Unit 1 — Melt origins and the thermodynamics of melting

Why partially molten rock behaves differently from its unmelted source.

Construct pressure–temperature–composition arguments without confusing a model line with a universal geological boundary. The central approach is to separate measurement, interpretation, and uncertainty before assigning any historical meaning to a rock. Petrography identifies minerals, textures and overprinting relationships; geochemistry expresses chemical patterns; field mapping constrains geometry and chronology; quantitative models test whether a proposed history is physically plausible. No one method can normally reconstruct the entire history of a complex terrain. The unit therefore uses deliberately simplified calculations alongside explicit alternatives and checks.

Recall that composition is not the same as mineral assemblage: two rocks can have similar bulk chemistry yet different minerals after differing thermal or pressure histories. Revisit the distinction between an intensive variable such as temperature or pressure and an extensive quantity such as mass or volume. When sketching diagrams, annotate axis scales and units and include the assumptions that make a boundary meaningful. For any result, ask whether equilibrium, a closed reservoir or ideal geometry was used. These assumptions should be stated before applying equations to natural rocks.

Begin with repeatable descriptions of a specimen or synthetic dataset. Next ask which process could account for those descriptions under plausible Earth conditions. Finally test a process model against a competing explanation. Even a good process model does not automatically identify a unique geographic origin. A strong field interpretation shows where each independent line of evidence enters, what could overturn it and which uncertainty is irreducible without new sampling. Use contextual evidence from the surrounding stratigraphy and structures to prevent a microscope-scale feature from being overinterpreted.

Mechanism: what physical or chemical change is being proposed?

Melting begins where the local geotherm and a composition-dependent solidus intersect; a rock can partially melt while most minerals remain solid. To reason quantitatively about sources of crustal and mantle melts, first distinguish the part of the system that is open to transport from the part treated as a closed parcel. Track changes in the mineral or melt assemblage, not just the name assigned to the whole rock. A rock records its latest preserved state together with some relics, so the working question is not simply “What rock is this?” but “What sequence of processes could have produced these specific observations?”

Evidence: what would a geologist actually measure?

Peridotite residues, xenoliths, basalt compositions and seismic anomalies provide evidence with different spatial scales. Organize the field notebook as a sequence of observation, measurement conditions and tentative interpretation. Geological evidence can come from hand specimens, thin sections, mapped contacts, electron-microprobe analyses, isotopes or dated mineral domains. The methods are complementary rather than interchangeable. Do not describe a map-scale contact as a microscopic mineral reaction, or a crystal core analysis as a whole-rock average.

Competing interpretations and a discriminating test

A mafic lava might reflect a mantle source, crustal mixing or fractionation of a different starting melt. The alternative is worth considering because two very different histories can converge on similar final textures or compositions. Compare trace-element ratios, isotope constraints, phenocryst cargo and regional tectonics instead of reading source directly from colour. A test must be designed before the final preferred interpretation is chosen: otherwise the analyst risks using every possible feature as evidence for the same story. Identify the response variable, a comparison sample and the result each proposed process would predict.

Change one assumption at a time when constructing an alternative model. This approach demonstrates whether the conclusion is stable, or whether a single unmeasured parameter controls the interpretation.

Worked quantitative example 1: Dry solidus temperature margin

Synthetic teaching inputs: Illustrative mantle temperature 1300 °c, assumed solidus 1230 °c; positive margin does not give melt fraction. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is 1300 - 1230. Substituting the stated values gives 70 °C. Check whether the result has appropriate units and physical order of magnitude before using it.

Why this inference can fail

An assumed dry mantle solidus ignores water, oxidation state and chemical variability. The scale of observation controls what the measured record can resolve. Two samples showing similar assemblages are not necessarily coeval; two mineral compositions agreeing within analytical precision are not necessarily in equilibrium. Evidence of replacement can survive after bulk chemistry has changed. Change one assumption at a time when constructing an alternative model. This approach demonstrates whether the conclusion is stable, or whether a single unmeasured parameter controls the interpretation. No degree of numerical polishing eliminates a missing source reservoir or undocumented sample context.

