Question 3 of 3: Earth Structure, Optical Mineralogy, Igneous and Metamorphic Processes

Question 3: Earth Structure, Optical Mineralogy, Igneous and Metamorphic Processes (Answer any 3 of 6 – 10 marks each: 30 total)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

a) Earth's internal structure and composition

Earth's internal composition is inferred largely indirectly, from several converging lines of evidence: (1) seismology — P- and S-wave velocity/density jumps at the Moho, 660 km, CMB and ICB mark first-order compositional and/or phase-transition boundaries, and the S-wave shadow zone (S waves do not propagate through the outer core) is the classic proof that the outer core is liquid, since shear waves cannot travel through a fluid; (2) meteorite analogy — chondritic meteorites are taken as a proxy for the bulk (undifferentiated) Earth's composition, while iron meteorites are taken as an analogue for the core; (3) high-pressure mineral physics — diamond-anvil-cell and shock experiments reproduce the P-T conditions of the deep interior and confirm which mineral phases (e.g. bridgmanite) are stable there, matching the density/velocity profile seismology requires; (4) direct sampling of the shallow upper mantle via mantle xenoliths in kimberlite pipes and ophiolites (obducted oceanic lithosphere); and (5) the Earth's moment of inertia and magnetic field (a self-sustaining dynamo requires a large, electrically conductive, convecting fluid region — the liquid outer core).

b) Classification of sedimentary rocks

Sedimentary rocks are classified into two principal groups: clastic (detrital/terrigenous) rocks, formed from mechanically transported and deposited rock/mineral fragments, and chemical/biochemical rocks, formed by precipitation (inorganic or biologically mediated) from solution.

• Clastic rocks are classified primarily by grain size (Wentworth scale) — conglomerate/breccia (> 2 mm, rounded vs. angular clasts), sandstone (0.0625–2 mm), siltstone (0.0039–0.0625 mm), and mudrock/shale (< 0.0039 mm) — and secondarily by composition/textural maturity, e.g. sandstones are further split by their quartz–feldspar–lithic (QFL) framework composition and matrix content into quartz arenite (>90% quartz, mature), arkose (feldspar-rich, immature, short transport/arid climate), and litharenite/greywacke (lithic-fragment- and matrix-rich, immature, often turbiditic).
• Chemical/biochemical rocks are classified by mineral composition and origin — carbonates (limestone, $\text{CaCO}_3$; dolostone, $\text{CaMg(CO}_3)_2$), evaporites (halite, gypsum, precipitated on saturation of restricted basin waters), chert ($\text{SiO}_2$, biogenic or chemical), coal (organic/plant material), and ironstone (Fe oxide/carbonate/silicate) — and by texture, distinguishing biochemical/bioclastic textures (fossiliferous limestone, coquina, chalk built from skeletal debris) from purely chemical precipitate textures (oolitic or crystalline/sparry limestone).

c) Biaxial negative interference figure, 2V = 10°

The melatopes are the points where the two optic axes emerge (where an isogyre crosses exactly through the centre of a set of isochromes); the isogyres are the dark brush-like extinction bands that sweep across the field as the stage is rotated; the isochromes are the concentric coloured interference-colour rings surrounding each melatope (closer rings = lower order, from a thin/low-birefringence mineral, spreading further apart for a highly birefringent one, as specified); and the 2V is the angle between the two optic axes, measured directly (with a universal stage) or estimated from the melatope separation relative to the field of view — a small 2V such as 10° puts the melatopes close together near the centre of the field, as drawn.

Whether a biaxial mineral is optically positive or negative is defined by which principal optical direction (X, the fast ray/smallest index α, or Z, the slow ray/largest index γ) coincides with the acute bisectrix (Bxa) — the bisector of the smaller angle between the two optic axes, which is also the direction the figure above is viewed down: if Bxa = Z (γ), the mineral is biaxial positive; if Bxa = X (α), the mineral is biaxial negative. This is determined at the microscope with an accessory (gypsum, "red I", or quartz wedge) plate inserted diagonally across the isogyres, oriented so its slow-ray direction runs NE–SW (parallel to the melatope/optic-plane line in this figure): in the NE and SW (melatope) quadrants, a shift to a higher interference colour (addition, toward blue) indicates the fast ray of the mineral lies NE–SW there — i.e. Bxa = Z — and the mineral is positive; a shift to a lower colour (subtraction, toward yellow/grey) in those same quadrants indicates Bxa = X and the mineral is negative. For the mineral in this question (specified biaxial negative), the gypsum-plate test would show subtraction (colour lowering) in the NE and SW melatope quadrants.

