norm_chisq function

Normalized Chi-Squared Test for Circular Data

A quantitative comparison between the predicted and observed directions of $SHmax$ is obtained by the calculation of the average azimuth and by a normalized $chi-squared$ test.

norm_chisq(obs, prd, unc)

Arguments

• obs: Numeric vector containing the observed azimuth of $SHmax$, same length as prd
• prd: Numeric vector containing the modeled azimuths of $SHmax$, i.e. the return object from model_shmax()
• unc: Uncertainty of observed $SHmax$, either a numeric vector or a number

Returns

Numeric vector

Details

The normalized $chi-squared$ test is

The value of the chi-squared test statistic is a number between 0 and 1 indicating the quality of the predicted $SHmax$

directions. Low values ($\le 0.15$) indicate good agreement, high values ($> 0.7$) indicate a systematic misfit between predicted and observed $SHmax$ directions.

Examples

data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na") # North America relative to
# Pacific plate
data(san_andreas)
point <- data.frame(lat = 45, lon = 20)
prd <- model_shmax(point, PoR)
norm_chisq(obs = c(50, 40, 42), prd$sc, unc = c(10, NA, 5))

data(san_andreas)
prd2 <- PoR_shmax(san_andreas, PoR, type = "right")
norm_chisq(obs = prd2$azi.PoR, 135, unc = san_andreas$unc)

References

Wdowinski, S., 1998, A theory of intraplate tectonics. Journal of Geophysical Research: Solid Earth, 103 , 5037-5059, doi: 10.1029/97JB03390.