude coefficient can be estimated. This technique is applicable for a class of geometrically simple anomalous bodies, including the semiinfinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The efficiency of this technique is demonstrated with gravity anomaly due to a theoretical model, in each case with and without random errors. Finally, the applicability is illustrated using the residual gravity anomaly of Mobrun ore body, situated near Noranda, QC, Canada. The interpreted depth and the other model parameters are in good agreement with the known actual values.

Shape and depth solutions from gravity data using correlation factors between successive least‐squares residuals

Geophysics ◽  
1993 ◽  
Vol 58 (12) ◽  
pp. 1785-1791 ◽  
Author(s):  
El‐Sayed M. Abdelrahman ◽  
Hesham M. El‐Araby
Keyword(s):  
Least Squares ◽  
Shape Factor ◽  
Gravity Data ◽  
Bouguer Anomaly ◽  
Vertical Cylinder ◽  
Gravity Anomalies ◽  
Horizontal Cylinder ◽  
Amplitude Coefficient ◽  
Regional Component ◽  
Correlation Factors

The gravity anomaly expression produced by most geologic structures can be represented by a continuous function in both shape (shape factor) and depth variables with an amplitude coefficient related to the mass. Correlation factors between successive least‐squares residual gravity anomalies from a buried vertical cylinder, horizontal cylinder, and sphere are used to determine the shape and depth of the buried geologic structure. For each shape factor value, the depth is determined automatically from the correlation value. The computed depths are plotted against the shape factor representing a continuous correlation curve. The solution for the shape and depth of the buried structure is read at the common intersection of correlation curves. This method can be applied to a Bouguer anomaly profile consisting of a residual component caused by local structure and a regional component. This is a powerful technique for automatically separating the Bouguer data into residual and regional polynomial components. This method is tested on theoretical examples and a field example. In both cases, the results obtained are in good agreement with drilling results.

scholarly journals Inversion of residual gravity anomalies using tuned PSO

2017 ◽  
Vol 6 (1) ◽  
pp. 71-79 ◽  
Author(s):  
Ravi Roshan ◽  
Upendra Kumar Singh
Keyword(s):  
Particle Swarm Optimization ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Gravity Anomalies ◽  
Optimization Method ◽  
Model Parameters ◽  
Swarm Optimization ◽  
Residual Gravity ◽  
Amplitude Coefficient ◽  
Improved Technique

Abstract. Many kinds of particle swarm optimization (PSO) techniques are now available and various efforts have been made to solve linear and non-linear problems as well as one-dimensional and multi-dimensional problems of geophysical data. Particle swarm optimization is a metaheuristic optimization method that requires intelligent guesswork and a suitable selection of controlling parameters (i.e. inertia weight and acceleration coefficient) for better convergence at global minima. The proposed technique, tuned PSO, is an improved technique of PSO, in which efforts have been made to choose the controlling parameters, and these parameters have been selected after analysing the responses of various possible exercises using synthetic gravity anomalies over various geological sources. The applicability and efficacy of the proposed method is tested and validated using synthetic gravity anomalies over various source geometries. Finally, tuned PSO is applied over field residual gravity anomalies of two different geological terrains to find the model parameters, namely amplitude coefficient factor (A), shape factor (q) and depth (z). The analysed results have been compared with published results obtained by different methods that show a significantly excellent agreement with real model parameters. The results also show that the proposed approach is not only superior to the other methods but also that the strategy has enhanced the exploration capability of the proposed method. Thus tuned PSO is an efficient and more robust technique to achieve an optimal solution with minimal error.

scholarly journals Depth and shape solutions from residual gravity anomalies due to simple geometric structures using a statistical approach

2017 ◽  
Vol 47 (2) ◽  
pp. 113-132 ◽  
Author(s):  
El-Sayed Abdelrahman ◽  
Mohamed Gobashy
Keyword(s):  
Gravity Data ◽  
Random Noise ◽  
Synthetic Data ◽  
Vertical Cylinder ◽  
Gravity Anomalies ◽  
Horizontal Cylinder ◽  
Random Errors ◽  
Residual Gravity ◽  
Characteristic Points ◽  
The Usa

