Transcript Gravity Summary - uni

Introduction to Earth System
Solid Earth part
Rocco Malservisi
[email protected]
Phone: 2180 4201
Elastic Waves
P waves
Elastic Waves
S waves
Elastic
Waves
Surface waves
Surface waves front expand as a cylindrical surface
Body waves front expand as a spherical surface
Since the energy is conserved, which one is decaying faster?
Body waves decay ~ as inverse of square of distance
Surface waves decay ~ as inverse of the distance
The same can be done with waves produced by earthquakes that
Can travel through the planet
PREM
Tomography
Flower, 2004
Data from Grand and
Van Der Hilst
Free oscillation Earth
http://web.ics.purdue.edu/~nowack/geos557/lecture16-dir/lecture16.htm
Toroidal
Spheroidal
3D-MODELLE DES ERDMANTELS
Kugelfunktionen
Zonale Komponente
Cnm: n = 2, m = 0
Die Eigenschwingungsmoden der
Erde lassen sich mit Hilfe von
Kugelfunktionen beschreiben.
Sektoral Komponente
Cnm: n = 2, m = 2
Terrassal Komponente
Cnm: n = 2, m = 0
Cnm sind die Kugelkoeffizienten
vom Grad n und Ordnung m
3D-MODELLE DES ERDMANTELS
Daten – III. Splitting der Eigenfrequenzen des Erdkörpers
Berechnet man die Fourier-Transformation sehr langer Seismogramme (24
Stunden und länger) so tauchen die Eigenfrequenzen der Erde als klare
Peaks im Spektrum auf.
Amplitudenspektrum, Irian-Java-Beben, 17. 2. 1996, Station
http://earthguide.ucsd.edu/mar/dec5/earth.html
Magnetic Field
We have a magnetic field
that it is very similar to
the one of a dipole.
Well in reality this is true
close to the surface if we
go far away enough it
looks more complex
Magnetopause 10Re Moon 60Re
Magnetic Field is a vector
It has an intensity (can be measured looking
At the oscillation of a compass)
And a direction
The direction change with the position
Magnetic Pole:
The place where the compass is pointing
Down
Magnetic Equator:
The place where the compass is horizontal
The Magnetic Poles are close to the geographical
Poles but do not coincide (~11 off)
The Earth’s Magnetic Field
B = (X, Y, Z)
Or
B = (F, I, D )
Or
B = (D, H, Z)
F: intensity
I: inclination
D: declination
H: Horizontal component
The seven elements of the (local) magnetic field
in the geographic coordinate system
I. Geomagnetic field – Local Geomagnetic Field Vector
The Earth’s Magnetic Field
From this:
Magnetic pole is the point where
H=0 D= +- 90
Magnetic Equator the point where
D=0
F: intensity
I: inclination
D: declination
H: Horizontal component
Where 3000nT<H<6000nT erratic zone (compass work badly)
Where H<3000nT unusable zone (compass does not work)
I. Geomagnetic field – Local Geomagnetic Field Vector
Tesla (T) Magnetic flux density = Wb/m^2
Weber (Wb) The weber may be defined in terms of Faraday's law, which relates a changing
magnetic flux through a loop to the electric field around the loop. A change in flux of one weber per second will
induce an tension of one volt.
T=N/Am
V velocity m/s
E electric field N/C V/m
B=N/Am
BiotSavart Law
The place where the axis of the dipole intersect the surface
Of the earth are called geomagnetic poles
The numerical interpolation of the data is called
Geomagnetic models. Every 5 yr a new model is released by
The international community now we have the IGRF 2005
From Press, 1992.
90% of spatial field distribution can be explained by a simple dipolar field
I. Geomagnetic field – Geocentric inclined dipole
Magnetic Observatory
http://www.ngdc.noaa.gov/seg/geomag/icons/Obs1999_lg.gif
FUR
http://www.geophysik.uni-muenchen.de/observatory/geomagnetism
Geomagnetic models: Interpolation of the observations
Using spherical harmonics.
If we do not have electrical charges and magnetic sources
We can have a potential. (otherwise it is not conservative
so no potenzial)
Gauss in 1830 thought that he can divide the field in internal
And external having 2 potentials.
The internal goes as r^-n the external as r^n
The potential can be expressed as:
a n 1 m
v i  a   gn cosm  hnm sinmPnm cos 
r 
n1 m 0

