We propose a new technique for passive seismic imaging via the direct application of operators to noise recordings. We propose a time-domain 2D scalar wave equation to describe the propagation of surface waves within a narrow frequency range. Outside the source region, this scalar wave equation relates the second-order spatial and second-order temporal derivatives of the wavefield with the local velocity. Different from seismic interferometry, this technique does not rely on cross-correlations to reveal the statistical coherence of a chaotic wavefield at two locations. Rather, it relies on the local measurements of velocity obtained directly from the ratio between temporal and spatial derivatives of the wavefield. The new method allows us to do passive imaging with much shorter passive recording. We apply this technique on ambient seismic recording made at a large and dense array installed over Ekofisk oil field, in the Norwegian North Sea. We are able to image a subsidence-induced geomechanical imprint on the Scholte wave velocities over Ekofisk.


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