AIRRLS: An Augmented Iteratively Re-weighted and Refined Least Squares Algorithm for Inverse Modeling of Magnetometry Data

Source:
By:Maysam Abedi

DOI: https://doi.org/10.30564/jgr.v1i3.1316

Abstract:

This work aims to examine the functionality of a new Augmented Iteratively Re-weighted and Refined Least Squares algorithm (AIRRLS) to generate a 3D model of magnetic susceptibility property from a potential field magnetometry survey. Whereby this algorithm ameliorates an lpnorm Tikhonov regularization cost function through replacing a set of weighted linear system of equations. It leads to constructing a magnetic susceptibility model that iteratively converges to an optimum solution, meanwhile the regularization parameter performs as a stopping criterion to finalize the iterations. To tackle and suppress the intrinsic tendency of a sought target responsible for generating a magnetic anomaly and to not be imaged at shallow depth in inverse modeling, a prior depth weighting function is imposed in the principle system of equations. The significance of this research lies in improvement of the performance of the inversion, where the running time of an lp norm problem after incorporating a pre-conditioner conjugate gradient solver (PCCG) in cases of large scale geophysical dataset. Forasmuch as this study attempts to image a geological target with low magnetic susceptibility property, it is assumed that there is no remanent magnetization. The applicability of the algorithm is tested for a synthetic multi-source data to demonstrate its performance in 3D modeling . Subsequently, a real case study in Semnan province of Iran, is investigated to image an embedded porphyry copper layer in a sequence of sediments. The sought target consists of a concealed arc-shaped porphyry andesite unit that may have potential of Cuoccurrences. Results prove that it extends down at depth, so exploratory drilling is highly recommended to get insights about its potential for Cu-bearing mineralization.

References:

