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Last data update: 2014.03.03

R: Zoeppritz Equations

zoeppritz

R Documentation

Zoeppritz Equations

Description

Calculate the P and S-wave scattering amplitudes for a plane wave at an interface.

Usage

zoeppritz(icoef, vp1, vp2, vs1, vs2, rho1, rho2, incw)

Arguments

`icoef`	type of out put Amplitude=1, Potential=2, Energy=3
`vp1`	P-wave Velocity of Upper Layer, km/s
`vp2`	P-wave Velocity of Lower Layer, km/s
`vs1`	S-wave Velocity of Upper Layer, km/s
`vs2`	S-wave Velocity of Lower Layer, km/s
`rho1`	Density of Upper Layer, kg/m3
`rho2`	Density of Lower Layer, kg/m3
`incw`	integer,Incident Wave: P=1, S=2

Details

Coeficiants are calculated at angles from 0-90 degrees. Zero is returned where coefficients are imaginary.

Value

List:

`angle`	Incident angles (degrees)
`rmat`	Matrix of 4 by n reflection coefficients for each angle
`rra`	Matrix of 4 by n real part of scattering matrix
`rra`	Matrix of 4 by n imaginary part of scattering matrix
`ang`	Matrix of 4 by n phase angle
`incw`	integer, from input parameter
`icoef`	integer, from input parameter

Note

Based on the fortran algorithm in Young and Braile. Uses a linear approximation by Aki and Richards.

Author(s)

Jonathan M. Lees<jonathan.lees@unc.edu>

References

Young, G.B., Braile, L. W. 1976. A computer program for the application of Zoeppritz's amplitude equations and Knott's energy equations, Bulletin of the Seismological Society of America, vol.66, no.6,1881-1885.

K. Aki and P.G. Richards.Quantitative seismology. University Science Books, Sausalito, Calif., 2nd edition, 2002.

Examples



#########  set up 2-layer model
 
 
 alpha1 = 4.98
  beta1 =  2.9
   rho1 = 2.667

  alpha2 = 8.0
   beta2 = 4.6
   rho2 = 3.38
###################  P-wave incident = 1
     incw=1;
   icoef=1

A =  zoeppritz(icoef, alpha1, alpha2, beta1, beta2, rho1,rho2,   incw)

plot(A$angle, A$rmat[,1], xlab="Incident Angle", ylab="Ratio of Amplitudes",
main="P-wave incident/P-wave Reflected" )

plot(A$angle, A$rmat[,2], xlab="Incident Angle", ylab="Ratio of Amplitudes",
main="P-wave incident/S-wave Reflected" )

plot(A$angle, A$rmat[,3], xlab="Incident Angle", ylab="Ratio of Amplitudes",
main="P-wave incident/P-wave Refracted" )

plot(A$angle, A$rmat[,4], xlab="Incident Angle", ylab="Ratio of Amplitudes",
main="P-wave incident/S-wave Refracted" )

###################  S-wave incident = 2
     incw=2
   icoef=1

A =  zoeppritz(icoef, alpha1, alpha2, beta1, beta2, rho1,rho2,   incw)

plot(A$angle, A$rmat[,1], xlab="Incident Angle", ylab="Ratio of Amplitudes",
main="S-wave incident/P-wave Reflected" )

plot(A$angle, A$rmat[,2], xlab="Incident Angle", ylab="Ratio of Amplitudes",
main="S-wave incident/S-wave Reflected" )

plot(A$angle, A$rmat[,3], xlab="Incident Angle", ylab="Ratio of Amplitudes",
main="S-wave incident/P-wave Refracted" )

plot(A$angle, A$rmat[,4], xlab="Incident Angle", ylab="Ratio of Amplitudes",
main="S-wave incident/S-wave Refracted" )