- Ground-motion model for shallow crustal is: and for upper mantle: where and y is in g, mc = 7.1 (from previous studies), Cmax = mc, c2 = 1.151 (from magnitude-fault length
relations), c1 = -3.224, c2 = 0.900, ccr = 1.0731, dcr = 0.200, FCRN = 0.3128, FumRV = -0.2024,
FumNS = 0.2519, bcr = 0.00907, gcr = -1.2603, gUM = -1.0999, gcrN = -0.4992, gcrL = 1.2656,
ecr = -0.00794, eum = -0.01083, ecrv = -0.00628, γcr = -9.0872, S2 = 0.2888, S3 = 0.1221,
S4 = 0.2081, σ = 0.556 (intra-event), τ = 0.391 (inter-event) and σT = 0.680 (total).
- Use 4 site classes (T is natural period of site):
- Rock, NEHRP site classes A+B+C, V s,30 > 600m∕s, T < 0.2s. 1968 records from crustal, 979 records
from upper mantle.
- Hard soil, NEHRP site class C, 300 < V s,30 ≤ 600m∕s, 0.2 ≤ T < 0.4s. 1064 records from crustal,
562 from upper mantle.
- Medium soil, NEHRP site class D, 200 < V s,30 ≤ 300m∕s, 0.4 ≤ T < 0.6s. 371 records from crustal,
137 from upper mantle.
- Soft soil, NEHRP site classes E+F, V s,30 ≤ 200m∕s, T ≥ 0.6s. 612 records from crustal, 264 from
Originally included some data from sites with inferred site classes but after initial testing excluded these
data as less reliable. Use site terms derived in previous studies that account for nonlinear response (see
article for details).
- Use 3 styles of faulting:
- 35 (2096 records) crustal and 26 (1021 records) upper-mantle earthquakes. Use FumRV .
- 17 (973 records) crustal and 5 (209 records) upper-mantle earthquakes. Use FumNS.
- 18 (946 records) crustal and 16 (712 records) upper-mantle earthquakes. Use FcrN for shallow
crustal and FumNS for upper mantle. Note that all crustal normal events occurred following Tohoku
earthquake in a small region and hence the applicability to other regions is not clear.
Find reverse and strike-slip events are statistically similar for shallow crustal events and strike-slip and
normal similar for upper mantle events (at 5% level).
- Partner model to those of Zhao et al. (2016a) and Zhao et al. (2016b). See Section 2.418 for details of
the data used and the approach.
- Choose functional form based on physics of earthquakes and previous studies. Remove term if not significant
at 5% level.
- Use data from shallow crustal (fault-top depth < 25km, 70 events) and upper-mantle (fault-top depth
25 ≤ h ≤ 64km, 47 events) earthquakes.
- Use some near-source data from outside Japan to derive magnitude-scaling for Mw > 7.1 and terms
controlling near-source spectrum.
- Exclude records below a straight line in magnitude-distance plot (Mw5.0-x = 124km to Mw7.3-x = 300km)
to avoid effects from untriggered stations. Data well distributed w.r.t. magnitude and distance. No
upper-mantle earthquakes with Mw > 7.
- Introduce xcro to avoid magnitude-distance oversaturation.
- Use term gcrL log e(x + 200) to avoid a positive anelastic attenuation rate. Choice of 200km as constant
significantly improves fit but note that it does not have a physical justification.
- Introduce term gN to eliminate near-source bias for Japan, which is related to use of foreign data to
constrain large-magnitude/near-source terms in model.
- Note that difficult to split variability into intra-site and inter-site as well as inter-event for many records.
Use approximate technique to compute these components.
- Find that predicted spectra from shallow-crustal and upper-mantle models differs by a factor up to
1.47 when evaluated for a depth of 25km. Propose depth-scaling functions: Scr = 1.0 for h ≤ h1,
Scr = (h2 - h)∕(h2 - h1) for h1 < h ≤ h2 and Scr = 0.0 for h > h2; and Sum = 0.0 for h ≤ h1,
Sum = (h - h1)∕(h2 - h1) for h1 < h ≤ h2 and Sum = 1.0 for h > h2; with h1 = 20km and h2 = 30km to
obtain continuously varying spectra as a function of depth, if required.
- Attempt to model hanging wall effect but insufficient data from Japan to obtain reliable results.
Recommend using models from California and then calibrated with Japanese data, if required.
- Believe model more suitable for soil sites with low impedance ratios (i.e. < 3) than for sites with high