Remote Sensing & GIS in Geology

Remote sensing and Geographic Information Systems (GIS) have revolutionized geological mapping and analysis. These technologies allow geologists to study Earth's surface and subsurface from a distance, providing unprecedented spatial and temporal coverage that enhances field-based investigations.

Remote Sensing Fundamentals

Electromagnetic Spectrum and Geological Applications

Where $E$ is energy, $h$ is Planck's constant, $\nu$ is frequency, $c$ is speed of light, and $\lambda$ is wavelength.

Spectral Ranges for Geological Applications

Visible (VIS): 0.4-0.7 μm

• Applications: Color variations in rocks, vegetation stress
• Sensors: Landsat TM bands 1-3, Sentinel-2 bands 2-4

Near Infrared (NIR): 0.7-1.3 μm

• Applications: Vegetation health, water content in soils
• Sensors: Landsat TM band 4, Sentinel-2 band 8

Shortwave Infrared (SWIR): 1.3-3.0 μm

• Applications: Hydration detection, mineral identification
• Sensors: Landsat TM bands 5-7, Sentinel-2 bands 11-12

Thermal Infrared (TIR): 8-14 μm

• Applications: Heat signatures, thermal inertia, rock identification
• Sensors: Landsat TM band 6, Landsat 8 TIRS bands 10-11

Spectral Signatures

Mineral Absorption Features

Where $R(\lambda)$ is reflectance at wavelength $\lambda$, $R_0$ is reference reflectance, $k(\lambda)$ is absorption coefficient, and $d$ is path length.

Diagnostic Absorption Bands

• OH/H₂O: 1.4, 1.9, 2.2 μm
• Carbonates: 2.3, 2.5 μm
• Clays: 2.2, 2.3 μm
• Ferro-magnesium minerals: 2.0-2.4 μm

Satellite Sensors and Platforms

Optical Sensors

Landsat Series

• Landsat 8/9: Operational Land Imager (OLI) and Thermal Infrared Sensor (TIRS)
  • Spatial resolution: 15-30 m (depending on band)
  • Spectral bands: 9 optical + 2 thermal
  • Temporal resolution: 16 days

Sentinel-2

• Spatial resolution: 10-60 m
• Spectral bands: 13 bands from VIS to SWIR
• Temporal resolution: 5 days (with two satellites)

ASTER (Advanced Spaceborne Thermal Emission Radiometer)

• Spectral coverage: VIS, NIR, SWIR, TIR
• Spatial resolution: 15-90 m
• Applications: Mineral mapping, temperature mapping

Radar Sensors

Synthetic Aperture Radar (SAR)

Where $\sigma^0$ is radar backscatter coefficient, $\lambda$ is wavelength, and $\theta$ is incidence angle.

Applications:

• Structural mapping: Penetrates vegetation cover
• Deformation monitoring: Interferometric SAR (InSAR)
• Surface roughness: Texture analysis

Image Processing Techniques

Preprocessing

Atmospheric Correction

Where $L_s$ is surface reflectance, $TOA_{radiance}$ is top-of-atmosphere radiance, $d$ is Earth-Sun distance, $ESUN$ is solar exoatmospheric irradiance, and $\theta_s$ is solar zenith angle.

Geometric Correction

• Ground Control Points: Known coordinates for image rectification
• Sensor Model: Mathematical relationship between image and ground coordinates

Enhancement Techniques

Principal Component Analysis (PCA)

Where $\mathbf{Z}$ is principal components, $\mathbf{X}$ is original data matrix, and $\mathbf{P}$ is principal component transformation matrix.

