Assuming a noise-free, autoregressive, non-stationary model,
the maximum-likelihood estimate of Q may be computed from a
single seismogram, using an iterative algorithm similar to
the prediction-error algorithm described in SEP-30 (Hale, 1982).
The only difference in the two algorithms is that the maximum-likelihood algorithm
is sensitive to the time-varying amplitude as well as color of a
seismogram, whereas the prediction-error algorithm is sensitive
to color variations only.
Maximum-likelihood estimation of Q for a seismogram contaminated
with ambient noise is more difficult.
The maximum-likelihood formulation of the estimation problem
leads to a set of equations which is highly non-linear in
the unknown parameters, including Q; and
no reasonably efficient algorithm has yet been found which solves
this estimation problem.
STANFORD