# CY08 Sub-Functions {nga}

CY08 Sub-Functions
Package:
nga
Version:
1.4-1

### Description

The sub-functions needed to estimate ground motions using the Chiou & Youngs NGA model. These functions are called by the main function used for calculations, `Sa.cy`.

### Usage

```LnYref.cy(M, Rrup, Rjb, Rx, Ztor, dip, Frv, Fnm, Fhw, AS, T)
NL.cy(Yref, Vs30, T)
Sigma.cy(M, Yref, Vs30, VsFlag, AS, T)
Tau.cy(M, T)
SigmaTot.cy(M, Yref, Vs30, VsFlag, AS, T)
SaMedian.cy(M, Rjb, Rrup, Rx, Ztor, Frv, Fnm, AS, Fhw, dip, Vs30, Z1.0, T)
```

### Arguments

M
Moment magnitude of earthquake.
Rjb
Horizontal distance to the surface projection of the rupture plane; Joyner-Boore distance (km).
Rrup
Closest distance to the rupture plane; rupture distance (km).
Rx
Horizontal distance to the surface projection of the top edge of the rupture plane, measured perpendicular to the strike; site coordinate (km).
Ztor
Depth to top of rupture (km).
Frv
Reverse style-of-faulting flag; equal to 1 for reverse faulting (`30 <= rake <= 150 deg`), and 0 otherwise.
Fnm
Normal style-of-faulting flag; equal to 1 for normal faulting (`-120 <= rake <= -60 deg`), and 0 otherwise.
AS
Aftershock flag; equal to 1 for aftershocks and 0 for mainshocks.
Fhw
Hanging wall flag; equal to 1 for sites on the hanging wall side of the fault (`Rx >= 0`) and 0 otherwise.
dip
Fault dip angle (deg).
Vs30
Time-averaged shear wave velocity over a subsurface depth of 30 meters (m/s).
VsFlag
Flag variable indicating how `Vs30` is obtained; equal to 1 if `Vs30` is measured, and 0 if `Vs30` is estimated or inferred.
Z1.0
Depth to Vs = 1.0 km/s (m).
Yref
Median ground motion for the reference rock site condition (g).
T
Spectral period (sec). Use 0 for PGA and -1 for PGV.

### Details

`LnYref.cy`
Median ground motion on reference rock site (Eqn 13a of Chiou and Youngs (2008)).
`NL.cy`
Nonlinear site response term (Eqns 10 and 21).
`Sigma.cy`
Intra-event standard deviation (Eqn 20).
`Tau.cy`
Inter-event standard deviation (Eqn 19).
`SigmaTot.cy`
Total standard deviation (Eqn 21).
`SaMedian.cy`
Median estimate of ground motion, with site response (Eqn 13b).

### Values

Returns values of the sub-functions for the Chiou & Youngs NGA model. The outputs of the functions are in log space, with the exception of `SaMedian.cy`, which outputs values in g (for Sa and PGA) or cm/s (for PGV).

### References

Chiou, B. S.-J., and R. R. Youngs (2008). An NGA Model for the Average Horizontal Component of Peak Ground Motion and Response Spectra. Earthquake Spectra 24, 173--215.

`coefs`, `coefs.t.cy`, `periods.cy`, `Sa.cy`, `Sa.nga`.