Anisotropic seismic noise gradiometry by elliptically-anisotropic wave equation inversion-an example at Ekofisk

We propose an anisotropic wavefield gradiometry technique to extract azimuthally anisotropic phase velocities from seismic noise that is dominated by a single surface wave mode. The method relies on a two-dimensional elliptical-anisotropic wave equation. This wave equation equates the spatial derivatives of the wavefield amplitudes with the temporal derivatives through the elements of a two-by-two matrix characterizing the medium parameters. The derivatives are evaluated using finite differences, and the system is inverted with a smoothness constraint. We test the procedure on ambient seismic noise recorded in a large and dense array installed over Ekofisk field. Because the station spacing is much larger cross-line then inline, the approximation error of the spatial finite difference results in an apparent anisotropy. From an experiment with synthetic isotropic plane waves, we define a Jacobian to correct the finite difference stencils. With the corrected finite difference stencils, we extracted anisotropic phase velocities at Ekofisk from as little as 10 minutes of seismic noise recordings. The azimuthal anisotropy forms a circular geometry around the production induced subsidence bowl. The methodology is a promising technique for studying changes in the subsurface geomechanical stress-state resulting from time-dependent phenomena operating at a short time-scales.