bvmed: Repeated medians regression for the determination of the...

In GRTo: Tools for the Analysis of Gutenberg-Richter Distributions of Earthquake Magnitudes

Description

This function determines the Gutenberg-Richter b-value from a set of magnitude values, using the repeated medians regression method.

Usage

bvmed(file, lis, hd = FALSE, colid = 1, nrep = 200, tm = NULL,
findtm = TRUE, title = "bvmed")

Arguments

file	file to be loaded
lis	list to be loaded
hd	whether file contains header or not
colid	field number for the magnitude values in file
nrep	number of replicates for the bootstrap (calculation of the standard-error for the b-value)
tm	threshold magnitude value
findtm	logical. Whether an automatic procedure is engaged to determine the threshold magnitude value tm or not
title	character. The title of the plot. The name for the PNG file that includes the plot begins with title

Details

This function reads magnitude values in the field which number is indicated by colid in file. Magnitude values are read in the list lis if the file does not exist. This function produces a plot showing the FMD and the linear model line. The plot is stored into a file with name file_bvmed.png (png format file). It includes the mblm function from the version 0.11 (2007) of the mblm library by Lukasz Komsta (known e-mail address : [e-mail]).

Value

A list containing the following components:

quantm	the 5%, 50% and 95% quantiles of the bootstrap replicates for the threshold magnitude value
mmed	the median of the bootstrap replicates for the threshold magnitude value
quantb	the 5%, 50% and 95% quantiles of the bootstrap replicates for the b-value
valid	the number of valid replicates
brm	the b-value
bse	the bootstrap standard-error value for the b-value
bme	the bootstrap margin of errors value for the b-value

Note

Thanks to Paul Friberg for telling us about the bug in the graphical part of bvmed.R. Thanks to Scott Kostyshak for telling us about the extra bootstrap package dependency. GRTo version 1.2 fixes these issues. Thanks to Andrew Barbour (USGS) for detecting and fixing minor problems of bvmed.R of version 1.2. In version 1.3, an option coded by Andrew Barbour allows the processing of data from a list. Willy Aspinall (University of Bristol) highlights bugs in the graphical parts of bvmed: An inappropriate magnitude shift in the FMD plot is definitely fixed in version 1.3. Many thanks to Willy!

Author(s)

Daniel Amorese <[e-mail]>, Paul A. Rydelek <[e-mail]> and Jean-Robert Grasso <[e-mail]>

Maintainer: Daniel Amorese <[e-mail]>

References

D. Amorese, J.-R. Grasso and P. A. Rydelek, "On varying b-values with depth: results from computer-intensive tests for Southern California", Geophys. J. Int. (2010) 180, 347-360

Siegel, A.F., "Robust regression using repeated medians", Biometrika (1982) 69, 242-244.

Examples

bvmed(file=system.file("extdata","IDYLLdeep.data.txt",package="GRTo"), colid = 15, nrep = 150, 
tm = NULL, findtm = TRUE, title = "IDYLLWILD")

Example output

The R bootstrap package is necessary

...You just have to wait...

Size of data set :  1214 events

M0 ('completeness') value or quantiles :
  5%  50%  95% 
0.93 1.10 1.40 

REPLICATES SHOWING UNDETERMINED M0: 23 

b-value or b-value quantiles :
   5%   50%   95% 
0.762 0.933 1.080 

 [1] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8
[20] 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7
[39] 3.8
 [1] 1214 1213 1209 1198 1198 1178 1076 1010 1010  933  847  747  521  521  291
[16]  291  222  141  141   89   89   69   59   39   32   32   27   25   17   15
[31]   15   14   12    7    4    4    2    2    1

b-value= 0.975 with standard-error 0.094 
Calculation over 747 magnitude values


Plot in IDYLLWILD_bvmed.png 

GRTo documentation built on May 2, 2019, 6:46 a.m.