Part 3: Geological Controls & Domain Definition

Connecting Numbers to Rocks - The Path to Robust Estimation Domains

EDA

Geological Domains

Domaining

Resource Estimation

Penulis

Ghozian Islam Karami

Diterbitkan

5 Oktober 2025

Introduction

We’ve validated our data (Part 1), explored spatial patterns, and characterized statistical distributions (Part 2). Now comes the most critical step: connecting numbers to geology.

Pillar 4: Geological Controls Analysis transforms statistical insights into geologically defensible estimation domains - the backbone of reliable resource models.

The Critical Question

“Where is mineralization located and WHY?”

This isn’t just about mapping high grades. It’s about understanding the geological controls that govern mineralization:

Which rock types host mineralization?
Are there geochemical relationships between elements?
How does grade behave at geological contacts?
What structural controls exist?

Why Geological Domains Matter

Poor domaining is a leading cause of resource estimation failure:

Mixed populations create unrealistic variograms
Inappropriate kriging produces smoothing artifacts
Classification confidence is compromised
Mining selectively targets become unrealistic

Good domains = Reliable estimates

Setup

Kode

library(dplyr)
library(tidyr)
library(ggplot2)
library(plotly)
library(DT)
library(RColorBrewer)
library(GGally)
library(patchwork)

# Create simulated drilling data with geological controls
set.seed(456)
n_holes <- 50

collar <- data.frame(
  hole_id = paste0("DDH", sprintf("%03d", 1:n_holes)),
  x = runif(n_holes, 500000, 501000),
  y = runif(n_holes, 9000000, 9001000),
  rl = runif(n_holes, 100, 200)
)

# Generate assay data with lithology-controlled grades
litho_codes <- c("Andesite", "Diorite", "Mineralized_Zone", "Altered_Volcanics")
litho_grade_means <- c(0.5, 0.8, 3.5, 2.0)  # Different grades by lithology

assay_list <- lapply(1:n_holes, function(i) {
  n_intervals <- sample(15:25, 1)
  depths <- seq(0, by = 2, length.out = n_intervals)
  
  # Assign lithology to each interval
  litho_idx <- sample(1:length(litho_codes), n_intervals - 1, replace = TRUE,
                     prob = c(0.3, 0.2, 0.3, 0.2))
  
  # Generate grades based on lithology
  au_grades <- sapply(litho_idx, function(idx) {
    max(0, rnorm(1, mean = litho_grade_means[idx], sd = 1.5))
  })
  
  # Correlated Ag and Cu
  ag_grades <- au_grades * runif(n_intervals - 1, 8, 12) + rnorm(n_intervals - 1, 0, 5)
  cu_grades <- au_grades * 0.3 + rnorm(n_intervals - 1, 0, 0.3)
  
  data.frame(
    hole_id = collar$hole_id[i],
    from = depths[-length(depths)],
    to = depths[-1],
    au_ppm = pmax(0, au_grades),
    ag_ppm = pmax(0, ag_grades),
    cu_pct = pmax(0, cu_grades),
    lithology = litho_codes[litho_idx]
  )
})

combined_data <- do.call(rbind, assay_list) %>%
  left_join(collar, by = "hole_id") %>%
  janitor::clean_names()

# Prepare standard formats
collar_std <- collar %>% janitor::clean_names()
assay_std <- combined_data %>% select(hole_id, from, to, au_ppm, ag_ppm, cu_pct)
lithology_std <- combined_data %>% select(hole_id, from, to, lithology)

PILLAR 4: Geological Controls Analysis

Part A: Lithology Analysis

Grade Distribution by Rock Type

The most fundamental control: which rocks contain ore?

Kode

# Calculate statistics by lithology
litho_summary <- combined_data %>%
  group_by(lithology) %>%
  summarise(
    n = n(),
    mean_au = mean(au_ppm, na.rm = TRUE),
    median_au = median(au_ppm, na.rm = TRUE),
    max_au = max(au_ppm, na.rm = TRUE),
    sd_au = sd(au_ppm, na.rm = TRUE)
  ) %>%
  arrange(desc(mean_au))

# Create color palette
n_litho <- length(unique(combined_data$lithology))
litho_colors <- setNames(
  brewer.pal(max(3, min(n_litho, 9)), "Set1")[1:n_litho],
  sort(unique(combined_data$lithology))
)

