Slide 1: In Memory of Professor Danie Krige
IN MEMORY OF PROFESSOR DANIE KRIGE WINFRED ASSIBEY-BONSU August 2015
Slide 2: Content
Content • Part 1: The Great man - Professor Danie Krige • Part 2: A summary of the basic tenets of evaluating the Mineral Resource assets of mining companies, as observed in Professor Krige’s pioneering work over half a century • Conclusion 2
Slide 3: Part 1 – The Great Man
Part 1 – The Great Man Professor Daniel Gerhardus Krige 26 August 1919 – 2 March 2013 3
Slide 4: A World Figure
A World Figure • Professor Danie Krige passed away on 2nd March 2013 at the age of 93. • His death was recorded in Wikipedia under notable deaths – a distinction shared with famous persons such as Margaret Thatcher – he was a true giant. 4
Slide 5: Professor Krige's Strong View on Life
Professor Krige’s Strong View on Life • This presentation would be incomplete without throwing light on some of the things Professor Krige held very dear in his life – taken from his 2012 interview with Professor R. C. A. Minnitt of the University of the Witwatersrand; • Professor Krige was a devout
Slide 6: The Six 'Gifts of Grace'
The Six ‘Gifts of Grace’ 1. A tribute to his parents for the practical application of a godly lifestyle, the establishment of a firm foundation, and a life philosophy that was modelled by them in every area of life. An example being, that even with the limited resources of a pastor, his parents saw
Slide 7: Professor Krige and Family (1930)
Professor Krige and Family (1930) 7
Slide 8: The Family Man
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Slide 9: Professor Krige's 90th Birthday with Ansie
Professor Krige’s 90th Birthday with Ansie 9
Slide 10: The Early Years
The Early Years • Professor Krige matriculated from Monument High School, South Africa at the age of 15; • In 1938 at the age of 19, he graduated as a Mining Engineer from the University of the Witwatersrand (“Wits University”); • It was clear early on, that he was destined for great achievements. •
Slide 11: The Early Years
The Early Years 11
Slide 12: Practitioner, Researcher and Teacher
Practitioner, Researcher and Teacher • Professor Krige worked with Anglo Transvaal on a number of gold mines in the Witwatersrand until 1943; • He then joined the Government Mining Engineering Department, where he worked for a further 8 years, and spent time studying data and developing mathematical
Slide 13: Initial World Recognition
Initial World Recognition • Professor Krige’s seminal papers published in the Journal of Chemical, Metallurgical and Mining Society of South Africa, led to additional fundamental research in France on “regionalized variables” by Professor George Matheron and his team; • Professor Matheron named the
Slide 14: Topics, Content and Effect of Papers
Topics, Content and Effect of Papers • The statistical explanation of conditional biases in block evaluation; • It stimulated the use of regression corrections for routine ore reserve evaluations by several mines; • This technique, in effect, was the first elementary basis of what is now known as “K
Slide 15: Significant Further Contributions
Significant Further Contributions Major inputs in the fields of investment, financial analysis and taxation, evidenced from various contributions, including: • the establishment of the original South African uranium contracts; • by a substantial number of local and overseas publications in this fiel
Slide 16: Academic Achievements and Awards
Academic Achievements and Awards • DSc (Eng) 1963, University of the Witwatersrand • DIng (HC) 1981, Honorary Degree, University of Pretoria • Honorary Doctorate Degree from Moscow State Mining University • Honorary Doctorate Degree from University of South Africa (UNISA) • Order of Meritorious Serv
Slide 17: Academic Achievements and Awards
Academic Achievements and Awards 17
Slide 18: Commitment to APCOM
Commitment to APCOM • Professor Krige was South Africa’s representative on the International APCOM Council from its inception; • He served as the Chairman of the International APCOM council, the 1st non-USA member to be elected to this position; • He initiated and was directly involved with all arra
Slide 19: APCOM and The Great Wall of China
APCOM and The Great Wall of China 19
Slide 20: Retirement
“Retirement” • Continued as a Professor of Mineral Economics at the University of the Witwatersrand, where he was responsible for postgraduate courses in geostatistics and mineral economics, and supervised many masters and doctoral theses; • Presented courses in geostatistics and/or lectured at loca
Slide 21: Publications
Publications • Published some 96 technical papers; • A 1951 paper, based on his MSc (Eng.) thesis at the University of the Witwatersrand, expounded his pioneering work in geostatistics in more detail; • Published Geostatistics Monograph, 1st in the series of the SAIMM; • A complete record of all his
Slide 22: Dedicated Service
Dedicated Service • As a Professional Engineer, Professor Krige served for many years on the mining committee of the Engineering Council of South Africa; • Served on the Council of SAIMM for many years; • A co-founder of the International Association of Mathematical Geology, GASA, GAA and the Statis
Slide 23: Part 2 – The Basic Tenets
