12.710 – Problem Set 4 solutions

1. What is “the geothermal gradient?” How has this relationship been established and what are some of the anchor points? Why are the subcontinental and suboceanic geothermal gradients postulated to be different?

“Geothermal gradient” refers to the temperature profile with depth in the Earth. Seismic data, experimental work, and heat calculations (e.g. adiabatic behavior in the convecting part of the mantle, heat conduction to the surface through the lithosphere) have helped to establish this pressure-temperature relationship. Anchor points for the profile include the temperature at the surface of the Earth; the core-mantle boundary (experiments and seismic velocity profiles); the upper mantle-lower mantle boundary and the transition zone (also experiments and velocity profiles), the crust-mantle boundary, and the base of the lithosphere. Because continental crust and lithosphere are thicker than oceanic lithosphere, their gradients must have different slopes.

2. What is “the adiabat?” What is the relationship between the adiabat and the Earth’s geothermal gradient?

The term “adiabat” refers to the condition under which heat is not exchanged outside of the system; this condition is such that with changes in pressure, the material behaves isentropically. In the context of the Earth, “the adiabat” generally refers to adiabatic conditions during up- or downwelling of material in the convecting mantle. Most processes in the convecting Earth occur adiabatically, and the geotherm closely approximates this adiabat. Likewise, materials upwelling or sinking in the mantle generally follow the geotherm and, thus, behave adiabatically.

3. What is “the solidus” and how does it vary with pressure? How does the addition of water into the mantle influence its solidus?

“The solidus” refers to the pressure and temperature conditions for a material at which the very last bit of liquid crystallizes (e.g. with cooling), or the very first increment of melt forms from a solid (e.g. with heating). A dry lherzolite solidus has a positive pressure/temperature slope. The addition of water to the mantle weakens the structure of the minerals in the rock and causes melting under higher pressure conditions – the wet solidus is deeper in the Earth than the dry solidus. The wet solidus also has a negative P/T slope.

4. Why does melting occur when solid mantle upwells?

Solid material upwelling adiabatically in the mantle at sufficiently high potential temperatures intersects its solidus and thus begins to melt.

5. Consider the olivine phase diagram shown below... According to this phase diagram, at what temperature will this particular melt begin to crystallize olivine? What will be the Fo composition of the crystallizing olivine at T=1500ºC, and what will be the proportion of crystals and liquid at this temperature?

In the olivine phase diagram shown, the melt at point O will begin to crystallize when it reaches the liquidus at point L at temperature T1, ~1630ºC. When the temperature has cooled to 1500ºC, the olivine crystallizing has a composition of Fo60 (60% forsterite, 40% fayalite). Using the lever rule, there is 55% liquid and 45% crystalline olivine (all Fo60) at this temperature.

6. The batch melting equation is... [Determine] the bulk partition coefficients for U and Th (i.e. DTh and DU) for a “garnet lherzolite” mantle composed of garnet (12%), olivine (59%), orthopyroxene (21%) and clinopyroxene (8%). Derive the batch melting expression for the ratio of two elements (i.e. ClA/ClB = ?). For a Th/U source ratio (CsTh/CsU) of 3.9, what is the Th/U in the melt (ClTh/ClU) if the total melt fraction (F) is 100%, 0%, 10%, 1%, 0.1%, and 0.001%? Make a plot of [Th/U]melt/[Th/U]mantle versus total melt fraction (F). Considering the relationship shown on this plot, what is the maximum melt fraction capable of fractionating Th from U during batch melting? Which of the above minerals is responsible for the observed fractionation of Th from U during melting? What would be different about the direction of Th/U fractionation (i.e. change during melting) if the solid mantle undergoing melting was composed of only olivine, orthopyroxene and clinopyroxene (i.e. no garnet)?

DThGt Lherz = 1.2e-3

DUGt Lherz = 2.4e-3

ClA/ClB = (CsA/CsB) * (F + (1-F)DB) / (F + (1-F)DA)

ClA/ClB = 3.9 (F=100%), 7.5 (0%), 3.9 (10%), 4.3 (1%), 5.9 (0.1%), 7.5 (0.001%)

According to the plot, F = 1% is the largest melt fraction capable of fractionating Th from U during batch melting. Although Cpx is capable of causing a small amount of fractionation, Gt dominates, since its DU and DTh values are very different. Without Gt present, Cpx would dominate the fractionation, but it fractionates Th and U in the opposite sense, such that [Th/U]melt/[Th/U]mantle would be <1 at small F.

7. The fractional crystallization equation is... For a magma which is crystallizing olivine only, use the above mineral/melt partition coefficients for olivine and plot the normalized Th concentration as a function of remaining melt fraction (i.e. ClTh/C0Th versus f), then on another graph plot the change in Th/U as a function of remaining melt fraction (i.e. [Th/U]remaining melt/[Th/U]original melt versus f). Now for a magma which is crystallizing orthopyroxene only, use the above mineral/melt partition coefficients for orthopyroxene and add to the first plot the change in Th concentration as a function of remaining melt fraction (i.e. ClTh/C0Th versus f), and then add to the second plot the change in Th/U as a function of remaining melt fraction (i.e. [Th/U]remaining melt/[Th/U]original melt versus f) and label these lines accordingly. Now do the same for clinopyroxene and again label these lines. Why does the relative Th concentration change, but the Th/U ratio remain constant during crystallization of olivine and orthopyroxene? What is different about clinopyroxene?

