Cover

Half-title

Title

Copyright

Contents

Preface

1 Introduction

1.1 Thermal history: the accumulation of thermochronological age

1.2 Cooling, denudation and uplift paths

1.3 Thermochronology in practice

Choice of thermochronometer

Sampling scale

Structural complexity

Mineralogy

Sample preparation

Sample quality

2 Basics of thermochronology: from t–T paths to ages

2.1 The isotopic age equation

2.2 Solid-state diffusion – the basic equation

2.3 Absolute closure-temperature approximation

2.4 Dodson’s method

2.5 Numerical solution

The spherical approximation

The finite-difference formulation

2.6 Determining the diffusion parameters

Tutorial 1

3 Thermochronological systems

3.1 Ar dating methods

Diffusion behaviour of Ar

Modelling routines

3.2 (U–Th)/He thermochronology

Diffusion behaviour of He

Mad_He.f90

3.3 Fission-track thermochronology

Annealing of fission tracks and confined track-length distributions

Annealing models

MadTrax.f

Tutorial 2

4 The general heat-transport equation

4.1 Heat transport within the Earth

4.2 Conservation of energy

4.3 Conduction

4.4 Advection

4.5 Production

4.6 The general heat-transport equation

4.7 Boundary conditions

4.8 Purely conductive heat transport

Conductive equilibrium – variable conductivity

Conductive equilibrium – the effect of heat production

Tutorial 3

5 Thermal effects of exhumation

5.1 Steady-state solution

Uplift and exhumation

Basic PDE: the steady-state case

The dimensionless form

Solution

5.2 Thermal effects of exhumation: transient solution

Basic PDE: the transient case

Solution

5.3 Thermal effects of exhumation: the general transient problem

Finite-element equations

The weak form

The weighted residual

The Galerkin method

Finite-element discretisation

Shape functions

Linear shape functions

Local coordinates

Quadratic shape functions

Two-dimensional elements

Shape-function derivatives

Which elements to use?

Numerical integration

The Newton–Cotes formula

Gauss quadrature

Which integration scheme?

Time-stepping algorithms

An explicit–implicit scheme

Limits on time-step length

Assembling the matrices

The complete matrix

Banded matrices and node numbering

Solution of the finite-element equations

Fixed-temperature boundary conditions

Positive-definite, symmetrical

Non-symmetrical A

Iterative methods

Heat1D

Comparison with analytical solutions

Tutorial 4

Tutorial 5

Tutorial 6

6 Steady-state two-dimensional heat transport

6.1 The effect of surface topography

Conductive equilibrium

Effects of exhumation

Another approximate solution

6.2 The age–elevation relationship – steady state

6.3 Relief change

Conclusion

Tutorial 7

7 General transient solution – the three-dimensional problem

7.1 Pecube

7.2 Time-varying surface topography

7.3 Surface relief in the Sierra Nevada

Tutorial 8

8 Inverse methods

8.1 Spectral analysis

8.2 An example based on synthetic ages

8.3 Application of the spectral method to the Sierra Nevada

8.4 Sampling strategy

8.5 Systematic searches

9 Detrital thermochronology

9.1 The basic approach

9.2 Deconvolution of detrital age distributions

9.3 Estimating denudation rates from detrital ages

9.4 Estimating relief from detrital ages

9.5 Interpreting partially reset detrital samples

10 Lateral advection of material

10.1 Lateral variability in tectonically active regions

10.2 Exhumation and denudation in multi-dimensional space

10.3 Consequences of lateral motion for thermochronology

Integrated effects on individual ages

Consequences for spatially dispersed datasets

10.4 Scaling of lateral significance with closure temperature

10.5 Evaluation of the significance of lateral variation

Regional estimation of significance: the Eta factor

Deconvolving lateral effects on the thermochronological record

Case study: the Olympic Mountains

Tutorial 9

Tutorial 10

11 Isostatic response to denudation

11.1 Local isostasy

11.2 Flexural isostasy

11.3 Periodic loading

11.4 Isostatic response to relief reduction

11.5 Effects on age distribution

11.6 Effects on age–elevation distributions

11.7 Application to the Dabie Shan

12 The evolution of passive-margin escarpments

12.1 Introduction

12.2 Early conceptual models: erosion cycles

12.3 Thermochronological data from passive margins

12.4 Models of landscape development at passive margins

12.5 Combining thermochronometers and modelling

13 Thermochronology in active tectonic settings

13.1 A simple model for continental collision

13.2 Heat advection in mountain belts

13.3 The Alpine Fault, South Island, New Zealand

13.4 Application of the Neighbourhood Algorithm to Southern Alps data

Appendix 1 Forward models of fission-track annealing

A1.1 Variable temperature history

Appendix 2 Fortran routines provided with this textbook

Appendix 3 One-dimensional conductive equilibrium with heat production

A3.1 The problem

A3.2 The basic equation

A3.3 The dimensionless form

A3.4 Analytical solution

A3.5 Temperature at the base of the crust

A3.6 The relationship between heat flux and heat production

Appendix 4 One-dimensional conductive equilibrium with anomalous conductivity

A4.1 The problem

A4.2 The basic equation

A4.3 The dimensionless form

A4.4 Analytical solution

A4.5 Temperature at the base of the crust

Appendix 5 One-dimensional transient conductive heat transport

A5.1 The problem

A5.2 The basic equation

A5.3 The dimensionless form

A5.4 Analytical solution

Appendix 6 Volume integrals in spherical coordinates

A6.1 Spherical integrals

Appendix 7 The complementary error function

Appendix 8 Pecube user guide

A8.1 How to compile and execute Pecube

A8.2 The input file

A8.3 create_Pecube_in

A8.4 Peclet_ geom

A8.5 Output files

Appendix 9 Tutorial solutions

A9.1 Tutorial 1

A9.2 Tutorial 2

A9.3 Tutorial 3

A9.4 Tutorial 4

A9.5 Tutorial 5

A9.6 Tutorial 6

A9.7 Tutorial 7

A9.8 Tutorial 8

A9.9 Tutorial 9

A9.10 Tutorial 10

References

Index