n

n


v e  a  ar g cosm  h sinm Pnm cos 
n
n1 m 0
*m
n
*m
n
a n 1 m
v i  a   gn cosm  hnm sinmPnm cos 
r 
n1 m 0

n

n


v e  a  ar g cosm  h sinm Pnm cos 
n
n1 m 0
*m
n
*m
n
This is not only an interpolation scheme but also the solution for
 the physical problem of the magnetic field due to an internal or
external source!
The coefficients are called Gauss coefficients
The internal field coef. start from r^-2 because we do not have
the magnetic monopole
The internal field represent 90% of the total field

a n 1 m
v i  a   gn cosm  hnm sinmPnm cos 
r 
n1 m 0

n

n


v e  a  ar g cosm  h sinm Pnm cos 
n
n1 m 0
*m
n
*m
n
Table 1. Spherical Harmonic Coefficient (in nT) of Terrestrial Magnetic Field (IGRF 1985)
Coefficient
Degree (m)
Order (n)
1
2
3
4
______________________________________________________
4
169
gnm
3
835
-426
2
1691
1244
363
______________________________________________________
1
-1903
2045
-2208
780
gno
0
-29877 -2073
1300
937
1
5497
-2191
-312
233
______________________________________________________
2
-309
284
-250
hnm
3
-296
68
4
-298
a n 1 m
v i  a   gn cosm  hnm sinmPnm cos 
r 
n1 m 0

n

n


v e  a  ar g cosm  h sinm Pnm cos 
n
n1 m 0
*m
n
*m
n
The internal field represent 90% of the total field

The coef. g with n=1 m=0 give the magnitude of the dipole
aligned with the rotation axis.
The coef. with n=1 give the magnitude of the dipole is the largest
one ~85% of the field. It is inclinated of ~11 degrees.
For n>12 the coef. are neglegible.
N=2 quadrupole etc… can be controlled by regional features.
The numerical interpolation of the data is called
Geomagnetic models. Every 5 yr a new model is released by
The international community now we have the IGRF 2005
From Press, 1992.
90% of spatial field distribution can be explained by a simple dipolar field
I. Geomagnetic field – Geocentric inclined dipole
Geomagnetic Field Intensity
Other units: Gauss=100000nT g=10000nT
I. Geomagnetic field – Worldwide Variation of F
Geomagnetic inclination (IGRF)
tan I = 2 tan 
I. Geomagnetic field – Worldwide Variation of I
Worldwide Distribution of Geomagnetic Declination according to IGRF 2000
I. Geomagnetic field – Worldwide Variation of D
The dipolar field is called the MAIN FIELD
It changing slowly (this is why we update the model
Every 5 yr by IAGA)
The external field can change quickly.
How does the field change:
http://www.geophysik.uni-muenchen.de/observatory/geomagnetism
Big diurnal variation and annual variation what can cause it?
Temporal (diurnal and secular) variations
other secular variation: reversal
10 nT / hour
From Butler,
Palaeomagnetism, 1992.
Magnetic storm
Slide
I. Geomagnetic field – Temporal Variations
other secular variation: reversal
From Butler,
Palaeomagnetism, 1992.
Slide
I. Geomagnetic field – Temporal Variations
Where the magnetic field came
from?
a) Dipole inside the Earth
can not have reversal
b-c) Uniformly magnetic mantle
Or core, mantle of silicate
too hot
d) Current in the core
Most likely
Where the magnetic field came
from?
Self Sustaining dynamo