Finally for a magma which is crystallizing olivine only, use the above mineral/melt partition coefficients for olivine and plot normalized Ni concentration as a function of remaining melt fraction (i.e. ClNi/C0Ni versus f). In the context of the observed differences in the change of Th and Ni concentrations in the remaining magma during olivine crystallization, discuss briefly what is meant by the terms compatible and incompatible elements.

The relative Th concentrations change for Ol and Opx with increasing f, but the Th/U ratios remain constant because DU and DTh are identical for both minerals. Clinopyroxene, on the other hand, has different DU and DTh values, so both the Th concentration and Th/U ratio changes with f.

Ni behaves compatibly in olivine – the DNiOl value is greater than 1, and with decreasing f it leaves the melt and enters the crystals rapidly. Th, on the other hand, is incompatible in olivine, and so Th concentrations increase with increasing f. Th remains in the liquid until the last remnant of melt crystallizes.

8. Briefly describe and explain the succession of igneous rocks expected in “normal” oceanic crust (i.e. give a description of ocean crust formed at mid-ocean ridges).

“Normal” ocean crust has an upper layer of pillow basalts, underlain by a sheeted dike complex, underlain by isotropic, foliated, and layered gabbros, underlain finally by ultramafic materials, including layered and unlayered “tectonite” peridotites. The pillow basalts are formed by extrusive flows on the ocean floor at ridges, and the sheeted dikes are the conduits feeding the volcanics. The gabbros represent the differentiating magma chamber beneath the ridge, and they are infiltrated by and overlie pods of cumulate material. The deepest peridotitic and harzburgitic rocks are the residuum of the uppermost part of the upwelling upper mantle beneath the ridge.

9. What is the difference between rhyolite, andesite, and basalt?

Rhyolite, andesite, and basalt are three types of low-alkalinity, extrusive (volcanic) igneous rocks, listed in order of decreasing silica content. Rhyolites are very silica-rich (felsic), andesites and dacites (not listed) are intermediate in composition, and basalt rocks are relatively silica-poor (mafic).

10. What is the fundamental difference between granite and rhyolite? Gabbro and basalt?

Granite and rhyolite have the same chemical composition, but granites cool more slowly beneath the Earth’s surface (intrusive or plutonic rocks), while rhyolites cool quickly after eruption on the surface (extrusive or volcanic rocks). Similarly, gabbro and basalt have the same composition; gabbros are intrusive, while basalts are extrusive.

11. Describe the three primary tectonic settings where volcanism occurs and discuss how differences in these settings result in different melting conditions, styles of volcanism and resulting melt compositions.

Volcanism occurs at divergent margins (spreading ridges), convergent margins (subduction zones or arcs), and intraplate settings (“hot spots”). Melts at spreading centers form by decompression melting of upwelling solids in the convecting mantle; most of the lavas erupted on earth erupt at ridges, the extent of melting is relatively high, lavas are low in volatiles, and lavas undergo moderate fractionation in magma chambers so that they are basaltic (tholeiitic) in composition. The basalts have relatively low viscosity and cool rapidly under the oceans. They show some isotopic and trace element variability, but not nearly as much as ocean island basalts. Melts at convergent margins are produced by “wet melting” of the mantle wedge due to the addition of water and other volatiles to the wedge overlying the wet subducting slab of crust. They can experience a lot of fractionation in the overlying crust, leading to differentiated melts ranging from basalts to rhyolites, and they are high in volatiles that can exsolve suddenly and generate explosive eruptions. Finally, intraplate or hot-spot volcanoes form seemingly independent of plate tectonics; some of these are probably formed by plumes of upwelling material from the mantle, while others may formed by some other process (this is hotly debated). They are generally low in volatiles and erupt as low-viscosity basalts. Their isotopic and trace element compositions are extremely variable and help us fingerprint heterogeneous mantle reservoirs. (Multiple answers will be accepted for this question since it is very open-ended.)

12. Please interpret this geologic cross-section in terms of the relative timing of the different igneous, metamorphic and geologic processes.

Depositional order:

Layer B

Layer A

Layer D

Layer C

(Sill occurs after C and before first Unconformity)

Lava1

Folding event

Angular Unconformity

Layer E

(Overturn occurs after E and before Lava2)

Coarse-grained Granite

Fault

Dike

(Angular Unconformity occurs after Dike and before Lava2)

Fine-grained Granite

Lava2

A possible scenario: Layers B (a limestone), A (layered mudstone or sandstone), D (shale), and C (finely-layered limestone) were deposited in a sedimentary basin as water levels changed over time. A volcanic eruption produced the flow Lava1 over Layer C, and either the same or another volcanic event injected the Sill between Layers A and C. The region underwent compression, folding the rocks, and then erosion created an angular unconformity above Lava1. Layer E (sandstone) was deposited. A coarse-grained Granite was intruded, perhaps as a magma chamber. The region was faulted, leading to what looks like extensional offset in this 2D view (in 3D it might not be the case, though). A dike intruded along the fault. A later, fine-grained Granite was then intruded across the other beds. Since Layer E was deposited, the entire region underwent an overturning tilting event, either between or concurrent with the granitic intrusions, faulting, and the dike intrusion. Following the overturn and either before or after the second granitic intrusion, another erosional event created a second angular unconformity. The lava flow Lava2 was deposited above this unconformity.