[1] Abdelrahman EM, Essa KS. Magnetic interpretation using a least-squares, depth shape curves method. Geophysics, 2005, 70: L23-L30. [2] Abdelrahman EM, Essa KS. A new method for depth and shape determinations from magnetic data. Pure Appl. Geophys, 2015, 172: 439-460. [3] Abedi M, Afshar A, Ardestani VE, Norouzi GH, Lucas C. Application of Various Methods for 2D Inverse Modeling of Residual Gravity Anomalies. Acta Geophys, 2010, 58: 317-336. [4] Abedi M, Gholami A, Norouzi GH, Fathianpour N. Fast inversion of magnetic data using Lanczos bidiagonalization method. J Appl Geophys, 2013a, 90: 126-137. [5] Abedi M, Norouzi GH, Fathianpour N, Gholami A. Approximate resistivity and susceptibility mapping from airborne electromagnetic and magnetic data, a case study for a geologically plausible porphyry copper unit in Iran. Journal of Mining & Environment, 2013b, 4: 133-146. [6] Abedi M, Gholami A, Norouzi GH. 3D inversion of magnetic data seeking sharp boundaries: a case study for a porphyry copper deposit from Now Chun in central Iran. Near Surface Geophysics, 2014, 12: 657-666. [7] Abedi M, Norouzi GH, Fathianpour N, Gholami A. Geological structure imaging from airborne electromagnetic and magnetic data, a case study in Kalat-eReshm area, Iran. Arab J Geosci, 2015, 8: 425-435. [8] Abedi M, Bahroudi A. A geophysical potential field study to image the Makran subduction zone in SE of Iran. Tectonophysics, 2016, 688: 119-134. [9] Bhattacharyya BK. Magnetic anomalies due to prism-shaped bodies with arbitrary polarization. Geophysics, 1964, 29: 517-531. [10] Bhattacharyya BK. A generalized multibody model for inversion of magnetic anomalies. Geophysics, 1980, 29: 517-531. [11] Boulanger O, Chouteau M. Constraints in 3D gravity inversion. Geophysical Prospecting, 2001, 49: 265-280. [12] Chasseriau P, Chouteau M. 3D gravity inversion using a model of parameter covariance. J Appl Geophys, 2003, 52: 59-74. [13] Clark DA. Magnetic petrology of igneous intrusions-Implications for exploration and magnetic interpretation. Exploration Geophysics, 1999, 20: 5-26. [14] Caratori Tontini F, Cocchi L, Carmisciano C. Depthto-the-bottom optimization for magnetic data inversion: Magnetic structure of the Latium volcanic region, Italy. Journal of Geophysical Research, 2006, 111: 1-17. [15] Essa KS. A simple formula for shape and depth determination from residual gravity anomalies. Acta Geophys, 2007a, 55: 182-190. [16] Essa KS. Gravity data interpretation using the s-curves method. J. Geophys. Eng. 2007b, 4: 204-213. [17] Essa KS. A new algorithm for gravity or self-potential data interpretation. J. Geophys. Eng. 2011, 8: 434-446. [18] Gholami A, Mohammadi Gheymasi H. Regularization of geophysical ill-posed problems by iteratively re-weighted and refined least squares. Comput Geosci, 2016. DOI: https://doi.org/10.1007/s10596-015-9544-1 [19] Gholami A, Siahkoohi HR. Regularization of linear and non-linear geophysical ill-posed problems with joint sparsity constraints. Geophys. J. Int. 2010, 180: 871-882. [20] Jin SG, van Dam T, Wdowinski S. Observing and understanding the Earth system variations from space geodesy. J. Geodyn. 2013, 72: 1-10. [21] John DA, Ayuso RA, Barton MD, Blakely RJ, Bodnar RJ, Dilles JH, Gray, Floyd, Graybeal FT, Mars JC, McPhee DK, Seal RR, Taylor RD, Vikre PG. Porphyry copper deposit model, chap. B of Mineral deposit models for resource assessment: U.S., Geological Survey Scientific Investigations Report, 2010, 2010–5070–B: 169 . [22] Lai M, Wang J. An unconstrained lq minimization with 0< q<1 for sparse solution of under-determined linear systems. SIAM J. Optim. 2011, 21: 82-101. [23] Last BJ, Kubik K. Compact gravity inversion. Geophysics, 1983, 48: 713-721. [24] Lelièvre PG, Oldenburg DW. A 3D total magnetization inversion applicable when significant, complicated remanence is present. Geophysics, 2009, 74: L21-L30. [25] Li Y, Shearer SE, Haney MM, Dannemiller N. Comperhensive approaches to 3D inversion of magnetic data affected by remanent magnetization. Geophysics, 2010, 75: L1-L11. [26] Li Y, Oldenburg DW. Fast inversion of large-scale magnetic data using wavelet transforms and logarithmic barrier methods. Geophys. J. Int. 2003, 152: 251-265. [27] Li Y, Oldenburg DW. 3-D inversion of gravity data.Geophysics, 1998, 63: 109-119. [28] Li Y, Oldenburg DW. 3-D inversion of magnetic data. Geophysics, 1996, 61: 394-408. [29] Lyu Q, Lin Z, She Y, Zhang C. A comparison of typical lp minimization algorithms. Neurocomputing, 2013, 119: 413-424. [30] Malehmir A, Thunehed H, Tryggvason A. Case History: the Paleoproterozoic Kristineberg mining area, northern Sweden: Results from integrated 3D geophysical and geologic modeling, and implications for targeting ore deposits. Geophysics, 2009, 74: B9-22. [31] Namaki L, Gholami A, Hafizi MA. Edge-preserved 2-D inversion of magnetic data: an application to the Makran arc-trench complex. Geophys. J. Int. 2011, 184: 1058-1068. [32] Oldenburg DW, Li Y, Ellis RG. Inversion of geophysical data over a copper gold porphyry deposit: A case history for Mt. Milligan. Geophysics, 1997, 62: 1419-1431. [33] Oskooi B, Abedi M. An airborne magnetometry study across Zagros collision zone along Ahvaz–Isfahan route in Iran. Journal of Applied Geophysics, 2015, 123: 112-122. [34] Pignatelli A, Nicolosi I, Chiappini M. An alternative 3D source inversion method for magnetic anomalies with depth resolution. Ann. Geophys. 2006, 49: 1021-1027. [35] Pilkington M. 3-D magnetic imaging using conjugate gradients. Geophysics, 1997, 62: 1132-1142. [36] Portniaguine O, Zhdanov MS. 3-D magnetic inversion with data compression and image focusing. Geophysics, 2002, 67: 1532-1541. [37] Rao DB, Babu NR. A rapid method for three-dimensional modeling of magnetic anomalies. Geophysics, 1991, 56: 1729-1737. [38] Shamsipour P, Chouteau M, Marcotte D. 3D stochastic inversion of magnetic data. J Appl Geophys, 2011, 73: 336-347. [39] Shirzaditabar F, Oskooi B. Recovering 1D conductivity from AEM data using Occam inversion. J Earth Space Phys. 2010, 37: 47–58. [40] Shirzaditabar F, Oskooi B. Approximate interpretation of airborne electromagnetic data using a halfspace model. J Earth Space Phys. 2011, 38: 1-12. [41] Shirzaditabar F, Bastani M, Oskooi B. Imaging a 3D geological structure from HEM, airborne magnetic and ground ERT data in Kalat-e-Reshm area, Iran. J Appl Geophys, 2011a, 75: 513-522. [42] Shirzaditabar F, Bastani M, Oskooi B. Study of the effects of the variables changes on the inversion of airborne electromagnetic data in frequency domain. Iranian J Geophys, 2011b, 5: 38-50. [43] Thoman MW, Zonge KL, Liu D. Geophysical case history of North Silver Bell, Pima County, Arizona-A supergene-enriched porphyry copper deposit, in Ellis, R.B., Irvine, R. & Fritz, F., eds., Northwest Mining Association 1998 Practical Geophysics Short Course Selected Papers on CD-ROM: Spokane. Washington, Northwest Mining Association, 2000, 4: 42 . [44] Tikhonov AN, Arsenin VY. Solutions of Ill-Posed Problems. Winston, Washington, D. C. [45] Van Wijk K, Scales JA, Navidi W, Tenorio L (2002) Data and model uncertainty estimation for linear inversion. Geophysics J. Int. 1977, 149: 625-632. [46] Zhang Y, Yan J, Li F, Chen C, Mei B, Jin S, Dohm JH. A new bound constraints method for 3-D potential field data inversion using Lagrangian multipliers. Geophys. J. Int. 2015, 201: 267-275.