Spatial Correlation

The excitation at two nodes can be fully correlated, fully uncorrelated, or partially correlated.

Partial correlation is based on the spatial distance Rij between two nodes. Depending on the relation between user defined parameters RMIN, RMAX and Rij:

1. Fully correlated: Distance R ij is smaller than the user defined R MIN ( R ij < R MIN ).

2. Fully uncorrelated: Distance R ij is larger than the user defined R MAX ( R ij > R MAX ).

3. Partially correlated: Distance R ij is between the user defined R MIN and R MAX  ( R MIN < R ij < R MAX ). The degree of correlation is constant for R MIN less or equal to R ij and decreases linearly for the interval R MAX - R MIN .

The above conditions are illustrated in the figure.

In the figure above:

The effect of the node distance on the cross-correlation terms (off-diagonal terms) of the section of the PSD excitation matrix that is related to two nodes (i) and (j) is written as:

(Eq.1)

where:

(Eq.2)