Part 2 – The Basic Tenet's Content: • Motivation – Capital intensiveness of mining • Data Integrity • Geology models • Change of Support • Efficiency of Estimates • Conditional bias and Smoothing Effect • Proposed Tools for the practitioner 23
Slide 24: Fundamental Assets of Mining Companies
Fundamental Assets of mining companies • Mineral Resources and Reserves are the fundamental assets of mining companies; • The intensive capital investments basically revolve around the fundamental Mineral Resource and Mineral Reserve assets in the ground – the strategic objective being to explore/ac
Slide 25: Capital Intensiveness of Mining
Capital Intensiveness of Mining Acquisition, mine development or Expansion cost (US$ billions) 38.1 27 Rio Tinto Billiton (2007) (2014) 25
Slide 26: Capital Intensiveness of Mining
Capital Intensiveness of mining Acquisition, mine development or Expansion cost (US$ billions) 8.5 2.5 2.3 1.1 Gold Fields Ltd Gold Fields Ltd Newmont Barrick (F2007) (2011) (2011) (2012) 26
Slide 27: Data Integrity
Data Integrity • Quality data is the lifeblood of evaluation; • Disastrous errors and critical risks include using bad data (‘GIGO - Garbage-In-Garbage-Out’) . Important aspects to consider include: • Data types and collation processes, including survey processes; • Ensure data quality; • Data valid
Slide 28: Geology Models
Geology models • Geology is the foundation of mineral resource and reserve modelling; • Geology should always be recognized as a vital element in deposit modelling; • Experience has shown that geostatistical assessment without proper geological input can be disastrous and will constitute a critical
Slide 29: Geology Modelling (Porphyry Cu & Au Ore body)
Geology Modelling (Porphyry Cu & Au Ore body) ● A view of the deposit showing geological domains – Cerro Corona, South America Oxide Supergene Mixed Hypogene Barren Diorite Cretaceous Sediments 29
Slide 30: 'Geo' in Geostatistics
‘Geo’ in Geostatistics A robust geological model is therefore a pre-requisite, and if the geostatistical model does not agree with the geological one, there are grounds for serious concern. Either one or both models should be critically re-examined so as to establish the essential correlation and va
Slide 31: Historical Background
Historical Background • In the field of mineral resource and reserve evaluation, geology and geostatistics are the two inseparable sides of the same coin; • As highlighted previously, on the one side geology concentrates on the physical features of the ore body, such as structures, source, depositio
Slide 32: Frequency Distribution
Frequency Distribution • The initial efforts in applying classical statistical procedures to ore evaluation in South Africa date back to 1919 (Watermeyer) and 1929 (Truscott); • It was only in the late 1940’s and early 1950’s that Sichel (1947, 1952) introduced the lognormal model for gold values, a
Slide 33: Professor Danie Krige and Herbert Sichel
Professor’s Danie Krige and Herbert Sichel 33
Slide 34: The Birth of Geostatistics
The Birth of Geostatistics • Geostatistics as such did not really originate until the basic concept of ore grades as a spatial variable with a spatial structure, was introduced in 1951/2 by Professor Krige; • This arose firstly in Professor Krige’s endeavour to explain the experience seen on the Sou
Slide 35: Explanation of Conditional Biases
Explanation of Conditional Biases 35
Slide 36: Spatial Concept and the Birth of Kriging
Spatial Concept and the Birth of “Kriging” • Professor Krige proposed and implemented corrective measures to eliminate these significant conditional biases; • The regression corrections were applied routinely to block estimates on several mines in the early 1950’s and represented the actual birth of
Slide 37: Spatial Structure and Variograms
Spatial Structure and Variograms • By 1963/66 (Krige, 1963, 1966) the spatial patterns were defined in far more detail; • These studies covered the spatial correlations between individual ‘point’ sample values, as well as that between regularized data blocks; • The corresponding correlograms or cova
Slide 38: Spatial Structure and Variograms
Spatial Structure and Variograms • Professor Krige’s pioneering work in early 1950’s aroused interest world wide, particularly in France where, under Professor Allais, Professor Krige’s papers were republished in French (Krige, 1955); • One of Professor Allais students, later to become world renowne
Slide 39: Conditional Unbiasedness
Conditional Unbiasedness • It is instructive to observe that on the South African gold mines, the improvement in the standard of block evaluations due to the elimination of conditional biases, accounts for some 70% of the total level of improvement achievable today, using the most sophisticated geos
Slide 40: What Contributes to Conditional Biases
What Contributes to Conditional Biases • It is a common knowledge concept that any increase in knowledge and available data relevant to any uncertainty being studied, will reduce the level of uncertainty, provided the knowledge is applied properly; • Knowledge will never be perfect and data never co
Slide 41: What Contributes to Conditional Biases
What Contributes to Conditional Biases 1. Insufficient data. As discussed in this presentation, in 1950 it was the use of only peripheral data for each block. Today, with geostatistics, the data search routine is still often inadequate, even with the complete data base available to the computer; 2.