# Boxplot with statistical annotations
p_litho_box <- ggplot(combined_data, aes(x = reorder(lithology, au_ppm, FUN = median), 
                                          y = au_ppm, 
                                          fill = lithology)) +
  geom_boxplot(outlier.alpha = 0.3) +
  stat_summary(fun = mean, geom = "point", shape = 23, size = 3, 
               fill = "red", color = "darkred") +
  scale_fill_manual(values = litho_colors) +
  labs(
    title = "Gold Grade Distribution by Lithology",
    subtitle = "Box = IQR, Diamond = Mean, Line = Median",
    x = "Lithology (ordered by median grade)",
    y = "Au (ppm)"
  ) +
  theme_minimal() +
  theme(
    axis.text.x = element_text(angle = 45, hjust = 1),
    legend.position = "none"
  )

p_litho_box

Statistical Summary by Lithology

Kode

datatable(litho_summary,
          caption = "Table 1: Gold Statistics by Lithology",
          options = list(pageLength = 10)) %>%
  formatRound(columns = c('mean_au', 'median_au', 'max_au', 'sd_au'), digits = 3) %>%
  formatStyle(
    'mean_au',
    background = styleColorBar(litho_summary$mean_au, 'lightblue'),
    backgroundSize = '100% 90%',
    backgroundRepeat = 'no-repeat',
    backgroundPosition = 'center'
  )

Geological Interpretation

From this analysis, identify:

Primary ore hosts: Lithologies with highest mean/median grades
Barren waste: Low-grade lithologies to exclude
Grade variance: High CV suggests mixed mineralization styles
Outlier behavior: Which rocks have extreme values?

Action: Candidate lithologies for separate estimation domains

Grade-Tonnage Curves by Lithology

Understanding the economic potential of each rock type.

Kode

# Calculate grade-tonnage curves
cutoffs <- seq(0, 5, by = 0.1)

gt_curves <- combined_data %>%
  expand_grid(cutoff = cutoffs) %>%
  filter(au_ppm >= cutoff) %>%
  group_by(lithology, cutoff) %>%
  summarise(
    tonnage_pct = n() / nrow(combined_data) * 100,
    avg_grade = mean(au_ppm, na.rm = TRUE),
    .groups = 'drop'
  )

# Plot tonnage vs cutoff
p_tonnage <- ggplot(gt_curves, aes(x = cutoff, y = tonnage_pct, color = lithology)) +
  geom_line(size = 1.2) +
  scale_color_manual(values = litho_colors) +
  labs(
    title = "Tonnage vs Cut-off Grade",
    x = "Cut-off Grade (ppm Au)",
    y = "Tonnage (% of total)"
  ) +
  theme_minimal() +
  theme(legend.position = "right")

# Plot grade vs cutoff
p_grade <- ggplot(gt_curves, aes(x = cutoff, y = avg_grade, color = lithology)) +
  geom_line(size = 1.2) +
  scale_color_manual(values = litho_colors) +
  labs(
    title = "Average Grade vs Cut-off",
    x = "Cut-off Grade (ppm Au)",
    y = "Average Grade (ppm)"
  ) +
  theme_minimal() +
  theme(legend.position = "right")

p_tonnage / p_grade

Part B: Element Correlation Analysis

Bivariate Relationships

Understanding element associations reveals mineralization processes.

Kode

# Select grade variables for correlation
grade_vars <- c("au_ppm", "ag_ppm", "cu_pct")

# Create scatter plot matrix
suppressWarnings({
  ggpairs(
    combined_data %>% select(all_of(grade_vars), lithology),
    mapping = aes(color = lithology, alpha = 0.5),
    upper = list(continuous = wrap("cor", size = 3)),
    lower = list(continuous = wrap("points", alpha = 0.3, size = 0.5)),
    diag = list(continuous = wrap("densityDiag", alpha = 0.5))
  ) +
    scale_color_manual(values = litho_colors) +
    scale_fill_manual(values = litho_colors) +
    theme_minimal() +
    labs(title = "Element Correlation Matrix by Lithology")
})

Regression Analysis: Au vs Ag

Kode

# Calculate regression by lithology
regression_data <- combined_data %>%
  filter(!is.na(au_ppm) & !is.na(ag_ppm)) %>%
  group_by(lithology) %>%
  filter(n() > 10) %>%
  nest() %>%
  mutate(
    model = purrr::map(data, ~lm(ag_ppm ~ au_ppm, data = .x)),
    r_squared = purrr::map_dbl(model, ~summary(.x)$r.squared),
    slope = purrr::map_dbl(model, ~coef(.x)[2]),
    intercept = purrr::map_dbl(model, ~coef(.x)[1])
  )

# Create scatter plot with regression lines
p_regression <- ggplot(combined_data, aes(x = au_ppm, y = ag_ppm)) +
  geom_point(aes(color = lithology), alpha = 0.5, size = 2) +
  geom_smooth(aes(color = lithology), method = "lm", se = FALSE, size = 1.2) +
  scale_color_manual(values = litho_colors) +
  labs(
    title = "Gold vs Silver: Correlation by Lithology",
    subtitle = "Different slopes suggest different mineralization styles",
    x = "Au (ppm)",
    y = "Ag (ppm)"
  ) +
  theme_minimal() +
  theme(legend.position = "right")

p_regression

Correlation Summary Table

Kode

regression_summary <- regression_data %>%
  select(lithology, r_squared, slope, intercept) %>%
  arrange(desc(r_squared)) %>%
  mutate(
    equation = paste0("Ag = ", round(slope, 2), " × Au + ", round(intercept, 2)),
    r_squared = round(r_squared, 3)
  ) %>%
  select(lithology, r_squared, equation)

datatable(regression_summary,
          caption = "Table 2: Au-Ag Correlation by Lithology",
          options = list(pageLength = 10, dom = 't')) %>%
  formatStyle(
    'r_squared',
    background = styleColorBar(regression_summary$r_squared, 'lightgreen'),
    backgroundSize = '100% 90%',
    backgroundRepeat = 'no-repeat',
    backgroundPosition = 'center'
  )

