| Title: | Seismic Reflection and Scattering Coefficients |
|---|---|
| Description: | Calculate and plot scattering matrix coefficients for plane waves at interface. |
| Authors: | Jonathan M. Lees [aut, cre] |
| Maintainer: | Jonathan M. Lees <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.0-9 |
| Built: | 2025-02-14 03:24:32 UTC |
| Source: | https://github.com/cran/zoeppritz |
Calculate and plot scattering matrix coefficients for plane waves at interface.
Jonathan M. Lees<[email protected]> Maintainer: Jonathan M. Lees<[email protected]>
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.
##### demo(ZOEP) ############# Incident wave in Low velocity layer alpha1 = 4.98 beta1 = 2.9 rho1 = 2.667 alpha2 = 8.0 beta2 = 4.6 rho2 = 3.38 App = pzoeppritz( "Amplitude" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "P", "ALL"); App = pzoeppritz( "Amplitude" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "S", "ALL"); App = pzoeppritz( "Energy" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "P", "ALL"); App = pzoeppritz( "Potential" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "P", "ALL"); ############# Incident wave in high velocity layer alpha1 = 8.0 beta1 = 4.6 rho1 = 3.38 alpha2 = 4.98 beta2 = 2.9 rho2 = 2.667 App = pzoeppritz( "Amplitude" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "P", "ALL"); App = pzoeppritz( "Amplitude" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "S", "ALL");##### demo(ZOEP) ############# Incident wave in Low velocity layer alpha1 = 4.98 beta1 = 2.9 rho1 = 2.667 alpha2 = 8.0 beta2 = 4.6 rho2 = 3.38 App = pzoeppritz( "Amplitude" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "P", "ALL"); App = pzoeppritz( "Amplitude" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "S", "ALL"); App = pzoeppritz( "Energy" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "P", "ALL"); App = pzoeppritz( "Potential" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "P", "ALL"); ############# Incident wave in high velocity layer alpha1 = 8.0 beta1 = 4.6 rho1 = 3.38 alpha2 = 4.98 beta2 = 2.9 rho2 = 2.667 App = pzoeppritz( "Amplitude" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "P", "ALL"); App = pzoeppritz( "Amplitude" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "S", "ALL");
Adds a small diagram showing two layers and labeled scattered ray paths.
piczoeppritz(LL = list(x = c(0, 1), y = c(0, 1)), chincw = "P")piczoeppritz(LL = list(x = c(0, 1), y = c(0, 1)), chincw = "P")
LL |
Bounds of Box for plotting |
chincw |
character for incident wave |
This code simply adds a small cartoon showing incoming and outgoing waves in scattering matrix.
Graphical side effect.
Jonathan M. Lees<[email protected]>
pzoeppritz
plot(c(0,1), c(0,1), type='n') piczoeppritz(LL = list(x = c(0.5, 0.75), y = c(0.5, 0.75)), chincw = "P")plot(c(0,1), c(0,1), type='n') piczoeppritz(LL = list(x = c(0.5, 0.75), y = c(0.5, 0.75)), chincw = "P")
Plot Scattering (Zoeppritz) Coefficients
plotzoeppritz(A, zoepcols = c("red", "green", "blue", "purple"), zoeplty = c(1, 1, 1, 1))plotzoeppritz(A, zoepcols = c("red", "green", "blue", "purple"), zoeplty = c(1, 1, 1, 1))
A |
list output of pzoeppritz or zoeppritz |
zoepcols |
vector of 4 colors |
zoeplty |
vector of 4 line types |
Used to plot the matrix of scattering coefficients with different colros and/or line types.
Graphical side effects.
Jonathan M. Lees<[email protected]>
zoeppritz, pzoeppritz, piczoeppritz
alpha1 = 4.98 beta1 = 2.9 rho1 = 2.667 alpha2 = 8.0 beta2 = 4.6 rho2 = 3.38 ############### create the scattering matrix: App = pzoeppritz( "Amplitude" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "P", "NONE"); ######### plot plotzoeppritz(App)alpha1 = 4.98 beta1 = 2.9 rho1 = 2.667 alpha2 = 8.0 beta2 = 4.6 rho2 = 3.38 ############### create the scattering matrix: App = pzoeppritz( "Amplitude" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "P", "NONE"); ######### plot plotzoeppritz(App)
Calculate and plot the P and S-wave scattering amplitudes for a plane wave at an interface.
pzoeppritz(chtype = "Amplitude", alpha1, alpha2, beta1, beta2, rho1, rho2, chincw = "P", choutkind = "ALL")pzoeppritz(chtype = "Amplitude", alpha1, alpha2, beta1, beta2, rho1, rho2, chincw = "P", choutkind = "ALL")
chtype |
character, type of output, one of: Amplitude, Potential, Energy |
alpha1 |
P-wave Velocity of Upper Layer, km/s |
alpha2 |
P-wave Velocity of Lower Layer, km/s |
beta1 |
S-wave Velocity of Upper Layer, km/s |
beta2 |
S-wave Velocity of Lower Layer, km/s |
rho1 |
Density of Upper Layer, kg/m3 |
rho2 |
Density of Lower Layer, kg/m3 |
chincw |
Incident Wave: P, S |
choutkind |
character, type of out put one of: P, S, ALL, NONE |
Front end for zoeppritz program.
List output of zoeppritz call:
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 |
alphacrit |
critical angle |
This front end is easier to call because it is more verbose. Creates a plot of the coefficients versus incident angle. If coefficients are complex, they are replaced with NA and they are thus not plotted.
Jonathan M. Lees<[email protected]>
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.
zoeppritz, pzoeppritz, piczoeppritz
############# Incident wave in Low velocity layer alpha1 = 4.98 beta1 = 2.9 rho1 = 2.667 alpha2 = 8.0 beta2 = 4.6 rho2 = 3.38 App = pzoeppritz( "Amplitude" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "P", "ALL"); App = pzoeppritz( "Amplitude" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "S", "ALL"); ############# Incident wave in high velocity layer alpha1 = 8.0 beta1 = 4.6 rho1 = 3.38 alpha2 = 4.98 beta2 = 2.9 rho2 = 2.667 App = pzoeppritz( "Amplitude" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "P", "ALL"); App = pzoeppritz( "Amplitude" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "S", "ALL");############# Incident wave in Low velocity layer alpha1 = 4.98 beta1 = 2.9 rho1 = 2.667 alpha2 = 8.0 beta2 = 4.6 rho2 = 3.38 App = pzoeppritz( "Amplitude" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "P", "ALL"); App = pzoeppritz( "Amplitude" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "S", "ALL"); ############# Incident wave in high velocity layer alpha1 = 8.0 beta1 = 4.6 rho1 = 3.38 alpha2 = 4.98 beta2 = 2.9 rho2 = 2.667 App = pzoeppritz( "Amplitude" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "P", "ALL"); App = pzoeppritz( "Amplitude" , alpha1, alpha2, beta1, beta2, rho1 ,rho2, "S", "ALL");
Calculate the P and S-wave scattering amplitudes for a plane wave at an interface.
zoeppritz(icoef, vp1, vp2, vs1, vs2, rho1, rho2, incw)zoeppritz(icoef, vp1, vp2, vs1, vs2, rho1, rho2, incw)
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 |
Coeficiants are calculated at angles from 0-90 degrees. Zero is returned where coefficients are imaginary.
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 |
Based on the fortran algorithm in Young and Braile. Uses a linear approximation by Aki and Richards.
Jonathan M. Lees<[email protected]>
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.
pzoeppritz, plotzoeppritz
######### 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" )######### 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" )