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vspprofile<-function(M=50, N=50, maxdepth = 1000, deltobs=20, noise = 2e-04, M1 = c(9000, -6, .001))
{
###### vertical seismic profile for inverse problem testing
### this is the quadratic mode: depth versus velocity
depth = seq(from=0, to=maxdepth, by=1)
### invert to get the velocity
vee = ( -M1[2] + sqrt( M1[2]^2 - 4*M1[3]*(M1[1]-depth) ) )/ (2*M1[3] )
dobs = seq(from=deltobs, to=maxdepth, by=deltobs)
tee = vector(length = length(dobs) )
for(i in 1:length(dobs) )
{
tee[i] = sum(1/vee[depth<=dobs[i]] )
}
### time with noise: ?
t2 = tee + noise*rnorm(length(tee) )
dd=maxdepth/N;
G=matrix( rep(0, length=M*N), nrow=M,ncol= N);
## k=1;
for(i in 1:M)
{
G[i, 1:(i) ] = rep(1,length=i)*dd;
}
return(list(G=G, tee=tee, t2=t2, depth=depth, vee=vee, N=N, M=M,maxdepth = maxdepth, deltobs=deltobs, noise = noise, M1 =M1) )
}
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