Baker and Jayaram (2008) inter-period correlation model

Computes the Pearson correlation coefficient between the residuals of ln(Sa) at two oscillator periods, using the canonical predictive equation of Baker and Jayaram (2008), Earthquake Spectra 24(1), 299-317 (DOI 10.1193/1.2857544), Eqs. 5 and 6 verbatim.

Usage

rhoBJ(Tn, T0 = 0.01, Rrup = 100)

Arguments

Tn

Numeric scalar. Target spectral period in seconds.

T0

Numeric scalar. Reference period in seconds. Default 0.01 (used as a numerical proxy for PGA). Values <= 0 are silently converted to 0.01.

Rrup

Numeric scalar. Not used; retained for backward compatibility.

Value

Numeric scalar correlation coefficient rho(T0, Tn).

Details

The model has no dependence on rupture distance or magnitude. Rrup is retained for signature compatibility and is silently ignored. Periods of zero are treated as 0.01 s (standard PGA proxy in B&J 2008).

Form (Eqs. 5-6 of B&J 2008): C1 = 1 - cos(pi/2 - 0.366 * ln(Tmax / max(Tmin, 0.109))) C2 = (1 - 0.105 * (1 - 1/(1 + exp(100*Tmax - 5))) * (Tmax-Tmin)/(Tmax-0.0099)) if Tmax < 0.2; else 0 C3 = C2 if Tmax < 0.109; else C1 C4 = C1 + 0.5 * (sqrt(C3) - C3) * (1 + cos(pi * Tmin / 0.109))

rho = C2 if Tmax < 0.109 = C1 else if Tmin > 0.109 = min(C2, C4) else if Tmax < 0.2 = C4 otherwise

Validity: 0.01 <= T1, T2 <= 10 s.

References

Baker, J. W. & Jayaram, N. (2008). Correlation of Spectral Acceleration Values from NGA Ground Motion Models. Earthquake Spectra, 24(1), 299-317. DOI: 10.1193/1.2857544.

Examples

rhoBJ(Tn = 0.3, T0 = 0.01)   # rho(PGA, 0.3 s)
#> [1] 0.7953519
rhoBJ(Tn = 1.0, T0 = 0.5)
#> [1] 0.7490206