Temperature is probably the parameter that most people associate with when they are introducted to the term heat flow. More importantly then temperature itself though is the change in temperature over a given distance. If we consider two points, $$T_1$$ and $$T_2$$, over a given distance, $$\Delta z$$, the thermal gradient is defined as $$\frac{\delta T}{\delta z} = (T_2 - T_1) / \Delta z$$. In other words, for geothermal purposes, the change in temperature with depth. Although thermal gradient exists as a vector comoponent in three dimensional space, if we assume the surface of the Earth to be a relatively flat, insulating layer (a reasonable assumption), then the solution to determining thermal gradient within the Earth can be reduced in most cases to only the vertical direction. SI units for thermal gradient are $$^\circ K/m$$, however, the official stance of the International Heat Flow Commission designates that thermal gradient be reported in $$^\circ C/km$$. While the unit change from $$^\circ K$$ to $$^\circ C$$ obvisouly has no effect on the resulting value, the change from $$m$$ to $$km$$ scales output to more intuitive values given the relatively low thermal gradients found across the globe.

## Global Distribution

Despite being a requirement for computing heat flow, thermal gradient is not always reported alongside heat flow measurements and therefore the number of entries in the database is less than that of heat flow. Despite this, we are still in possession of over 40,000 corrected and uncorrected thermal gradient data which is more than enough for statistical insight across a wide range of categorization. However, like heat flow, such analysis suffers from substantial spatial bias which should be considered. Again, we see wide swathes of missing or low data counts throughout central Africa while South America, Antartica and even Australia all feature relatively low counts across the board. *Calculating statistic across the major oceans suffers the same shortcomings as heat flow in that spatial bias is pervasive so the numbers found here should again be used with caution.

*We are actively working on a better way to visually display heat flow variations throughout the oceans.

## Continental vs Oceanic

Unlike heat flow itself, thermal gradient features two distinct distributions depending on whether the measurements are oceanic or continental in origin. Continental crust has a median gradient of around 34$$^\circ C/km$$ while oceanic crust is almost double that at 66$$^\circ C/km$$ (or 62$$^\circ C/km$$ if we exclude hydrothermal effects by limitings data to less than 200). This is probably an expected result given the difference in crustal thickness between oceanic (~7km) and continental crust (~40km).

## Age Distributions

In terms of juvenile age, thermal gradient shows a relatively similar trend to heat flow from ~1000 Ma and older. At ages younger than 1000 Ma, gradient values are relatively constant around 30$$^\circ C/km$$. This is in contrast to heat flow where a marked increase is observed over the same time interval. Thermotectonic age seems to have little effect on thermal gradient with values relatively constant around 35$$^\circ C/km$$ across the board barring age groups with less than a dozen or data points. An exception is the Jurassic period, however, like some of the points in the heat flow plot, this one is largely determined by a single geological province, the Mantiqueira Province, in eastern Brazil.

## Tectonic Environment

The tectonic environment in which thermal gradient is measured has a large influence on the expected value. The general trends are roughly the same as those of heat flow whereby higher values are found in active environments such as rifts and volcanic arcs and lower values are found in stable environments such as shields and cratons. There also tends to be much less variability in stable terrains compared to active environments where measured gradients can vary by hundreds of degrees.