tectonicr (version 0.4.6)

norm_chisq: Normalized Chi-Squared Test for Circular Data

Description

A quantitative comparison between the predicted and observed directions of ${\sigma }_{Hmax}$ is obtained by the calculation of the average azimuth and by a normalized ${\chi }^2$ test.

Usage

norm_chisq(obs, prd, unc)

Value

Numeric vector

Arguments

obs

Numeric vector containing the observed azimuth of ${\sigma }_{Hmax}$, same length as prd

prd

Numeric vector containing the modeled azimuths of ${\sigma }_{Hmax}$, i.e. the return object from model_shmax()

unc

Uncertainty of observed ${\sigma }_{Hmax}$, either a numeric vector or a number

Details

The normalized ${\chi }^2$ test is $$Norm{\chi }_i^2==\frac{\sum _{i=1}^M{\left(\frac{{\alpha }_i-{\alpha }_{predict}}{{\sigma }_i}\right)}^2}{\sum _{i=1}^M{\left(\frac{90}{{\sigma }_i}\right)}^2}$$ The value of the chi-squared test statistic is a number between 0 and 1 indicating the quality of the predicted ${\sigma }_{Hmax}$ directions. Low values ($\le 0.15$) indicate good agreement, high values ($>0.7$) indicate a systematic misfit between predicted and observed ${\sigma }_{Hmax}$ directions.

References

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

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)