PEIP (version 2.2-5)

vspprofile: Vertical Seismic Profile In 1D

Description

Example vertical 1-dimensional seismic profile used for setting up examples for inverse theory.

Usage

vspprofile(M = 50, N = 50, maxdepth = 1000, deltobs = 20,
noise = 2e-04, M1 = c(9000, -6, 0.001))

Value

list:

G

M by N design matrix

tee

true travel times from model

t2

travel times with noise added

depth

depth samples of model

vee

velocity at the depths indicated

M

input M

N

input N

maxdepth

input maxdepth

deltobs

input delta observation

noise

input noise

M1

True model used for depth versus velocity

Arguments

M

integer, number of rows in in design matrix G, default=50

N

integer, number of columns in design matrix G, default=50

maxdepth

Maximum depth of model, default = 1000

deltobs

integer, sampling interval in depth, default=20

noise

gausian noise multiplier, default=2e-04

M1

3-vector, linear model for velocity versus depth model

Author

Jonathan M. Lees<[e-mail]>

Details

Vertical seismic profile in 1D dimension used for setting up examples in PEIP. Given a simple velocity profile, defined by input parameter M1 create the travel times and designe matrix used for solving an inverse problem. The velocity model is defined as depth versus velocity, and the function inverts that from the slowness. Any model could be used to replace this model. The default model here is taken from an inversion in the Aster book.

References

Aster, R.C., C.H. Thurber, and B. Borchers, Parameter Estimation and Inverse Problems, Elsevier Academic Press, Amsterdam, 2005.

Examples

V = vspprofile()
### plot quadratic velocity profile
plot(V$vee, -V$depth, main="VSP: velocity increasing with depth")
dobs = seq(from=V$deltobs, to=V$maxdepth, by=V$deltobs)
### plotdepth versus time (not linear)
plot(dobs, V$t2)
abline(lm(V$t2 ~ dobs) )