Geochemical Insights

Strong correlations indicate:

Coupled mineralization: Elements deposited together
Common sources: Shared ore fluids or processes
Domain boundaries: Changes in correlation suggest domain breaks

Weak correlations may indicate:

Different mineralization events: Overprinting
Remobilization: Secondary processes
Mixed populations: Need for further domain subdivision

Part C: Contact Analysis

Grade Behavior at Geological Boundaries

How does grade change across lithology contacts?

Kode

# Identify contact zones (simplified approach)
contact_zones <- combined_data %>%
  arrange(hole_id, from) %>%
  group_by(hole_id) %>%
  mutate(
    next_litho = lead(lithology),
    is_contact = lithology != next_litho & !is.na(next_litho),
    contact_type = if_else(is_contact, 
                          paste(lithology, "→", next_litho), 
                          NA_character_)
  ) %>%
  filter(is_contact) %>%
  ungroup()

# Plot grade at contacts
if(nrow(contact_zones) > 0) {
  p_contacts <- ggplot(contact_zones, aes(x = contact_type, y = au_ppm)) +
    geom_boxplot(fill = "lightcoral", alpha = 0.7) +
    geom_jitter(width = 0.2, alpha = 0.5, size = 2) +
    labs(
      title = "Gold Grades at Lithology Contacts",
      subtitle = "Understanding grade behavior at geological boundaries",
      x = "Contact Type",
      y = "Au (ppm)"
    ) +
    theme_minimal() +
    theme(axis.text.x = element_text(angle = 45, hjust = 1))
  
  print(p_contacts)
} else {
  cat("No contact zones identified in the dataset.\n")
}

Contact Zone Interpretation

Sharp grade changes at contacts may indicate:

Structural controls: Faults or shears
Alteration halos: Gradational vs sharp boundaries
Domain boundaries: Where to draw estimation domains
Dilution zones: Material to exclude from ore domains

Domain Definition Workflow

Combining All Evidence

Now we synthesize findings from all analyses:

Kode

# IMPROVED: More realistic domain classification
# Step 1: Classify each interval
domain_definition <- combined_data %>%
  mutate(
    interval_domain = case_when(
      lithology == "Mineralized_Zone" & au_ppm >= 1.5 ~ "High Grade Ore",
      lithology == "Mineralized_Zone" & au_ppm >= 0.3 ~ "Low Grade Ore",
      lithology == "Altered_Volcanics" & au_ppm >= 0.8 ~ "Altered Ore",
      au_ppm < 0.3 ~ "Waste",
      TRUE ~ "Transitional"
    )
  )

# Step 2: Summarize by hole (dominant domain approach)
hole_summary <- domain_definition %>%
  group_by(hole_id) %>%
  summarise(
    n_intervals = n(),
    avg_au = mean(au_ppm, na.rm = TRUE),
    max_au = max(au_ppm, na.rm = TRUE),
    has_high_grade = any(interval_domain == "High Grade Ore"),
    pct_ore = sum(interval_domain %in% c("High Grade Ore", "Low Grade Ore", "Altered Ore")) / n() * 100,
    .groups = 'drop'
  )

# Step 3: Final hole-level domain classification
hole_domains <- hole_summary %>%
  mutate(
    hole_domain = case_when(
      has_high_grade & avg_au >= 1.0 ~ "High Grade Ore",
      avg_au >= 0.8 ~ "Low Grade Ore",
      avg_au >= 0.5 | pct_ore >= 30 ~ "Altered Ore",
      avg_au >= 0.3 ~ "Transitional",
      TRUE ~ "Waste"
    )
  )

# Summary by domain
domain_summary <- domain_definition %>%
  group_by(interval_domain) %>%
  summarise(
    Intervals = n(),
    `Mean Au` = mean(au_ppm, na.rm = TRUE),
    `Median Au` = median(au_ppm, na.rm = TRUE),
    `Mean Ag` = mean(ag_ppm, na.rm = TRUE),
    `Mean Cu` = mean(cu_pct, na.rm = TRUE),
    .groups = 'drop'
  ) %>%
  arrange(desc(`Mean Au`)) %>%
  mutate(across(where(is.numeric) & !Intervals, ~round(.x, 3)))

datatable(domain_summary,
          caption = "Table 3: Proposed Estimation Domains (Interval-Based)",
          options = list(pageLength = 10, dom = 't'))

