I am trying to simulate two seismic traces and represented as two 1D vectors. I want the correlation between and to be a constant i.e. 0.9 and In order to simulate these two trases I am wondering how to make this into a positive definite covariance matrix.
and is both spatially dependent, so I have introduced a gaussian correlation function and is on the form
let for j=1,2
and I though I could create a covariance matrix B where
Why is this wrong? Why is this not positive definite?
I also tried with
Which is indeed positive definite, but the simulation from this looks all wrong, and the second trace just got a super small variation around the mean compared to the first trace.
I think there is something wrong with my trail of thought here, any tip is appreciated.