Chapter 4

Physical Quantities, Fields, Dimensions, and Scaling

Earth's crust under the state of Texas is lifted by a crane in this cartoon from M. King Hubbert's (1945) paper on scaling laws in which he demonstrates that the good state of Texas is utterly incapable of self support. In this chapter define the basic physical quantities used to investigate the origins of earth structures and agree on their units of measure. We discuss the material continuum that forms the basis for most of our thinking about the spatial and temporal variations of these physical field quantities. Next we consider physical dimensions and explain, using the same ideas that Hubbert used in the last century, how to check the consistency of equations and to construct graphs of physical quantities. Dimensional analysis provides the tools to understand the scaling of structural phenomena, and to set up scaled laboratory experiments to model the development of structures.

Exercises

Concepts from Chapter 4

These exercises explore concepts from Chapter 4 including fundamental and derived units of measurement, SI units, dimensionally consistent equations, dimensional analysis, dimensionless groups, and scaling relations.