Abstract
Cuckoo Search Algorithm (CSA) is a nature-inspired metaheuristic optimization algorithm. The optimization algorithm was inspired by the life story of a family of birds called the Cuckoo. In this paper, an application of the CSA, is implemented to estimate model parameters of deep-seated faults by using gravity anomalies. To increase the efficiency of the algorithm, parameter tuning studies are carried out for the optimum algorithm-based control parameters. In addition, the reliability and possible uncertainties of the obtained solutions were examined using probability density function analysis. The model parameters (z1, z2, α, x0 and ρ) for noisy and noise-free synthetic models were obtained by using CSA. These obtained parameters are very compatible with the true model parameters for noise-free data, similarly well-nigh compatible results for noisy data. As a result we can say that the method works successfully when applied to synthetic data. The technique is tested on three widely studied benchmark field data including gravity anomaly [Garber Fault (USA), Gazal Fault (Egypt), Mersa Matruh Fault (Egypt)]. In previous studies, various solution techniques have been used for the inversion of these field data and the compatibility of the model parameters obtained in this study with the values obtained from previous studies was compared. The results demonstrate that the CSA is a very effective and robust approach for the optimization of gravity anomalies.
Similar content being viewed by others
Data availability
The author confirms that the data supporting the findings of this study are available within the article.
References
Abdelrahman, E. M., & Bayoumi, A. I. (1989). Nomograms for delineating fault parameters from gravity data application to the Mersa Matruh Basin Egypt. Journal of African Earth Sciences, 9, 455–459.
Abdelrahman, E. M., Bayoumi, A. I., Abdelhady, Y. E., Gobashy, M. M., & El-Araby, H. M. (1989). Gravity interpretation using correlation factors between successive least-squares residual anomalies. Geophysics, 54(12), 1614–1621.
Abdelrahman, E. M., & El-Araby, T. M. (1996). Shape and depth solutions from moving average residual gravity anomalies. Journal of Applied Geophysics, 36, 89–95.
Abdelrahman, E. M., El-Araby, T. M., El-Araby, H. M., & Abo-Ezz, E. R. (2001a). Three least squares minimization approaches to depth, shape, and amplitude coefficient determination from gravity data. Geophysics, 66, 1105–1109.
Abdelrahman, E. M., El-Araby, T. M., El-Araby, H. M., & Abo-Ezz, E. R. (2001b). A new method for shape and depth determinations from gravity data. Geophysics, 66, 1774–1780.
Abdelrahman, E. M., El-Araby, T. M., & Essa, K. S. (2003). Shape and depth solutions from third moving average residual gravity anomalies using the window curves method. Kuwait Journal of Science and Engineering, 30, 95–108.
Abdelrahman, E. M., & Essa, K. S. (2015). Three least-squares minimization approaches to interpret gravity data due to dipping faults. Pure and Applied Geophysics, 172, 427–438.
Abdelrahman, E. M., Essa, K. S., & Abo-Ezz, E. R. (2013). A least-squares window curves method to interpret gravity data due to dipping faults. Journal of Geophysics Engineering, 10, 025003.
Abdelrahman, E. S., Gobashy, M., Abo-Ezz, E., & El-Araby, T. (2019). A new method for complete quantitative interpretation of gravity data due to dipping faults. Contributions to Geophysics and Geodesy, 49, 133–151.
Abdelrahman, E. M., Radwan, A. H., Issawy, E. A., El-Araby, H. M., El-Araby, T. M., & Abo-Ezz, E. R. (1999). Gravity interpretation of vertical faults using correlation factors between successive least-squares residual anomalies. In Mining pribram symposium on mathematical methods in geology, MC2 (pp. 1–6).
Abdelrahman, E. M., & Sharafeldin, S. H. M. (1995). A least-squares minimization approach to shape determination from gravity data. Geophysics, 60, 589–590.
Abdelrahman, E. M., Tealeb, A., & Ahmed, H. A. (1991). Gravity map of Kalabsha area, northwest of Aswan Lake, and its structural significance. Journal of Geodynamics, 14(1–4), 125–135.
Alkan, H., & Balkaya, C. (2018). Parameter estimation by differential search algorithm from horizontal loop electromagnetic (HLEM) data. Journal of Applied Geophysics, 149, 77–94.