Band Ratios

Common geological ratios:

• Fe content: Band 5 / Band 4 (Landsat TM)
• Clay content: Band 5 / Band 7 (Landsat TM)
• Vegetation: (NIR - Red) / (NIR + Red) (NDVI)

Geological Applications

Structural Analysis

Lineament Detection

Techniques:

• Edge detection: Sobel, Canny, Laplacian operators
• Texture analysis: Gray-level co-occurrence matrices (GLCM)
• Frequency domain: Fourier transforms for pattern recognition

Fracture Analysis

• Rose diagrams: Directional analysis of structural features
• Spacing analysis: Statistical distribution of fracture spacing
• Intensity mapping: Density of structural features

Lithological Mapping

Spectral Classification

• Supervised classification: Training sites with known lithology
• Unsupervised classification: Clustering algorithms (K-means, ISODATA)
• Spectral angle mapper: Angular distance in n-dimensional space

Mineral Mapping

Techniques:

• Spectral unmixing: Linear combinations of endmembers
• Continuum removal: Isolate absorption features
• Absorption band analysis: Center wavelength and depth

Hydrothermal Alteration Mapping

Alteration Assemblage Detection

• Alunite/Kaolinite/Aluminum: ASTER bands 6/(5/4)
• Ferrous Iron: ASTER band 4/band 2
• Silica: ASTER band 6 (1.65 μm) depth

Digital Terrain Analysis

Topographic Attributes

Slope and Aspect

Curvature Analysis

Where $s$ is direction of maximum slope and $u$ is direction perpendicular to $s$.

Terrain Analysis Applications

Structural Geology

• Drainage pattern analysis: Rectangular, trellis, radial patterns
• Valley floor mapping: Identifies potential structural lows
• Escarpment analysis: Identifies resistant rock units

Engineering Geology

• Slope stability: Steepness and aspect analysis
• Landslide susceptibility: Curvature and slope analysis
• Stream gradient analysis: Erosion potential assessment

GIS in Geological Applications

Spatial Analysis

Overlay Analysis

Where $w_i$ is weight of factor $i$ and $r_i$ is rating of factor $i$.

Proximity Analysis

• Buffer analysis: Distance zones around features
• Viewshed analysis: Visibility from specific locations
• Cost distance: Minimum cost path analysis

Database Management

Attribute Tables

• Lithology codes: Standardized rock type classification
• Age assignments: Temporal information
• Structural data: Orientation measurements
• Sample information: Geochemical and geochronological data

Change Detection

Multi-Temporal Analysis

Normalized Difference Vegetation Index (NDVI)

Normalized Difference Built-up Index (NDBI)

Landform Evolution Analysis

Integration with Field Data

Ground Truth Validation

Field-to-Satellite Scaling

• Pixel integration: Averaging field measurements over pixel area
• Up-scaling: Extrapolating field observations to satellite scale
• Down-scaling: Refining satellite interpretations with field data

Applications in Mineral Exploration

Target Identification

Exploration Planning

• Accessibility analysis: Route planning from satellite data
• Prioritization: Ranking target areas based on evidence
• Cost optimization: Efficient field campaign planning

Emerging Technologies

Hyperspectral Imaging

• AVIRIS: Airborne Visible/Infrared Imaging Spectrometer
• EnMAP: Environmental Mapping and Analysis Program
• PRISMA: Hyperspectral Precursor and Application Mission

LiDAR Applications

• DEM generation: High-resolution topography
• Vegetation penetration: Sub-canopy mapping
• Deformation monitoring: mm-scale precision

Real-World Application: Structural Mapping Using Remote Sensing

Remote sensing is particularly valuable for mapping geological structures in areas with limited field access.

Lineament Analysis Example

# Structural analysis using remote sensing data
struct_analysis = {
    'image_resolution': 15,    # meters (pixel size)
    'study_area': 1000,        # km² (total area)
    'lineament_density': 2.5,  # km/km² (lineaments per unit area)
    'average_length': 1.2,     # km (average lineament length)
    'dominant_azimuth': 45,    # degrees (most common direction)
    'preferred_directions': [45, 135, 225, 315],  # degrees (common directions)
    'confidence_level': 0.85   # unitless (rating of interpretation confidence)
}

# Calculate total lineament length
total_lineament_length = struct_analysis['lineament_density'] * struct_analysis['study_area']  # km
number_of_lineaments = total_lineament_length / struct_analysis['average_length']  # count

