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The angle has a statistical interpretation. Effectively,
with the definition of *P*_{1,k,T}, we see that:
Notice first that .
Moreover *A*'_{1,k,T}*A*_{1,k,T} contains the lags of the
autocorrelation of the data: thus, it is the covariance matrix *R*^{y}_{k,T}
of the data (up to time *T*). So, the value
can be compared to the probability of the sequence
according to the covariance matrix
*R*^{y}_{k,T}:
A small value of means that the previous samples don't
deviate from the general statistics of the data. On the contrary, a sudden
burst of noise, or a new strong seismic arrival, will produce a large value of
. This occurrence will also perturb strongly the
covariances
, *R*^{r}_{k,T}, and the correlation , whose
updatings
involve a division by (small in that case).
So the variable can be assimilated to a likelihood
variable, and used for detection of unexpected events.

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** Up:** THE LSL ALGORITHM
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Stanford Exploration Project

1/13/1998