Retrieving the earth's reflection response by multi-dimensional deconvolution of ambient seismic noise

A major assumption for retrieving the earth's reflection response with seismic interferometry by cross-correlation of ambient noise is that subsurface sources are uniformly distributed It has been shown that interferometry by multi-dimensional deconvolution can cope with non-uniform source arrays, but implementation of this concept requires a separation of the incident wavefield from the free-surface multiples. For transient passive sources, this separation can be implemented by time-gating in the recorded transmission panels before cross-correlation, but such methodology cannot be applied for simultaneously acting noise sources. Here we show that time-gating can also be applied after an intermediate cross-correlation step. In cross-correlated data, we isolate events around t=0, which inhabit the illumination imprint of the subsurface sources. Next, we apply multi-dimensional deconvolution with the isolated events to the events away from t=0. In this way we can effectively correct for the effects of a non-uniform subsurface source distribution in data that is already cross-correlated. With this new approach, multidimensional deconvolution becomes feasible for simultaneously acting noise sources.