# Analyze directional clustering
direction_tolerance = 10  # degrees (acceptable variation from preferred directions)

# Calculate structural index
# Factor in density, length, and clustering around preferred directions
structural_complexity = (struct_analysis['lineament_density'] * 
                         struct_analysis['average_length'] * 
                         len(struct_analysis['preferred_directions']) / 4)

print(f"Structural analysis results:")
print(f"  Study area: {struct_analysis['study_area']} km²")
print(f"  Lineament density: {struct_analysis['lineament_density']} km/km²")
print(f"  Total lineament length: {total_lineament_length} km")
print(f"  Estimated number of structures: {number_of_lineaments:.0f}")
print(f"  Dominant direction: {struct_analysis['dominant_azimuth']}°")
print(f"  Structural complexity index: {structural_complexity:.2f}")
print(f"  Confidence level: {struct_analysis['confidence_level']:.2f}")

# Interpret tectonic significance
if structural_complexity > 3:
    tectonic_setting = "Highly deformed - complex tectonic environment"
elif structural_complexity > 1.5:
    tectonic_setting = "Moderately deformed - multiple deformation events"
else:
    tectonic_setting = "Low deformation - stable cratonic setting"
    
print(f"  Tectonic interpretation: {tectonic_setting}")

# Geological implications
if struct_analysis['dominant_azimuth'] in [0, 180] or struct_analysis['dominant_azimuth'] in [90, 270]:
    stress_pattern = "Orthogonal stress system (likely maximum compression)"
else:
    stress_pattern = "Oblique stress system"

print(f"  Stress pattern: {stress_pattern}")

Integration with Field Data

Combining remote sensing with field observations enhances geological understanding.

Your Challenge: Lithological Classification Using Spectral Data

Analyze multispectral satellite data to classify and map different rock types in an area.

Goal: Use spectral analysis techniques to identify and map lithological units from satellite data.

Satellite Data

import math

# Multispectral data for sample areas
# Simulated data for different rock types (reflectance values in different bands)
spectral_data = [
    {'name': 'Area A', 'band1': 0.15, 'band2': 0.22, 'band3': 0.32, 'band4': 0.45, 'band5': 0.55, 'band7': 0.65, 'rock_type': 'unknown'},
    {'name': 'Area B', 'band1': 0.25, 'band2': 0.35, 'band3': 0.42, 'band4': 0.52, 'band5': 0.75, 'band7': 0.85, 'rock_type': 'unknown'},
    {'name': 'Area C', 'band1': 0.12, 'band2': 0.18, 'band3': 0.25, 'band4': 0.35, 'band5': 0.45, 'band7': 0.52, 'rock_type': 'unknown'},
    {'name': 'Area D', 'band1': 0.35, 'band2': 0.45, 'band3': 0.58, 'band4': 0.72, 'band5': 0.82, 'band7': 0.88, 'rock_type': 'unknown'},
    {'name': 'Area E', 'band1': 0.20, 'band2': 0.30, 'band3': 0.38, 'band4': 0.48, 'band5': 0.68, 'band7': 0.78, 'rock_type': 'unknown'},
]

# Known training sites for supervised classification
training_data = {
    'granite': {'band1': 0.22, 'band2': 0.32, 'band3': 0.42, 'band4': 0.55, 'band5': 0.72, 'band7': 0.82},
    'basalt': {'band1': 0.15, 'band2': 0.22, 'band3': 0.28, 'band4': 0.38, 'band5': 0.48, 'band7': 0.55},
    'sandstone': {'band1': 0.25, 'band2': 0.35, 'band3': 0.45, 'band4': 0.58, 'band5': 0.75, 'band7': 0.85},
    'limestone': {'band1': 0.18, 'band2': 0.28, 'band3': 0.35, 'band4': 0.45, 'band5': 0.58, 'band7': 0.68}
}

# Calculate spectral distance for each sample to each training class
classifications = []
for sample in spectral_data:
    distances = {}
    for rock_type, train_vals in training_data.items():
        # Calculate Euclidean distance in spectral space
        sum_sq_diff = 0
        for band in ['band1', 'band2', 'band3', 'band4', 'band5', 'band7']:
            diff = sample[band] - train_vals[band]
            sum_sq_diff += diff**2
        distance = math.sqrt(sum_sq_diff)
        distances[rock_type] = distance
    
