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Chapter 6 • Theory & Derivations

Unit 6 — Metamorphic facies, fabric and pressure–temperature paths

Reconstruct metamorphic histories rather than memorize rock names.

§6.1 Central question

Reconstruct metamorphic histories rather than memorize rock names.

§6.2 Unit outcomes and perspective

Bring together mineral reactions, deformation and geochronology to infer how crust moves and changes. 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.

§6.3 Prior knowledge and the logic of the lesson sequence

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.

§6.4 Evidence ladder for this unit

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.

§6.5 Facies and the role of protolith

Mechanism: what physical or chemical change is being proposed?

Metamorphic facies group broadly comparable stability conditions inferred from mineral assemblages, with exact phases depending on composition. To reason quantitatively about facies and the role of protolith, 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?

Mafic rocks progressing from greenschist toward amphibolite may develop systematic changes in amphibole and plagioclase. 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 mica-rich metapelite does not contain the same index assemblage as a basalt at equal P and T. The alternative is worth considering because two very different histories can converge on similar final textures or compositions. Cross-check mineral chemistry, protolith indicators and mapped regional gradients. 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 26: Mafic mineral mode

Synthetic teaching inputs: 48 observed mafic-mineral points out of 100; thin-section sampling limited. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is 100*48/(48+52). Substituting the stated values gives 48 vol %. Check whether the result has appropriate units and physical order of magnitude before using it.

Why this inference can fail

Reaction hysteresis and late fluids complicate simple facies assignment. 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 facies and the role of protolith and record it without a causal verb.
  2. Sketch the predicted field or thin-section expression of the principal mechanism: metamorphic facies group broadly comparable stability conditions inferred from mineral assemblages, with exact phases depending on composition.
  3. Describe an observation that would be expected under the rival: a mica-rich metapelite does not contain the same index assemblage as a basalt at equal P and T.
  4. Propose the sampling or measurement comparison: cross-check mineral chemistry, protolith indicators and mapped regional gradients.
  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: Specify a facies field cautiously, with explicit composition assumptions. 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 facies and the role of protolith, 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?

§6.6 Blueschist and eclogite in subduction zones

Mechanism: what physical or chemical change is being proposed?

High-pressure assemblages can develop where cold crust is transported to depth before heating fully equilibrates. To reason quantitatively about blueschist and eclogite in subduction zones, 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?

Glaucophane-bearing rocks and garnet–omphacite eclogite can constrain subduction metamorphism. 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 high-pressure mineral in a loose block does not locate the original subduction interface. The alternative is worth considering because two very different histories can converge on similar final textures or compositions. Combine mineral compositions, structural context and exhumation ages to build a coherent history. 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 27: Approximate pressure–depth conversion

Synthetic teaching inputs: Constant rock density 3000 kg/m³; overburden pressure only. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is (1e9/(3000*9.81))/1000. Substituting the stated values gives 33.9789 km/GPa. Check whether the result has appropriate units and physical order of magnitude before using it.

Why this inference can fail

Pressure estimates from a single phase can be ambiguous or reset. 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 blueschist and eclogite in subduction zones and record it without a causal verb.
  2. Sketch the predicted field or thin-section expression of the principal mechanism: high-pressure assemblages can develop where cold crust is transported to depth before heating fully equilibrates.
  3. Describe an observation that would be expected under the rival: a high-pressure mineral in a loose block does not locate the original subduction interface.
  4. Propose the sampling or measurement comparison: combine mineral compositions, structural context and exhumation ages to build a coherent history.
  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: Distinguish the rock’s peak conditions from its later exhumation route. 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 blueschist and eclogite in subduction zones, 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?

§6.7 Contact metamorphism and aureole gradients

Mechanism: what physical or chemical change is being proposed?

Heating adjacent to intrusions can produce hornfels and composition-specific metamorphic assemblages. To reason quantitatively about contact metamorphism and aureole gradients, 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?

Distance from pluton contact, mineral assemblage and textural changes provide an aureole transect. 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 narrow baked margin may reflect short heating or a low-permeability wall rock, not a universally small intrusion. The alternative is worth considering because two very different histories can converge on similar final textures or compositions. Measure transects and simulate transient conduction with variable thermal properties. 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 28: Thermal diffusion distance

Synthetic teaching inputs: Thermal diffusivity 10^-6 m²/s over 600 yr; not aureole edge. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is math.sqrt(1e-6600365.25*86400). Substituting the stated values gives 137.6029 m. Check whether the result has appropriate units and physical order of magnitude before using it.

Why this inference can fail

Fluids, emplacement pulses and erosion disturb an ideal concentric aureole. 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 contact metamorphism and aureole gradients and record it without a causal verb.
  2. Sketch the predicted field or thin-section expression of the principal mechanism: heating adjacent to intrusions can produce hornfels and composition-specific metamorphic assemblages.
  3. Describe an observation that would be expected under the rival: a narrow baked margin may reflect short heating or a low-permeability wall rock, not a universally small intrusion.
  4. Propose the sampling or measurement comparison: measure transects and simulate transient conduction with variable thermal properties.
  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: Estimate conditions with error bars, not a single universal radius. 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 contact metamorphism and aureole gradients, 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?

§6.8 Foliation, lineation and strain history

Mechanism: what physical or chemical change is being proposed?

Anisotropic stress and mineral growth during deformation organize planar and linear fabrics. To reason quantitatively about foliation, lineation and strain history, 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?

Schistosity, crenulation, stretched pebbles and mineral lineations may mark different deformation stages. 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 planar mineral fabric is not necessarily parallel to original bedding or the latest shortening direction. The alternative is worth considering because two very different histories can converge on similar final textures or compositions. Use oriented samples and overprinting relations to separate fabrics in a relative deformation history. 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 29: Finite marker extension ratio

Synthetic teaching inputs: Marker length change 10 to 16 mm, assumed finite passive strain. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is 16/10. Substituting the stated values gives 1.6 stretch ratio. Check whether the result has appropriate units and physical order of magnitude before using it.

