Global GeophysicsGlobal Geophysics

Lecture partLecture part

Rocco MalservisiRocco Malservisi

roccom@lmu.de

Phone: 2180 4201Phone: 2180 4201

NASA photo from Apollo 17

Is it really a sphere?Is it really a sphere? Is it an ellipsoid?Is it an ellipsoid? Is it flat?Is it flat? The shape of our The shape of our

system depend on the system depend on the problem we want to problem we want to study and the required study and the required precision!!precision!!

How big is the planet?How big is the planet?

By definition 40000 km!!By definition 40000 km!!

1m=1/4e6 length of a 1m=1/4e6 length of a meridian.meridian.

Or 60x360 nautical miles Or 60x360 nautical miles (21600 nm).(21600 nm).

How big is the planet?How big is the planet?

By definition 40000 km!!By definition 40000 km!!

The first one to measure it The first one to measure it correctly Erstosthenes correctly Erstosthenes measuring the distance measuring the distance from Alexandria and from Alexandria and Syene (5000 stadia) and Syene (5000 stadia) and the angles in figure, he the angles in figure, he computed a circumference computed a circumference of 250000 stadia 39300kmof 250000 stadia 39300km

From Marshak, 2005

How big is the planet?How big is the planet?By definition 40000 km!!By definition 40000 km!!

Today we say that the radius Today we say that the radius of the Spherical Earth of the Spherical Earth equivalent to the volume of equivalent to the volume of the planet is:the planet is:

6371 km6371 km

We also know that an We also know that an ellipsoid is a better ellipsoid is a better approximation:approximation:

Eq radius: 6378 kmEq radius: 6378 kmPol Radius: 6356 kmPol Radius: 6356 kmFlattening: 1/298Flattening: 1/298

From Marshak, 2005

We are attracted to it and We are attracted to it and there is gravitythere is gravity

http://www.jadetower.org/muses/wlsimages/gravity-newton.jpg

We are attracted to it and We are attracted to it and there is gravitythere is gravity

And if we look at the And if we look at the satellite it is “falling in satellite it is “falling in to the Earth” attracted to the Earth” attracted by a force that is by a force that is proportional to the proportional to the mass of the planet.mass of the planet.

From the orbit parameter From the orbit parameter we can compute the we can compute the massmass

http://www.jadetower.org/muses/wlsimages/gravity-newton.jpg

Well even from the Well even from the ground if we know the ground if we know the constant G and our constant G and our distance from the distance from the center of the Earth we center of the Earth we can measure the can measure the gravity acceleration gravity acceleration thus the mass of the thus the mass of the Earth (ex a pendulum) Earth (ex a pendulum)

M=gRM=gR22/G/Gg=9.8msg=9.8ms-2 -2

G=6.67e-11 mG=6.67e-11 m33kgkg-1-1ss-2-2

R=6371kmR=6371kmM=6e24 kgM=6e24 kg

http://www.jadetower.org/muses/wlsimages/gravity-newton.jpg

So can we say So can we say something about the something about the interior of the planet?interior of the planet?

what is the average what is the average density?density?

Mass = 6e24 kgMass = 6e24 kg

Volume = ?Volume = ?

So what is the average So what is the average density?density?

Mass 6e24 kgMass 6e24 kg

Volume=4/3Volume=4/3RR33==

1.08e21 m1.08e21 m33

So its density isSo its density is

~5500 kg m~5500 kg m-3-3

Density of surface rocks?Density of surface rocks?

So what is the average So what is the average density?density?

Mass 6e24 kgMass 6e24 kgVolume=4/3Volume=4/3RR33==1.08e21 m1.08e21 m33

So its density isSo its density is~5500 kg m~5500 kg m-3-3

Density of surface rocks?Density of surface rocks?~1.5-3.5 g/cc~1.5-3.5 g/ccDensity Iron ~7g/ccDensity Iron ~7g/cc

http://earthguide.ucsd.edu/mar/dec5/earth.html

Which shape has the Which shape has the planet?planet?

What can we see What can we see (colors)?(colors)?

What can we measure?What can we measure?

We have a magnetic field We have a magnetic field that it is very similar to that it is very similar to the one of a dipole.the one of a dipole.

Well in reality this is true Well in reality this is true close to the surface if close to the surface if we go far away we go far away enough it looks more enough it looks more complexcomplex

Magnetopause 10Re Moon 60Re

Variation of Magnetic field on Variation of Magnetic field on oceansoceans

Looking for subs the British and Americans developed a map ofMagnetic anomalies of the sea floor, in 1961 Harry Hess explained It using seafloor spreading theory.

Magnetic and gravity anomalies and topo/bathymetry

Müller et al. 2006

GGM01S, GRACE missionwww.csr.utexas.edu/grace/gravity/

Let’s try to look more in details the brownish regions

Some area are more brownish then otherSome area are flat and some are roughSome areas look like if someone enjoyed to fold it

Let’s try to look more in details the gravity

What does influence this variation of gravity field?

So as first approximation So as first approximation the Earth is a planet the Earth is a planet that looks like a sphere that looks like a sphere with a density higher with a density higher than we would expect than we would expect looking only at the looking only at the surface, with regions of surface, with regions of different colors at the different colors at the surface and able to surface and able to generate a dipolar generate a dipolar magnetic field. That magnetic field. That does not appear to be does not appear to be constant.constant.

So it does not look any longer as an homogeneous sphere!!On second approximation it is an ellipsoid6357 km (polar) 6378 km (equatorial)

And it looks like if some processes are shaping the brownishregions….

We will spend the rest of the semester to look at these processes and to figure out how we can observe them

PLATE TECTONICSPLATE TECTONICS

Plate Tectonic is a theory that unify different previous geological theories (CONTINENTAL DRIFT and OCEAN SPREADING) and that can explain the majority of the solid earth system observations.

Basic concept:The outermost layer (LITHOSPHERE) is divided in a small number of “rigid” plates in relative motion one respect to the other and that are moving on a weak ASTHENOSPHERE

PLATE TECTONICSPLATE TECTONICSBasic concept:The outermost layer (LITHOSPHERE) is divided in a small number of “rigid” plates in relative motion one respect to the other and that are moving on a weak ASTHENOSPHERE

Basic Assumptions:The astenosphere viscosity is low enough to allow on long time scale for viscous flow;The generation of new plate material occurs by sea floor spreading;The new oceanic lithosphere form part of a rigid plate that may or may not include continental material;Earth’s surface area remains constant; this means that seafloor spreading must be balanced by consumption of plate elsewhere;Lithospheric plate are capable of transmitting stress over great horizontal scale. In other words plates are rigid and the deformation is concentrated along the boundaries.