Anderson, N., Essa, K. S., & Elhussein, M. (2020). A comparison study using particle swarm optimization inversion algorithm for gravity anomaly interpretation due to a 2D vertical fault structure. Journal of Applied Geophysics, 179, 104120.
Balkaya, Ç. (2013). An implementation of differential evolution algorithm for inversion of geoelectrical data. Journal of Applied Geophysics, 98, 160–175.
Barakat, M. G., & Darwish, M. (1987). Contribution to the lithostratigraphy of the lower cretaceous sequence in Mersa Matruh area, north Western Desert, Egypt. M.E.R.C Ain Shams University. Earth Science Series, 1, 48–66.
Ben, U. C., Akpan, A. E., Enyinyi, E. O., & Awak, E. (2021). Novel technique for the interpretation of gravity anomalies over geologic structures with idealized geometries using the Manta ray foraging optimization. Journal of Asian Earth Sciences, 6, 100070.
Bowin, C., Scheer, E., & Smith, W. (1986). Depth estimates from ratios of gravity, geoid, and gravity gradient anomalies. Geophysics, 51, 123–136.
Braitenberg, C., Sampietro, D., Pivetta, T., Zuliani, D., Barbagallo, A., Fabris, P., et al. (2016). Gravity for detecting caves: Airborne and terrestrial simulations based on a comprehensive karstic cave benchmark. Pure and Applied Geophysics, 173, 1243–1264.
Chakravarthi, V., Mallesh, K., & Ramamma, B. (2017). Basement depth estimation from gravity anomalies: Two 2.5D approaches coupled with the exponential density contrast model. Journal of Geophysics and Engineering, 14, 303–315.
Chakravarthi, V., & Sundararajan, N. (2004). Ridge-regression algorithm for gravity inversion of fault structures with variable density. Geophysics, 69(6), 1394–1404.
Chakravarthi, V., & Sundararajan, N. (2005). Invgrafalt: A Fortran code for Marquardt inversion of gravity anomalies of faulted beds with varying density. Computers & Geosciences, 31(10), 1234–1240.
Civicioglu, P., & Besdok, E. (2013). A conceptual comparison of the cuckoo-search, particle swarm optimization, differential evolution and artificial bee colony algorithms. Artificial Intelligence Review, 39, 315–346.
Coelho, A. C. Q. M., Menezes, P. T. L., & Mane, M. A. (2021). Gravity data as a faulting assessment tool for unconventional reservoirs regional exploration: The Sergipe-Alagoas Basin example. Journal of Natural Gas Science and Engineering, 94, 104077.
Davis, J. C. (1973). Statistics and data analysis in geology (p. 550). Wiley.
Eiben, A. E., & Smit, S. K. (2011). Parameter tuning for configuring and analyzing evolutionary algorithms. Swarm and Evolutionary Computation, 1(1), 19–31.
Ekinci, Y. L., Balkaya, Ç., & Göktürkler, G. (2019). Parameter estimations from gravity and magnetic anomalies due to deep-seated faults: Differential evolution versus particle swarm optimization. Turkish Journal of Earth Sciences, 28(6), 860–881.
Ekinci, Y. L., Balkaya, Ç., Göktürkler, G., & Özyalın, Ş. (2021). Gravity data inversion for the basement relief delineation through global optimization: A case study from the Aegean Graben System, western Anatolia, Turkey. Geophysical Journal International, 224(2), 923–944.
Eshaghzadeh, A., Dehghanpour, A., & Kalantari, R. A. (2019). Fault strike detection using satellite gravity data decomposition by discrete wavelets: A case study from Iran. Journal of Sciences, Islamic Republic of Iran, 30(1), 41–50. https://doi.org/10.22059/jsciences.2019.69631
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 and Engineering Geophysics, 25(4), 463–476. https://doi.org/10.32389/JEEG20-003
Eshaghzadeh, A., & Hajian, A. (2021). 2-D gravity inverse modelling of anticlinal structure using improved particle swarm optimization (IPSO). Arabian Journal of Geosciences, 14, 1378. https://doi.org/10.1007/s12517-021-07798-6
Eshaghzadeh, A., & Hajian, A. (2022). Modelling of residual gravity data due to a near surface dyke structure using damped SVD and marquardt inverse methods. Geofísica Internacional, 61(4), 325–350. https://doi.org/10.22201/igeof.00167169p.2022.61.4.2203
Essa, K. S. (2013). Gravity interpretation of dipping faults using the variance analysis method. Journal of Geophysics and Engineering, 10, 015003.
