Comparison of the Third- order moving average and least square methods for estimating of shape and depth residual magnetic anomalies

Subject Areas : Mineralogy

Mohammad Fouladi ¹ , Mirsattar Meshinchi Asl ^{2 *} , Mahmoud Mehramuz ³ , Nima Nezafati ⁴

1 - Department of Earth Sciences, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of Earth Sciences, Science and Research Branch, Islamic Azad University, Tehran, Iran
3 - Department of Earth Sciences, Science and Research Branch, Islamic Azad University, Tehran, Iran
4 - Department of Earth Sciences, Science and Research Branch, Islamic Azad University, Tehran, Iran

Received: 2020-06-30 Accepted : 2021-05-05 Published : 2021-07-01

Keywords: third- order moving average, Variance, least square method, residual magnetic anomalies, standard deviation,

Abstract :

In the current study, we have developed a new method called the third- order moving average method to estimate the shape and depth of residual magnetic anomalies. This method, calculates a nonlinear relationship between depth and shape factor, at seven points with successive window length. It is based on the computing standard deviation at depths that are determined from all residual magnetic anomalies for each value of the shape factor. The method was applied to the synthetic model by geometrical shapes both as horizontal cylinder and combination of horizontal cylinder, sphere and thin sheet approaches, with and without noise. It was tested by real data in Geological Survey of Iran (GSI). In this study, least square methods were applied to interpret the magnetic field so that we can compare the results of this methods with the third- order moving average method. This method is applied to estimate the depth using second horizontal derivative anomalies obtained numerically from magnetic data with successive window lengths. This method utilizes the variance of the depths as a scale for calculation of the shape and depth. The results showed that the third- order moving average method is a powerful tool for estimating shape and depth of the synthetic models in the presence and absence of noise compared to least square method. Moreover, the results showed that this method is very accurate for real data while the least square method did not lead to feasible results.In this study, least square methods were applied to interpret the magnetic field so that we can compare the results of this methods with the third- order moving average method. This method is applied to estimate the depth using second horizontal derivative anomalies obtained numerically from magnetic data with successive window lengths. This method utilizes the variance of the depths as a scale for calculation of the shape and depth.The results showed that the third- order moving average method is a powerful tool for estimating shape and depth of the synthetic models in the presence and absence of noise compared to least square method. Moreover, the results showed that this method is very accurate for real data while the least square method did not lead to feasible results.

References:

1. Abdelrahman EM, Abo-Ezz ER (2001) Higher derivatives analysis of 2-D magnetic data, Geophysics 66: 205–212.


2. Abdelrahman EM, Abo-Ezz ER, Essa KS, El-Araby TM, Soliman KS (2007) A new least-squares minimization approach to depth and shape determination from magnetic data, Geophysical Prospecting 55: 433–446.


3. Abdelrahman EM, Essa KS (2015) A new method for depth and shape determinations from magnetic data, Pure and Applied Geophysics 172: 439–460.


4. Abdelrahman EM, Essa KS, El-Araby TM, Abo-Ezz ER (2016) Depth and shape solutions from second moving average residual magnetic anomalies, Exploration Geophysics 43: 178–189.


5. Atchuta Rao DA, Ram Babu HV (1980) Properties of the relation figures between the total, vertical, and horizontal field magnetic anomalies over a long horizontal cylinder ore body, Current Science 49: 584–585.


6. Essa KS, Elhussein M (2018) PSO (Particle Swarm Optimization) for Interpretation of Magnetic Anomalies Caused by Simple Geometrical Structures, Pure and Applied Geophysics 175(2).


7. Essa KS, Elhussein M (2019) Interpretation of Magnetic Data Through Particle Swarm Optimization: Mineral Exploration Cases Studies, Natural Resources Research 29: 521-537.


8. Gay P (1963) Standard curves for interpretation of magnetic anomalies over long tabular bodies, Geophysics, 28: 161–200.


9. Gay P (1965) Standard curves for interpretation of magnetic anomalies over long horizontal cylinders, Geophysics 30: 818–828.


10. Hartman RR, Teskey DJ, Friedberg JL (1971) A system for rapid digital aeromagnetic interpretation, Geophysics 36: 891–918.


11. Hinze WJ (1990) The role of gravity and magnetic methods in engineering and environmental studies, Geotechnical and Environmental Geophysics 75–126.


12. Jain S (1976) An automatic method of direct interpretation of magnetic profiles, Geophysics 41: 531–541.


13. McGrath PH, Hood PJ (1970) The dipping dike case: A computer curve-matching method of magnetic interpretation, Geophysics 35:831–848.


14. Paul PA (1964) Depth rules for some geometric bodies for interpretation of aeromagnetic anomalies, Geophysics Research Bulletin 2:15–21.


15. Pengfei L, Tianyou L,  Peimin Z, Yushan Y, Qiaoli Z, Henglei Z, Guoxiong C (2017) Depth Estimation for Magnetic/Gravity Anomaly Using Model Correction, Pure and Applied Geophysics 174: 1729–1742.


16. Prakasa Rao TKS, Subrahmanyan M, Srikrishna Murthy A (1986) Nomograms for the direct interpretation of magnetic anomalies due to long horizontal cylinders, Geophysics 51: 2156–2159.


17. Prakasa Rao TKS, Subrahmanyan M (1988) Characteristic curves for inversion of magnetic anomalies of spherical ore bodies, Pure and Applied Geophysics 126: 69–83.


18. Radhakrishna Murthy IV (1967) Note on the interpretation of magnetic anomalies of spheres, I. G. U. 4: 41–42.


19. Reid AB, Allsop JM, Granser H, Millett AJ, Somerton IW (1990) Magnetic interpretation in three dimensional using Euler deconvolution, Geophysics 55: 80–91.


20. Stanley JM (1977) Simplified magnetic interpretation of the geologic contact and thin dike, Geophysics 42: 1236–1240.


21. Steenland NC, Slack HA, Lynch VM, Langan L (1968) Discussion on The geomagnetic gradiometer, Geophysics 32: 877– 892.


22. Thompson DT (1982) EULDPH a new technique for making computer-assisted depth estimates from magnetic data, Geophysics 47: 31–37.


23. Werner S (1953) Interpretation of Magnetic Anomalies of Sheet-like Bodies, Sveriges Geologiska Underok Series C 43: N6.