earthquakes {ridgetorus}

Japanese earthquakes dataset

Description

Pre-earthquake direction of steepest descent and the direction of lateral ground movement before and after, respectively, an earthquake in Noshiro (Japan) in 1983.

Usage

earthquakes

Format

A data frame with 678 rows and 2 variables:

theta1

Direction of steepest descent.

theta2

Direction of lateral ground movement.

Details

The direction is measured in radians in [0, 2\pi) with 0 / \frac{\pi}{2} / \pi / \frac{3\pi}{2} / 2\pi representing the East / North / West / South / East directions.

References

Hamada, M. and O'Rourke, T. (1992). Case Studies of Liquefaction & Lifeline Performance During Past Earthquake. Volume 1: Japanese Case Studies. Technical Report NCEER-92-0001. National Center for Earthquake Engineering Research, University at Buffalo. doi:10.1016/0886-7798(93)90146-m

Jones, M. C., Pewsey, A., and Kato, S. (2015). On a class of circulas: copulas for circular distributions. Annals of the Institute of Statistical Mathematics, 67(5):843–862. doi:10.1007/s10463-014-0493-6

Rivest, L.-P. (1997). A decentred predictor for circular-circular regression. Biometrika, 84(3):717–726. doi:10.1093/biomet/84.3.717

Examples

# Load data
data("earthquakes")

# Transform the data into [-pi, pi)
earthquakes <- sdetorus::toPiInt(earthquakes)
plot(earthquakes, xlab = expression(theta[1]), ylab = expression(theta[2]),
     xlim = c(-pi, pi), ylim = c(-pi, pi), axes = FALSE)
sdetorus::torusAxis()


# Perform TR-PCA
fit <- ridge_pca(x = earthquakes)
show_ridge_pca(fit)