Directional structure tensors in estimating seismic structural and stratigraphic orientations

Estimating orientations of seismic structures (reflections) and stratigraphic features (channels) is important for seismic interpretation, subsurface interpolation and geophysical inversion. Structure tensors, constructed as smoothed outer products of amplitude gradients, are commonly used to estimate seismic reflection normals, which uniquely define the reflection orientations. However, this conventional structure-tensor method often generates significant errors in estimating orientations of the reflections with steep and rapidly varying slopes. To better estimate reflection orientations, we propose to construct structure tensors in a new space, where the reflections are mostly flat or only slightly dipping and the variation of reflection slopes is reduced. We use these constructed structure tensors to compute reflection normals in this new space and then transform the normals back to obtain a better estimation of reflection orientations in the original space. Seismic stratigraphic features such as channels are often aligned within dipping reflections. It is not discussed previously by others to estimate orientations of such features directly from a seismic image. An ideal way to estimate stratigraphic orientations is to first extract a horizon surface with stratigraphic features, and then construct structure tensors with gradients on the surface to estimate the orientations of the features. However, extracting horizon surfaces can be a difficult and time-consuming task in practice. Fortunately, computing gradients on a horizon surface is only a local operation and is equivalent to directly compute directional derivatives along reflection slopes without picking horizons. Based on this observation, we propose to use an equivalent but more efficient way to estimate seismic stratigraphic orientations by using structure tensors constructed with the directional derivatives along reflections. We demonstrate the methods of estimating structural and stratigraphic orientations using 3-D synthetic and real examples.