Guided field or laboratory investigation

1. Define the most diagnostic feature for sources of crustal and mantle melts and record it without a causal verb.
2. Sketch the predicted field or thin-section expression of the principal mechanism: melting begins where the local geotherm and a composition-dependent solidus intersect; a rock can partially melt while most minerals remain solid.
3. Describe an observation that would be expected under the rival: a mafic lava might reflect a mantle source, crustal mixing or fractionation of a different starting melt.
4. Propose the sampling or measurement comparison: compare trace-element ratios, isotope constraints, phenocryst cargo and regional tectonics instead of reading source directly from colour.
5. Recompute the quantitative case after changing its largest uncertain input by a plausible amount; describe which conclusion survives.
6. Produce a short evidence matrix that ranks the explanations as supported, consistent-but-not-unique, contradicted or untested.

Interpretive outcome: Explain why generating melt does not imply melting the entire host rock. A strong answer states both the observation that supports a conclusion and the observation still needed to reject an alternative.

Review questions

• Which measured variable provides the strongest test of sources of crustal and mantle melts, and which confounder is most threatening?
• Why might the competing hypothesis produce an apparently similar rock, and what data would discriminate?
• Which parameter in the worked numerical example is least securely known in a real field setting?
• Can a preserved texture be assigned to one instant in time, or might it be a record of overprinting?
• What conclusion would you withdraw if a second laboratory contradicted the key measurement?

Mechanism: what physical or chemical change is being proposed?

Upwelling mantle can cross its solidus when pressure decreases faster than temperature changes; decompression is not the same as adding heat. To reason quantitatively about decompression melting at spreading ridges, first distinguish the part of the system that is open to transport from the part treated as a closed parcel. Track changes in the mineral or melt assemblage, not just the name assigned to the whole rock. A rock records its latest preserved state together with some relics, so the working question is not simply “What rock is this?” but “What sequence of processes could have produced these specific observations?”

Evidence: what would a geologist actually measure?

Ridge-axis basalts, mantle upwelling geometry and melt extraction pathways constrain the process. Organize the field notebook as a sequence of observation, measurement conditions and tentative interpretation. Geological evidence can come from hand specimens, thin sections, mapped contacts, electron-microprobe analyses, isotopes or dated mineral domains. The methods are complementary rather than interchangeable. Do not describe a map-scale contact as a microscopic mineral reaction, or a crystal core analysis as a whole-rock average.

Competing interpretations and a discriminating test

Basalt at an oceanic ridge need not be generated at one pressure or with one degree of melting. The alternative is worth considering because two very different histories can converge on similar final textures or compositions. Build a pressure–temperature sketch with a family of mantle paths and compare plausible primary melt compositions. A test must be designed before the final preferred interpretation is chosen: otherwise the analyst risks using every possible feature as evidence for the same story. Identify the response variable, a comparison sample and the result each proposed process would predict.

Use two samples at contrasting spatial scales where possible: a local thin section and a regional outcrop pattern. Agreement across scales is more informative than repeated estimates of a single proxy.

Worked quantitative example 2: Pressure decrease in an upwelling column

Synthetic teaching inputs: 12 km ascent at fixed assumed bulk density; actual pressure path is not strictly hydrostatic. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is (33009.8112000)/1e6. Substituting the stated values gives 388.476 MPa. Check whether the result has appropriate units and physical order of magnitude before using it.

Why this inference can fail

A one-dimensional steady plume model omits lateral flow, heat extraction and heterogeneous mantle. The scale of observation controls what the measured record can resolve. Two samples showing similar assemblages are not necessarily coeval; two mineral compositions agreeing within analytical precision are not necessarily in equilibrium. Evidence of replacement can survive after bulk chemistry has changed. Use two samples at contrasting spatial scales where possible: a local thin section and a regional outcrop pattern. Agreement across scales is more informative than repeated estimates of a single proxy. No degree of numerical polishing eliminates a missing source reservoir or undocumented sample context.

Guided field or laboratory investigation

1. Define the most diagnostic feature for decompression melting at spreading ridges and record it without a causal verb.
2. Sketch the predicted field or thin-section expression of the principal mechanism: upwelling mantle can cross its solidus when pressure decreases faster than temperature changes; decompression is not the same as adding heat.
3. Describe an observation that would be expected under the rival: basalt at an oceanic ridge need not be generated at one pressure or with one degree of melting.
4. Propose the sampling or measurement comparison: build a pressure–temperature sketch with a family of mantle paths and compare plausible primary melt compositions.
5. Recompute the quantitative case after changing its largest uncertain input by a plausible amount; describe which conclusion survives.
6. Produce a short evidence matrix that ranks the explanations as supported, consistent-but-not-unique, contradicted or untested.

