| bvalue.contour {ssEDA} | R Documentation |
This function calculates b-value contours at a pre-specified depth.
bvalue.contour(events, divs=c(15, 15, 15), h=c(0.5, 0.5, 15),
threshold=30, depth=10)
events |
defines the events to be plotted. It is an object of class "subset", generally created by subsetcircle, subsetpolygon, subsetrect or subsetsphere.
|
divs |
a vector of length three. It specifies the grid points where b-values are calculated. The first, second and third entries of this vector correspond to the number of divisions on the longitude, latitude and depth axes respectively. |
h |
a vector of length three. This specifies the bandwidths for the kernel function (see Details). |
threshold |
the minimum number of events needed to evaluate pointwise b-values (see Details). |
depth |
specifies the longitude-latitude plane where the b-value contours are plotted. |
The b-values are calculated in two steps. First, they are evaluated on a 3D grid using the maximum likelihood method (Utsu, 1965). The MLE estimate at (x,y,z) (corresponds to longitude, latitude and depth respectively) only utilises data that lie in S=(x-divs[1],x+divs[1],y-divs[2],y+divs[2], z-divs[3],z+divs[3]). However, if the number of points in S is less than that specified by the threshold parameter, the closest threshold number of points to (x,y,z) are used. The resulting b-value estimates are smoothed using local linear regression technique described in Ruppert and Wand (1994) using a standard trivariate normal kernel. The smoothness of the contours is controlled by the bandwidths of the kernel.
NULL
Edwin Choi (ANU), 1997
Ruppert, D. & Wand, M.P. (1994). Multivariate locally weighted least squares regression. Ann. Statist. 22, 1346–1370.
Utsu, T. (1965). A method for determining the value of b in a formula log n = a - bM showing the magnitude frequency relation for earthquakes. Geophys. Bull. Hokkaido University 13, 99–103 (in Japanese).
# This example requires the NZ catalogue
require(ssNZ)
# Remember the parameters of the graphics device
par.reset <- par(no.readonly=TRUE)
# Make the Wellington Catalogue
as.catalogue(subsetrect(NZ, minlat=-42.2, maxlat=-40.5,
minlong=173.6, maxlong=176.0, minday=julian(1,1,1978)),
catname="Wellington")
b <- subsetrect(Wellington, maxdepth=100, minmag=3,
minlat=-42.2, maxlat=-40.5, minlong=173.6, maxlong=176.0,
minday=julian(1,1,1980), maxday=julian(1,1,2000))
par(pty="s")
bvalue.contour(b, h=c(0.25, 0.2, 2), depth=10)
map("nz", add=TRUE, col="red")
par(par.reset)