Essa, K. S. (2021). Evaluation of the parameters of fault-like geologic structure from the gravity anomalies applying the particle swarm. Environmental Earth Sciences, 80, 489.
Essa, K. S., & Gèraud, Y. (2020). Parameters estimation from the gravity anomaly caused by the two-dimensional horizontal thin sheet applying the global particle swarm algorithm. Journal of Petroleum Science and Engineering, 193, 107421.
Essa, K. S., Géraud, Y., & Diraison, M. (2021b). Fault parameters assessment from the gravity data profiles using the global particle swarm optimization. Journal of Petroleum Science and Engineering, 207, 109129.
Essa, K. S., Mehanee, S. A., & Elhussein, M. (2021a). Gravity data interpretation by a two-sided fault-like geologic structure using the global particle swarm technique. Physics of the Earth and Planetary Interiors, 311, 106631.
Essa, K. S., Mehanee, S. A., Soliman, K. S., & Diab, Z. E. (2020). Gravity profile interpretation using the R-parameter imaging technique with application to ore exploration. Ore Geology Reviews, 126, 103695.
Essa, K. S., & Munschy, M. (2019). Gravity data interpretation using the particle swarm optimization method with application to mineral exploration. Journal of Earth System Science, 128(5), 123.
Evans, K., Beavan, J., & Simpson, D. (1991). Estimating aquifer parameters from analysis of forced fluctuations in well level: An example from the Nubian Formation near Aswan, Egypt: 1. Hydrogeological background and large-scale permeability estimates. Journal of Geophysical Research, 96, 12127–12137.
Fat-Helbary, R. E., & Tealeb, A. A. (2002). A study of seismicity and earthquake hazard at the proposed Kalabsha Dam Site, Aswan, Egypt. Natural Hazards, 25, 117–133.
Ferris, C. (1987). Gravity anomaly resolution at the Garber field. Geophysics, 52, 1570–1579.
Fister, I., Yang, X. S., Fister, D., & Fister, I. (2014). Cuckoo search: a brief literature review. In X. S. Yang (Ed.), Cuckoo search and firefly algorithm. Studies in computational intelligence (Vol. 516, pp. 49–62). Springer.
Gämperle, R., Müller, S. D., & Koumoutsakos, P. (2002). A parameter study for differential evolution. In A. Grmela & N. E. Mastorakis (Eds.), Advances in intelligent systems, fuzzy systems, evolutionary computation (pp. 293–298). WSEAS Press.
Grant, F. S., & West, G. F. (1965). Interpretation theory in applied geophysics (p. 584). New York: McGraw Hill Co.
Gupta, O. P. (1983). A least-squares approach to depth determination from gravity data. Geophysics, 48, 357–360.
Issawi, B. (1969). The geology of Kurkur-Dungul area. Geological Survey of Egypt Paper, 46, 102.
Joshi, A. S., Kulkarni, O., Kakandikar, G. M., & Nandedkar, V. M. (2017). Cuckoo search optimization—A review. Materials Today: Proceedings, 4, 7262–7269.
Kirkland, D. W., Denison, R. E., & Rooney, M. A. (1995). Diagenetic alteration of Permian strata at oil fields of south central Oklahoma, USA. Marine and Petroleum Geology, 12(6), 629–644.
Lelièvre, P. G., Farquharson, C. G., & Hurich, C. A. (2012). Joint inversion of seismic traveltimes and gravity data on unstructured grids with application to mineral exploration. Geophysics, 77(1), K1–K15.
Lichoro, C. M., Árnason, K., & Cumming, W. (2019). Joint interpretation of gravity and resistivity data from the Northern Kenya volcanic rift zone: Structural and geothermal significance. Geothermics, 77, 139–150.
