fluid, 90% iron solidified iron km ,00012,000 Mg(Fe) silicates phase changes basaltic-granitic crust chemical stratification and differentiation

upper mantle outer core inner core D”, core-mantle boundary layer km ,00012,000 lower mantle core-mantle boundary transition zone crust Structure of Earth as imaged by seismic waves radius of earth = 6371 km

Seismic waves involve stress, strain, and density Two important types of stresses and strains:  Pressure, P and volume change per unit volume,  V/V  Shear stress and shear strain

For linear elasticity, Hooke’s law applies: stress = elastic_constant x strain

For elastic waves, two elastic constants are key: And density of the material,   = mass/volume

Two types of elastic waves Compressional or P waves  involve volume change and shear Shear or S waves  involve only shear P wave particle motions S wave particle motions Click on these links to see particle motions:

Elastic wave velocities determined by material properties P wave velocity S wave velocity

epicenter expanding wavefront at some instant of time after earthquake occurrence ray perpendicular to wavefront seismograph station Earth surface Earth center

epicenter ray seismograph station   = epicentral distance in degrees Earth surface Earth center tt(  ) = total travel time along ray from earthquake to station

Globally recorded earthquakes during the past 40 years earthquake depth 0-33 km

Partial map of modern global seismograph network

2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km. These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page distance, degrees time, minutes

These lines represent plus or minus one minute errors in reading arrival times P diffracted P PKIKP PKP PcP PP PPP ScS SKS S PcS SS SSS PS PPS PKPPKP PKKP PKS SKKS PPP surface waves water waves click on link to P and S phases in the earthP and S phases in the earth

Nomenclature for seismic body phases c = reflection at core mantle boundary K P or S I or J i = reflection at inner core-outer core boundary P wave segments in blue S wave segments in red inner core outer core mantle

P S Mantle Inner core Outer core Single path refracted through mantle seismic wave source

2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km. These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page distance, degrees time, minutes P S P diffracted around core

PP SS Mantle Outer core Single reflection at surface Inner core

2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km. These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page distance, degrees time, minutes PP SS

PcP Single reflection at core-mantle boundary reflection

ScS Single reflection at core-mantle boundary

PcSPcS Single reflection with conversion of P to S

2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km. These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page distance, degrees time, minutes PcP ScS PcS

PKP P in mantle, refracting to P in the outer core (K) and out through the mantle as P P K P

PKIKP P segments in mantle, P segments in outer core (K), and P segment in inner core (I) P K P K I

2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km. These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page distance, degrees time, minutes PKIKP PKP

SKSSKS S in mantle, refracting and converting to P in outer core, then refracting back out and converting back to S in the mantle S K S

SKKS S in mantle, refracting and converting to P in outer core, P reflects once at inner side of core-mantle boundary, then refracting back out back with conversion to S in the mantle S K S K reflection

2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km. These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page distance, degrees time, minutes SKS S SKKS

outer core inner core lower mantle upper mantle km/sec km transition zone D’’ layer depth seismic wave velocity Compressional (P) and Shear (S) wave velocities, Vp and Vs

outer core inner core lower mantle upper mantle km/sec km transition zone D’’ layer depth seismic wave velocity Compressional (P) and Shear (S) wave velocities, Vp and Vs No Shear waves in outer core!

From Vp and Vs to seismic parameter 

For self compression of homogeneous material  (R) =  /   = - dP/(dV/V) = dP/(d  /  ) dP = - g  dR where R = radius to a point in the earth, and g = gravitational acceleration at that radius g = GM R /R 2 where M R = mass within sphere of radius R d  /dR = -  /  g

For self compression of homogeneous material d  /dR = -  /  g This is the gradient in density determined by the seismic wave velocities. To obtain density, one must integrate by fixing the density, , and gravity, g, at the top of the layer and calculating both  and g as one proceeds downwards. The calculation assumes  a simple compression of material that does not change chemistry or phase.  the compression as one goes deeper produces an adiabatic temperature increase.

For self compression of homogeneous material d  /dR = -  /  g The method is applied to the following layers:  upper mantle  lower mantle  outer core  inner core To determine the jumps in density between these layers, the following constraints are used: Mass of earth Moment of Inertia of Earth Periods of free oscillations of Earth

Density,  core-mantle boundary kg/m 3 km depth, km

Gravitational acceleration, g core-mantle boundary km m/s 2 depth, km

Pressure, P core-mantle boundary GPa. km depth, km

Density vrs pressure GPa. kg/m 3

Density vrs pressure GPa. kg/m 3 compression composition change phase changes liquid to solid mantle density crustal density core-mantle boundary Inner core/outer core boundary 1 mbar

fluid, 90% iron solidified iron km ,00012,000 Mg(Fe) silicates phase changes basaltic-granitic crust Chemical stratification

upper mantle “Peridotite”: 65% olivine: (Mg,Fe) 2 SiO 4 25% orthopyroxene (Mg,Fe) 2 Si 2 O 6 10% clinopyroxene (Ca,Mg,Fe) 2 Si 2 O 6 + garnet (Mg,Fe) 3 AL 2 Si 3 O 12 phase changes through transition zone lower mantle 85% Perovskite: (Mg 0.9 Fe 0.1 )SiO 3 15% magnesiowustite (Mg 0.9 Fe 0.1 )O + Ca Perovskite ( Ca, Mg, Fe )SiO 3 + Corundum Al 2 O 3 outer core 90% Fe (Ni) 10% lighter alloy (FeO, S, Si, ?) inner core solid Fe + ? oceanic crustcontinental crust MOHO CMB

upper mantle lower mantle transition zone outer core CMB D” Temperature, degrees C iron melting Adiabatic gradient near surface thermal boundary layer = lithosphere D” = Lower mantle thermo-chemical boundary layer mantle convection advective heat flow conductive heat flow Temperature in mantle ? mantle melting

Temperature profile through entire earth

cool, strong lithospheric boundary layer slowly convecting mantle: plate tectonic engine rapidly convecting outer core: geomagnetic dynamo solid inner core subduction seafloor spreading core-mantle thermo-chemical boundary layer km ,00012,000 crust Earth’s convective systems

inner core km ,00012,000 crust mantle The geomagnetic dynamo: turbulent fluid convection electrically conducting fluid fluid flow-electromagnetic interactions effects of rotation of earth Generation of Earth’s magnetic field in the outer core outer core

Geomagnetic field