Introduction Geodynamics course - part 1 Physics 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/geodynamics Schedule: 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 computerlab preparation

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 programs in Earth Sciences at Utrecht University

Focus on geophysical model development

Topical subdivision: Earth’s structure and composition Internal 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

∂P Resulting pressure profile P(r), ∂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,..., n Constrained by geological , astronomical data - Ch. 2.8 lecture notes Pressure P Treated in connection with density & gravity profile in lectures 1+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 from mineral physics theory and HPT experiments

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

Phase transitions linked to sharp transitions in seismic wave speed 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

1 Radial(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 material properties. For example density ρ,

ρ(r, θ, φ) = ρr (r)+∆ρ(r, θ, φ)

Typically ∆ρ << 1 (∼ 10−2) ρr Often the horizontal average over a spherical surface Sr of radius r, is used as a reference profile Z 1 2 ρr (r) =ρ ¯(r) = 2 ρ(r, θ, φ)r sin(θ)dθdφ 4πr Sr 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: ¯ 3 T (r, θ, φ) = T (r) + ∆T (r, θ, φ), ∆T . 10 K

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: ¯ 3 T (r, θ, φ) = T (r) + ∆T (r, θ, φ), ∆T . 10 K Expressed in linearized equation of state, ρ(T ) ≈ ρ(T¯ )(1 − α(T − T¯ )), ∆ρ = −αρ(T¯ )∆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: ¯ 3 T (r, θ, φ) = T (r) + ∆T (r, θ, φ), ∆T . 10 K Expressed in linearized equation of state, ρ(T ) ≈ ρ(T¯ )(1 − α(T − T¯ )), ∆ρ = −αρ(T¯ )∆T ∆ρ = −α∆T 2 · 10−5 × 103 = 2 · 10−2 ρ(T¯ ) .

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: ¯ 3 T (r, θ, φ) = T (r) + ∆T (r, θ, φ), ∆T . 10 K Expressed in linearized equation of state, ρ(T ) ≈ ρ(T¯ )(1 − α(T − T¯ )), ∆ρ = −αρ(T¯ )∆T ∆ρ = −α∆T 2 · 10−5 × 103 = 2 · 10−2 ρ(T¯ ) . Conclusion: Small ∼ 1% density perturbutions are significant in 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: ¯ 3 T (r, θ, φ) = T (r) + ∆T (r, θ, φ), ∆T . 10 K Expressed in linearized equation of state, ρ(T ) ≈ ρ(T¯ )(1 − α(T − T¯ )), ∆ρ = −αρ(T¯ )∆T ∆ρ = −α∆T 2 · 10−5 × 103 = 2 · 10−2 ρ(T¯ ) . Conclusion: Small ∼ 1% density perturbutions are significant in driving mechanism of plate tectonics Temperature perturbations also induce perturbations in seismic 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, 2010

A.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