Lines, L. R., & Treitel, S. (1984). A review of least-squares inversion and its application to geophysical problems. Geophysical Prospecting, 32, 159–186.
Martínez-Moreno, F. J., Galindo-Zaldívar, J., Pedrera, A., González-Castillo, L., Ruano, P., Calaforra, J. M., et al. (2015). Detecting gypsum caves with microgravity and ERT under soil water content variations (Sorbas, SE Spain). Engineering Geology, 193, 38–48.
Mohan, N. L., Anandababu, L., & Rao, S. (1986). Gravity interpretation using the Melin transform. Geophysics, 51, 114–122.
Mulugeta, B. D., Fujimitsu, Y., Nishijima, J., & Saibi, H. (2021). Interpretation of gravity data to delineate the subsurface structures and reservoir geometry of the Aluto-Langano geothermal field, Ethiopia. Geothermics, 94, 102093.
Murthy, R. I. V., & Krishnamacharyulu, S. K. G. (1990). Automatic inversion of gravity anomalies of faults. Computers & Geosciences, 16, 539–548.
Nettleton, L. L. (1976). Gravity and magnetic in oil exploration. Mc. Graw Hill Publication Co.
Njeudjang, K., Essi, J. M. A., Kana, J. D., Teikeu, W. A., Nouck, P. N., Djongyang, N., et al. (2020). Gravity investigation of the Cameroon Volcanic Line in Adamawa region: Geothermal features and structural control. Journal of African Earth Sciences, 165, 103809.
Obasi, A. I., Onwuemesi, A. G., & Romanus, O. M. (2016). An enhanced trend surface analysis equation for regional–residual separation of gravity data. Journal of Applied Geophysics, 135, 90–99.
Odegard, M. E., & Berg, J. W. (1965). Gravity interpretation using the Fourier integral. Geophysics, 30, 424–438.
Pallero, J., Fernandez-Martinez, J. L., Bonvalot, S., & Fudym, O. (2015). Gravity inversion and uncertainty assessment of basement relief via particle swarm optimization. Journal of Applied Geophysics, 116, 180–191.
Pawlowski, R. S. (1994). Green’s equivalent-layer concept in gravity band-pass filter design. Geophysics, 59, 69–76.
Pham, L. T., Oksum, E., & Do, T. D. (2018). GCH_gravinv: A MATLAB-based program for inverting gravity anomalies over sedimentary basins. Computers and Geosciences, 120, 40–47.
Price, K. V., Storn, R. M., & Lampinen, J. A. (2005). Differential evolution: A practical approach to global optimization. Springer-Verlag.
Rao, K., & Biswas, A. (2021). Modeling and uncertainty estimation of gravity anomaly over 2D fault using very fast simulated annealing global optimization. Acta Geophysica, 69(5), 1735–1751.
Rao, M. M. M., Murty, R. T. V., Murthy, K. S. R., & Vasudeva, R. Y. (2003). Application of natural generalised inverse technique in reconstruction of gravity anomalies due to a fault. Indian Journal of Pure and Applied Mathematics, 34, 31–47.
Reid, A. B., Allsop, J. M., Granser, H., Millet, A. J., & Somerton, I. W. (1990). Magnetic interpretation in three dimensions using Euler deconvolution. Geophysics, 55, 80–91.
Rogers, S. M. (2001). Deposition and diagenesis of Mississippian chat reservoirs, North-Central Oklahoma. AAPG Bulletin, 85(1), 115–129.
Rönkkönen, J., Kukkonen, S., & Price, K. (2005). Real-parameter optimization with differential evolution. In Proceedings of the IEEE congress on evolutionary computation (pp. 506–513), Edinburgh, UK.
Roy, A., Dubey, P. C., & Prasad, M. (2021). Gravity inversion for heterogeneous sedimentary basin with b-spline polynomial approximation using differential evolution algorithm. Geophysics, 86, F35–F47.
Roy, A., & Kumar, T. S. (2021). Gravity inversion of 2D fault having variable density contrast using particle swarm optimization. Geophysical Prospecting, 69(6), 1358–1374.
Roy, L., Agarwal, B. N. P., & Shaw, R. K. (1999). Estimation of shape factor and depth from gravity anomalies due to some simple sources. Geophysical Prospecting, 47, 4–158.
