Introduction Geodynamics course - part 1Physics of the Earth’s Interior

A.P. van den Berg

February 2015

A.P. van den Berg Introduction Geodynamics course - part 1 Physics of the Earth’s Interior

Overview

Organisation and credit

Documentation available on course website:www.geo.uu.nl/∼berg/geodynamicsSchedule: Outline 2015.pdf

Content: lecturenotes.pdf computerlabs.pdf

Introduction lecture:Earth’s global internal structure (lecture notes section 2)

A.P. van den Berg Introduction Geodynamics course - part 1 Physics of the Earth’s Interior

Organisation and course credit of part 1

6 lecture sessions:50% credit - midterm exam. Wed. March 4(based on home work problem exercises, course notes)

4 computer lab sessions:40% credit labreports (2-student teams)10% individual homework summaries of computerlabpreparation

A.P. van den Berg Introduction Geodynamics course - part 1 Physics of the Earth’s Interior

Subject of the of the geodynamics course

Internal structure and dynamics of the Earth

Branch of research- and educational programsin Earth Sciences at Utrecht University

Focus on geophysical model development

Topical subdivision:

Earth’s structure and compositionInternal dynamics - thermal state and evolution

A.P. van den Berg Introduction Geodynamics course - part 1 Physics of the Earth’s Interior

Models of Earth’s internal structure

Radial distribution of density ρ(r)

Corresponding gravity field g(r) - selfgravitation

Resulting pressure profile P(r), ∂P∂r = −ρg

These items are subject of lectures 1+2 and computerlab 1

A.P. van den Berg Introduction Geodynamics course - part 1 Physics of the Earth’s Interior

Observational constraints on interior models 1/2

Model calculation of physical material properties requires:

Material composition, weight fractions Wi , i = 1, . . . , nConstrained by geological , astronomical data - Ch. 2.8lecture notes

Pressure PTreated in connection with density & gravity profile in lectures1+2 and computerlabs

Internal temperature T (r)Models for thermal state and eveolution - lectures 5,6

A.P. van den Berg Introduction Geodynamics course - part 1 Physics of the Earth’s Interior

Observational constraints on interior models 2/2

Model predictions of internal P,T must be consistent with:

Mineral phase diagrams of candidate mantle materials frommineral physics theory and HPT experiments

This way mineral phase transitions are predicted(∼ 410, 660 km depth)

Phase transitions linked to sharp transitions in seismic wavespeed constrain internal T and P - lecture 4

A.P. van den Berg Introduction Geodynamics course - part 1 Physics of the Earth’s Interior

Internal temperature thermal state and evolution

Internal (radioactive) heating / secular cooling

Heat transport processes - conduction / convection

Impact of mineral phase transitions on dynamics of the mantle

Topics treated in lectures 5,6, lecture notes Ch. 3

A.P. van den Berg Introduction Geodynamics course - part 1 Physics of the Earth’s Interior

Earth’s 1-D global structure - PREM model

1

1Radial(depth) distribution of density ρ, seismic velocities vp and vs , gravity acceleration g and pressure P in

the PREM model (Dziewonski and Anderson, 1981).

A.P. van den Berg Introduction Geodynamics course - part 1 Physics of the Earth’s Interior

First order internal structure (1)1-D reference profile ρr (r)

Radially symmetrical (one dimensional) geometry and materialproperties. For example density ρ,

ρ(r , θ, φ) = ρr (r)+∆ρ(r , θ, φ)

Typically ∆ρρr<< 1 (∼ 10−2)

Often the horizontal average over a spherical surface Sr

of radius r , is used as a reference profile

ρr (r) = ρ̄(r) =1

4πr 2

∫Sr

ρ(r , θ, φ)r 2 sin(θ)dθdφ

A.P. van den Berg Introduction Geodynamics course - part 1 Physics of the Earth’s Interior

First order internal structure (2)Importance of small local perturbations on 1-D structure

Density variation in cold slabs (thermal contraction) ⇒driving mechanism of plate tectonics.

Density effect of thermal contraction/expansion:T (r , θ, φ) = T̄ (r) + ∆T (r , θ, φ), ∆T . 103K

A.P. van den Berg Introduction Geodynamics course - part 1 Physics of the Earth’s Interior

First order internal structure (3)Importance of small local perturbations on 1-D structure

Density variation in cold slabs (thermal contraction) ⇒driving mechanism of plate tectonics.

Density effect of thermal contraction/expansion:T (r , θ, φ) = T̄ (r) + ∆T (r , θ, φ), ∆T . 103K

Expressed in linearized equation of state,ρ(T ) ≈ ρ(T̄ )(1− α(T − T̄ )), ∆ρ = −αρ(T̄ )∆T

A.P. van den Berg Introduction Geodynamics course - part 1 Physics of the Earth’s Interior

First order internal structure (4)Importance of small local perturbations on 1-D structure

Density variation in cold slabs (thermal contraction) ⇒driving mechanism of plate tectonics.

Density effect of thermal contraction/expansion:T (r , θ, φ) = T̄ (r) + ∆T (r , θ, φ), ∆T . 103K

Expressed in linearized equation of state,ρ(T ) ≈ ρ(T̄ )(1− α(T − T̄ )), ∆ρ = −αρ(T̄ )∆T

∆ρρ(T̄ )

= −α∆T . 2 · 10−5 × 103 = 2 · 10−2

A.P. van den Berg Introduction Geodynamics course - part 1 Physics of the Earth’s Interior

First order internal structure (5)Importance of small local perturbations on 1-D structure

Density variation in cold slabs (thermal contraction) ⇒driving mechanism of plate tectonics.

Density effect of thermal contraction/expansion:T (r , θ, φ) = T̄ (r) + ∆T (r , θ, φ), ∆T . 103K

Expressed in linearized equation of state,ρ(T ) ≈ ρ(T̄ )(1− α(T − T̄ )), ∆ρ = −αρ(T̄ )∆T

∆ρρ(T̄ )

= −α∆T . 2 · 10−5 × 103 = 2 · 10−2

Conclusion: Small ∼ 1% density perturbutions are significantin driving mechanism of plate tectonics

A.P. van den Berg Introduction Geodynamics course - part 1 Physics of the Earth’s Interior

First order internal structure (6)Importance of small local perturbations on 1-D structure

Density variation in cold slabs (thermal contraction) ⇒driving mechanism of plate tectonics.

Density effect of thermal contraction/expansion:T (r , θ, φ) = T̄ (r) + ∆T (r , θ, φ), ∆T . 103K

Expressed in linearized equation of state,ρ(T ) ≈ ρ(T̄ )(1− α(T − T̄ )), ∆ρ = −αρ(T̄ )∆T

∆ρρ(T̄ )

= −α∆T . 2 · 10−5 × 103 = 2 · 10−2

Conclusion: Small ∼ 1% density perturbutions are significantin driving mechanism of plate tectonics

Temperature perturbations also induce perturbations inseismic wave speeds that are imaged in seismic tomography(part 2 geodynamics course).

A.P. van den Berg Introduction Geodynamics course - part 1 Physics of the Earth’s Interior

Perturbation of 1-D structure - tomographic images

a,c 1325 km depth, 120 Ma, b,d 2650 km depth, 240 Ma

van der Meer et al., Nature Geoscience, 2010A.P. van den Berg Introduction Geodynamics course - part 1 Physics of the Earth’s Interior

Great circle cross section ∼ 1% wave speed perturbations

A.P. van den Berg Introduction Geodynamics course - part 1 Physics of the Earth’s Interior