- Ground-motion model is: where Y is in cm∕s2, τ is inter-event variability, a = 3.90119, c1 = -1.5472, c2 = 0.203801, h = 6.78654,
b1 = 0.157748, b2 = -0.0375241, b3 = 0, e1 = 0, e2 = 0.183962, e3 = 0.265793, e4 = 0.223751, f1 =
-0.0467904, f2 = 0.0184746, f3 = 0, Mref = 5.5, Mh = 6.75, Rref = 1;
τ1 = 0.311636, τ2 = 0.180874, τ = 0.171510 (homoscedastic) and ϕ = 0.305205 for repi; and τ1 = 0.299730,
τ2 = 0.177908, τ = 0.170688 (homoscedastic) and ϕ = 0.303741 for rjb.
- Use 4 Eurocode 8 site classes (to be able to use most about of French data):
- FA = 1, FB = FC = FD = 0.
- FB = 1, FA = FC = FD = 0.
- FC = 1, FA = FB = FD = 0.
- Poorly represented compared to other classes. FD = 1, FA = FB = FC = 0.
Note that many French and other stations lack measured V s,30. 40% of records have V s,30. Try regressing
using a continuous V s,30-based site term and find negligible differences in terms of σ.
- Use 3 styles of faulting:
- Most data. EN = 1, ER = ES = 0.
- Second most data. ES = 1, EN = ER = 0.
- About half of normal events. ER = 1, EN = ES = 0.
- Use data from RESORCE-2013 database. Focus of study is French (432 records from 65 events) and Swiss
- Note that metadata from small events generally less accurate in terms of Mw and fault mechanism. Swiss
data are reliable because of time-domain moment-tensor inversion. Seek to obtain consistent Mw for French
data from previous studies but some uncertainty and potential slight overestimation. Mechanisms from
literature or from dominant stress regime and seismotectonic zonation. Note that this is a rough approach.
- Exclude data from: events with depth > 30km, repi > 200km, Mw < 3, stations that are known not to
be in free-field (e.g. from galleries or dams), bad-quality records or those lacking a horizontal component,
stations without V s,30 or site class, events with only converted Mw, singly-recorded events and records
filtered with low-pass corner frequency ≤ 20Hz and for each period records with high-pass corner frequency
- Most data with M > 4 from Italy and Turkey, with smaller amount from Greece. Most smaller events are
from France and Switzerland.
- Do not include anelastic attenuation term because not statistically different from zero.
- Choose Mref = 5.5 because it is close to 50th percentile of cumulative number of records v. Mw.
- Use Mh = 6.75 based on previous studies and by inspection of plots of magnitude scaling. Note that lack
of data from Mw > 6.5 so magnitude scaling poorly constrained. Find that when b3 is constrained to be
non-negative it is found not to be statistically significant so constrain it to zero in final regression. Note
that no magnitude oversaturation is found.
- Do not consider other terms (e.g. hanging/foot wall, depth to top of rupture) due to lack of information.
- Do not find any bias or trends in inter-event residuals w.r.t. Mw nor in intra-event residuals w.r.t. R. Do
not find evidence for regional dependency between French intra-event residuals and other regions, which
note may be due to lack of data. Do not find evidence for trend in intra-event residuals w.r.t. κ0 estimated
in previous studies.
- Find large variability in residuals from French and Swiss data at small magnitudes. Find inter-event
residuals correlated with stress parameter and different groups of residuals for different parts of France
and Switzerland: Swiss Alps and Foreland; French Alps and Rhine Graben; and Pyrenees. Derive an
empirical correction for the base-case model that is a function of the stress parameter based on the model
of Yenier and Atkinson (2015b), which find to match observations at small magnitudes. Find reductions
in inter-event variability for French and Swiss small-magnitude events because of this correction. Find
reduced magnitude-dependency of τ because of this correction.
- Compute ϕSS for all stations and only considering French stations when each stations has ≥ 5 records.