Quantitative Skills > Teaching Resources > Activities > BotEC: Depth of Buried Metamorphic Rock

# Back-of-the-Envelope Calculations: Depth of Buried Metamorphic Rock

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#### Summary

Question

In many high-grade metamorphic belts around the world, rocks were buried 20-30 km beneath the surface during deformation and metamorphism. How deep is that relative to the cruising altitude of a typical commercial airplane flying across the country?

## Assessment

A typical transcontinental airliner flies at 30-35,000 feet, or roughly 10,000 meters (10 km) above sea level. Rocks in many orogenic belts were deformed and metamorphosed at depths equivalent to two to three times the distance above the surface that a transcontinental airliner flies! And all of that rock had to be removed by erosion in order for us to see those rocks exposed now at the surface of the Earth.

## References and Resources

This SERC page describes the use of Back of the Envelope Calculations

A View from the Back of the Envelope : This site has a good number of easy simulations and visualizations of back of the envelope calculations.

The Back of the Envelope : This page outlines one of the essays in the book "Programming Pearls" (ISBN 0-201-65788-0). The book is written for computer science faculty and students, but this portion speaks very well to back of the envelope calculations in general.

## Controlled Vocabulary Terms

Subject: Geoscience:Geology:Igneous and Metamorphic Petrology:Metamorphic Processes
Resource Type: Activities:Classroom Activity:Short Activity
Special Interest: Quantitative
Grade Level: High School (9-12), College Lower (13-14)
Quantitative Skills: Estimation