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Bedding Angle Identification from BIF Marker Shales via Modified Dynamic Time Warping

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Abstract

When modelling a stratified orebody, accurately representing the dip and dip direction is important for accurate resource estimation. In the banded iron formation-hosted iron ore deposits in the Pilbara region of Western Australia, these quantities can be determined using marker shales from nearby holes. These marker shales are identified using natural gamma logs and are generally manually processed. Therefore, an automated method for matching natural gamma logs between holes is desirable. Dynamic time warping (DTW) can match two signals where there is stretching or distortion. This study presents a modified, iterative version of DTW for matching downhole natural gamma logs. This new method accounts for large differences in length of the two signals by comparing different segments of the signals. Several metrics were then used to rank potential matches between signals. The proposed iterative DTW method had an accuracy of 90%, compared with 67% for the standard DTW. Once matched, signals can be used to estimate the bedding angle at each hole. A point in one hole was matched to as many nearby holes as possible, creating a set of points located on the same surface. A localized plane was then fitted to these points. These bedding angles were used to reconstruct a surface representing the bedding. While the signal matching was accurate, the sparsity of correctly matched holes limits the accuracy of the calculated surface. Even with sparse gradient fields, a reasonable approximation of the bedding could be achieved.

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References

  • Agrawal R, Lin K-I, Sawhney H, Shim K (1997) Fast similarity search in the presence of noise, scaling, and translation in time-series databases. Paper presented at the 21st international conference on very large databases, Zurich, Switzerland

  • Bubnova A, Ors F, Rivoirard J, Cojan I, Romary T (2020) Automatic determination of sedimentary units from well data. Math Geosci 52:213–231. https://doi.org/10.1007/s11004-019-09793-w

    Article  Google Scholar 

  • Clifford D et al (2009) Alignment using variable penalty dynamic time warping. Anal Chem 81:1000–1007. https://doi.org/10.1021/ac802041e

    Article  Google Scholar 

  • Dalstra HJ, Rosiere CA (2008) Structural controls on high-grade iron ores hosted by banded iron formation: a global perspective. In: Hagemann S, Rosiere C, Gutzmer J, Beukes NJ (eds) Banded iron formation-related high-grade iron ore, vol 15. Reviews in Economic Geology. Society of Econimic Geologists, INC, Littleton, CO, pp 73–106

    Google Scholar 

  • D'Errico J (2012) inpaint_nans. MATLAB Central File Exchange

  • Harker M, O'Leary P (2013) Surface Reconstruction from Gradient Fields: grad2Surf Version 1.0. MATLAB Central File Exchange

  • Harmsworth RA, Kneeshaw M, Morris RC, Robinson CJ, Shrivastava PK (1990) BIF-derived iron ores of the Hamersley province. In: Hughes FE (ed) Geology of the mineral deposits of Australia and Papua New Guinea. The Australasian Institute of Mining and Metallurgy, Melbourne, pp 617–642

    Google Scholar 

  • Hill EJ, Robertson J, Uvarova Y (2015) Multiscale hierarchical domaining and compression of drill hole data. Comput Geosci 79:47–57

    Article  Google Scholar 

  • Hill EJ, Pearce MA, Stromberg JM (2021) Improving automated geological logging of drill holes by incorporating multiscale spatial methods. Math Geosci 53:21–53. https://doi.org/10.1007/s11004-020-09859-0

    Article  Google Scholar 

  • Kadkhodaie A, Rezaee R (2017) Intelligent sequence stratigraphy through a wavelet-based decomposition of well log data. J Nat Gas Sci Eng 40:38–50. https://doi.org/10.1016/j.jngse.2017.02.010

    Article  Google Scholar 

  • Keogh E, Pazzani M (2002) Derivative dynamic time warping. First SIAM international conference on data Mining, vol 1, https://doi.org/10.1137/1.9781611972719.1

  • Keogh E, Ratanamahatana CA (2005) Exact indexing of dynamic time warping. Knowl Inf Syst 7:358–386. https://doi.org/10.1007/s10115-004-0154-9

