PSI - Issue 78

Fadel Ramadan et al. / Procedia Structural Integrity 78 (2026) 859–866

863

)

(

where

b M

M

M

M

−



    

)

(

1

W

h

W

h

(2)

,

F

M

SOF

f

SOF

=

+

)

(

M

W

j

j

where

b M

M

M

M

−



2

W

h

W

h

)

(

  

  

  

+  

(3)

2 2 2 2 R h c R h + + +

,

log

F

M

R c M =

M

c

−

1

2

10

3

D

W

W

ref

for

/ 1500

V V =

V

m s



S 0 ,30

,30

S

V 800 0

   

   

(4)

 =  

  

log

F

V

k

,30

10

S

S

/ 1500

for

/ 1500

V

m s

V

m s

=



0

,30

S

2

2

2

(5)

2    = + + S S



0

Y is the observed IM, i.e. the vertical FAS ordinates in the frequency (f) range 0.1–30Hz. The explanatory variables are the moment magnitude MW, the source-to-site distance R, the shear wave velocity VS,30 and the styles of faulting SOFj, which are dummy variables, introduced to specify strike-slip (j=1), reverse (j=2), and normal (j=3) fault types. To ensure consistency with the horizontal component, the same reference magnitude (Mref= 5) and hinge magnitude (Mh=6) are retained. The coefficients a, b1, b2, c1, c2, c3, k and fj (f1 for strike-slip, f2 for thrust fault, and f3 for normal fault) are derived by a mixed-effect linear regression (Bates et al. 2015). The random-effects are applied to stations and events, in order to estimate the partially non- ergodic sigma according to Al Atik et al (2010), where τ and phi_S2S represent between-event and site-to-site variability, respectively, and phi_0 is the standard deviation of the event- and site- corrected residuals. We derived two different sets of coefficients for Joyner-Boore (R=RJB) and rupture (R=Rrup) distances. The results of this regression, including detailed coefficient values is provided upon request. Figure 4.2 illustrates the predicted FAS spectra computed using the ITA18-FAS model for both horizontal and vertical components under a strike-slip scenario with Vs30 = 300 m/s. Two sets of comparisons are presented: (a) for a fixed magnitude (Mw = 5.5) and varying rupture distances (Rjb = 1 km, 20 km, and 50 km), and (b) for a fixed distance (Rjb = 20 km) and varying magnitudes (Mw = 4.5, 5.5, and 7.0). The results clearly highlight the frequency-dependent behavior of the vertical and horizontal spectral content. At frequencies below 10 Hz, the horizontal component consistently is higher that the vertical one across all distances and magnitudes. Conversely, for frequencies above 10 Hz, the vertical component tends to exceed the horizontal, particularly at closer distances and lower magnitudes. This inversion is confirmed by the higher vertical PGAs with respect to horizontal counterparts, typically observed in recordings in near-source conditions. These findings support the need to account for vertical motion in structural design, especially for short-period-sensitive systems or components. The standard deviation of both components, horizontal and vertical, and for the different terms, is comparable. The detailed results are provided in Appendix A.

5