The first order operator can be further approximated as a cascade of three operators.

pre-multiplying, pre-multiplying,

The separation procedure has three stages.

*A*1- A rotation about the
*z*-axis to separate the two S-wavetypes. *A*2- An operator to separate
*P*from*S*. This operator has two free parameters that need to be estimated._{1} *A*3- An operator to separate
*P*from*S*. This operator also has two free parameters that need to be estimated._{2}

12/18/1997