Indicator Variograms as an Aid for Geological Interpretation and Modeling of Ore Deposits
2. Materials and Methods
2.1. Indicator Modeling
2.2. Theoretical Indicator Direct Variogram
2.3. Experimental Indicator Direct Variogram
2.4. Theoretical Indicator Cross-Variogram
2.5. Experimental Indicator Cross-Variogram
2.6. Link between Indicator Direct and Cross-Variograms
2.7. Ratio of Indicator Cross-to-Direct Variograms and Edge Effects
- : due to Equations (19) and (20), where is a point located close to x. Knowing that x belongs to Dk decreases the probability that x’ belongs to Dk′, given that it does not belong to Dk This means that the contact area between Dk and Dk′ is smaller than it would be in the absence of edge effect, i.e., there is a propensity for both domains not to be in contact (Figure 4A,B).
- : the contact area between domains Dk and Dk′ coincides with the expected contact area in the absence of edge effect (no preferential contact) (Figure 4C,D).
- : the contact area between Dk and Dk′ is larger than it would be in the absence of edge effect. There is a propensity for both domains to be in contact together (Figure 4E,F).
3. Case Study and Results
3.1. Presentation of the Deposit
- Andesite (code 1): this volcanic rock is distributed as an interbedded sequence spread over the whole deposit and consists of lavas, auto-breccias and ocoites, with porphyritic to aphanitic texture and, locally, with amygdaloidal to ocoitic texture.
- Other volcanic rocks (code 2): this is a sequence of differentiated volcanic rocks with textures that vary from porphyritic to tuffaceous with an aphanitic matrix.
- Sedimentary rocks (code 3): this rock type includes undifferentiated, volcaniclastic and calcareous sediments, which are mostly interbedded with dacite and andesite, forming the host rock of the intrusive porphyry.
- Granodioritic porphyry (code 4): this is a medium grain granodiorite of Triassic age.
- Monzonitic porphyry (code 5): this porphyry rock is associated with the hypogene mineralization.
- Hydrothermal breccia (code 6) with tourmaline, quartz, chalcopyrite and pyrite cements, which can be found in the contact between the monzonitic porphyry with the host rock as a breccia with intrusive fragments.
3.2. Data Presentation and Pre-Processing
3.3. Indicator Direct Variograms
3.3.1. Existence of a Sill
3.3.2. Shape and Anisotropy
3.3.3. Slope at the Origin
3.4. Indicator Cross-Variograms
3.4.1. Behavior at Large Distances
3.4.2. Behavior at Short Distances
3.5. Ratios of Indicator Cross-to-Direct Variograms
4.1. Geological Interpretation and Modeling
4.2. Geostatistical Modeling and Simulation
Conflicts of Interest
- : the contact area between Dk and Dk′ when moving along vector u (i.e., leaving Dk at x and reaching Dk′ at ) is smaller than it would be in the absence of a directional edge effect.
- : the contact area between Dk and Dk′ when moving along vector u is equal to the expected area in the absence of a directional edge effect.
- : the contact area between Dk and Dk′ when moving along vector u is larger than it would be in the absence of an edge effect.
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Maleki, M.; Emery, X.; Mery, N. Indicator Variograms as an Aid for Geological Interpretation and Modeling of Ore Deposits. Minerals 2017, 7, 241. https://doi.org/10.3390/min7120241
Maleki M, Emery X, Mery N. Indicator Variograms as an Aid for Geological Interpretation and Modeling of Ore Deposits. Minerals. 2017; 7(12):241. https://doi.org/10.3390/min7120241Chicago/Turabian Style
Maleki, Mohammad, Xavier Emery, and Nadia Mery. 2017. "Indicator Variograms as an Aid for Geological Interpretation and Modeling of Ore Deposits" Minerals 7, no. 12: 241. https://doi.org/10.3390/min7120241