Kode

# Hole-level summary
hole_domain_summary <- hole_domains %>%
  group_by(hole_domain) %>%
  summarise(
    Holes = n(),
    `Avg Au (ppm)` = mean(avg_au),
    `Max Au (ppm)` = max(max_au),
    .groups = 'drop'
  ) %>%
  arrange(desc(`Avg Au (ppm)`)) %>%
  mutate(across(where(is.numeric) & !Holes, ~round(.x, 3)))

datatable(hole_domain_summary,
          caption = "Table 4: Domain Classification by Drillhole",
          options = list(pageLength = 10, dom = 't'))

Domain Spatial Distribution

Kode

# Create color palette for domains
domain_colors <- c(
  "High Grade Ore" = "#d32f2f",
  "Low Grade Ore" = "#ff9800",
  "Altered Ore" = "#ffd54f",
  "Transitional" = "#9e9e9e",
  "Waste" = "#e0e0e0"
)

# Merge hole domains with collar data
domain_spatial <- hole_domains %>%
  left_join(collar_std, by = "hole_id")

p_domain_map <- ggplot(domain_spatial, aes(x = x, y = y, color = hole_domain)) +
  geom_point(size = 4, alpha = 0.8) +
  scale_color_manual(values = domain_colors) +
  coord_equal() +
  labs(
    title = "Proposed Domain Distribution - Plan View",
    subtitle = "Dominant domain per drillhole",
    x = "Easting (m)",
    y = "Northing (m)",
    color = "Domain"
  ) +
  theme_minimal() +
  theme(legend.position = "right")

p_domain_map

The Birth of Robust Geological Domains

Before EDA

Without systematic EDA:

Random data points without geological context
Mixed populations in estimation
Unreliable variograms
Poor mining selectivity

After EDA: The 4 Pillars Converge

flowchart TB
    P1[Pillar 1:<br/>Clean, Validated Data] --> D[Robust<br/>Geological<br/>Domains]
    P2[Pillar 2:<br/>Spatial Understanding] --> D
    P3[Pillar 3:<br/>Statistical Populations] --> D
    P4[Pillar 4:<br/>Geological Controls] --> D
    
    D --> E1[Reliable Estimation]
    D --> E2[Realistic Mine Plans]
    D --> E3[Confident Classification]
    
    style D fill:#4caf50,color:#fff
    style P1 fill:#e3f2fd
    style P2 fill:#fff3e0
    style P3 fill:#f3e5f5
    style P4 fill:#e8f5e9

Domain Validation Checklist

Defensible Domains Must Have:

✓ Geological justification: Rock types, alteration, structure ✓ Statistical support: Distinct populations, different variability ✓ Spatial continuity: Mappable in 3D space ✓ Grade differences: Economically meaningful ✓ Sample support: Adequate data density ✓ Clear boundaries: Definable contacts

Summary: From Data to Domains

What We Accomplished

Through the 4 Pillar EDA framework, we:

Validated data integrity (Pillar 1)
Understood spatial distribution (Pillar 2)
Characterized grade populations (Pillar 3)
Identified geological controls (Pillar 4)

Result: Scientifically defensible estimation domains ready for resource modeling.

Next Steps in Resource Estimation

With robust domains defined, you can proceed to:

Compositioning: Regularize sample support within domains
Variography: Model spatial continuity per domain
Estimation: Kriging with appropriate search parameters
Classification: Measured, Indicated, Inferred categories
Validation: Check estimates against reality

Key Takeaways

Remember These Principles

EDA is not optional - It’s mandatory for JORC compliance
Data quality = Model reliability - GIGO always applies
Geology drives domains - Statistics support, geology defines
Document everything - Auditors will ask for justification
Use modern tools - Automate routine tasks, focus on interpretation

Impact on Business Decisions

Good EDA and domaining directly impact:

Resource confidence: Better classification categories
Mine planning: Realistic extraction sequences
Grade control: Achievable selectivity
Investor confidence: Defensible, auditable reports
Project value: Reduced risk = higher valuations

The Foundation of Trust

“In mining, we don’t get second chances. The quality of our EDA determines whether we build a mine or lose millions in poor decisions.”

Every successful operation starts with understanding the data.

Tools and Resources

GeoDataViz Application

All analyses demonstrated here are available in GeoDataViz:

GitHub: github.com/ghoziankarami/GeoDataViz
Zenodo: doi.org/10.5281/zenodo.17142676
License: MIT (Open Source)

Contact

Author: Ghozian Islam Karami
Email: ghoziankarami@gmail.com
LinkedIn: linkedin.com/in/ghoziankarami

Series Complete

You’ve completed the comprehensive EDA workflow:

← Part 1: Foundation & Data Validation
← Part 2: Spatial & Statistical Analysis
Part 3: Geological Controls & Domain Definition (You are here)

You now have the tools and knowledge to build trusted geological models from raw drilling data.

“Quality data, systematic analysis, geological thinking - the foundation of every successful mine.”

