Correlation energy between surface and borehole stations at the Valhall field

Discussion

There is definitely coherent correlated energy between borehole and surface stations. Although the results in Figure 4 appear noisy, the correlations between a single surface station and all five borehole stations are very similar to each other. However, a resemblance between the cross-correlation signal and the Green's function remains to be discussed. As previously mentioned, seismic interferometry says that, under certain conditions, the Green's function between two stations can be extracted by cross-correlating recordings of the ambient seismic field at both stations. One of the primary conditions is that the ambient seismic field satisfies energy equipartition, which means that energy propagates equally in all directions. This seems to be more or less satisfied for wave modes along the surface but does not usually seem to hold in 3D for body waves (Artman, 2007).

The seismic Green's function between borehole stations and the surface stations is unknown, especially at these low frequencies. The wave propagation between stations in the borehole and stations at the surface is obviously affected by the presence of the borehole, as it can act as a wave-guide. It is not inconceivable that the waves propagate from a virtual source in the borehole, first moving up to the surface along the borehole and then outward along the surface. This would explain why the apex of the event at causal times lies at the platform rather than at the surface coordinates of the borehole stations. However, this does not explain the non-physical nature of the apex not lying at $t=0$  s but at approximately $t=-2$  s, nor why the signal we retrieve is not time-symmetric (not even around approximately $t=-2$  s).

The diagram in Figure 6 shows a possible mechanism for the coherent energy observed at low frequencies between the borehole and surface stations. The diagram depicts energy, excited by distant sources, in both directions along the surface. Energy that reaches the entrance of the borehole both excites the waves down to the borehole stations and continues to the surface stations. This would account for the apex of the (mostly) causal events lying at a small negative correlation lag. Energy that enters the borehole under the platform and travels down can lead to multiple bounces up and down the borehole, which would cause the repetitive signal in the acausal time window. This mechanism of seismic energy does not satisfy the conditions of seismic interferometry, thus we cannot interpret the cross-correlation signals as inter-station Green's functions.

diagram
Figure 6. Illustration of the ambient seismic noise environment at Valhall.

Correlation energy between surface and borehole stations at the Valhall field