Bathymetry on software

Meeresspiegeländerungen und Batimetrie aus

Satellitenbeobachtungen

FU Berlin, Januar 2003Carla Braitenberg

Dipartimento Scienze della Terra, Università di Trieste, Via Weiss 1, 34100 Trieste

Berg@units.itTel +39-040-5582258 fax +39-040-575519

Übungen am Rechner.

Program-Exercizes on PC:

• 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.