Imaging under salt: Illumination compensation by regularized inversion

Imaging in areas of strong velocity contrasts is an increasingly important problem in the search for hydrocarbons. The multipathing and poor illumination that occur in such areas render conventional imaging techniques inadequate. Traditional imaging techniques use a migration operator to reverse the wavefield propagation. Unfortunately, migration alone cannot properly image areas of poor illumination. This problem has been overcome with an iterative inversion that uses an imaging operator and its adjoint along with a regularization operator.; The imaging operator used in the inversion process is a linear operator relating reflectivities to data (a migration operator). This operator creates an image that includes angle domain (or offset ray parameter) common image gathers (ADCIGs). I regularize the image space using two different regularization schemes. In the first scheme, called the geophysical scheme, the regularization operator acts horizontally along the ray parameter axis. This assumes that there is no moveout along the ray parameter axis, meaning that the correct velocity model has been used by the imaging operator. The geophysical regularization operator penalizes large changes in amplitude along offset ray parameters, which are assumed to be caused by poor illumination. The second regularization scheme, called the geological scheme, combines the first regularization operator with a second regularization operator that acts along specified dips at every point in the X-Z plane. This geological regularization tends to create events with the user-specified dip at each point in the X-Z plane. This allows information from a seismic interpretation or geological model to be included in the inversion.; The images obtained with both of my regularized inversion schemes are cleaner than the result of migration alone and the events in areas of poor illumination are stronger and more consistent in amplitude. The geophysical regularization scheme is demonstrated on real 2-D and 3-D data and the geological regularization is demonstrated on real 2-D data.