- Ground-motion model is:
where PSA(f) is in m∕s2, a = -5.08210, b = 2.06210, c = -0.11966, d = -0.00319, e = 0.00488, S = -0.01145
and σ = 0.32257 for borehole stations (S applies for stations at 200m) and a = -4.884, b = 2.18080, c = -0.12964,
d = -0.00397, e = 0.01226, SB = 0.16101, SC = 0.27345, SD = 0.45195 and σ = 0.35325 for surface
Experiments on magnitude dependency of decay and σ reported below conducted using:
Do not report coefficients of these models.
- Use four site classes (based on Eurocode 8) for surface stations:
- V s,30 > 800m∕s.
- 360 < V s,30 < 800m∕s. Use coefficient SB.
- 180 < V s,30 < 360m∕s. Use coefficient SC.
- V s,30 < 180m∕s. Use coefficient SD.
- Use data from boreholes to reduce influence of nonlinear site effects for investigating magnitude-dependent
decay. Also derive models using surface records.
- Only use data from < 100km.
- Only retain events with depth < 25km to exclude subduction earthquakes.
- Note relatively good magnitude-distance coverage.
- Visually inspect records to retain only main event if multiple events recorded and to check for glitches.
Bandpass Butterworth (four poles and two passes) filter records with cut-offs 0.25 and 25Hz. Longest
usable period of model is less than 3s due to filtering.
- Derive equations using data from small (Mw ≤ 5) earthquakes (3376 records from 310 events) and large
(Mw ≥ 5) earthquakes (518 records from 27 events) to examine ability of models to predict ground
motions outside their magnitude range of applicability. Find ground motions from small events attenuate
faster than from large events. Predict ground motions for Mw 4.0, 5.0 and 6.5 and 10, 30 and 99km.
Find overestimation of ground motions for Mw4.0 using model derived using data from Mw ≥ 5 and
overestimation of ground motions for Mw6.5 using model derived using data from Mw ≤ 5. Predictions
for Mw5.0 are similar for both models. Also compare predictions from both models and observations for
Mw4.1, 4.6, 5.2, 5.7, 6.5 and 7.3 and find similar results.
- Also derive models for 11 magnitude ranges: 4.0–4.2, 4.2–4.4, 4.4–4.6, 4.6–4.8, 4.8–5.0, 5.0–5.2, 5.2–5.4,
5.6–5.8, 5.8–6.8 and 6.8–7.3. Compare predictions with observations for each magnitude range and find
good match. Find that decay rate depends on Mw with faster decay for small events. Plot σs from each
model w.r.t. Mw and find that it has a negative correlation with Mw.
- Examine residuals w.r.t. distance. Find slight increase at large distances, which relate to magnitude
dependency of attenuation.
- Note that goal of analysis was not to compete with existing models but to compare magnitude dependency
of ground motions at depth and surface.
- Examine residuals w.r.t. distance and magnitude of final model. Find no trends.
- Find that σs for surface motions are larger (by about 9%) than those for motions at depth.