--- title: "Part 3: Geological Controls & Domain Definition" subtitle: "Connecting Numbers to Rocks - The Path to Robust Estimation Domains" author: "Ghozian Islam Karami" date: "2025-10-05" categories: [EDA, Geological Domains, Domaining, Resource Estimation] image: "Part3.png" format: html: code-fold: true code-tools: true toc: true toc-depth: 3 --- ## Introduction We've validated our data ([Part 1](../Data Validation/)), explored spatial patterns, and characterized statistical distributions ([Part 2](../Spatial Statistics/)). Now comes the most critical step: **connecting numbers to geology**. **Pillar 4: Geological Controls Analysis** transforms statistical insights into geologically defensible estimation domains - the backbone of reliable resource models. ## The Critical Question > **"Where is mineralization located and WHY?"** This isn't just about mapping high grades. It's about understanding the **geological controls** that govern mineralization: - Which rock types host mineralization? - Are there geochemical relationships between elements? - How does grade behave at geological contacts? - What structural controls exist? ::: {.callout-important} ## Why Geological Domains Matter Poor domaining is a leading cause of resource estimation failure: - Mixed populations create unrealistic variograms - Inappropriate kriging produces smoothing artifacts - Classification confidence is compromised - Mining selectively targets become unrealistic **Good domains = Reliable estimates** ::: ## Setup ```{r} #| message: false #| warning: false library(dplyr) library(tidyr) library(ggplot2) library(plotly) library(DT) library(RColorBrewer) library(GGally) library(patchwork) # Create simulated drilling data with geological controls set.seed(456) n_holes <- 50 collar <- data.frame( hole_id = paste0("DDH", sprintf("%03d", 1:n_holes)), x = runif(n_holes, 500000, 501000), y = runif(n_holes, 9000000, 9001000), rl = runif(n_holes, 100, 200) ) # Generate assay data with lithology-controlled grades litho_codes <- c("Andesite", "Diorite", "Mineralized_Zone", "Altered_Volcanics") litho_grade_means <- c(0.5, 0.8, 3.5, 2.0) # Different grades by lithology assay_list <- lapply(1:n_holes, function(i) { n_intervals <- sample(15:25, 1) depths <- seq(0, by = 2, length.out = n_intervals) # Assign lithology to each interval litho_idx <- sample(1:length(litho_codes), n_intervals - 1, replace = TRUE, prob = c(0.3, 0.2, 0.3, 0.2)) # Generate grades based on lithology au_grades <- sapply(litho_idx, function(idx) { max(0, rnorm(1, mean = litho_grade_means[idx], sd = 1.5)) }) # Correlated Ag and Cu ag_grades <- au_grades * runif(n_intervals - 1, 8, 12) + rnorm(n_intervals - 1, 0, 5) cu_grades <- au_grades * 0.3 + rnorm(n_intervals - 1, 0, 0.3) data.frame( hole_id = collar$hole_id[i], from = depths[-length(depths)], to = depths[-1], au_ppm = pmax(0, au_grades), ag_ppm = pmax(0, ag_grades), cu_pct = pmax(0, cu_grades), lithology = litho_codes[litho_idx] ) }) combined_data <- do.call(rbind, assay_list) %>% left_join(collar, by = "hole_id") %>% janitor::clean_names() # Prepare standard formats collar_std <- collar %>% janitor::clean_names() assay_std <- combined_data %>% select(hole_id, from, to, au_ppm, ag_ppm, cu_pct) lithology_std <- combined_data %>% select(hole_id, from, to, lithology) ``` --- # PILLAR 4: Geological Controls Analysis ## Part A: Lithology Analysis ### Grade Distribution by Rock Type The most fundamental control: **which rocks contain ore?** ```{r} #| fig-width: 10 #| fig-height: 6 #| warning: false # Calculate statistics by lithology litho_summary <- combined_data %>% group_by(lithology) %>% summarise( n = n(), mean_au = mean(au_ppm, na.rm = TRUE), median_au = median(au_ppm, na.rm = TRUE), max_au = max(au_ppm, na.rm = TRUE), sd_au = sd(au_ppm, na.rm = TRUE) ) %>% arrange(desc(mean_au)) # Create color palette n_litho <- length(unique(combined_data$lithology)) litho_colors <- setNames( brewer.pal(max(3, min(n_litho, 9)), "Set1")[1:n_litho], sort(unique(combined_data$lithology)) ) # Boxplot with statistical annotations p_litho_box <- ggplot(combined_data, aes(x = reorder(lithology, au_ppm, FUN = median), y = au_ppm, fill = lithology)) + geom_boxplot(outlier.alpha = 0.3) + stat_summary(fun = mean, geom = "point", shape = 23, size = 3, fill = "red", color = "darkred") + scale_fill_manual(values = litho_colors) + labs( title = "Gold Grade Distribution by Lithology", subtitle = "Box = IQR, Diamond = Mean, Line = Median", x = "Lithology (ordered by median grade)", y = "Au (ppm)" ) + theme_minimal() + theme( axis.text.x = element_text(angle = 45, hjust = 1), legend.position = "none" ) p_litho_box ``` ### Statistical Summary by Lithology ```{r} datatable(litho_summary, caption = "Table 1: Gold Statistics by Lithology", options = list(pageLength = 10)) %>% formatRound(columns = c('mean_au', 'median_au', 'max_au', 'sd_au'), digits = 3) %>% formatStyle( 'mean_au', background = styleColorBar(litho_summary$mean_au, 'lightblue'), backgroundSize = '100% 90%', backgroundRepeat = 'no-repeat', backgroundPosition = 'center' ) ``` ::: {.callout-note} ## Geological Interpretation From this analysis, identify: - **Primary ore hosts**: Lithologies with highest mean/median grades - **Barren waste**: Low-grade lithologies to exclude - **Grade variance**: High CV suggests mixed mineralization styles - **Outlier behavior**: Which rocks have extreme values? **Action**: Candidate lithologies for separate estimation domains ::: ### Grade-Tonnage Curves by Lithology Understanding the economic potential of each rock type. ```{r} #| fig-width: 10 #| fig-height: 6 #| warning: false # Calculate grade-tonnage curves cutoffs <- seq(0, 5, by = 0.1) gt_curves <- combined_data %>% expand_grid(cutoff = cutoffs) %>% filter(au_ppm >= cutoff) %>% group_by(lithology, cutoff) %>% summarise( tonnage_pct = n() / nrow(combined_data) * 100, avg_grade = mean(au_ppm, na.rm = TRUE), .groups = 'drop' ) # Plot tonnage vs cutoff p_tonnage <- ggplot(gt_curves, aes(x = cutoff, y = tonnage_pct, color = lithology)) + geom_line(size = 1.2) + scale_color_manual(values = litho_colors) + labs( title = "Tonnage vs Cut-off Grade", x = "Cut-off Grade (ppm Au)", y = "Tonnage (% of total)" ) + theme_minimal() + theme(legend.position = "right") # Plot grade vs cutoff p_grade <- ggplot(gt_curves, aes(x = cutoff, y = avg_grade, color = lithology)) + geom_line(size = 1.2) + scale_color_manual(values = litho_colors) + labs( title = "Average Grade vs Cut-off", x = "Cut-off Grade (ppm Au)", y = "Average Grade (ppm)" ) + theme_minimal() + theme(legend.position = "right") p_tonnage / p_grade ``` ## Part B: Element Correlation Analysis ### Bivariate Relationships Understanding element associations reveals mineralization processes. ```{r} #| fig-width: 10 #| fig-height: 8 #| warning: false #| message: false # Select grade variables for correlation grade_vars <- c("au_ppm", "ag_ppm", "cu_pct") # Create scatter plot matrix suppressWarnings({ ggpairs( combined_data %>% select(all_of(grade_vars), lithology), mapping = aes(color = lithology, alpha = 0.5), upper = list(continuous = wrap("cor", size = 3)), lower = list(continuous = wrap("points", alpha = 0.3, size = 0.5)), diag = list(continuous = wrap("densityDiag", alpha = 0.5)) ) + scale_color_manual(values = litho_colors) + scale_fill_manual(values = litho_colors) + theme_minimal() + labs(title = "Element Correlation Matrix by Lithology") }) ``` ### Regression Analysis: Au vs Ag ```{r} #| fig-width: 10 #| fig-height: 6 #| warning: false # Calculate regression by lithology regression_data <- combined_data %>% filter(!is.na(au_ppm) & !is.na(ag_ppm)) %>% group_by(lithology) %>% filter(n() > 10) %>% nest() %>% mutate( model = purrr::map(data, ~lm(ag_ppm ~ au_ppm, data = .x)), r_squared = purrr::map_dbl(model, ~summary(.x)$r.squared), slope = purrr::map_dbl(model, ~coef(.x)[2]), intercept = purrr::map_dbl(model, ~coef(.x)[1]) ) # Create scatter plot with regression lines p_regression <- ggplot(combined_data, aes(x = au_ppm, y = ag_ppm)) + geom_point(aes(color = lithology), alpha = 0.5, size = 2) + geom_smooth(aes(color = lithology), method = "lm", se = FALSE, size = 1.2) + scale_color_manual(values = litho_colors) + labs( title = "Gold vs Silver: Correlation by Lithology", subtitle = "Different slopes suggest different mineralization styles", x = "Au (ppm)", y = "Ag (ppm)" ) + theme_minimal() + theme(legend.position = "right") p_regression ``` ### Correlation Summary Table ```{r} regression_summary <- regression_data %>% select(lithology, r_squared, slope, intercept) %>% arrange(desc(r_squared)) %>% mutate( equation = paste0("Ag = ", round(slope, 2), " × Au + ", round(intercept, 2)), r_squared = round(r_squared, 3) ) %>% select(lithology, r_squared, equation) datatable(regression_summary, caption = "Table 2: Au-Ag Correlation by Lithology", options = list(pageLength = 10, dom = 't')) %>% formatStyle( 'r_squared', background = styleColorBar(regression_summary$r_squared, 'lightgreen'), backgroundSize = '100% 90%', backgroundRepeat = 'no-repeat', backgroundPosition = 'center' ) ``` ::: {.callout-tip} ## Geochemical Insights Strong correlations indicate: - **Coupled mineralization**: Elements deposited together - **Common sources**: Shared ore fluids or processes - **Domain boundaries**: Changes in correlation suggest domain breaks Weak correlations may indicate: - **Different mineralization events**: Overprinting - **Remobilization**: Secondary processes - **Mixed populations**: Need for further domain subdivision ::: ## Part C: Contact Analysis ### Grade Behavior at Geological Boundaries How does grade change across lithology contacts? ```{r} #| fig-width: 10 #| fig-height: 6 #| warning: false # Identify contact zones (simplified approach) contact_zones <- combined_data %>% arrange(hole_id, from) %>% group_by(hole_id) %>% mutate( next_litho = lead(lithology), is_contact = lithology != next_litho & !is.na(next_litho), contact_type = if_else(is_contact, paste(lithology, "→", next_litho), NA_character_) ) %>% filter(is_contact) %>% ungroup() # Plot grade at contacts if(nrow(contact_zones) > 0) { p_contacts <- ggplot(contact_zones, aes(x = contact_type, y = au_ppm)) + geom_boxplot(fill = "lightcoral", alpha = 0.7) + geom_jitter(width = 0.2, alpha = 0.5, size = 2) + labs( title = "Gold Grades at Lithology Contacts", subtitle = "Understanding grade behavior at geological boundaries", x = "Contact Type", y = "Au (ppm)" ) + theme_minimal() + theme(axis.text.x = element_text(angle = 45, hjust = 1)) print(p_contacts) } else { cat("No contact zones identified in the dataset.\n") } ``` ::: {.callout-note} ## Contact Zone Interpretation Sharp grade changes at contacts may indicate: - **Structural controls**: Faults or shears - **Alteration halos**: Gradational vs sharp boundaries - **Domain boundaries**: Where to draw estimation domains - **Dilution zones**: Material to exclude from ore domains ::: ## Domain Definition Workflow ### Combining All Evidence Now we synthesize findings from all analyses: ```{r} #| warning: false # IMPROVED: More realistic domain classification # Step 1: Classify each interval domain_definition <- combined_data %>% mutate( interval_domain = case_when( lithology == "Mineralized_Zone" & au_ppm >= 1.5 ~ "High Grade Ore", lithology == "Mineralized_Zone" & au_ppm >= 0.3 ~ "Low Grade Ore", lithology == "Altered_Volcanics" & au_ppm >= 0.8 ~ "Altered Ore", au_ppm < 0.3 ~ "Waste", TRUE ~ "Transitional" ) ) # Step 2: Summarize by hole (dominant domain approach) hole_summary <- domain_definition %>% group_by(hole_id) %>% summarise( n_intervals = n(), avg_au = mean(au_ppm, na.rm = TRUE), max_au = max(au_ppm, na.rm = TRUE), has_high_grade = any(interval_domain == "High Grade Ore"), pct_ore = sum(interval_domain %in% c("High Grade Ore", "Low Grade Ore", "Altered Ore")) / n() * 100, .groups = 'drop' ) # Step 3: Final hole-level domain classification hole_domains <- hole_summary %>% mutate( hole_domain = case_when( has_high_grade & avg_au >= 1.0 ~ "High Grade Ore", avg_au >= 0.8 ~ "Low Grade Ore", avg_au >= 0.5 | pct_ore >= 30 ~ "Altered Ore", avg_au >= 0.3 ~ "Transitional", TRUE ~ "Waste" ) ) # Summary by domain domain_summary <- domain_definition %>% group_by(interval_domain) %>% summarise( Intervals = n(), `Mean Au` = mean(au_ppm, na.rm = TRUE), `Median Au` = median(au_ppm, na.rm = TRUE), `Mean Ag` = mean(ag_ppm, na.rm = TRUE), `Mean Cu` = mean(cu_pct, na.rm = TRUE), .groups = 'drop' ) %>% arrange(desc(`Mean Au`)) %>% mutate(across(where(is.numeric) & !Intervals, ~round(.x, 3))) datatable(domain_summary, caption = "Table 3: Proposed Estimation Domains (Interval-Based)", options = list(pageLength = 10, dom = 't')) # Hole-level summary hole_domain_summary <- hole_domains %>% group_by(hole_domain) %>% summarise( Holes = n(), `Avg Au (ppm)` = mean(avg_au), `Max Au (ppm)` = max(max_au), .groups = 'drop' ) %>% arrange(desc(`Avg Au (ppm)`)) %>% mutate(across(where(is.numeric) & !Holes, ~round(.x, 3))) datatable(hole_domain_summary, caption = "Table 4: Domain Classification by Drillhole", options = list(pageLength = 10, dom = 't')) ``` ### Domain Spatial Distribution ```{r} #| fig-width: 10 #| fig-height: 6 #| warning: false # Create color palette for domains domain_colors <- c( "High Grade Ore" = "#d32f2f", "Low Grade Ore" = "#ff9800", "Altered