# Isostasy and Global Elevation Patterns

#### Summary

This investigation explores the basic process of isostasy and its explanatory power for the observed bimodal distribution for global elevations. In Part A, the densities of representative rock samples of granite and basalt are determined experimentally and compared to typical crustal values. In Part B, the concept of isostasy is examined through a continent-to-ocean transect by determining if the hydrostatic pressure at a common asthenosphere depth is approximately equal under four different "columns" of overlying material. In Part C, a dynamic web-based isostasy model is used to predict elevations for lithospheric columns of different crustal thickness and density. In Part D, the bimodal distribution of global elevations is explicitly explored and connected to the fundamental components of isostasy as explored in Parts A, B, and C.

## Context

#### Audience

Developed for an undergraduate non-major general-education course in oceanography, but readily applicable to a variety of major and non-major courses within the geological sciences.

#### Skills and concepts that students must have mastered

Students are assumed to have mastered the basic principles of plate tectonics, the process of unit conversion, and the relationships among mass, density, and volume.

#### How the activity is situated in the course

This investigation generally scaffolds upon knowledge gained from earlier plate-teconic-focused lectures and laboratories that explore minerals, rocks, the two basic types of crust, etc.

## Goals

#### Content/concepts goals for this activity

- Quantify the relationships between mass, volume, and density
- Calculate the density of basalt and granite hand-samples from measurements of their mass and volume
- Calculate the mean and standard deviation of density for granite and basalt hand-sample populations
- Generalize basalt and granite hand-samples as representative of typical oceanic and continental crust

#### Higher order thinking skills goals for this activity

- Visualize Archimedes' principle that a floating object displaces a volume of liquid equal to the object's mass

- Explain the bimodal distribution of global elevations as result of isostatic equilibrium among oceanic and continental crust

- Explain the bimodal distribution of global elevations as result of isostatic equilibrium among oceanic and continental crust

#### Other skills goals for this activity

- Demonstrate proficiency in determining volume by displacement and determining mass by balance.

- Demonstrate proficiency in unit conversion and basic algebraic calculations.

- Demonstrate proficiency in unit conversion and basic algebraic calculations.

## Description and Teaching Materials

The pdf and Word files below contain the complete laboratory investigation. Note that Part E is a bit of a cognitive stretch for oceanography, but may be of interest to instructors and students in some circumstances.

Investigation: Isostasy and Global Elevation (Microsoft Word 1MB Jun16 13)

Investigation: Isostasy and Global Elevation (Acrobat (PDF) 1.2MB Jun16 13)

Investigation: Isostasy and Global Elevation (Microsoft Word 1MB Jun16 13)

Investigation: Isostasy and Global Elevation (Acrobat (PDF) 1.2MB Jun16 13)

## Teaching Notes and Tips

The investigation does not delve into the various complexities of isostasy, but strives to provide a first-order approach to the concept. Instructor should ensure that the hand-samples are representative of continental and oceanic crust (e.g., granite and basalt, but one must ensure that the basalt is not vesicular!). Operationally, the greatest challenge and source of greatest uncertainty is the volumetric determination of the hand-specimens. While the methods for determining mean and standard deviation are provided, in many cases the number of samples will be fairly small and caution is advised in their usage. One could expand/modify this investigation to focus on comparing small sample sizes with non-parametric statistics and/or 95% confidence-intervals if so inclined. Finally, for multiple laboratory sections, one could compile replicate density determinations and present in subsequent lecture session for a discussion of reproducibility and precision.

## Assessment

- Students calculate hydrostatic pressure at common depth from multiple sections to predict equilibrium or non-equilibrium conditions.

- Students are presented with a novel situation of adding significant ice-volume to a region to predict the general isostatic response during accumulation, steady-state, and subsequent melting.

- Students are presented with a novel situation of adding significant ice-volume to a region to predict the general isostatic response during accumulation, steady-state, and subsequent melting.

## References and Resources

The flash-based model below is an excellent means to introduce the general concept of Archimedes' Principle and then expand towards isostasy:

http://www.geo.cornell.edu/hawaii/220/PRI/interactive/isostasy_2.swf

http://www.geo.cornell.edu/hawaii/220/PRI/interactive/isostasy_2.swf