Interpretive outcome: Separate the onset of melting from the amount of melt that reaches the surface. A strong answer states both the observation that supports a conclusion and the observation still needed to reject an alternative.

Review questions

• Which measured variable provides the strongest test of decompression melting at spreading ridges, and which confounder is most threatening?
• Why might the competing hypothesis produce an apparently similar rock, and what data would discriminate?
• Which parameter in the worked numerical example is least securely known in a real field setting?
• Can a preserved texture be assigned to one instant in time, or might it be a record of overprinting?
• What conclusion would you withdraw if a second laboratory contradicted the key measurement?

Mechanism: what physical or chemical change is being proposed?

Water-rich fluids released by a subducting plate can lower melting temperatures in the overlying mantle wedge. To reason quantitatively about flux melting in subduction systems, first distinguish the part of the system that is open to transport from the part treated as a closed parcel. Track changes in the mineral or melt assemblage, not just the name assigned to the whole rock. A rock records its latest preserved state together with some relics, so the working question is not simply “What rock is this?” but “What sequence of processes could have produced these specific observations?”

Evidence: what would a geologist actually measure?

Arc-front positions, water-rich volcanic products and slab geometry collectively bear on the mechanism. Organize the field notebook as a sequence of observation, measurement conditions and tentative interpretation. Geological evidence can come from hand specimens, thin sections, mapped contacts, electron-microprobe analyses, isotopes or dated mineral domains. The methods are complementary rather than interchangeable. Do not describe a map-scale contact as a microscopic mineral reaction, or a crystal core analysis as a whole-rock average.

Competing interpretations and a discriminating test

A hydrated arc magma is not proof that all its water came from a single slab mineral. The alternative is worth considering because two very different histories can converge on similar final textures or compositions. Use fluid-mobile versus immobile element patterns and petrological evidence for hydrous mineral breakdown. A test must be designed before the final preferred interpretation is chosen: otherwise the analyst risks using every possible feature as evidence for the same story. Identify the response variable, a comparison sample and the result each proposed process would predict.

An independent mineralogical check can be more valuable than simply increasing precision of an already biased major-element measurement. Plan discrimination first, then precision.

Worked quantitative example 3: Illustrative volatile mass fraction

Synthetic teaching inputs: 1.4 g dissolved equivalent in 72 g melt with no post-entrapment loss. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is 100*1.4/72. Substituting the stated values gives 1.9444 wt %. Check whether the result has appropriate units and physical order of magnitude before using it.

Why this inference can fail

Water contents can change through degassing, storage and alteration after melt generation. The scale of observation controls what the measured record can resolve. Two samples showing similar assemblages are not necessarily coeval; two mineral compositions agreeing within analytical precision are not necessarily in equilibrium. Evidence of replacement can survive after bulk chemistry has changed. An independent mineralogical check can be more valuable than simply increasing precision of an already biased major-element measurement. Plan discrimination first, then precision. No degree of numerical polishing eliminates a missing source reservoir or undocumented sample context.

Guided field or laboratory investigation

1. Define the most diagnostic feature for flux melting in subduction systems and record it without a causal verb.
2. Sketch the predicted field or thin-section expression of the principal mechanism: water-rich fluids released by a subducting plate can lower melting temperatures in the overlying mantle wedge.
3. Describe an observation that would be expected under the rival: a hydrated arc magma is not proof that all its water came from a single slab mineral.
4. Propose the sampling or measurement comparison: use fluid-mobile versus immobile element patterns and petrological evidence for hydrous mineral breakdown.
5. Recompute the quantitative case after changing its largest uncertain input by a plausible amount; describe which conclusion survives.
6. Produce a short evidence matrix that ranks the explanations as supported, consistent-but-not-unique, contradicted or untested.

Interpretive outcome: State which observations indicate a hydrous system and which support the proposed source of water. A strong answer states both the observation that supports a conclusion and the observation still needed to reject an alternative.

