The initial stress field

The initial stress field is determined as follows: A tensional stress acting N103$^\circ$E (nearly parallel to the SISZ; cf. DeMets et al. 1990) is assumed, due to ridge push or basal drag of the adjacent plates. This rifting induces shear stresses in the region of the transform fault. The stress magnitude, which is unknown, is set to a value that produces left-lateral shear stresses in E-W direction as large as the stress drop determined for the largest event (M=7.1) in the studied earthquake sequence.

Tensional stresses at both ridges are modelled as constantly being released to have zero values at the rifts. These are the major disturbances of the unknown background stresses.

On this initial field, the stress changes due to earthquakes are iteratively superposed as well as the stress changes due to further spreading at the ridge segments based on an opening of 2 cm/year. This value is taken from DeMets et al. (1990). As the simplest assumption, lacking other data, the spreading rate is taken to be constant during the modelled time period, even though this can be questioned as for instance the present debate on the stress increase in the New Madrid seismic zone shows.

The stress field before every event is thus the sum of the initial field, the stress drop of all preceding events, and the plate tectonic stress build-up since the starting time of the model, which is set to 1706, when the first event in the series occurred.

Results were calculated for 56x44 test-points covering 280 km in E-W direction and 220 km in N-S direction. Stresses were computed for a homogeneous half-space, as a starting model. Although surface stress changes are calculated, these should be representative for crustal stresses using values for the moduli, that are typical for oceanic crust [19] and not for sedimentary layers at the surface.

 

Table: Earthquakes M$\ge$6 since 1706 in the South Iceland seismic zone. 1) Data taken from Stefánsson et al. 1993. 2) Position in the model coordinate system with origin at 64$^\circ$N, 24$^\circ$W. 3) Calculated via the magnitude moment relationship $\log M_0$ [dyne cm] $= 1.5M_S - (11.8 - \log(\sigma_a/\mu))$ with the apparent stress $\sigma _a = 150$ MPa and the shear modulus $\mu =0.39\cdot 10^{11}$ Pa [37], followed by using the values of $\mu$ above, the rupture length as given in the table as well as a vertical fault width of 14 km east of 21$^\circ$W and 7 km between 21$^\circ$W and 21.2$^\circ$W. Finally, the values were reduced by a factor of 2, following the discussion in Hackman et al. 1990. 4) Calculated using $\log L$ [km] = 0.5 M -2 [40] which results in slightly lower values compared to e.g. Schick 1968.

Date1	Magnitude1	Epicenter1		South end of		Co-seismic	Rupture
				rupture2		slip3	length4
		Lat. $^\circ$N	Long. $^\circ$W	x [km]	y [km]	U0 [m]	L [km]
1706	6.0	64.0	21.2	131	-5	0.30	10
1732	6.7	64.0	20.1	183	-11	0.77	22
1734	6.8	63.9	20.8	150	-23	0.96	25
14.08.1784	7.1	64.0	20.5	164	-18	1.9	35
16.08.1784	6.7	63.9	20.9	145	-22	0.77	22
26.08.1896	6.9	64.0	20.2	178	-14	1.2	28
27.08.1896	6.7	64.0	20.1	183	-11	0.77	22
05.09.1896	6.0	63.9	21.0	140	-16	0.30	10
05.09.1896	6.5	64.0	20.6	159	-9	0.48	18
06.09.1896	6.0	63.9	21.2	131	-16	0.30	10
06.05.1912	7.0	63.9	20.0	187	-27	1.5	32