Iranian Journal of Geophysics

Iranian Journal of Geophysics

Using the grey wolf optimization algorithm for estimating parameters of buried geometric objects with gravity data: A case study - Humble salt dome

Document Type : Research Article

Authors
Mona Ahmadi 1
Ali Nejati Kalate 2
Afshin Akbari 3
1 Ph.D. Student, Department of Petroleum, Mining and Materials Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran
2 Associate Professor, Department of Mining, Petroleum, and Geophysics, Shahrood University of Technology, Shahrood, Iran
3 Assistant Professor, Department of Petroleum, Mining and Materials Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran
10.30499/ijg.2024.420648.1547
Abstract
In this article, the Grey Wolf Optimization (GWO) algorithm is discussed, which is considered a global optimization technique capable of improving the global search of particles across the entire search space. The Grey Wolf Algorithm is a relatively new algorithm inspired by the hunting behavior of grey wolves and was first introduced by Mirjalili and his colleagues in 2014. This algorithm has been applied in a few cases to geophysical data. The main goal of the Grey Wolf Optimization Algorithm is to optimize objective functions by drawing inspiration from the behavior of wolf packs to reach better and optimal solutions. Therefore, each of the wolves represents a model with dimensions corresponding to the number of model parameters. The parameters of each wolf (model) include amplitude Coefficient (A), Depth (z), Shape Factor (q), and Center of Mass (x0). The designed algorithm is run for 300 iterations with 30 search agents (wolves), and it is tested on the objective function 10 times, taking the average optimal solution provided by the software as the final parameter.
   To evaluate the performance of  this method, the gravity field of three synthetic  models, namely a sphere, a horizontal cylinder, and a vertical cylinder, both with and without the addition of random noise, is analyzed. Frequency domain estimation of the model parameters is used for each of these models. The results show that the proposed algorithm can accurately estimate the model parameters. Subsequently, the Grey Wolf Optimization Algorithm is applied to analyze the gravity field of the Humble salt dome area in the United States. The results for the studied region indicate that the buried object's center of mass is approximately 4.76 kilometers deep, the domain coefficient is 294.25 units, and its approximate shape is calculated to be similar to a sphere with a calculated shape factor of 1.47, which aligns well with previous studies. The advantage of  GWO inversion is its ability to fine-tune the parameters quickly, avoid local minima, and estimate the optimal parameter values.
   In this study, the Root Mean Square (RMS) statistical measure is used to compare the measured gravity field and the gravity field calculated based on the estimated parameters. The error between the gravity field values of the synthetic  models and the values calculated from the optimal parameters obtained by the Grey Wolf  Optimization Algorithm is very small, indicating the algorithm's good performance. Furthermore, the sensitivity of this algorithm to various  levels of random noise is investigated, and the results indicate the algorithm's stability against random noise.
 
Keywords
Simple geometric shapes
grey wolf optimization algorithm
gravity anomaly
salt dome
inverse modeling

