Velocity estimation after removing offsets from the time series

To estimate the plate velocities we need to remove the coseismic displacements due to the SISZ 2000 earthquake sequence. By removing the coseismic displacements from the time series the resulting velocities are representing the interseismic velocities at the stations. Those velocities are expected to decrease when approaching a central axis of a plate boundary because most of the displacement within the plate boundary deformation zone is accommodated with coseismic displacements or rifting (see Figure 21).

 

Table 7: Calculated velocities of the stations in east, north and up, relative to REYK, using data from the beginning of measurements at each station until December 31, 2001. Offsets due to radome installation and the June 2000 SISZ earthquake sequence have been removed from the data before the velocities are calculated, except at HLID* where it is not possible to estimate the coseismic displacements. See Table 6 for explanation of the columns.

		Velocities [mm/yr]			Uncertainties [mm/yr]			WSTD [mm]			Chi squared
Station	N	Ve	Vn	Vu	dVe	dVn	dVu	e	n	u	$\chi^{2}_{\nu e}$	$\chi ^{2}_{\nu n}$	$\chi^{2}_{\nu u}$
AKUR	102	-5.5	4.9	3.0	2.5	3.1	12.8	1.3	1.7	7.0	1.7	1.2	1.8
HLID*	460	22.0	-2.5	11.5	0.4	0.2	0.7	3.1	1.3	5.5	10.1	0.7	0.9
HOFN	873	20.3	-5.7	8.9	0.2	0.2	0.6	2.7	2.0	7.0	3.3	1.6	1.4
HVER	914	5.9	-0.5	3.4	0.1	0.1	0.5	1.4	1.6	5.6	2.1	1.0	0.9
HVOL	635	17.8	-7.7	9.2	0.3	0.3	0.9	2.3	2.3	7.0	4.2	2.1	1.4
KIDJ	330	10.2	2.5	5.4	0.4	0.5	2.0	1.0	1.1	4.8	1.3	0.7	0.9
OLKE	814	1.6	-0.4	4.7	0.1	0.2	0.6	1.6	1.8	5.6	2.7	1.5	1.0
RHOF	128	18.0	0.1	-6.2	2.5	2.8	10.5	1.6	1.8	7.1	1.8	1.1	1.6
SKRO	416	2.7	1.1	16.1	0.5	0.5	2.4	1.8	1.6	8.4	3.1	1.4	2.7
SOHO	696	16.8	-7.7	5.6	0.3	0.4	0.9	2.5	3.4	6.8	4.8	4.5	1.3
THEY	500	20.9	-5.0	3.2	0.3	0.4	1.3	1.4	1.9	6.4	2.1	1.8	1.5
VMEY	497	20.0	-6.1	3.8	0.3	0.3	1.1	1.3	1.3	5.1	1.8	0.9	0.9
VOGS	925	15.9	-3.0	7.0	0.1	0.1	0.4	1.8	1.4	5.0	3.2	0.8	0.7

 

In the second set of velocities (Table 7) they are calculated in the same manner as in Table 6, except the offsets due to the June 2000 earthquake sequence have been removed from the time series before estimating the velocities. The coseismic offsets are estimated by differencing the average coordinates of the stations approximately 10 days before and after the earthquakes - see Section 4.6 and Table 9 for details. It was not possible to calcuate the coseismic displacements at HLID since the station had not been in operation several months before the earthquakes, reflected as a large gap in the time series. For the stations which were not operational before the June 2000 earthquake sequence (AKUR, KIDJ, RHOF, SKRO and VMEY), the results in Table 7 are excactly the same as in Table 6.

The results in Table 7 generally agree with the NUVEL-1A plate motion model (Figures 24 and 25). The largest discrepancies between the observed and predicted velocities are observed in the Mýrdalsjökull area. This could be due to a pressure increase below the Katla caldera and will be discussed in more detail in Section 4.4. From Figure 24 it seems like the Eastern volcanic zone is taking up much of the spreading between the North-American and Eurasian plates because SKRO is moving with the North-American plate, as suggested in previous studies [Sigmundsson et al. (1995)]. A denser network with stations on both sides of the Western and Eastern volcanic zones is needed to give a more complete picture of how the plate spreading is divided between the two volcanic zones. The reference station REYK is on the North-American plate along with OLKE, SKRO and AKUR moving WNW at velocities similar to the predicted NUVEL-1A velocities. The stations RHOF, HOFN, HVOL, SOHO, THEY, VMEY and VOGS are on the Eurasian plate moving towards ESE or SE. The stations HVER and KIDJ are within the plate boundary deformation zone moving at intermediate velocities (Figure 25).

The velocity uncertainties stated in Table 6 are rather small, at least for the longer time series, as we already expected (Section 4.2.1). The horizontal velocity uncertainties for VOGS are 0.15 mm/yr east and 0.12 mm/yr north. According to [Sella et al. (2002)] the velocity uncertainties for a site with three years of data should be of the order of 1-2 mm/yr in the horizontal components. Their data processing is done on a global scale, whereas the ISGPS processing is on a local scale and coordinates are expected to be more precise. However, it is not likely that the different scales of the networks result in a factor 10 in the velocity uncertainty estimates.

The WSTD and $\chi^{2}_{\nu}$ values in Table 4 generally have lower values in Table 7 than in Table 6, except for station HLID which still includes the offsets from the earthquakes. Generally the standard deviation of the residual (WSTD) is lowest in the east and north components and highest in the vertical component. KIDJ has the lowest standard deviation of the residuals, 1.0 mm, 1.1 mm and 4.8 mm in east, north and up respectively. It is evident that the time series for KIDJ (Figure 13) is well behaved, in the sense that a straight line fits well to the data. This is also reflected in the $\chi^{2}_{\nu}$ values for KIDJ.

The $\chi^{2}_{\nu}$ values are strongly dependent on the scaling factors (Section 3.1). The scaling factors obtained in Section 3.1 differed between stations and also between coordinate components. Thus the choice of a single scale factor for all the stations is likely to affect the $\chi^{2}_{\nu}$ values in Tables 6 to 8. In Section 3.1 the same scale factor was chosen for the east and north components although Table 4 indicates that the scale factor should be slightly higher for the east component. This would cause smaller $\chi^{2}_{\nu}$for the east component. The time series (Figures 8 to 20) show that at some stations, like HOFN and VOGS, a straight line does not represent the data in the east component (see also Figure 6). There are some stations with $\chi^{2}_{\nu}$ below 1 in the north and vertical velocity components indicating that the scaling factor is too large for those stations. Stations SOHO and HVOL have unusually high standard deviation of the residuals and $\chi^{2}_{\nu}$ values for the horizontal components in Table 7. This is probably caused by the deformation signal due to the Hekla eruption (Figures 12 and 17, Section 4.5).

  

Figure 24: Velocities for the permanent GPS stations, as in Table 7, assuming REYK is moving at velocity 9.6 mm/yr west and 2.1 mm/yr north (black arrows) compared to the NUVEL-1A plate motion model velocities (orange arrows). The velocities are based on data without the offsets caused by the June 2000 earthquakes. Confidence limits are at the 2$\sigma$ level.

  

Figure 25: As in Figure 24 for the Hengill area. The observed motion of HLID is not shown here since the time series for HLID include coseismic offsets due to the June 2000 earthquake sequence.