AbstractWe have developed a simple and fast quantitative method for depth and shape determination from residual gravity anomalies due to simple geometrical bodies (semi-infinite vertical cylinder, horizontal cylinder, and sphere). The method is based on defining the anomaly value at two characteristic points and their corresponding distances on the anomaly profile. Using all possible combinations of the two characteristic points and their corresponding distances, a statistical procedure is developed for automated determination of the best shape and depth parameters of the buried structure from gravity data. A least-squares procedure is also formulated to estimate the amplitude coefficient which is related to the radius and density contrast of the buried structure. The method is applied to synthetic data with and without random errors and tested on two field examples from the USA and Germany. In all cases examined, the estimated depths and shapes are found to be in good agreement with actual values. The present method has the capability of minimizing the effect of random noise in data points to enhance the interpretation of results.

scholarly journals Inversion of Residual Gravity Anomalies using Tuned-PSO Technique

2016 ◽  
Author(s):  
Ravi Roshan ◽  
Upendra Kumar Singh
Keyword(s):  
Particle Swarm Optimization ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Gravity Anomalies ◽  
Optimization Method ◽  
Model Parameters ◽  
Swarm Optimization ◽  
Residual Gravity ◽  
Amplitude Coefficient ◽  
Improved Technique

Abstract. Many kinds of particle swarm optimization (PSO) technique are now available and various efforts have been made to solve linear and non linear problems as well as one dimensional and multidimensional problem of geophysical data. Particle swarm optimization is a Meta heuristic optimization method that requires the intelligent guess and suitable selection of controlling parameters (i.e. Inertia weight and acceleration coefficient) for better convergence at global minima. The proposed technique Tuned–PSO is an improved technique of PSO, in which effort has been made for choosing the controlling parameters and these parameters have selected after analysing the response of various possible exercises using synthetic gravity anomalies over various geological sources. The applicability and efficacy of the proposed method is tested and also validated using synthetic gravity anomalies over various source geometries. Finally Tuned-PSO is applied over field residual gravity anomalies of two different geological terrains to find out the model parameters namely amplitude coefficient factor (A), shape factor (q) and depth (z). The analysed results have been compared with published results obtained by different methods that show a significantly excellent agreement with real model parameters. The results also show that the proposed approach is not only superior to the other methods but also shows that the strategy has enhanced the exploration capability of proposed method. Thus Tuned–PSO is an efficient and more robust technique to achieve optimal solution with minimal error.

Three least‐squares minimization approaches to depth, shape, and amplitude coefficient determination from gravity data

Geophysics ◽  
2001 ◽  
Vol 66 (4) ◽  
pp. 1105-1109 ◽  
Author(s):  
E. M. Abdelrahman ◽  
H. M. El‐Araby ◽  
T. M. El‐Araby ◽  
E. R. Abo‐Ezz
Keyword(s):  
Least Squares ◽  
Shape Factor ◽  
Least Squares Method ◽  
Gravity Data ◽  
Synthetic Data ◽  
Gravity Anomalies ◽  
Maximum Error ◽  
The United States ◽  
Random Errors ◽  
Amplitude Coefficient

Three different least‐squares approaches are developed to determine, successively, the depth, shape (shape factor), and amplitude coefficient related to the radius and density contrast of a buried structure from the residual gravity anomaly. By defining the anomaly value g(max) at the origin on the profile, the problem of depth determination is transformed into the problem of solving a nonlinear equation, [Formula: see text]. Formulas are derived for spheres and cylinders. Knowing the depth and applying the least‐squares method, the shape factor and the amplitude coefficient are determined using two simple linear equations. In this way, the depth, shape, and amplitude coefficient are determined individually from all observed gravity data. A procedure is developed for automated interpretation of gravity anomalies attributable to simple geometrical causative sources. The method is applied to synthetic data with and without random errors. In all the cases examined, the maximum error in depth, shape, and amplitude coefficient is 3%, 1.5%, and 7%, respectively. Finally, the method is tested on a field example from the United States, and the depth and shape obtained by the present method are compared with those obtained from drilling and seismic information and with those published in the literature.

Regional‐residual gravity anomaly separation using the minimum‐curvature technique

Geophysics ◽  
1991 ◽  
Vol 56 (2) ◽  
pp. 279-283 ◽  
Author(s):  
K. L. Mickus ◽  
C. L. V. Aiken ◽  
W. D. Kennedy
Keyword(s):  
Gravity Anomaly ◽  
Gravity Anomalies ◽  
Bouguer Gravity ◽  
Bouguer Gravity Anomaly ◽  
Residual Gravity ◽  
Residual Gravity Anomaly ◽  
Gravity Interpretation ◽  
Minimum Curvature

One of the most difficult problems in gravity interpretation is the separation of regional and residual gravity anomalies from the Bouguer gravity anomaly. This study discusses the application of the minimum‐curvature method to determine the regional and residual gravity anomalies.

