Geostatistics with Applications in Earth Sciences

Title Page\r......Page 3
Copyright Page\r......Page 4
Preface to the Second Edition......Page 6
Preface to the First Edition......Page 7
Table of Contents\r......Page 9
Some Important Symbols Used in the Text......Page 13
1.1.1 Sampling, Data Collection and Sample Design......Page 16
1.1.2 Sample Design and the Various Steps......Page 17
1.1.5 Different Types of Sample Design......Page 18
1.1.6 Analysis Aspects......Page 20
1.2 HYPOTHESIS......Page 25
1.3 QUANTIFICATION AND PREDICTION IN EARTH SCIENCES......Page 26
1.5 PROBABILITY......Page 27
1.6 FREQUENCY FUNCTION, JOINT FREQUENCY FUNCTION, CONTINUOUS FREQUENCY FUNCTION AND JOINT CONTINUOUS FREQUENCY FUNCTION......Page 28
Review Questions......Page 30
2.2 FREQUENCY ANALYSIS......Page 31
2.3 GRAPHICAL REPRESENTATION OF FREQUENCYDISTRIBUTION......Page 33
2.4.1 Measure of Central Location......Page 44
2.4.3 Skewness and Kurtosis......Page 45
2.5 CORRELATION AND REGRESSION......Page 46
2.5.1 Correlation Coefficient......Page 47
(b) Multiple Linear Regression......Page 48
(c) Polynomial Regression......Page 49
2.6.1 Introduction......Page 50
2.6.3 Limitations of Simulation Techniques......Page 51
2.7.1 Applications to Inventory Control......Page 52
2.7.2 Applications to Gold Mineralisation......Page 55
Review Questions......Page 56
3.1.1 Salient Features of Normal Distribution and Normal Probability Law......Page 57
3.1.2 Confidence Limits for the Mean (z)......Page 59
3.2.1 Estimates for the Mean......Page 60
3.2.2 Confidence Limits for the Mean......Page 62
3.3 THE CHI-SQUARE (X2) TEST......Page 64
3.4 APPLICATIONS......Page 65
3.4.1 Bauxite Example: Distribution of Fe203 Element......Page 66
3.4.2 Gold Ore Distribution......Page 67
3.4.3 Copper Example......Page 70
3.5 CASE OF REJECTION OF NORMAL DISTRIBUTION......Page 75
Review Questions......Page 76
4.1.1 Stochastic Processes......Page 77
4.1.2 The Autocorrelation Function (acf)......Page 78
4.2 STOCHASTIC MODELLING (TIME SERIES ANALYSIS)......Page 79
4.2.1 Physical Significance in Relation to Estimation of Blocks of Ore......Page 80
4.2.2 Estimation of Parameters of A.R Process of Order p [AR(p)]......Page 81
4.2.4 Auto-regressive and Moving Average Process of Order p, q [ARMA(p, q)]......Page 82
4.3.1 Bauxite Example (Fe203)......Page 83
4.3.2 Gold Mineralisation......Page 84
4.4.1 Spectrum, Discrete Fourier Transform (OFT) and Fast Fourier Transform (FFT)......Page 86
B. Sectioning of Time Series......Page 87
4.4.3 Spectral Density and Entropy......Page 89
Review Questions......Page 92
5.1 INTRODUCTION......Page 93
5.2.1 Stationarity......Page 94
5.3 VARIOGRAM......Page 95
1. Range......Page 96
5.3.2 Anisotropies......Page 97
2. Zonal (or stratified) anisotropy......Page 98
5.3.4 Presence of a Drift......Page 99
5.3.6 Other Features......Page 100
5.4 COMMONLY USED VARIOGRAM MODELS......Page 101
5.5 CHANGE OF SUPPORT, REGULARISATION AND ESTIMATION VARIANCE......Page 102
5.6 EXAMPLES OF VARIOGRAM COMPUTATION......Page 104
5.7 EXAMPLES OF VARIOGRAMS IN OTHER FIELDS OF EARTH SCIENCES......Page 107
Review Questions......Page 109
6.1 INTRODUCTION......Page 110
6.2 DIFFERENT SITUATIONS......Page 112
6.4 EXAMPLE: Fe203 ELEMENT VALUES FOR CORE LENGTH OF L = 0.5 m......Page 115
6.5.1 Example: Lode 0: gold field 1......Page 120
6.5.2 Example: Lode Z: gold field 2......Page 121
6.6 THE WITHIN VARIATION IN CORE LENGTH L: DIFFERENT CASES......Page 122
6.7 DISTRIBUTIONS BASED ON CORE SAMPLE STATISTICS AND DERIVED ONES FOR POINT SAMPLES......Page 123
6.8 CASE OF LOGNORMAL DISTRIBUTION ANDBLOCKS OF SIZE V......Page 126
6.8.1 Distributions Based on Point Samples and Derived Statistics for Blocks......Page 127
6.8.2 Grade Tonnage Computations Based on Log-transformed Statistics and Economic Implications......Page 128
Review Questions......Page 130
7.1.1 Variance of Point Samples within Volume V......Page 133
7.1.2 Variance of vwithin V......Page 135
7.2 EXTENSION VARIANCE......Page 136
7.3 ESTIMATION VARIANCE......Page 138
Review Questions......Page 139
8.1 TOWARDS KRIGING VARIANCE......Page 140
8.2 KRIGING PROCEDURE......Page 142
8.4 SIMPLE KRIGING (ALSO KNOWN AS LINEAR KRIGING WITH KNOWN EXPECTATION)......Page 145
8.5.1 Punctual Kriging......Page 146
8.5.2 Block Kriging......Page 148
Review Questions......Page 153
9.1 INTRODUCTION......Page 154
9.2.1 Universal Kriging......Page 155
9.2.2 Disjunctive Kriging......Page 156
9.2.3 Disjunctive Kriging Estimator......Page 157
9.3 ESTIMATION BASED ON CONDITIONAL SIMULATION......Page 158
9.4.1 Median Polish Kriging......Page 159
9.4.2 Example......Page 160
Review Questions......Page 165
10 Computer Software......Page 166
PROGRAM: NORMAL.FOR......Page 168
PROGRAM: LN.FOR......Page 173
PROGRAM: AR.FOR......Page 178
PROGRAM: MA1.FOR......Page 185
PROGRAM: VGRAM.FOR......Page 191
PROGRAM: ORDKRIG.FOR......Page 199
Bibliography......Page 210
Index......Page 218