But back to heat flow. In my last blog post, I basically gave a primer on how surface heat flow is measured and how surface heat flow is used to infer temperature at depth, at least within the upper part of the Earth's thermal boundary layer.
Here are some data, taken from a classic paper by Blackwell et al. on the heat flow in the Oregon Cascade range. Let's focus on just the heat flow data and ignore the gravity data (the gravity data represent Bouguer gravity anomalies, which to first order reflect topography due to the mass deficits associated with the roots of mountains). We can see that heat flow through the Juan de Fuca plate is high - 150 mW/m^2 and then it decreases slightly as we move away from the Juan de Fuca-Pacific spreading ridge until we reach the accretionary prism, after which surface heat flow drops precipitously down to 50 mW/m^2, more typical of cratonic geotherms. Heat flow stays low as we go across the fore-arc basin (Willamette valley) and continues to stay low in the western Cascade range. Heat flow then rises abruptly across the transition from the western Cascade reigon to the high Cascades, which is the volcanically active part of the arc today.
The high heat flow in the Juan de Fuca plate are just associated with the very thin, hot and young lithosphere there. The low heat flow in the accretionary prism and forearc basin presumably are associated with refrigeration from the top of the subducting oceanic lithosphere, which is cold. The high heat flow in the high Cascades is due to the presence of magma chambers in the area. What is more difficult to explain is why the heat flow is low in the western Cascades and why there is such an abrupt thermal contrast between the western Cascades and the high Cascades.
This low heat flow in the western cascades turns out be a very important number. If this heat flow is real and temperatures can be extrapolated to depth, it places a very strict constraint on the thermal state of the mantle wedge below. The mantle wedge here cannot be too hot. And because it cannot be too hot, it makes it difficult for geodynamic models that invoke T-dependent and non-Newtonian viscosity because such models generate a hote nose rather than a cold nose. So one way to stop the nose of the wedge from getting too hot is to decouple the subducting slab from the mantle wedge in the region of the nose. If you eliminate viscous coupling, then the sinking of the slab no longer drives how mantle into the nose. Only below the decoupling depth is there viscous coupling, which drives flow witihn the athsnoerphic mantle wedge. Exactly what this decoupling lengthscale means is unclear, but its magnitude does influence the thermal evolution of the slab surface. Thus, it is important for us to better understand the origin of the low heat flow in the western Cascades.
The night before I headed down to Scripss, my dad and I discussed this issue. My dad is a heat flow expert. The results of our discussion are shown below, mixed in with some sketches of dinosaurs that my mother did for my 2 year old nephew. Ignore the dinosaurs.
If you recall, surface heat flow is almost never directly measured. It's inferred from the temperature gradient in a borehole multiplied by the thermal conductivity of the rock. If, however, some of the heat is being advected out, say be fluid flow, then the total heat flow is the sum of the conductive heat flow plus the advected component, that is,
q tot = k*dT/dz + rho*c*deltaT*V
the first term on the right is the conductive heat flow as determined from the temperature-depth relationships. The second term on the right is the advective heat flow, where V is the velocity of the fluid, delta T is the temperature difference with respect to the ambient, c is heat capacity, and rho is density of the fluid. As you can see, if V = 0, then the measured temperature profile can be used to get the total heat flow, but if V is not equal to zero, then any temperature-depth measurement underestimates the total heat flow.
So if there is an advective component of heat flow, then the inferred surface heat flows shown above are all apparent heat flows and surely minimum bounds on the total heat flow. The question is how much heat flow is advective. This is a very difficult number to quantify. One way to do it is to measure the temperature of hot springs and their flow rates. But hot springs tend to be highly localized, so it's not clear how to take such data and extrapolate over a regional surface.
Another way is to make some estimate of what total q might actually be. This would of course be model-dependent, but one can certainly place bounds here. Then the deficit would be the adveticve component. And once one has the advective component, one might be able to get average V. One would have to get delta T, but this can be done by looking at the difference between the projected temperature at depth = 0 and the time-averaged temperature of the Earth's surface (correcting of course for the adiabatic lapse rate if topography is varying). If we can do this, we get V.
V, the velocity of the fluid, has units of m/s. This is equivalent to m^3/m^2/s, which is equal to the volume flux rate of water. And if we multiply by density, this is the mass flux of water. And if we know how much water enters the vadose zone in the high Cascades (this is the annual precipitation minus the direct runoff and the evaporation rate), then we effectively know the velocity of groundwaters in the recharge zone. If the velocity of groundwaters in discharge zones (this is the effective velocity we get after estimating the advective heat flow) is known, then we can get some idea of the extent to which the flow paths have diverged or converged. If discharge V is lower than the recharge V, the flow lines have diverged. The extent of divergence may give a quantitative, albeit with huge error bars, estimate of how deep groundwater circulation penetrates the volcanic edifice.
My interest is how much hydrothermal weathering and alteration takes place in volcanic arcs, in continental and island arcs. This is important because once you build a volcano, topographic effects drive fluid flow. Fluid flow alters the volcano such that any subsequent magmas emplaced into this evolving volcanic edifice will interact with the altered rock. We talk a lot about magmas cannabilizing the volcanic edifice through which they pass, and as a consequence, their compositions shouldn't change much. You are what you eat. However, if the what you eat is slightly altered, you are what you eat plus some. Take an island arc as an example. Fluid flow will likely introduce seawater derived sulfate into the volcanic edifice. Any magmas that pass through this sulfate-laced edifice will very likely inherit these sulfates, given how soluble sulfates are in aqueous fluids.
This is why I am interested in heat flow.
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