A least‐squares minimization approach to depth determination from moving average residual gravity anomalies

Geophysics ◽  
1993 ◽  
Vol 58 (12) ◽  
pp. 1779-1784 ◽  
Author(s):  
El‐Sayed M. Abdelrahman ◽  
Tarek M. El‐Araby
Keyword(s):  
Least Squares ◽  
Gravity Data ◽  
Moving Average ◽  
Gravity Anomalies ◽  
The United States ◽  
Random Errors ◽  
Minimization Method ◽  
Residual Gravity ◽  
Average Residual ◽  
Least Squares Minimization

We have developed a least‐squares minimization method to estimate the depth of a buried structure from moving average residual gravity anomalies. The method involves fitting simple models convolved with the same moving average filter as applied to the observed gravity data. As a result, our method can be applied not only to residuals but also to the Bouguer gravity data of a short profile length. The method is applied to synthetic data with and without random errors. The validity of the method is tested in detail on two field examples from the United States and Senegal.

scholarly journals Interpretation of gravity anomalies due to simple geometric-shaped structures based on quadratic curve regression

2018 ◽  
Vol 48 (2) ◽  
pp. 161-178 ◽  
Author(s):  
Mohammed Tlas ◽  
Jamal Asfahani
Keyword(s):  
Gaussian White Noise ◽  
Synthetic Data ◽  
Gravity Anomalies ◽  
Real Data ◽  
Real Field ◽  
Model Parameters ◽  
Data Set ◽  
Simple Method ◽  
Residual Gravity ◽  
Quadratic Curve

Abstract An easy and very simple method to interpret residual gravity anomalies due to simple geometrical shaped models such as a semi-infinite vertical rod, an infinite horizontal rod, and a sphere has been proposed in this paper. The proposed method is mainly based on the quadratic curve regression to best-estimate the model parameters, e.g. the depth from the surface to the center of the buried structure (sphere or infinite horizontal rod) or the depth from the surface to the top of the buried object (semi-infinite vertical rod), the amplitude coefficient, and the horizontal location from residual gravity anomaly profile. The proposed method has been firstly tested on synthetic data set corrupted and contaminated by a Gaussian white noise level to demonstrate the capability and the reliability of the method. The results acquired show that the estimated parameters values derived by this proposed method are very close to the assumed true parameters values. Next, the validity of the presented method is demonstrated on synthetic data set and 3 real data sets from Cuba, Sweden and Iran. A comparable and acceptable agreement is indicated between the results derived by this method and those from the real field data information.

Multivariable Modified Teaching Learning Based Optimization (MM-TLBO) Algorithm for Inverse Modeling of Residual Gravity Anomaly Generated by Simple Geometric Shapes

2020 ◽  
Vol 25 (4) ◽  
pp. 463-476
Author(s):  
Ata Eshaghzadeh ◽  
Alireza Hajian
Keyword(s):  
Gravity Anomaly ◽  
Gravity Data ◽  
Optimal Solution ◽  
Model Parameters ◽  
Major Purpose ◽  
Residual Gravity ◽  
Tlbo Algorithm ◽  
Residual Gravity Anomaly ◽  
Teaching Learning Based Optimization ◽  
Teaching Learning

This paper presents an improved nature-based algorithm, namely multivariable modified teaching learning based optimization (MM-TLBO) algorithm, as in an iterative process can estimates the best values for the model parameters in a multi-objective problem. The algorithm works in two computational phases: the teacher phase and the learner phase. The major purpose of the MM-TLBO algorithm is to improve the value of the learners and thus, improving the value of the model parameters which leads to the optimal solution. The variables of each learner (model) are the radius ( R), depth ( h), shape factor ( q), density contrast ( ρ) and axis location ( x0) parameters. We apply MM-TLBO and TLBO methods for the residual gravity anomalies caused by the buried masses with a simple geometry such as spheres, horizontal and vertical cylinders. The efficiency of these methods are also tested by noise corruption synthetic data, as the acceptable results were obtained. The obtained results indicate the better performance the MM-TLBO algorithm than the TLBO algorithm. We have utilized the MM-TLBO for the interpretation of the six residual gravity anomaly profiles from Iran, USA, Sweden and Senegal. The advantage of the MM-TLBO inversion is that it can estimates the best solutions very fast without falling into local minimum and reaches to a premature convergence. The considered primary population for the synthetic and real gravity data are thirty and fifty models. The results show which this method is able to achieve the optimal responses even if a small population of learners had been considered.

Sign in / Sign up

Export Citation Format

Share Document