Slide 42: Conditional Biases – Testing Tools
Conditional Biases – Testing Tools Mineral Resources for a new or an existing Mine covers two major stages: • At the initial or first stage the data is limited and is obtained either from a broad drill hole grid or from an initial main development grid; • During the second or final stage more data b
Slide 43: Conditional Biases – Testing Tools
Conditional Biases – Testing Tools • At both stages of evaluation, the evaluation technique should ensure minimum error variances / uncertainty; • These requirements are linked closely to the expected slopes of regression of the eventual follow-up values on the original block estimates; • Slopes of
Slide 44: Block Estimate Efficiency and Slope of Regression
Block Estimate Efficiency and Slope of Regression Professor Krige in 1996 proposed to define and measure the efficiency as follows: Efficiency = (BV-KV)/BV expressed as a percentage. Where: BV = Block Variance (i.e. the variance of actual block values, calculated from a variogram), and KV = Kriging
Slide 45: Efficiency of Block Evaluations
Efficiency of Block Evaluations • An extensive study of some 70 cases by Professor Krige covering a wide range of spatial and data patterns used, indicated a correlation between kriging efficiency and the regression slope (actuals on estimates) of 87.5% (Krige 1996); • Thus the slope (or the extent
Slide 46: Slope of Regression
Slope of Regression TEST FOR CONDITIONAL BIASES – REGRESSION SLOPE BV = Block Variance, ie. variance of actual kriged blocks, computed from the variogram KV = Respective Kriging Variance of kriged block estimates. LM = Respective Lagrange multiplier for Ordinary Kriging. Regression Slope = (BV – KV
Slide 47: Smoothing Effect of Kriging
Smoothing Effect of Kriging • The absence of conditional biases is unavoidably accompanied by some smoothing and it is a fallacy to use the data search routine for block evaluation in an endeavour to reduce or eliminate smoothing. 47
Slide 48: Smoothing is Inevitable and Essential for Conditional Unbiased Estimates
Smoothing is Inevitable and Essential for Conditional Unbiased Estimates Theoretical Explanation: The definition of the slope of the line of regression of actuals (Y) on estimated block values (X), i.e. Slope = r (σy/σx) If the Slope is to be unity, (i.e. Slope = ~1) for unbiased block estimates and
Slide 49: Smoothing Effect of Kriging
Smoothing Effect of Kriging • Various post-processing techniques are available to remove smoothing effects (e.g., Krige and Assibey-Bonsu, 1999; Journel et al, 2000) and should be applied only to block or panel estimates that are conditionally unbiased. 49
Slide 50: Part 3 - Conclusion
Part 3 - Conclusion Professor Krige’s outstanding influence on the worldwide mining industry is visible everyday, as shown by the decision making processes followed by international mining companies. Professor Krige’s Basic Points of Advice 1. Ensure data integrity; 2. Establish all the necessary ge
Slide 51: Conclusion (cont'd.)
Conclusion (cotd.) The industry seems to be going backwards in certain areas, with a widely spread misunderstanding of the causes and consequences of conditional biases. The following are some of the possible causes: • In certain universities, as well as training provided elsewhere in the industry,
Slide 52: Conclusion (cont'd.)
Conclusion (cotd.) “ … after half a century of phenomenal developments in geostatistics, conditional biases which gave birth to this subject, are still encountered in practical applications… the main concern is that this record will be tarnished by the all too ready acceptance [in certain cases] of
Slide 53: A Final Personal Tribute
A Final Personal Tribute • I am privileged to have had an association with Professor Krige for more than two decades, first as his student during my doctorate programme at the University of the Witwatersrand, and secondly, as my mentor and ‘father figure’ over these years. He has been an immense sou
Slide 54: You Made the World a Better Place
You Made the World a Better Place Professor Daniel Gerhardus Krige 26 August 1919 – 2 March 2013 54