Meeresspiegeländerungen und Batimetrie aus Satellitenbeobachtungen FU Berlin, Januar 2003 Carla Braitenberg Dipartimento Scienze della Terra, Università di Trieste, Via Weiss 1, 34100 Trieste Berg @ units . it Tel +39-040-5582258 fax +39-040- 575519 Übungen am Rechner.
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Meeresspiegeländerungen und Batimetrie aus
Satellitenbeobachtungen
FU Berlin, Januar 2003Carla Braitenberg
Dipartimento Scienze della Terra, Università di Trieste, Via Weiss 1, 34100 Trieste
• Scope of exercize: familiarize with flexure response of crust.
• Load: bathymetry• The flexure model is tested trough the observed gravity
field. Procedure: Take Bouguer anomaly over sea. This field is representative of crustal thickness variations. Invert field by downward continuation-you obtain first approximation of Moho.
• Apply bathymetric load to flexure model. Choose parameters for crust and mantle density, and elastic thickness. Test different Te’s.
• Calculate the difference field of inverted and modelled CMI. Find which Te gives best results. Describe where the deviations are greatest, and the model does not seem to be appropriate.
Program-Exercizes on PC:
• At last calculate isostatic gravity residual. This field can be used for correcting the bathymetry.
• Programs necessary:• Surfer for visualization and handling grids• Simple file-editor• Downward continuation program: invertonly• Forward calculation of gravity field: parker• Flexure calculation: modflex• Input grids: bathymetry grid, gravity anomaly
grid, gravity Bouguer grid.
(Spangler Nissen and Hayes, 1995)
Età del Bacino del M. Cinese Merid. :
NE: 17-32 Ma
SW: 15.5-24 Ma
Espansione:
NE: asse direzione EW
SW: direzione NE-SW
Database
• Gravità: 2’x2’ Database Cinese. Da osservazioni satellitari.
• Topografia iniziale per il calcolo della correzione di Bouguer, analisi flessurale: ETOPO5
• Rilevamenti batimetrici da nave: Database Sandwell (UCSD)
Grids in input
Bathymetry:bat.grd
equivalent load:load.grd
observed gravity:grav.grd
Bouguer:boug.grd
Programs:
parker.exe parker.inp
invertonly.exe invertonly.inp
modflex.exe modflex.inp
Input files examples:input file for modflex.for (modflex.inp)
load.grd ! input file
22 ! reference depth(km)
3 ! Te (km)
input file for program parker.for
22.,0.5 !ref.depth (km), density (g/cm3)
flexure.grd !Moho
outg.grd ! gravity output
0 !again(1)
Input files examples:Input file for invertonly.for (invertonly.inp):
dx, dy, nn(1), nn(2), pmin, basex, basey
4., 4., 350, 276, 100., 40, 40
d, rhov
22, -.5
First step: describe given fields and maps
• Use program surfer• overlay field maps with
topograhy/bathymetry• Topo-contour: create only
one level (0-2500m), color= yellow. Bring to front
• Modify color-scale: contours-levels-level and fill.
• Change foreground colors.• Alos: use *.lvl files
1) create maps of observed gravity anomaly and Bouguer gravity. Save maps. Give short description of properties of fields.
2) Make map of ETOPO5 topography/bathymetry
Gravity anomaly
ETOPO5
Bouguer
37800 38000 38200 38400 38600 38800 39000
(km )
600
800
1000
1200
1400
1600
(km
)
-20
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
340
m gal
10
15
110 115 120
Bouger fie ld
Second step: estimate of crust-mantle interface undulations
• Downward continuation: invertonly.exe
• check input file with editor
• Test 3 different cut-off wavelengths: 200, 100,50 km
1)Downward continuation of Bouguer gravity field
-parameters:
reference depth= 22 km
density contrast= - 0.5 103 kg/m3
Cut-off wavelength=100 km
2) Describe features of CMI. Save plot. (Overlay with topography for orientation).