Review questions

• Which measured variable provides the strongest test of flux melting in subduction systems, and which confounder is most threatening?
• Why might the competing hypothesis produce an apparently similar rock, and what data would discriminate?
• Which parameter in the worked numerical example is least securely known in a real field setting?
• Can a preserved texture be assigned to one instant in time, or might it be a record of overprinting?
• What conclusion would you withdraw if a second laboratory contradicted the key measurement?

Mechanism: what physical or chemical change is being proposed?

Heating or introduction of fluid can partially melt fertile crustal rocks, producing leucosomes and melt-depleted residues. To reason quantitatively about crustal anatexis and migmatites, first distinguish the part of the system that is open to transport from the part treated as a closed parcel. Track changes in the mineral or melt assemblage, not just the name assigned to the whole rock. A rock records its latest preserved state together with some relics, so the working question is not simply “What rock is this?” but “What sequence of processes could have produced these specific observations?”

Evidence: what would a geologist actually measure?

Layer-parallel leucosomes, restitic assemblages, and cross-cutting melt veins preserve different stages of melt movement. Organize the field notebook as a sequence of observation, measurement conditions and tentative interpretation. Geological evidence can come from hand specimens, thin sections, mapped contacts, electron-microprobe analyses, isotopes or dated mineral domains. The methods are complementary rather than interchangeable. Do not describe a map-scale contact as a microscopic mineral reaction, or a crystal core analysis as a whole-rock average.

Competing interpretations and a discriminating test

A pale vein could be injected granite rather than melt generated in the adjacent host. The alternative is worth considering because two very different histories can converge on similar final textures or compositions. Inspect contact relations, mineral reaction textures and chemical mass balance over the host–leucosome pair. A test must be designed before the final preferred interpretation is chosen: otherwise the analyst risks using every possible feature as evidence for the same story. Identify the response variable, a comparison sample and the result each proposed process would predict.

Document negative evidence as carefully as positive evidence. A predicted reaction product that is absent from an adequately sampled rock deserves an explanation rather than being silently ignored.

Worked quantitative example 4: Leucosome volume proportion

Synthetic teaching inputs: Measured volumes in one idealized host transect; volume change neglected. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is 100*16/(16+64). Substituting the stated values gives 20 vol %. Check whether the result has appropriate units and physical order of magnitude before using it.

Why this inference can fail

Original melt compositions may have changed by crystal entrainment and subsequent deformation. The scale of observation controls what the measured record can resolve. Two samples showing similar assemblages are not necessarily coeval; two mineral compositions agreeing within analytical precision are not necessarily in equilibrium. Evidence of replacement can survive after bulk chemistry has changed. Document negative evidence as carefully as positive evidence. A predicted reaction product that is absent from an adequately sampled rock deserves an explanation rather than being silently ignored. No degree of numerical polishing eliminates a missing source reservoir or undocumented sample context.

Guided field or laboratory investigation

1. Define the most diagnostic feature for crustal anatexis and migmatites and record it without a causal verb.
2. Sketch the predicted field or thin-section expression of the principal mechanism: heating or introduction of fluid can partially melt fertile crustal rocks, producing leucosomes and melt-depleted residues.
3. Describe an observation that would be expected under the rival: a pale vein could be injected granite rather than melt generated in the adjacent host.
4. Propose the sampling or measurement comparison: inspect contact relations, mineral reaction textures and chemical mass balance over the host–leucosome pair.
5. Recompute the quantitative case after changing its largest uncertain input by a plausible amount; describe which conclusion survives.
6. Produce a short evidence matrix that ranks the explanations as supported, consistent-but-not-unique, contradicted or untested.

Interpretive outcome: Differentiate melt generation, segregation, migration and final emplacement. A strong answer states both the observation that supports a conclusion and the observation still needed to reject an alternative.

Review questions

• Which measured variable provides the strongest test of crustal anatexis and migmatites, and which confounder is most threatening?
• Why might the competing hypothesis produce an apparently similar rock, and what data would discriminate?
• Which parameter in the worked numerical example is least securely known in a real field setting?
• Can a preserved texture be assigned to one instant in time, or might it be a record of overprinting?
• What conclusion would you withdraw if a second laboratory contradicted the key measurement?

