- Ground-motion model is
where PGA is in g, a = -2.26, b = 1.28, c = -2.85, d = -0.0437, e = -d∕a = -0.0194, g = -b∕a = 0.569, k = 0.0309 and σ = 0.302.

- Detailed information on site conditions is not available hence do not include site terms in model.
- Focal depths between 0.04 and 9.49km with most ≤ 6km.
- Use data from SIL national seismic network (3-component velocimeters) converted to acceleration. Most instruments are short-period Lennartz sensors (7 with corner frequency of 1Hz and 35 with corner frequency of 0.2Hz). 6 to 8 broadband sensors (CMG-3T, CMG-40T, CMG-ESP and STS2 with corner frequencies at 0.008 and 0.033Hz). Full-scale amplitude of stations between 0.3cm∕s and 1.25cm∕s. Hence, at near-source distances records are often saturated and unusable. Most data have sampling rate of 100Hz but some records are sampled at 20Hz. First, remove instrument response. Next, high-pass filter (for short-period records use cut-off of 0.15Hz and for broadband used 0.1Hz). Finally, differentiate velocity to obtain acceleration. Do not use data sampled at 20Hz nor data from distances > 100Hz from Lennartz 1Hz sensors.
- Note that magnitudes of earthquaks with M > 3 are generally underestimated by SIL system, which is
designed to monitor microseismicity. Therefore, use 5 of 6 largest earthquakes with teleseismic (Global
CMT) M
_{w}estimates to calibrate the local moment magnitudes M_{Lw}used for study. - Develop model for use in ShakeMap and real-time aftershock hazard mapping applications.
- Most earthquakes from the Hengill region in 1997 and 1998. 7 are on Reykjanes Peninsula and 6 in the South Iceland Seismic Zone (mainly from sequence in 2000, which provides three largest earthquakes used).
- Note that model of Ágústsson et al. (2008) is significantly flawed. Use same data but remove data from Reykjanes Ridge and Myrdalsjokull because of uncertainties in magnitude estimates for these earthquakes.
- Data selected based on magnitude and number and quality of usable waveforms.
- Most data from M
_{Lw}≤ 5 and r_{epi}> 20km and distribution shows effect of saturation of records for larger (M_{Lw}> 5) earthquakes for r_{epi}< 20km. Correlation coefficient between M_{Lw}and log r_{epi}is 0.24. 39% of data is from 5 to 50km. - Also derive most using simpler functional form: log
_{10}(PGA) = -2.08log_{10}(r)-0.0431M^{2}+1.21M -2.96 with σ = 0.304. - In SW Iceland large earthquakes usually occur on NS faults. Hence, examine effect of radiation pattern. Add radiation pattern variable to model so that all earthquakes were assumed to take place on NS-striking vertical strike-slip faults. Find that, as predicted by theory, the coefficient multiplying this term was close to unity and standard deviation was significantly reduced. However, find that this term led to worse fit for some earthquakes and so it was dropped.
- Examine effect of instrument type using residual plots. Find that data from Lennartz 1Hz sensors and Nanometrics RD3 0.5Hz digitizers from > 100km were lower than predicted, which led to them being excluded.
- Find that observations from hve station are consistently lower than predicted, which relate to strong attenuation in Western Volcanic Zone. Make similar observations for ada, bru and mok, which relate to propagation through crust and upper mantle of Eastern Volcanic Zone. Find data from snb station is consistently higher due to strong Moho relections from Hengill region earthquakes at about 130km.
- Try form log
_{10}(PGA) = alog_{10}+ bM + c but find very small k. Also try form of Fukushima and Tanaka (1990) but find higher standard deviations. - Discuss the theoretical basis of coefficient g and its constraints w.r.t. a and b. Initial regression with g as free parameter led to coefficients very close to g = -b∕a (PGA independent of M at source) and, therefore, impose this as constraint.
- Try weighted regression to correct for uneven magnitude and distance distribution but these are dropped since data follows magnitude distribution expected in SW Iceland and also run risk of putting too much emphasis on erroneous recordings.
- Find that residuals are approximately normally (in terms of log
_{10}) distributed, using normal Q-Q plots. - Compare predictions and observations for some magnitude ranges and for each earthquake grouped by geographical region.
- Fit log
_{10}(PGA) = alog r_{epi}+… using only data from < 150km and M_{Lw}> 4.7 and find a = -1.70. Relate difference in distance scaling to lack of far-field data. - Believe that model can be used between 0 and 380km.