Input files examples:Input file for invertonly.for (invertonly.inp):
dx, dy, nn(1), nn(2), pmin, basex, basey
4., 4., 350, 276, 100., 40, 40
d, rhov
22, -.5
Moho from inversion
37800 38000 38200 38400 38600 38800
(km )
800
1000
1200
1400
1600(k
m)
1112
99
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
km
10
110 115
Inversion Moho
Third step: apply load to flexural isostasy model
• Flexure: modflex.exe• check input file with editor• Test different Te’s • Te=0, 3, 10, 30, 60 km
• In surfer: calculate difference between the the gravity and flexure CMI:– Grid-math– plot residual. Reduce min-max
contours. Take notice of border-effects– use grid-editor to find specific values
on grid.
1)Flexure loading: calculate the flexure of thin plate model with topographic load. Test different values of Te.
-parameters:
reference depth= 22 km
density contrast= - 0.5 103 kg/m3
2) Describe features of flexure-CMI. Save plot. (Overlay with topography for orientation).
Modello Te
37800 38000 38200 38400 38600 38800
(km )
800
1000
1200
1400
1600(k
m)
1
3
5
7
9
11
13
15
17
19
km
10
110 115Elastic th ickness
Moho from flexure model
37800 38000 38200 38400 38600 38800
(km )
800
1000
1200
1400
1600
(km
)
1112
99
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
km
10
110 115
Flexure Moho
Difference between gravity and flexure Moho
37800 38000 38200 38400 38600 38800
(km )
800
1000
1200
1400
1600
(km
)
-4
-3
-2
-1
0
1
2
3
4
km
10
110 115
Residual Moho
Fourth step: calculate gravity field of flexure CMI
• Gravity field: parker.exe
• check input file with editor
• In surfer: calculate difference between the the Bouguer gravity and flexure CMI. Where are the greatest anomalies. Give some clues to the reasons.
1)calculate gravity of flexure:
-parameters:
reference depth= 22 km
density contrast= 0.5 103 kg/m3
2) Describe features of gravity field and of residual. Save plot. (Overlay with topography for orientation).
Parker.for input file
input file for program parker.for
22.,0.5 !ref.depth (km), density (g/cm3)
flexure.grd !Moho
outg.grd ! gravity output
0 !again(1)
Fifth step: observed anomaly minus gravity of flexure CMI
• Calculate residual between gravity anomaly and field of flexure CMI. What can we obtain from the inversion of this residual?
• Describe features of gravity field and of residual. Save plot. (Overlay with topography for orientation).
Sixth step: downward continue the residual from step 5
• Invert the residual gravity field. This gives a first order approximation of the bathymetry.
• Compare the resulting bathymetry with the bathymetry from ETOPO5.
• Save the plots. Overlay land-areas on plot.
• Describe results. Where are the greatest dicrepancies?
• What are the short-wavelength differences due to?
• Notice the feature along the rift.
Input file for the downward continuation of the bathymetry
Input file for invertonly.for (invertonly.inp):
dx, dy, nn(1), nn(2), pmin, basex, basey
4., 4., 350, 276, 8., 40, 40
d, rhov
0, -1.64
Residual gravity ready for inversion of bathymetry
Inverted bathymetry. Should be integrated with ship-tracks.
Profile AA’
0 200 400 600 800profile AA' (km )
-5000
-4000
-3000
-2000
-1000
0
(m)
-100
0
100
200
300
400
(mga
l)
gravity
Bathym etry
0
20
40
(km
)
flexure
gravity
Bouguer
F lexure
Free a ir
Inversion
Sandw ell
E topo5
ship
CMI
S N
Discussion• The flexure-CMI gives a physical model of the long-
wavelength component of the gravity field. It gives an alternative to the “remove-restore” method.
• It is apt where there are control points for the Moho. • Improvements in the “real application”:
– spatially varying Te– replace downward continuaton with inversion process.
Downward continuation gives only an approximation.– Use model of sediment thickness variations.