Mechanism: what physical or chemical change is being proposed?

A solidus marks the first appearance of melt for a specified composition and conditions; a liquidus marks complete melting. To reason quantitatively about phase diagrams and the meaning of a solidus, first distinguish the part of the system that is open to transport from the part treated as a closed parcel. Track changes in the mineral or melt assemblage, not just the name assigned to the whole rock. A rock records its latest preserved state together with some relics, so the working question is not simply “What rock is this?” but “What sequence of processes could have produced these specific observations?”

Evidence: what would a geologist actually measure?

Binary eutectic experiments and natural mineral assemblages provide complementary information. Organize the field notebook as a sequence of observation, measurement conditions and tentative interpretation. Geological evidence can come from hand specimens, thin sections, mapped contacts, electron-microprobe analyses, isotopes or dated mineral domains. The methods are complementary rather than interchangeable. Do not describe a map-scale contact as a microscopic mineral reaction, or a crystal core analysis as a whole-rock average.

Competing interpretations and a discriminating test

A two-component eutectic picture does not accurately capture every multicomponent magma. The alternative is worth considering because two very different histories can converge on similar final textures or compositions. Apply the lever rule to a controlled two-phase example, then identify why natural systems depart from its assumptions. A test must be designed before the final preferred interpretation is chosen: otherwise the analyst risks using every possible feature as evidence for the same story. Identify the response variable, a comparison sample and the result each proposed process would predict.

Do not infer time from spatial distance without independent constraints; a cooling front, reaction isograd and intrusive contact are different physical objects.

Worked quantitative example 5: Binary lever-rule liquid proportion

Synthetic teaching inputs: Bulk x=62, solid x=52, liquid x=72 on one tie-line; binary equilibrium only. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is 100*(62-52)/(72-52). Substituting the stated values gives 50 % liquid. Check whether the result has appropriate units and physical order of magnitude before using it.

Why this inference can fail

Pressure, volatile content and imperfect equilibrium shift the phase boundaries. The scale of observation controls what the measured record can resolve. Two samples showing similar assemblages are not necessarily coeval; two mineral compositions agreeing within analytical precision are not necessarily in equilibrium. Evidence of replacement can survive after bulk chemistry has changed. Do not infer time from spatial distance without independent constraints; a cooling front, reaction isograd and intrusive contact are different physical objects. No degree of numerical polishing eliminates a missing source reservoir or undocumented sample context.

Guided field or laboratory investigation

1. Define the most diagnostic feature for phase diagrams and the meaning of a solidus and record it without a causal verb.
2. Sketch the predicted field or thin-section expression of the principal mechanism: a solidus marks the first appearance of melt for a specified composition and conditions; a liquidus marks complete melting.
3. Describe an observation that would be expected under the rival: a two-component eutectic picture does not accurately capture every multicomponent magma.
4. Propose the sampling or measurement comparison: apply the lever rule to a controlled two-phase example, then identify why natural systems depart from its assumptions.
5. Recompute the quantitative case after changing its largest uncertain input by a plausible amount; describe which conclusion survives.
6. Produce a short evidence matrix that ranks the explanations as supported, consistent-but-not-unique, contradicted or untested.

Interpretive outcome: Use diagrams as constrained models, not as universal thermometers. A strong answer states both the observation that supports a conclusion and the observation still needed to reject an alternative.

Review questions

• Which measured variable provides the strongest test of phase diagrams and the meaning of a solidus, and which confounder is most threatening?
• Why might the competing hypothesis produce an apparently similar rock, and what data would discriminate?
• Which parameter in the worked numerical example is least securely known in a real field setting?
• Can a preserved texture be assigned to one instant in time, or might it be a record of overprinting?
• What conclusion would you withdraw if a second laboratory contradicted the key measurement?

The five lessons in this unit share a logic of observation → explanation → discrimination → calculation → qualified conclusion. Submit the five worked calculations with their units, three alternative-hypothesis comparisons and an annotated conceptual diagram. The diagram should distinguish arrows that represent measured directions from arrows that indicate proposed process pathways. Your final statement should name the observation that would most efficiently falsify your preferred account. A final confidence label is required, but the label is not a substitute for the written justification.