Esci 203, Earth Structure and Deformation Heat flow and faulting

Esci 203, Earth Structure and DeformationHeat flow and faulting John Townend EQC Fellow in Seismic Studies john.townend@vuw.ac.nz

Overview • Why bother taking the Earth’s temperature? • Conductive heat flow • Describing heat flow in financial terms • Describing heat flow with the heat flow equation • Determining surface heat flow • The relationship between temperature and rheology (how rocks deform)

Why measure temperature? • Many geological phenomena depend on temperature; some key questions include • How did the Earth form? • What controls the depth of the oceans? • At what depths do different metamorphic reactions occur? • How fast does rock deform? • Have these rocks been cooked enough? • What controls earthquake depths?

q = – k dT dz Conductive heat flow • “Fourier’s law of conduction” • q is the heat flow per unit area (W m–2) • k is the thermal conductivity (W m–1K–1) dT/dz is the thermal gradient (°C m–1, K m–1)

Budgeting with money Min = income DM = Min–Mout = increase in wealth Mout = expenses Gain in money per unit time

Budgeting with heat Hin = a q(z) area a Hprod = a  A  z DH = Hprod + Hin–Hout = increase in heat Hout = a q(z+z) Gain in heat per unit time

The heat conduction equation • Rate of temperature change • Variations in temperature gradient • Effects of heat generation • k: thermal diffusivity (m2 s–1)

Radioactive elements This is the heat generation that goes into the conduction equation

Rutherford at the Royal Society • To my relief, Kelvin fell fast asleep, but as I came to the important point, I saw the old bird sit up, open an eye and cock a baleful glance at me! Then a sudden inspiration came, and I said Lord Kelvin had limited the age of the earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium! Behold! the old boy beamed upon me. — Ernest Rutherford, 1904

The geotherm Temperature (T) geothermal gradient (“geotherm”) = T/z T z Depth (z) The geotherm is an approximation to what is commonly a non-linear temperature profile

Horner diagram T(t) ln (1+tc/t) Measuring temperature thermister Lister-type probe borehole

q = – k T  z Heat flow We represent the amount of heat travelling through the Earth’s crust using Fourier’s conduction relation: That is, heat flow density (“heat flow”) equals the thermal conductivity of the rock times the geotherm Heat flow is expressed in watts per square metre (W m–2) or milliwatts per square metre (mW m–2)

Surface heat flow Effect of volcanism • We typically map surface heat flow • By convention, surface heat flow is expressed as a positive number • q0 = –q(z=0) • This avoids lots of minus signs Effect of subduction Effect of rock uplift

Steps in calculating heat flow • First, calculate the average thermal gradient • Fit a line to T–z data • Then estimate the average conductivity • Best to use the “harmonic mean” • Finally, multiply the two together! ki, zi Z

Calculating a geotherm and heat flow Harmonic mean = 2.4 W m–1 K–1

Other heat flow indicators • Groundwater geochemistry • e.g. silica solubility • Curie depth • Determined magnetically • Mantle resistivity • Depends strongly on temperature • Xenoliths • Mineralogical assemblages Decreasing reliability

Heat flow map examples

Brittle (frictional faults) Ductile (viscous flow) Brittle–ductile transition • What happens to the rheology of crustal rocks as temperature increases? Temperature Seismicity ~15–20 km crust ~350ºC mantle

The BDZ Lin et al., Tectonophysics, 2005

A preliminary map of the New Zealand seismogenic thickness Susan Ellis, GNS Science, pers. comm.

Suggested reading material • Fowler (2004) • Chapter 7, particularly §7.1, (7.2–7.3), 7.5.1, 7.8 • Mussett and Khan • Chapter 17, particularly §17.1, 17.2, 17.4 • Beardsmore and Cull (2001) • Any or all of chapters 1–3 • Turcotte and Schubert (1982) • Section 4.1 Not on reserve (see me)

Esci 203, Earth Structure and Deformation Heat flow and faulting