Tables
Table 1: Summary of analysis
including model label, hypothesis, and equations used to estimate
distance, space-modified time and growth rate. Where \(r_{t,i}\) is the
log difference growth rate of centroid i at time t, \(\alpha_{1}\) is
the intercept term, \(\epsilon\) is the Normal distributed residual
error, \(T\) is day since start of study, \(f\) is used to represent
thin-plate smoothing splines with a maximum of 12 bases (\(f_{1}\),\(f_{2}\), \(f_{\text{North}}\), and \(f_{\text{South}}\)), \(f_{p}\) is
a thin-plate tensor product with a maximum of ten bases in each
dimension, \(X\) is the mean centred easting coordinate (UTM), \(Y\) is
the mean centred northing coordinate (UTM), \(D\) is the distance of a
centroid from either a planar angle or radial epicentre, \(\theta\) is
the angle of a planar wave (radian), \(\rho\) is the space-modified time
variable, \(\zeta\) is the constant speed of the wave, \(\gamma\) and\(\psi\) are the easting and northing coordinates of a radial wave
epicentre (mean centred UTM), \(N\) and \(S\) denote north and south of
the Duero river. The number of additional travelling wave parameters for
each model are included.