    # Assign to closest class
    closest_class = min(distances, key=distances.get)
    sample['rock_type'] = closest_class
    sample['confidence'] = 1.0 / (1.0 + distances[closest_class])  # Higher confidence for smaller distances
    classifications.append((sample['name'], closest_class, sample['confidence']))

# Calculate commonly used geological indices
for sample in spectral_data:
    # Iron content index
    sample['fe_index'] = sample['band5'] / sample['band4']
    
    # Clay content index (albedo ratio for clay minerals)
    sample['clay_index'] = sample['band5'] / sample['band7']
    
    # Silica content proxy (band 7 response)
    sample['silica_index'] = sample['band7']

# Evaluate quality of classification
avg_confidence = sum([s['confidence'] for s in spectral_data]) / len(spectral_data)

Analyze the spectral data to classify lithologies and identify geological patterns.

Hint:

• Use spectral distance calculations to match unknown samples to known rock types
• Calculate geological indices (Fe, clay, silica) from spectral ratios
• Consider how different rock types have characteristic reflectance patterns
• Assess classification confidence based on spectral similarity

# TODO: Calculate classification results
classification_results = []  # List of (area, rock_type, confidence) tuples
dominant_rock_type = ""      # Most common rock type identified
geological_pattern = ""      # Pattern of rock distribution
confidence_level = 0         # Average confidence level

# Calculate geological indices for each area
indices_results = []
for sample in spectral_data:
    area_name = sample['name']
    fe_content = sample['fe_index']
    clay_content = sample['clay_index']
    silica_content = sample['silica_index']
    rock_type = sample['rock_type']
    confidence = sample['confidence']
    
    indices_results.append({
        'area': area_name,
        'rock_type': rock_type,
        'fe_index': fe_content,
        'clay_index': clay_content,
        'silica_index': silica_content,
        'confidence': confidence
    })

# Determine dominant rock type
rock_type_counts = {}
for sample in spectral_data:
    rock_type = sample['rock_type']
    rock_type_counts[rock_type] = rock_type_counts.get(rock_type, 0) + 1

dominant_rock_type = max(rock_type_counts, key=rock_type_counts.get)
dominant_percentage = rock_type_counts[dominant_rock_type] / len(spectral_data) * 100

# Calculate average confidence
confidence_level = sum([sample['confidence'] for sample in spectral_data]) / len(spectral_data)

# Assess geological pattern
if len(set([s['rock_type'] for s in spectral_data])) == 1:
    geological_pattern = "Homogeneous - single rock type dominates"
elif dominant_percentage > 60:
    geological_pattern = f"Moderately heterogeneous - {dominant_rock_type} dominant"
else:
    geological_pattern = "Heterogeneous - multiple rock types, no clear dominance"

# Print results
print(f"Classification results:")
for result in indices_results:
    print(f"  {result['area']}: {result['rock_type']} (conf: {result['confidence']:.2f})")
    
print(f"\nDominant rock type: {dominant_rock_type} ({dominant_percentage:.1f}%)")
print(f"Average classification confidence: {confidence_level:.2f}")
print(f"Geological pattern: {geological_pattern}")

# Geological interpretation
if 'basalt' in dominant_rock_type:
    interpretation = "Mafic igneous terrain - possible volcanic or plutonic mafic rocks"
elif 'granite' in dominant_rock_type:
    interpretation = "Felsic igneous terrain - granitic plutonic rocks"
elif 'sandstone' in dominant_rock_type:
    interpretation = "Sedimentary terrain - clastic sedimentary rocks"
elif 'limestone' in dominant_rock_type:
    interpretation = "Sedimentary carbonate terrain"
else:
    interpretation = "Mixed lithologies - complex geological setting"

print(f"Geological interpretation: {interpretation}")

How might the geological setting identified through remote sensing compare with what you might expect from the tectonic setting of the region?