Why this inference can fail

Rotation during growth and later folding limit simple kinematic interpretations. 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 foliation, lineation and strain history and record it without a causal verb.
  2. Sketch the predicted field or thin-section expression of the principal mechanism: anisotropic stress and mineral growth during deformation organize planar and linear fabrics.
  3. Describe an observation that would be expected under the rival: a planar mineral fabric is not necessarily parallel to original bedding or the latest shortening direction.
  4. Propose the sampling or measurement comparison: use oriented samples and overprinting relations to separate fabrics in a relative deformation history.
  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: Describe observable fabric and inferred stress conditions in separate sentences. 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 foliation, lineation and strain history, 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?

§6.9 Clockwise and counterclockwise P–T paths

Mechanism: what physical or chemical change is being proposed?

Mineral inclusions, reaction rims and diffusion profiles can reveal segments of burial–heating–exhumation histories. To reason quantitatively about clockwise and counterclockwise p–t paths, 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?

Core-to-rim zoning, reaction boundaries and dated minerals anchor parts of a pressure–temperature trajectory. 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

Similar peak conditions can arise along distinct clockwise or counterclockwise paths. The alternative is worth considering because two very different histories can converge on similar final textures or compositions. Combine thermobarometry and geochronology with petrographic sequence, retaining alternate path families. 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 30: Geotherm slope

Synthetic teaching inputs: Straight-line model between 4 and 19 km; not universal metamorphic geotherm. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is (620-170)/(19-4). Substituting the stated values gives 30 °C/km. Check whether the result has appropriate units and physical order of magnitude before using it.

Why this inference can fail

Diffusion and retrogression can erase early segments or create apparent loops. 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 clockwise and counterclockwise p–t paths and record it without a causal verb.
  2. Sketch the predicted field or thin-section expression of the principal mechanism: mineral inclusions, reaction rims and diffusion profiles can reveal segments of burial–heating–exhumation histories.
  3. Describe an observation that would be expected under the rival: similar peak conditions can arise along distinct clockwise or counterclockwise paths.
  4. Propose the sampling or measurement comparison: combine thermobarometry and geochronology with petrographic sequence, retaining alternate path families.
  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: Distinguish time-ordered evidence from a freehand path drawn through unrelated estimates. 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 clockwise and counterclockwise p–t paths, 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?

§6.10 Unit 6 summary and assessment

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.

THREE WORKED QUESTIONS

Step-by-Step Petrology Solutions

Three original questions connect calculations, definitions and interpretation. Open each solution to follow the reasoning.

Solved Problem Example 6.1: Mafic mineral mode

Synthetic teaching inputs: 48 observed mafic-mineral points out of 100; thin-section sampling limited. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is 100*48/(48+52). Substituting the stated values gives 48 vol %. Check whether the result has appropriate units and physical order of magnitude before using it.

Step

Synthetic teaching inputs: 48 observed mafic-mineral points out of 100; thin-section sampling limited. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is 100*48/(48+52). Substituting the stated values gives 48 vol %. Check whether the result has appropriate units and physical order of magnitude before using it.

Solved Problem Example 6.2: Approximate pressure–depth conversion

Synthetic teaching inputs: Constant rock density 3000 kg/m³; overburden pressure only. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is (1e9/(3000*9.81))/1000. Substituting the stated values gives 33.9789 km/GPa. Check whether the result has appropriate units and physical order of magnitude before using it.

Step

Synthetic teaching inputs: Constant rock density 3000 kg/m³; overburden pressure only. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is (1e9/(3000*9.81))/1000. Substituting the stated values gives 33.9789 km/GPa. Check whether the result has appropriate units and physical order of magnitude before using it.

Solved Problem Example 6.3: Thermal diffusion distance

Synthetic teaching inputs: Thermal diffusivity 10^-6 m²/s over 600 yr; not aureole edge. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is math.sqrt(1e-6600365.25*86400). Substituting the stated values gives 137.6029 m. Check whether the result has appropriate units and physical order of magnitude before using it.

Step

Synthetic teaching inputs: Thermal diffusivity 10^-6 m²/s over 600 yr; not aureole edge. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is math.sqrt(1e-6600365.25*86400). Substituting the stated values gives 137.6029 m. Check whether the result has appropriate units and physical order of magnitude before using it.

Solved Problem Example 6.4: Finite marker extension ratio

Synthetic teaching inputs: Marker length change 10 to 16 mm, assumed finite passive strain. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is 16/10. Substituting the stated values gives 1.6 stretch ratio. Check whether the result has appropriate units and physical order of magnitude before using it.

Step

Synthetic teaching inputs: Marker length change 10 to 16 mm, assumed finite passive strain. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is 16/10. Substituting the stated values gives 1.6 stretch ratio. Check whether the result has appropriate units and physical order of magnitude before using it.

Solved Problem Example 6.5: Geotherm slope

Synthetic teaching inputs: Straight-line model between 4 and 19 km; not universal metamorphic geotherm. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is (620-170)/(19-4). Substituting the stated values gives 30 °C/km. Check whether the result has appropriate units and physical order of magnitude before using it.

Step

Synthetic teaching inputs: Straight-line model between 4 and 19 km; not universal metamorphic geotherm. Treat the listed inputs as constructed exercise values, not measurements from a real locality. The mathematical relation in this intentionally simplified calculation is (620-170)/(19-4). Substituting the stated values gives 30 °C/km. Check whether the result has appropriate units and physical order of magnitude before using it.