    Article  Google Scholar 

  • Lascelles DF (2000) Marra Mamba Iron Formation stratigraphy in the eastern Chichester Range, Western Australia. Aust J Earth Sci 47:799–806. https://doi.org/10.1046/j.1440-0952.2000.00810.x

    Article  Google Scholar 

  • Mueen A, Keogh E (2016) Extracting optimal performance from dynamic time warping. Paper presented at the Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining, San Francisco, California, USA, https://doi.org/10.1145/2939672.2945383

  • Quiniou T, Selmaoui N, Christine L-M (2007) Calculation of bedding angles inclination from drill core digital images. Paper presented at the IAPR conference on machine vision applications, Tokyo, Japan

  • Rabiner L, Juang B-H (1993) Fundamentals of speech recognition. Prentice-Hall, Inc., Englewood Cliffs

  • Ratanamahatana C, Keogh E (2004) Everything you know about dynamic time warping is wrong. Paper presented at the 3rd international workshop on mining temporal and sequential data (TDM-04), Seattle, USA

  • Silversides KL, Melkumyan A (2016) A Dynamic Time Warping based covariance function for Gaussian Processes signature identification. Comput Geosci 96:69–76. https://doi.org/10.1016/j.cageo.2016.08.001

    Article  Google Scholar 

  • Silversides K, Melkumyan A, Wyman D (2015a) Automated lithological recognition using DTW signal processing of natural gamma logs. Paper presented at the application of computers and operations research in the mineral industry (APCOM 2015), Alaska, USA

  • Silversides K, Melkumyan A, Wyman D, Hatherly P (2015b) Automated recognition of stratigraphic marker shales from geophysical logs in iron ore deposits. Comput Geosci 77:118–125. https://doi.org/10.1016/j.cageo.2015.02.002

    Article  Google Scholar 

  • Sommerville B, Boyle C, Brajkovich N, Savory P, Latscha AA (2014) Mineral resource estimation of the Brockman 4 iron ore deposit in the Pilbara region. Appl Earth Sci 123:135–145. https://doi.org/10.1179/1743275814Y.0000000038

    Article  Google Scholar 

  • Taylor D, Dalstra HJ, Harding AE, Broadbent GC, Barley ME (2001) Genesis of high-grade hematite orebodies of the Hamersley province, Western Australia. Econ Geol Bull Soc Econ Geol 96:837–873. https://doi.org/10.2113/gsecongeo.96.4.837

    Article  Google Scholar 

  • Thorne W, Hagemann S, Webb A, Clout J (2008) Banded iron formation-related iron ore deposits of the Hammersley Province, Western Australia. In: Hagemann S, Rosiere C, Gutzmer J, Beukes N (eds) Reviews in economic geology: banded iron formation-related high-grade iron ore, vol 15. Society of Economic Geologists. Westminster, USA, pp 197–221

    Google Scholar 

  • Tofallis C (2014) Add or multiply? A tutorial on ranking and choosing with multiple criteria. INFORMS Trans Edu 14:109–119. https://doi.org/10.1287/ited.2013.0124

    Article  Google Scholar 

  • Trendall AF, Blockley JG (1968) Stratigraphy of the dales gorge member of the Brockman iron formation, in the Precambrian Hamersley Group of Western Australia. Western Australia Geological Survey

  • Zaiontz C (2012) Real statistics using excel. http://www.real-statistics.com/correlation/basic-concepts-correlation/.

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Acknowledgements

This work has been supported by the Australian Centre for Field Robotics and the Rio Tinto Centre for Mine Automation.

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Correspondence to Katherine L. Silversides.

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George, M.A., Silversides, K.L., Zigman, J. et al. Bedding Angle Identification from BIF Marker Shales via Modified Dynamic Time Warping. Math Geosci 53, 1567–1585 (2021). https://doi.org/10.1007/s11004-021-09936-y

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  • DOI: https://doi.org/10.1007/s11004-021-09936-y

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