Kinematics in iterated correlations of a passive acoustic experiment

Iterated correlation after muting

The terms in group 2 cannot uniquely be separated from those of groups 1. Time-domain muting of $C^{(2)}_{B,X}$ and $C^{(2)}_{B,X}$ can exclude the leading order event 4.1, but would also exclude parts of terms 4.2 and 4.3. The black lines in Figures 7(a) and 7(b) indicate the travel time of an event between station $A$ or $B$ and each auxiliary station. The dominant term in $C^{(2)}$ will always reside in this window, see Figure 4(a). We now mute each $C^{(2)}$ according to these limits to obtain the two correlograms in Figures 10(a) and 10(b).

The $C^{(3)}_{B,A}$ is evaluated for each auxiliary station to obtain the correlogram in Figure 11(a), this panel is summed and multiplied with a phase-modifying according to equation 18 to retrieve the signal in Figure 11(b).

The resulting signal resembles the true result slightly better than evaluating the terms of equation 15 group 2 without muting; the spurious event arriving at $t=.8$s is slightly smaller. This is because, for the present geometry, the auxiliary stations where the spurious event is absent, would have contributed more strongly to the spurious event without muting before evaluating $C^{(3)}_{B,A}$. (The geometrical spreading factors vary for the contribution of each auxiliary station.)

corrC2c,corrC2d
Figure 10. Muted $C^{(2)}_{A,X}$ in a) and $C^{(2)}_{B,X}$ in b). These are the input for the evaluation of $C^{(3)}_{B,A}$. $\mathbf{[ER]}$

corrC4ABc,resultC4c
Figure 11. a) Correlogram of $C^{(3)}_{B,A}$ evaluated after muting $C^{(2)}$, as a function of each auxiliary station-position angle $\phi$. b) Comparison of retrieved Green's function with the true result, after summation of $C^{(3)}_{B,A}$ over all auxiliary stations. $\mathbf{[ER]}$

Kinematics in iterated correlations of a passive acoustic experiment