Nuclide concentration in a vertically mixed soil

Compute nuclide concentration in a vertically-mixed steady-state soil, using the approach of Foster et al. (2015)

conc_soil_mixing(h, E, rhos, rhob, p, L, S, fqz = 1)

Arguments

h

soil thickness (cm)

E

erosion rate (m/Ma)

rhos

soil density (g/cm3)

rhob

bedrock density (g/cm3)

p

production and decay parameters for the nuclide (4 elements vector)

  • p[1] unscaled spallation production rate (at/g/a)

  • p[2] unscaled stopped muons production rate (at/g/a)

  • p[3] unscaled fast muons production rate (at/g/a)

  • p[4] decay constant (1/a)

L

Attenuation length (3 elements vector in g/cm2)

  • L[1] neutrons

  • L[2] stopped muons

  • L[3] fast muons

S

scaling factors (2 elements vector)

  • S[1] scaling factor for spallation

  • S[2] scaling factor for muons

fqz

quartz enrichment factor (default 1)

Value

Nuclide concentration in soil (at/g)

Examples

#' data("prm") # production and decay data
p = prm
data("Lambda") # attenuation length data
L = Lambda
altitude = 1000 # site elevation in m
latitude = 20 # site latitude in degrees
P = atm_pressure(alt=altitude,model="stone2000") # atmospheric pressure at site
S = scaling_st(P,latitude) # Stone 2000 scaling parameters
rhob = 2.65 # bedrock density (g/cm3)
rhos = rhob/2 # soil density  (g/cm3)
E = 10^seq(log10(0.1),log10(100),length.out = 100) # denudaton rate (m/Ma)
plot(NA,xlim=range(E),ylim=c(0.02,6),log="xy",
    xlab="Denudation rate (m/Ma)",ylab="Concentration (10^6 at/g)")
h = 100 # soil depth (cm)
C = conc_soil_mixing(h,E,rhos,rhob,p[,1],L,S)
lines(E,C/1e6)
h = 200 # soil depth (cm)
C = conc_soil_mixing(h,E,rhos,rhob,p[,1],L,S)
lines(E,C/1e6,col="red")
h = 1000 # soil depth (cm)
C = conc_soil_mixing(h,E,rhos,rhob,p[,1],L,S)
lines(E,C/1e6,col="green")
legend("topright",c("1 m","2 m","10 m"),lty=1,col=c("black","red","green"),title="Mixing depth")