Model-based Spatial Data integration

MODELS

OUTPUT MAP = ∫ (Two or More Maps)• The integrating function is estimated using

either:– Theoretical understanding of physical and

chemical principles, or– Based on observational data

MODELS – Deterministic Models

OUTPUT MAP = ∫ (Two or More Maps)For example, you want to derive a map of water

circulation in a lake:• Velocity field = ∫ water depth, bottom slope, inflow,

outflow, wind orientation and direction• Apply Navier-Stokes equation to get the output.

MODELS – Stochastic ModelsOUTPUT MAP = ∫ (Two or More Maps)

• For example, you want to derive a map of groundwater potential in an area. Conceptually, we can say:Ground water potential = ∫ Ground water recharge, discharge

• And further:

Groundwater recharge = ∫ availability of water for recharging; percolation of water to the aquifers

Ground water discharge = ∫ evapo-transpiration; extraction for human use.

• There are no theoretical equation available to combine these maps.• So what do we do?

MODELS – Empirical Models• Groundwater recharge = ∫Water availability, Water percolation• Water availability – how do we map?

– Rainfall maps– Wide rivers in late stage, proximity to rivers

• Percolation– water flow velocity – we use slope maps– drainage density, – Landuse– soil and rock permeability, – structural permeability – density of faults, joints; proximity to faults etc

• These maps are said to serve as spatial proxies for the two factors, water availability and water percolation. We call them predictor maps.

• Groundwater discharge= ∫Evapo-transpiration, extraction humans• Proxies for evapo-transpiration:

– Vegetation density– Humidity distribution – Wind velocity– Temperature distribution– Agriculture intensity– Population density

Now we redefine the model in terms of proxies.Ground water potential = ∫ Ground water recharge, discharge

= ∫ (Rainfall maps, proximity to rivers, slope maps, drainage density, land-use, soil and rock

permeability, density of faults, joints; proximity to faults etc)

AND (vegetation density, humidity distribution, wind

velocity, temperature distribution, agriculture intensity, population density)

MODELS – Empirical Models

How do derive output groundwater potential map?

• We combine the proxies or predictor maps• We can overlay the above maps in a simplistic way,

and add them up.• But the problem is, all the factors do not contribute

equally to water recharge, do they?• So we need to provide weights before combining

them.

How do derive the output groundwater potential map?

• We can either assign weights based on our Knowledge about groundwater recharge/discharge

Or we can use empirical observations to determine the weights. The empirical observations are used as training points.

• Based on whether we use our knowledge to assign weight to the map, or we use empirical observation to determine the weights, we call a model knowledge-driven or data-driven.

• A third category of models are called hybrid models, which use both knowledge and data

Knowledge-driven model

• Boolean overlay• Index overlay• Fuzzy set theroy• Dempster-shafer belief theory

Data-driven model

• Bayesian Probabilistic (weights of evidence)• Logistic regression• Artificial neural networks

Hybrid models

• Adaptive fuzzy inference systems

Input data preparation

SCALE

Ligand source

Metal source

Model I

Model II

Model III

Trap Region

Energy(Driving Force)

Transporting fluid

ResidualFluid Discharge

Mineral System(≤ 500 km) Deposit Halo

Deposit(≤ 10 km)

(≤ 5 km)

COMPONENTS 1. Energy 2. Ligand 3. Source 4. Transport 5. Trap 6. Outflow

INGR

EDIE

NTS

Deformation MetamorphismMagmatism

Connate brinesMagmatic fluidsMeteoric fluids

Enriched source rocksMagmatic fluids

Structures Permeable zones

Structures Chemical traps

Structures aquifers

MAP

PABL

E CR

ITER

IA

Link processes to predictor maps

Metamorphic grade, igneous intrusions, sedimentary thickness

Evaporites, Organics, isotopes

Radiometric anomalies, geochemical anomalies, whole-rock geochemistry

Fault/shear zones, folds geophysical/ geochemical anomalies, alteration

Dilational traps, reactive rocks, geophyiscal/ geochemical anomalies, alteration

magnetic/ radiometric/ geochemical anomalies, alteration, structures

SPAT

IAL

PROX

IES

Predictor maps• A GIS data layer that can predict the presence of a mineral deposit is

called a predictor map.• Also called evidential maps because they provide spatial evidence for

processes that form mineral deposits.

Primary datasets typically available for mineral exploration

• Geological map (rocks types, rock description, stratigraphic groupings; typically vector polygon map + attribute table)

• Structural maps (type of structures e.g., Faults, folds, joints, lineament etc; typically vector line map + attribute table) • Geochemical maps (multi-element concentration values at irregularly distributed sample locations + attribute table)

• Geophysical images (gravity and magnetic field intensity, ratser images, no attribute tables)

• Remote sensing images (multispectral/hyperspectral, no attribute tables)

Geology

Structures

Geochemistry

MAGNETIC DATA

GRAVITY DATA

Gamma-ray Spectrometric data

LANDSAT TM data

Predictor maps

Process Possible predictor map(s) GIS processingEnergy for driving fluid circulation

Map of granites Querying geological map for granites and associated igneous rocks; Extraction

Map of metamorphic grades Querying geological maps for specific metamorphic minerals that indicate the grade of metamorphism; Reclassification

Isopach map of sedimentary rocks Interpolation of sediment thickness in boreholes

Ligand source

Presence of evaporite (mainly halites) diapirs

Querying geological map for halites/salt domes/evaporites; Extraction

Metal source

Map of granites Querying geological map for granites and associated igneous rocks; Extraction; Euclidean distance calculation

PathwaysProximity to faults Querying for faults, Euclidean distance calculationProximity to lineaments Querying for lineaments, distance calculation

Physical traps

Proximity to fold axes Querying for fold axes, Euclidean distance calculationHigh fault density Line density estimationHigh fault intersection density Extraction of fault intersections, point density estimationsHigh geological contact density Line density estimationHigh competency contrast across geological contacts

Assign rheological strength values to all rocks on the geological map, Assign rheological difference values across each geological contact to the geological contact;

Predictor maps

Process Possible predictor map(s) GIS processingChemical traps

Map of Chemical reactivity (Fe anomalies) Interpolation of Fe values from geochemical data

Gold anomalies Interpolation of Au values from geochemical data

As, Sb, Cu, Bi anomalies Interpolation of Au values from geochemical data

Energy source/Metal source:Distance to granites

Pathways:Distance to Faults

Physical trap:Fault density

Physical trap:Fault intersection density

Physical trap:Competency contrast

Chemical trap:Fe Concentration

Chemical trap:As Concentration

Chemical trap:Sb Concentration

Chemical trap:Au Concentration

Gold deposits