Correlation energy between surface and borehole stations at the Valhall field

Passive Seismic Interferometry

In passive seismic interferometry, receivers record data from passive sources such as ambient seismic noise. Under appropriate conditions, cross-correlating two receiver recordings recovers a Green's function and its time-reversed version between the two receivers, convolved with the autocorrelation of a source function such as noise (Wapenaar et al., 2010). In equation form

$$[G(x_B,x_A,t) + G(x_B,x_A,-t)] \ast S_N(t) = \langle u(x_B,t) \ast u(x_A,-t) \rangle \mbox \ \ \ ,$$ (1)

where $G$ is the Green's function between two receiver locations ($x_A,x_B$ ), $S_N(t)$ is the autocorrelation of the source function (here it is noise), and $u$ is the observed wavefield at a given receiver location. Convolving the Green's function with the autocorrelation of the source function can reveal the time it takes for a virtual source signal at one receiver to reach the other receiver of interest, whether directly or after reflecting in the subsurface. If investigating direct waves, the travel-time information with the known distance between the two receivers produces an estimate of the average velocity along the path traveled. Using only surface stations and direct waves, de Ridder and Dellinger (2011) successfully constructed a velocity model of the shallow subsurface at Valhall. Now we want to incorporate recordings at borehole stations into our passive seismic interferometry. To determine whether we can extract the Green's functions between borehole and surface stations, we start by looking at spectrograms and by cross-correlating the borehole and surface station recordings.

Correlation energy between surface and borehole stations at the Valhall field