Ore" = "#ffd54f", "Transitional" = "#9e9e9e", "Waste" = "#e0e0e0" ) # Merge hole domains with collar data domain_spatial <- hole_domains %>% left_join(collar_std, by = "hole_id") p_domain_map <- ggplot(domain_spatial, aes(x = x, y = y, color = hole_domain)) + geom_point(size = 4, alpha = 0.8) + scale_color_manual(values = domain_colors) + coord_equal() + labs( title = "Proposed Domain Distribution - Plan View", subtitle = "Dominant domain per drillhole", x = "Easting (m)", y = "Northing (m)", color = "Domain" ) + theme_minimal() + theme(legend.position = "right") p_domain_map ``` ## The Birth of Robust Geological Domains ### Before EDA Without systematic EDA: - Random data points without geological context - Mixed populations in estimation - Unreliable variograms - Poor mining selectivity ### After EDA: The 4 Pillars Converge ```{mermaid} flowchart TB P1[Pillar 1: Clean, Validated Data] --> D[Robust Geological Domains] P2[Pillar 2: Spatial Understanding] --> D P3[Pillar 3: Statistical Populations] --> D P4[Pillar 4: Geological Controls] --> D D --> E1[Reliable Estimation] D --> E2[Realistic Mine Plans] D --> E3[Confident Classification] style D fill:#4caf50,color:#fff style P1 fill:#e3f2fd style P2 fill:#fff3e0 style P3 fill:#f3e5f5 style P4 fill:#e8f5e9 ``` ### Domain Validation Checklist ::: {.callout-important} ## Defensible Domains Must Have: ✓ **Geological justification**: Rock types, alteration, structure ✓ **Statistical support**: Distinct populations, different variability ✓ **Spatial continuity**: Mappable in 3D space ✓ **Grade differences**: Economically meaningful ✓ **Sample support**: Adequate data density ✓ **Clear boundaries**: Definable contacts ::: ## Summary: From Data to Domains ### What We Accomplished Through the 4 Pillar EDA framework, we: 1. **Validated data integrity** (Pillar 1) 2. **Understood spatial distribution** (Pillar 2) 3. **Characterized grade populations** (Pillar 3) 4. **Identified geological controls** (Pillar 4) **Result**: Scientifically defensible estimation domains ready for resource modeling. ### Next Steps in Resource Estimation With robust domains defined, you can proceed to: 1. **Compositioning**: Regularize sample support within domains 2. **Variography**: Model spatial continuity per domain 3. **Estimation**: Kriging with appropriate search parameters 4. **Classification**: Measured, Indicated, Inferred categories 5. **Validation**: Check estimates against reality ### Key Takeaways ::: {.callout-tip} ## Remember These Principles 1. **EDA is not optional** - It's mandatory for JORC compliance 2. **Data quality = Model reliability** - GIGO always applies 3. **Geology drives domains** - Statistics support, geology defines 4. **Document everything** - Auditors will ask for justification 5. **Use modern tools** - Automate routine tasks, focus on interpretation ::: ## Impact on Business Decisions Good EDA and domaining directly impact: - **Resource confidence**: Better classification categories - **Mine planning**: Realistic extraction sequences - **Grade control**: Achievable selectivity - **Investor confidence**: Defensible, auditable reports - **Project value**: Reduced risk = higher valuations ::: {.callout-important} ## The Foundation of Trust "In mining, we don't get second chances. The quality of our EDA determines whether we build a mine or lose millions in poor decisions." **Every successful operation starts with understanding the data.** ::: ## Tools and Resources ### GeoDataViz Application All analyses demonstrated here are available in GeoDataViz: - **GitHub**: [github.com/ghoziankarami/GeoDataViz](https://github.com/ghoziankarami/GeoDataViz/) - **Zenodo**: [doi.org/10.5281/zenodo.17142676](https://doi.org/10.5281/zenodo.17142676) - **License**: MIT (Open Source) ### Contact - **Author**: Ghozian Islam Karami - **Email**: ghoziankarami@gmail.com - **LinkedIn**: [linkedin.com/in/ghoziankarami](https://linkedin.com/in/ghoziankarami) --- ## Series Complete You've completed the comprehensive EDA workflow: - [← Part 1: Foundation & Data Validation](../Data Validation/) - [← Part 2: Spatial & Statistical Analysis](../Spatial Statistics/) - **Part 3: Geological Controls & Domain Definition** (You are here) You now have the tools and knowledge to build **trusted geological models** from raw drilling data. --- *"Quality data, systematic analysis, geological thinking - the foundation of every successful mine."*