GATE Igneous Petrology Numericals
The specific problems may vary from year to year, but they generally focus on the quantitative
aspects of igneous rock formation, composition, and interpretation. In the exam these appear most
often as short calculation problems based on standard petrological principles.
1. Magma Composition Calculations
Problems involving the calculation of the composition of magma based on the proportions of
different minerals or components (CIPW).
Calculating the composition of a magma after fractional crystallization or assimilation
(addition and subtraction diagrams).
Determining the modal mineralogy from thin section analysis.
Calculation of magma mixing and mingling proportions: two‐end member mixing – solving
for proportions of magma A and B required to achieve a given bulk composition (linear mixing of
oxide abundances). Calculation of the composition of a hybrid magma formed by the mixing of two
or more distinct magmas (using mass balance equations and the application of mixing models).
Calculation of the density and viscosity of magmas (Giordano‐Russell model or simplified
empirical relations) based on their composition and temperature. Bulk density calculations from
mineral or melt proportions. Understanding how these properties affect magma movement and
eruption dynamics.
Calculations related to the volatile content of magmas and the implications for eruption style
and explosivity. Estimating the amount of gas released during volcanic eruptions based on magma
composition.
Problems that involve calculating the thermal conductivity of igneous rocks and the heat
flow associated with magmatic processes.
Calculating the volume of volcanic eruptions from deposit thicknesses and areas.
2. Melting and Crystallization
Calculations related to the melting of rocks and the crystallization of minerals from magma.
Problems may involve determining the percentage of melting or the temperature at which certain
minerals crystallize.
From the initial composition of a magma, calculate the composition of the residual liquid
and the crystallized minerals at different stages of fractional crystallization. This may involve the use
of phase diagrams and the application of Bowen's Reaction Series. Calculating how much of each
mineral crystallizes from a given magma batch to consume specific oxides. Re-distributing major‐
element oxides into sets of minerals by stoichiometry.
Modelling of magmatic differentiation and crustal contamination.
Estimating the degree of melting (F) required to produce a melt of known composition from
a given source composition, using batch or fractional melting equations.
3. Geothermometry and Geobarometry
Using geothermometers to estimate the temperature of magma crystallization. Using
geobarometers to estimate the pressure of magma crystallization.
Numerical problems that require the use of mineral compositions to estimate the
temperature (geothermometry) and pressure (geobarometry) of formation.
Application of specific equations or calibration curves based on mineral pairs. Calculation of
pressure and temperature conditions of magma crystallization using thermo-barometric equations.
Determination of magma depth and volatile content.
Estimation of temperature and pressure conditions of formation of an igneous rock based on
the mineral assemblage and the chemical composition. [This can involve the use of various
geothermometers and geobarometers, such as the two-pyroxene geothermometer or the Al-in-
hornblende geobarometer. Two‐pyroxene thermometry: using the compositional exchange reaction
between coexisting orthopyroxene + clinopyroxene to compute temperature (Brey & Köhler or
Lindsley equations). Plagioclase‐liquid or two‐feldspar geothermometers: deriving T from An% in
plagioclase coexisting with melt or K‐feldspar. Amphibole geothermobarometry: using Al–in–
hornblende barometers/thermometers.]
Simple isochemical exchange reactions to solve for P or T given known mineral
compositions.
4. Phase Equilibria
Use of phase diagrams to determine the stability fields of minerals at various temperatures
and pressures (conditions of formation).
Calculating the temperature and pressure conditions from phase diagrams.
Numerical problems that require the interpretation of phase diagrams and the calculation of
phase relationships in igneous systems.
Calculation of phase boundaries and stability fields using equations. Determination of
reaction rates and timescales.
Applying Gibbs’ phase rule F = C – P + 2 (or +1 for T=constant) to mineral assemblages,
identifying degrees of freedom F.
Reading binary (e.g. diopside–anorthite) or ternary (e.g. join in the CaO–MgO–SiO₂
system) phase diagrams to find liquidus/solidus boundaries.
Using the lever rule on a binary diagram to compute proportions of melt vs. crystals at a
given T.
Calculating the Gibbs free energy, enthalpy, and entropy changes during igneous processes.
Using thermodynamic data to model the stability of minerals and melts.
[Use the appropriate mass‐balance or exchange equation. Identify given variables and what
you need to solve for. Rearrange algebraically to isolate the unknown. Keep track of units (wt %,
mole %, partition coefficients, temperature in °C or K, pressure in kbar)].
5. Isotope Geochemistry
Problems involving the calculation of isotopic ratios (and ages) and their implications for the
source and evolution of magmas.
Using isotopic data to trace the sources of magmas and the processes involved in their
formation.
Calculate the age of an igneous rock using radiometric dating techniques, such as the U-Pb
or Rb-Sr methods. This can involve the application of radioactive decay equations and the
interpretation of isotopic ratios.
Solving two‐component mixing equations for isotopic ratios (Sr, Nd), given end‐member
concentrations and ratios.
Calculating isotopic ratios and using them to determine the age of igneous rocks.
6. Trace Element Geochemistry
Calculation of element partitioning and distribution coefficients.
Interpretation of trace element composition of an igneous rock and its implications for the
petrogenesis and tectonic setting. This may involve the calculation of various trace element ratios
and the use of geochemical discrimination diagrams.
Applying the Rayleigh fractionation equation or its variants, to track how trace‐element
concentrations change as magma crystallizes.
Estimating residual melt composition given a fraction of crystals removed (f ) and partition
coefficient (D).
Using mass‐balance equations for batch melting, contrast with fractional melting
formulations to calculate melt and residue compositions.
Computing bulk partition coefficients for trace elements given modal mineral proportions
and mineral‐melt Kᴅ values.
Predicting element depletion/enrichment in residual melt. Determining the degree of partial
melting from the composition of the melt and the source rock.
7. Tectonic Settings and Magma Generation
Numerical problems that may involve calculating the conditions under which different types
of magmas are generated in various tectonic settings (mid-ocean ridges, subduction zones).
8. Igneous Rock Classification:
Chemical composition of an igneous rock and IUGS classification and other schemes. This
may involve the calculation of various indices and parameters used in the classification process.
Using modal analyses or CIPW norms for the QAPF classification diagram.
9. Petrogenetic Grids
Using petrogenetic grids to determine the conditions of magma formation and evolution.
Calculating the composition of magmas at different stages of differentiation.
10. Chemical Weathering and Alteration
Calculating the degree of chemical weathering from the composition of weathered rocks.
Determining the composition of altered rocks from their original composition and the
alteration processes.
11. Melt Inclusion Studies
Calculating the composition of melts trapped in inclusions. Using melt inclusions to
determine the conditions of magma formation and evolution.
Phase Diagram Analysis
Using a phase diagram for the system Anorthite (An) - Diopside (Di) - Forsterite (Fo),
determine the temperature and pressure conditions at which a rock with the composition
An40Di30Fo30 would be in equilibrium.
Magma Differentiation
Given an initial magma composition and the composition of a mineral that crystallizes from
it, calculate the composition of the residual magma after 50% crystallization.
Geothermometry
Using the two-pyroxene geothermometer, calculate the temperature of crystallization of a
rock containing orthopyroxene (En80Fs20) and clinopyroxene (En40Fs10Wo50).
Isotopic Age Determination
Given the isotopic ratios of 87Sr/86Sr = 0.705 and 87Rb/86Sr = 0.1, calculate the age of the rock
using the Rb-Sr isotopic system.