Subjects

اسحق زاده ع.، حاجیان ع.، خلیلی ش.،1396، مدل سازی وارون دو بعدی میدان گرانی باقی مانده با استفاده از شبکه عصبی پیشخور مدولار : مطالعه موردی یک معدن کرومیت، نشریه پژوهشهای ژئوفیزیک کاربردی،43-60.
Abdelrahman EM, Bayoumi AI, Abdelhady YE, Gobash MM, EL-Araby HM., 1989,Gravity interpretation using correlation factors between successive leastsquares residual anomalies. Geophysics 54, 1614e1621.
Abdelrahman, E. M., Bayoumi, A. I., and El-Araby, H. M., 1991. A least-squares minimization approach to invert gravity data. Geophysics, 56, 115-l 18.
Abdelrahman, E.M., El-Araby, T.M., El-Araby, H.M. and Abo-Ezz, E.R., 2001, A new method for shape and depth determinations from gravity data. Geophysics, 66, 1774–1778.
Agarwal, A. C., S. Shalivahan, and R. K. Singh, 2017, GreyWolf Optimizer: A new strategy to invert geophysical data sets: Geophysical Prospecting, accepted.
Asfahani, J., Tlas, M., 2012. Fair function minimization for direct interpretation of residual gravity anomaly profiles due to spheres and cylinders. Pure and Applied Geophysics 169, 157e165.
Barbosa,V. C. F., and Joao,B., 1994, Generalized compact gravity inversion: Geophysics, 59,57-68.
  Biswas A.,2015, Interpretation of residual gravity anomaly caused by simple shaped bodies using very fast simulated annealing global optimization, Geoscience Frontiers 6:875-893
Chandra, A., Agarwal, A. & Singh, R. K.,2017, Grey wolf optimisation for inversion of layered earth 451 geophysical datasets. Near Surf. Geophys. 15(5), 499-513 https://doi.org/10.3997/1873- 452 0604.2017017 .
 Eshaghzadeh. A Seyedi Sahebari.,S.,2020, Multivariable teaching-learning-based optimization (MTLBO) algorithm for estimating the structural parameters of the buried mass by magnetic data. Journal of  Geofizika 37(2):213-235
 Eshaghzadeh.A. Hajian.,A.,2020, Multivariable Modified Teaching Learning Based Optimization (MM-TLBO) Algorithm for Inverse Modeling of Residual Gravity Anomaly Generated by Simple Geometric Shapes. Journal of Environmental & Engineering Geophysics 25(4):463-476
Essa, K. S., and Elhussein, M., 2018, PSO (Particle Swarm Optimization) for interpretation of magnetic anomalies caused by simple geometrical structures: Pure and Applied Geophysics, 175(10), 3539-3553.
Essa, K.S., 2013. Gravity interpretation of dipping faults using the variance analysis method. J. Geophys. Eng. 10, 015003
Essa, K.S., 2014. New fast least-squares algorithm for estimating the best-fitting parameters Geophysics 30, 424e438.
Gupta, O.P., 1983, A least-squares approach to depth determination from gravity data, Geophysics, 48(3), 357-360.
Hartmann, R.R., Teskey, D., Friedberg, I., 1971. A system for rapid digital aeromagnetic interpretation. Geophysics 36, 891e918.
Mehanee, S.A., 2014. Accurate and efficient regularised inversion approach for the interpretation of isolated gravity anomalies. Pure and Applied Geophysics 171, 1897e1937. http://dx.doi.org/10.1007/s00024-013-0761-z.
Miensopust MP .,2017, Application of 3-D electromagnetic inversion in practice: challenges, pitfalls and solution approaches. Surv Geophys 38(5):869–933
Mirjalili S, S. M. Mirjalili and A. Lewis., 2014 , Grey Wolf Optimizer, Advances in Engineering Software, Vol.69, pp.46-61.
Muro C, R. Escobedo, L. Spector and R.
 
Coppinger.,2011, “Wolf-pack (Canis Lupus) Hunting  Strategies Emerge from Simple Rules in Computational Simulations,” Behavioural Processes, Vol.88, No.3, pp.192-197.
Nandi, B.K., Shaw, R.K. and Agarwal, N.P., 1997, A short note on identification of the shape of simple causative sources from gravity data. Geophys. Prospect., 45, 513–520.
Odegard, M.E., Berg, J.W., 1965. Gravity interpretation using the Fourier integral. Roshan R., Singh U. K., 2017: Inversion of residual gravity anomalies using tuned PSO. Geosci. Instrum. Methods Data Syst., 6, 1, 71–79, doi: 10.5194/gi-6-71-2017.
Roshan R., Singh U. K., 2017, Inversion of residual gravity anomalies using tuned PSO. Geosci. Instrum. Methods Data Syst., 6, 1, 71–79, doi: 10.5194/gi-6-71-2017.
Salem, A., Elawadi, E. and Ushijima, K., 2003, Short note: depth determination from residual anomaly using a simple formula. Computer Geosci., 29, 801–804.
Santos, F. A. M.,2010, Inversion of self – potential of idealized bodies’ anomalies using particle swarm optimization, Comput. Geosci., 36, 1185–1190.
Sen, M.K., Stoffa, P.L., 2013. Global Optimization Methods in Geophysical Inversion. Cambridge University Press, Cambridge, p. 289.
Sharma, B. and Geldart, L.P., 1968, Analysis of gravity anomalies of two dimensional faults using Fourier transforms. Geophys. Prospect., 16, 77–93.
Snieder R .,1998,The role of nonlinearity in inverse problems." Inverse Problems 14.3.
Song, Xianhai, Tang, Li, Zhao, Sutao, Zhang, Xueqiang, Li, Lei, Huang, Jianquan, & Cai, Wei., 2015, Grey wolf optimizer for parameter estimation in surface waves. Soil Dynamics and Earthquake Engineering, 75, 147-157.
Tarantola A.,2005, Inverse problem theory and methods for model parameter estimation. Society for Industrial and Applied Mathematics.
Thompson, D. T. (1982): EULDPH A new technique for making computer-assisted depth estimates from magnetic data, Geophysics, 47, p. 31, https://doi.org/10.1190/1.1441278.
Tlas, M., Asfahani, J., Karmeh, H., 2005. A versatile nonlinear inversion to interpret gravity anomaly caused by a simple geometrical structure. Pure and Applied Geophysics 162, 2557e2571.
Yuan S, Shangxu W, Nan T .,2009, Swarm intelligence optimization and its application in geophysical data inversion. Applied Geophysics 6.2: 166-174.
Iranian Journal of Geophysics
Volume 18, Issue 4
September and October 2024
Pages 59-77