Annual cycles in deformationEinar Ragnar Sigurðsson

Leveling lines: monitoring of Katla

• Eysteinn Tryggvason in two time periods:1967-19731986-1995

• Monitoring of underground processes preceding eruption in Katla

Ref. Tryggvason, 1973

Signal from leveling observation

• Amount of yearly tilting 1.4 to 4.5mrad• Direction changing

every year

Ref. Tryggvason, 1973

Possible causesof annual variations• Atmosphere changes• Soil moisture and groundwater variation• Temperature variations • nontidal ocean loading• Variation in ice and snowload

Ref. Tryggvason, 1973 and Geirsson et al, 2006

Simple model for variable snow load Use of various data• Precipitation data from the nearest

weather stations• Increased precipitation with elevation• Temperature profile same as measured at

Keflavik

clear correlation• Little or none time delay• Calculated R coefficient for correlation:

highest for 0 days delay, R=0.63• Elastic plate over a liquid substratum

modeling gave plate thicknes 6.8 to 8.5km• 99% confident the seasonal leveling is true

and not caused by magmatic movements

Ref. Tryggvason, 1973 and Tryggvason, 2000

GPS network• First station in year

1995• Monitoring of

crustal movements related to:• Plate spreading• Magmatic

movements • Earthquakes

They show annual cycles in deformation as well.

Ref. Geirsson et al, 2006

A cosinus model for crustal displacement

• The varying position, function of time in years: y(t)

• Initial position: a• Linear trend: b*t• Annual factor for cycles in

deformation:Amplitude: Aperiod: 2ptphase:

Ref. Geirsson et al, 2006

Skrokkalda (SKRO) rel. to REYK, uplift

Year

mm

Elastic half space and Green’s functionsFor an elastic halfspace after having convolved Green’s functions with the load we have the horizontal and vertical displacement as:

at a point ȓ. The variables are r for the density of a load with thickness h integrated over the area R making the load. Poisson ratio is taken to be n = 0.25 and g is the gravity acceleration

Ref. Grapenthin et al, 2006

Snow load on each glacier

• Constant load over each glacierVatnajökull, Mýrdalsjökull, Hofsjökull and Langjökull

• Good data of snow (water equivalent) thickness• Raster size for modeling area of glaciers: 50x50m

Ref. Grapenthin et al, 2006

The variable snow loadthe snow load is taken to be of constant thickness over each glacier but varying with time. So the ice load thickness at a point ȓ‘ at time t is:

where thm is the phase for maximum ice thickness and hm is the maximum ice thickness and

With this equation for h and the other two for displacement used with data for displacement from CGPS stations, the only unknown, free parameter will be the Young modulus E.

Ref. Grapenthin et al, 2006

Young modulus E

Ref. Grapenthin et al, 2006

The model fit

Ref. Grapenthin et al, 2006

HÖFN-REYK SAUD-REYK

SOHO-REYK SKRO-REYK

Annual displacement cycle according to the model• Maximum vertical

displacement in center of Vatnajökull: 37mm• Maximum horizontal

displacement on east end of Vatnajökull: 6mm• Note the low horizontal

displacement areas on the three smaller glaciers on side to Vatnajökull

Ref. Grapenthin et al, 2006

Possible improvements of the model

• The uniform thickness of snow load on glaciers• The same

melting and accumulating time -> cosinus function is not the best model• Other seasonal

causes of deformation

Ref. Grapenthin et al, 2006 Ref. Veðurstofa Íslands, 2013

References• Geirsson, H., T. Árnadóttir, C. Völksen, W. Jiang, E. Sturkell, T. Villemin, P. Einarsson, F.

Sigmundsson, and R. Stefánsson (2006), Current plate movements across the Mid-Atlantic Ridge determined from 5 years of continuous GPS measurements in Iceland, J. Geophys. Res., 111, B09407, doi:10.1029/2005JB003717.

• Grapenthin, R., F. Sigmundsson, H. Geirsson, T. Árnadóttir, and V. Pinel (2006), Icelandic rhythmics: Annual modulation of land elevation and plate spreading by snow load, Geophys. Res. Lett., 33, L24305, doi:10.1029/2006GL028081.

• Tryggvason, 1973. Surface Deformation and Crustal Structure in the Mýrdalsjökull Area of South Iceland. Journal of geophysical research, vol 78, No 14, p. 2488 – 2497.

• Tryggvason, 2000. Ground deformation of Katla: Result of precision levellings 1967-1995. Jökull No 48, p. 1-8

• Vedurstofa Íslands, 2013. http://brunnur.vedur.is/myndir/harmonie/ downloaded 22.04.2013