I am interested in all aspects of seismic processing, and I work with students on projects that span processing technology from the early pre-processing steps like multiple suppression ( Alvarez et al., 2004 ), to post-imaging interpretation tools ( Lomask et al., 2004 ). I also occasionally work with students and colleagues on seismic imaging applications other than hydrocarbon exploration. Examples of this research activity are: the imaging of teleseismic data for crustal studies ( see program of workshop ( Bridging the gap between Exploration, Crustal, and Earthquake Seismology ), the use of seismic data for monitoring water storage and recovery, and the proposal for acquiring 3-D seismic data in the area where a well is being drilled through the San Andreas Fault ( SAFOD project ).

The most of my research activity is however focused on seismic imaging of structurally complex areas. In these areas seismic-imaging technology meets its most difficult challenges, and algorithmic progress has the largest impact when it helps to produce a high-quality image from data that could not be satisfactorily imaged with conventional methods.

In complex areas, finite-frequency wave propagation is unlikely to be accurately modeled by numerical methods based on high-frequency approximations, such as raytracing. Therefore, in the past several years I found myself naturally gravitating toward wavefield imaging methods ( Wave-Equation Migration , Wave-Equation MVA ). Wavefield-imaging methods work best when the data are regularly sampled. Since 3-D acquisition geometries never fulfill this requirement, the regularization of 3-D data is another important topic of research related to imaging in complex areas. ( Aliasing and shadow zones ).

The estimation of migration velocity, and in some cases of anisotropic migration velocity, is the most challenging problem in seismic imaging of complex structures. An inaccurate velocity function is the most likely culprit when seismic imaging fails. Many of the early failures of wave-equation migration to produce better images than conventional Kirchhoff migration are likely to be caused by the lack of migration velocity analysis (MVA) methods that worked in conjunction with wave-equation migration. This technological gap motivated me to work on methods for performing MVA after wave-equation migration ( Migration Velocity Analysis ).

If raytracing is insufficiently accurate for computing migration operators, it should not be used for velocity updating either. Therefore, the future of MVA in complex areas belongs to methods that use a wave-equation operator to update the velocity ( Wave-Equation MVA ). At the present, these methods are too computationally expensive to be used in practice, but algorithmic and computer progress are likely to make them affordable before long.

Finally, I also believe that in complex areas we must go beyond simple migration when imaging reflectors that are poorly illuminated, or when reflection amplitudes are required for petrophysical analysis. In these situations, the linear operator that links the data and reflectivity is singular, and the adjoint (migration) is a poor approximation of the inverse. The application of a diagonal operator to equalize the amplitudes (amplitude-preserving migration) is a step in the right direction, but it is usually insufficient. To fully solve the problem we must apply better approximations to the true inverse operator than a normalized adjoint. When inverting a singular operator we must be careful to properly constraint the solution, otherwise noise in the null space can easily destroy our image. ( Aliasing and shadow zones ). The introduction of effective geological constraints to this inverse process is still beyond our skills, but it is likely to be extremely beneficial in the future.