Gravity inversion and isostasy- an integrated system. Trieste, 17-20. February 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. Topics. Different aspects of isostasy:
Trieste, 17-20. February 2003
Dipartimento Scienze della Terra,
Università di Trieste, Via Weiss 1, 34100 Trieste
Tel +39-040-5582258 fax +39-040-575519
E = 1011 N/m2
An arbitrary topography can be built as the sum of sine-functions (Fourier-Transormation)
The flexure of the plate is then :
With very low flexural rigidity or for small wave-numbers (great wave-lengths) the regional isostasy goes into the Airy Isostasy:
With very high rigidity or for small wave-numbers (small wave-lengths) the load does not deform the plate.
Maximum ice-thickness during LGM in scandinavia and North-America estimated to max 2000-2500 m (Lambeck and Chappell, 2001).
Gives: r of 600-760 m
In occasion of a measured sealevel fall of about
120 m, you obtain r of 40m.
The hydro-isostatic effect of MSL-change is then:
The comparison with the observations in the Mediterranean shows that the hydro-isostatic effect calculated in the Airy model is over-estimated.
Lambeck and Bard, 2000
(Lambeck and Bard, 2000)
Flexure of the crust/lithosphere in frequency space related to topography:
Problems in recovering H(k):
Low spectral energies in topography
Poor spatial resolution caused by required window size in spectral analysis
Limitations posed by rectangular window
Flexure point load response
Obtained from inverse FT of flexure transfer function
Load: refers to total load, being the sum of surface and subsurface load.
Lburied inner-crustal loads, hi thickness of the i-th layer, i density of the i-th layer and c the density of the reference crust.
Equivalent topography: total load divided by reference density
Sampling (dr in km)
Number of elements along the baselength of the square grid (N)
Minimum filter extension (Rmax in km) required to reach percentage point 10% and 1% of the maximum value of the impulse response
Te f0 (1/km) dr (km) N Rmax (km) Rmax (km)
1 4.00 10-25 500 19 42
2 2.38 10-25 841 33 68
5 1.20 10-210 836 65 135
10 7.11 10-315 938 105 230
20 4.23 10-320 1183 180 400
30 3.12 10-320 1604 245 520
40 2.51 10-330 1326 310 650
50 2.13 10-330 1568 360 760
60 1.85 10-330 1798 400 870
given load and Te spatial variation: obtain expected flexure
given load and observed CMI variation: obtain spatial variations of Te
Resolution: 5 km
Size of Moho: 550 km by 500 km
On square overlapping windows: for Te=0,...30 km (dTe = 0.5 km) calculate difference between flexure and synthetic Moho
Choose Te that minimizes rms
Moho Grid: 550km by 500km.
Topo: enlarged grid 1200km by 1500 km
Te-input model: constant on 15km by 15km cells
Moho with noise: noise has rms with 5% of maximal excursion
Final Te resolution in space: 30-45 km