vspprofile: Vertical Seismic Profile In 1D

In PEIP: Geophysical Inverse Theory and Optimization

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))

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

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.

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

Author(s)

Jonathan M. Lees<[e-mail]>

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) )

PEIP documentation built on Aug. 21, 2023, 9:10 a.m.