- Ground-motion model is:
where y is in m∕s2, for horizontal PGA b1 = -0.659, b2 = 0.202, b3 = -0.0238, bA = 0.020, bS = 0.029 and
σ = 0.214 and for vertical PGA b1 = -0.959, b2 = 0.226, b3 = -0.0312, bA = 0.024, bS = 0.075 and
σ = 0.270.
Assume decay associated with anelastic effects due to large strains and cannot use both log d and d because
highly correlated in near field.
- Use four site categories (often use shear-wave velocity profiles):
- Very soft soil: approximately V s,30 < 180m∕s, (combine with category S) ⇒ SA = 0,SS = 1, 4
- Soft soil: approximately 180 ≤ V s,30 < 360m∕s ⇒ SA = 0,SS = 1, 87 records.
- Stiff soil: approximately 360 ≤ V s,30 < 750m∕s ⇒ SA = 1,SS = 0, 68 records.
- Rock: approximately V s,30 > 750m∕s ⇒ SA = 0,SS = 0, 23 records.
where V s,30 is average shear-wave velocity to 30m. Know no site category for 14 records.
- Use only records from ‘near field’ where importance of vertical acceleration is greatest. Select records with
Ms ≥ 5.8, d ≤ 15km and focal depth h ≤ 20km. Do not use magnitude dependent definition to avoid
correlation between magnitude and distance for the records.
- Focal depths, 1 ≤ h ≤ 19km.
- Majority (133 records, 72%) of records from W. N. America, 40 records (22%) from Europe and rest from
Canada, Nicaragua, Japan and Taiwan.
- Consider three source mechanisms but do not model:
- Normal, 8 earthquakes, 16 records.
- Strike-slip, 18 earthquakes, 72 records.
- Thrust, 16 earthquakes, 98 records.
- Use only free-field records using definition of Joyner and Boore (1981), include a few records from
structures which violate this criterion but feel that structure did not affect record in period range of
- Records well distributed in magnitude and distance so equations are well constrained and representative of
entire dataspace. Note lack of records from normal earthquakes. Correlation coefficient between magnitude
and distance is -0.10.
- Use same correction procedure (elliptical filter with pass band 0.2 to 25Hz, roll-off frequency 1.001Hz,
sampling interval 0.02s, ripple in pass-band 0.005 and ripple in stop-band 0.015 with instrument correction)
for almost all records. Use 19 records available only in corrected form as well because in large magnitude
range. Think different correction procedures will not affect results.
- Try both one-stage and two-stage regression method for horizontal PGA; find large differences in b2 but
very similar b3. Find that (by examining cumulative frequency distribution graphs for magnitude scaling of
one-stage and two-stage methods) that two-stage better represents large magnitude range than one-stage
method. Examine plot of amplitude factors from first stage of two-stage method against Ms; find that
amplitude factor of the two Kocaeli (Ms = 7.8) records is far below least squares line through the amplitude
factors. Remove the two Kocaeli records and repeat analysis; find b2 from two-stage method is changed
by a lot but b2 from one-stage method is not. Conclude two-stage method is too greatly influenced by the
two records from Kocaeli and hence use one-stage method.
- Find b2 and b3 significantly different than 0 at 5% level but bA and bS not significant.