GLG 490/598 - Subduction Zones Fall, 2003
Profs. Simon Peacock and Matt Fouch
Problem Set #3 - Temperatures and Shear Stresses in Subduction-Zone Forearcs
Due Tuesday, September 16
The plate boundary separating a subducting plate ifrom the overriding plate is a major
thrust fault. Molnar and England (1990, J. Geophys. Res., v. 95, 4833-4956) investigated the
thermal structure near major thrust faults and their analytical expressions may be used to gain
insight into the thermal structure of subduction zones. The steady-state thermal structure of
the hanging wall (upper plate) depends on:
(1) the magnitude and distribution of three heat sources:
(a) conduction from below
(b) radioactivity
(c) shear heating along the thrust fault
(2) the rate at which movement of the footwall (lower plate) advectively moves heat
(3) physical properties of the rocks, particularly thermal conductivity and thermal
diffusivity.
Assuming negligible radioactive heating, temperatures within the hanging wall may
be calculated using analytical expressions derived by Molnar and England (1990):
T=(Q0
+
Qsh )z
/
k
S
(1)
where T = temperature (°C), Q0 = basal heat flux (W/m2), Qsh = rate of shear heating
(W/m2), z = depth (m), k = thermal conductivity (W/m-K), and S = a divisor that accounts for
advection given by:
S = 1 + b V z
δ
f sin
κ
(2)
where b = a constant (≈1 based on numerical experiments), V = slip rate (m/s), zf = depth to
the fault (m),
δ
= angle of subduction, and
κ
= thermal diffusivity (m2/s). The numerator in
equation (1) represents the steady-state temperatures in the absence of advection and the
denominator, S, represents the effect of advection (i.e., cooling of the hanging wall resulting
from underthrusting).
For a constant shear stress along the thrust fault, the rate of shear heating (Qsh) is
given by:
Qsh =
τ
V (3)
where
τ
= shear stress (Pa) and V = slip rate along the fault (m/s).
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