Roy, L., Sen, M. K., Blankenship, D. D., Stoffa, P. L., & Richter, T. G. (2005). Inversion and uncertainty estimation of gravity data using simulated annealing: An application over Lake Vostok East Antarctica. Geophysics, 70(1), J1–J12.
Saibi, H., & Toushmalani, R. (2015). Gravity inversion of a fault by Cuckoo optimization. In Near-surface Asia Pacific conference, Waikoloa, Hawaii, 7–10 July 2015. https://doi.org/10.1190/nsapc2015-052
Sawires, R., Peláez, J. A., Fat-Helbary, R. E., Ibrahim, H. A., & García Hernández, M. T. (2015). An updated seismic source model for Egypt. In A. Moustafa (Ed.), Earthquake engineering—From engineering seismology to optimal seismic design of engineering structures. Intech Open.
Shaw, R. K., & Agarwal, P. (1990). The application of Walsh transforms to interpret gravity anomalies due to some simple geometrical shaped causative sources: A feasibility study. Geophysics, 55, 843–850.
Silva, J. B., Costa, D. C., & Barbosa, V. C. (2006). Gravity inversion of basement relief and estimation of density contrast variation with depth. Geophysics, 71(5), J51–J58.
Singh, A. (2020). Triangular grid-based fuzzy cross-update inversion of gravity data: Case studies from mineral exploration. Natural Resources Research, 29, 459–471.
Thompson, D. T. (1982). EULDPH—A new technique for making computer-assisted depth estimates from magnetic data. Geophysics, 47, 31–37.
Toushmalani, R. (2013). Gravity inversion of a fault by particle swarm optimization (PSO). Springerplus, 2(1), 315.
Toushmalani, R., Parsa, Z., & Esmaeili, A. (2014a). Comparison result of inversion of gravity data of a fault by cuckoo optimization and Levenberg–Marquardt methods. Research Journal of Pharmaceutical, Biological and Chemical Sciences, 5(1), 418–427.
Toushmalani, R., Parsa, Z., & Esmaeili, A. (2014b). Comparison result of inversion of gravity data of a fault by particle swarm optimization and cuckoo optimization methods. Research Journal of Pharmaceutical, Biological and Chemical Sciences, 5(1), 428–437.
Turan-Karaoğlan, S., & Göktürkler, G. (2021). Cuckoo search algorithm for model parameter estimation from self-potential data. Journal of Applied Geophysics, 194, 104461.
Yang, X. S. (2014). Nature-inspired metaheuristic algorithms. Luniver Press. ISBN 978-0-12-416743-8.
Yang, X.S., & Deb, S. (2009). Cuckoo search via Lévy flights. In: IEEE world congress on nature and biologically inspired computing (NaBIC) (pp. 210–214), Coimbatore, India.
Yuan, B., Song, L., Han, L., An, S., & Zhang, C. (2018). Gravity and magnetic field characteristics and hydrocarbon prospects of the Tobago Basin. Geophysical Prospecting, 66, 1586–1601.
Zhou, X. (2013). Gravity inversion of 2D bedrock topography for heterogeneous sedimentary basins based on line integral and maximum difference reduction methods. Geophysical Prospecting, 61(1), 220–234.
Acknowledgements
The authors thank to Dr. Reza Toushmalani and anonymous reviewer for their suggestions and many constructive comments, which significantly improved the earlier version of the paper. The CSA algorithm was implemented by using the MATLAB®, the software for numerical computation (http://www.mathworks.com/).
Funding
No funding has been received from any organization.
Author information
Authors and Affiliations
Contributions
Both authors contributed to the study, conception, and design. The authors’ detailed responsibilities are as follows: ŞÖ: methodology, data processing, code editing, figure preparation, writing; AT: data research, investigation, supervision, writing, reviewing and editing.
Corresponding author
Ethics declarations
Conflict of Interest
The authors declare no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Özyalın, Ş., Tunçel, A. Estimation of Deep-Seated Faults Parameters from Gravity Data Using the Cuckoo Search Algorithm. Pure Appl. Geophys. 180, 4147–4173 (2023). https://doi.org/10.1007/s00024-023-03368-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00024-023-03368-x