Heatflow of Oceanic Lithosphere, Reading: T & S 4-16

GG 652: Homework 12

Heatflow of Oceanic Lithosphere, Reading: T & S 4-16

Due Friday 4/19/13

One prediction of the lithosphere rejuvenation model for the Hawaiian hotspot swell is that there should be an immediate increase in seafloor heat flow. But this is not observed, in fact the heat flow near Big Island looks like that for normal 90 Myr-old seafloor. A different process must be creating the Hawaiian swell. Olson [1990] proposed that the lithosphere is cold and rigid so that it does not thin very much, and certainly not instantaneously. The anomalous uplift is caused by a buoyant mantle plume pushing up on the base of the lithosphere, but the temperature of the lithosphere, and therefore heatflow is largely unchanged near Big Island. But, as the lithosphere moves away from the mantle plume, it drags a layer of hot plume material with it, and eventually heat from the plume layer diffuses into and heat up the lithosphere. A heat flow anomaly is bound to appear at some time or distance away from Big Island (the lithospheric plate is moving away from the plume at ~80 km/m.y.).

To test this model, you propose to do a heatflow survey someplace along the Hawaiian hotspot chain. First and foremost, you must determine where to do the survey, i.e., how far away from Big Island should a heat flow anomaly be detectable? To do this you will need to predict the anomalous heat flow at the surface due to the heat conducting from the hot layer into the lithosphere. Because you only care about the changes introduced by the plume, you can neglect the background heat flow and normal thermal structure of the lithosphere cooling with age.

To construct your thermal model let’s assume that time t = 0 Myr at Big Island where the plume first impacts the lithosphere. At this point, the lithosphere has a thickness of b (~100 km) and a normal temperature so the temperature anomaly DT=0°C everywhere in the lithosphere. Below the lithosphere, the plume introduces an excess temperature DTmax.. Now compute the diffusion of the excess temperature DT from the plume into the lithosphere. With that solution compute the excess heatflow Dq at the seafloor versus distance (or time) up the chain away from Big Island.

Produce 3 plots: (1) DT vs. depth at three different times or distances from Big Island, (2) Dq vs. depth for the same three times/distances, and (3) Dq at the surface versus distance along the chain. The accuracy of your heatflow probes are such that the minimum heatflow anomaly you can possibly detect is ~2-3 mW/m3. Is the Hawaiian plume likely to be detectable with your heat flow probes? If so, where along the chain should you place your probes? Below are two methods of solving the problem.

Method 1: T&S problem 4-36 forms a great basis for approaching this problem. For example, a rather crude approximation would be to assume the plume layer is much thicker than the lithosphere (i.e., it extends to infinite depth). The initial condition is that the temperature anomaly DT = 0°C in the lithosphere (i.e., DT=T0=T1 = 0°C, 0 < y b) and the temperature anomaly is maximum just below the base of the lithosphere (i.e., DT = T2 = DTmax, y > b). The boundary conditions are no temperature anomaly at the surface (DT =T0 = 0°C at y = 0) and temperature anomaly is maximum deep in the plume layer (DT = T2 = DTmax at y = ).
Solve for DT as a function of depth below the seafloor y and time t, with b= 100 km.
Method 2: The better way to do the problem is to model a plume layer of finite thickness. By superposing error function solutions, or alternatively, by using Fourier transforms, you can simulate the temperature structure shown to the right. In the coordinates of T&S 4-36, the seafloor would be at y = -b, the base of the lithosphere would be at y = 0, and the base of the plume layer would be at y = b. The initial condition is DT = 0°C (-b y 0) and DT = DTmax (0 y b). The boundary conditions are DT = 0°C at y = -b and y = . Assume b= 100 km. /