Q and Adaptive Prediction Error Filters
, by Dave Hale
We first specify an auto-regressive model for a seismic trace which includes the effects of attenuation and spherical divergence. From this model, we determine how an adaptive prediction error filter (APEF) should change with time as it "deconvolves" our model, non-stationary seismogram.
Most APEF algorithms developed to cope with non-stationarity are not based on a model of the physical processes which cause the non-stationarity. We applied two such algorithms to our model seismogram, attempting not only to deconvolve the data, but also to estimate Q from changes in the APEF with time. Both algorithms yielded reasonable deconvolved traces along with rough estimates of Q, although one algorithm performed significantly better than the other.
We also derive an APEF algorithm based on (in fact, constrained by) our model of attenuation. When applied to the model seismogram, this algorithm produced a better deconvolved trace and a more accurate estimate of Q than either of the two unconstrained algorithms; it is, however, limited by its inability to adapt to the time-varying signal-to-noise ratio present in our model (and in real seismic data as well).
STANFORD