Applications of curvelets/surfacelets to seismic data processing

In this talk we explore several applications of the curvelet and surfacelet transforms to seismic data processing. The first application is stable signal recovery in the physical domain - seismic data acquisition is often limited by physical and economic constraints, and the goal is to interpolate the data from a given subset of seismic traces. The second application is signal recovery in a transform domain - we assume that our data comes in a form of a random subset of temporal frequencies and the goal is to recover the missing frequencies from this data. Since seismic signals are generally not bandwidth limited, this in fact becomes an anti-aliasing problem. In both these problems the recovery is resolved via a robust $\ell$_1 solver that exploits the sparsity of the signals in curvelet/surfacelet domains. In the last application we explore the problem of primary-multiple separation by simple thresholding.