d) Factors controlling magma viscosity

• Silica content / melt polymerization — $\text{SiO}_2$ tetrahedra link into progressively longer, more cross-linked chain/network polymers as silica content rises, sharply raising resistance to flow: rhyolitic melts (>68% $\text{SiO}_2$) are orders of magnitude more viscous than basaltic melts (<52% $\text{SiO}_2$) at the same temperature.
• Temperature — viscosity falls (roughly exponentially/Arrhenius-like) as temperature rises, because thermal agitation breaks up the polymerized silicate network; this is why a basaltic lava flows readily near its (relatively high) eruption temperature but a cooling flow front stiffens rapidly.
• Dissolved volatiles, especially water — dissolved $\text{H}_2\text{O}$ (and to a lesser extent $\text{CO}_2$, F, Cl) breaks Si–O–Si bridging bonds, depolymerizing the melt and dramatically lowering viscosity even at a few weight percent; conversely, degassing on ascent/eruption sharply raises viscosity, which is central to why volatile-rich, silicic magmas can transition abruptly from effusive to explosive behaviour as they degas and stiffen near the surface.
• Crystal content (crystallinity) — suspended crystals raise the bulk/effective viscosity of the magma; above a critical crystal fraction (commonly cited around 40–60% by volume) the magma behaves less like a Newtonian liquid and more like a crystal mush or solid, losing eruptibility.
• Pressure and bubble (vesicle) content — secondary controls: rising vesicularity can either lower apparent viscosity (bubbles deform and slip) or raise it (bubble interference at high vesicularity), and pressure principally matters through its control on dissolved-volatile solubility rather than acting on viscosity directly.

e) Metamorphic assemblages, peak conditions, and P-T paths for crustal thickening

The claim that metamorphic mineral assemblages record peak metamorphic conditions is only partly valid, and the P-T path above shows why. Pure-shear crustal thickening loads rock mechanically (burial) much faster than heat can conduct into the thickened pile (rock has low thermal diffusivity), so peak pressure is reached first, followed — after continued burial has stopped and the pile begins to thermally relax and/or erode — by peak temperature at a later time, when pressure has already started to decrease. This produces the characteristic clockwise P-T-t loop of England & Thompson-type thermal models. Because prograde metamorphic reactions (dehydration, mineral growth) generally proceed efficiently as temperature rises, while retrograde reactions on cooling are commonly sluggish or incomplete (limited fluid availability, slow reaction kinetics at falling T), the mineral assemblage that actually gets "frozen in" and preserved typically approximates conditions near the thermal maximum (peak T) — not the true pressure maximum, which occurred earlier along the path at a different (lower) temperature. In other words, assemblages more reliably record peak T than true peak P; a P-T estimate read directly off a preserved assemblage using geothermobarometry should therefore be interpreted as a point somewhere on the retrograde/near-peak-T part of the loop, not necessarily the absolute maximum burial depth the rock experienced.

f) Depth of melting above a subducting slab and arc rock type

Melting above a subducting slab is driven primarily by flux (fluid-fluxed) melting: as the slab descends and heats, dehydration reactions in the subducted crust and sediments release aqueous fluids upward into the overlying mantle wedge, lowering the wedge peridotite's solidus and triggering partial melting once the wedge is hot enough for the flux to work — this typically occurs at a depth-to-slab of roughly 100–150 km, which sets the characteristic distance of the volcanic front from the trench for a given slab dip angle. Magma composition then varies systematically with the depth to the slab (and hence, indirectly, with the thickness/nature of overriding crust the magma must traverse): shallower slab depths beneath the arc front (thinner or more oceanic overriding crust, less time/distance for the ascending magma to fractionate or assimilate crust) favour more mafic, basaltic to basaltic-andesitic magmas, while progressively deeper slab depths and thicker, more continental overriding crust (greater opportunity for fractional crystallization and crustal assimilation en route to the surface) favour more evolved, silica-rich andesitic to dacitic/rhyolitic magmas — the well-documented global correlation between slab depth beneath the volcanic front and average arc magma silica content (England, Engdahl & Thatcher, 2004).