We revisit Smith’s frame of curvelets and discretize it making use of the USFFT as developed by Dutt and Roklin, and Beylkin. In the discretization, we directly approximate the underlying dyadic parabolic decomposition, its (rotational) symmetry, and approximate all the necessary decay estimates in phase space with arbitrary accuracy. Numerically, our transform is unitary. Moreover, if we apply...

We discuss a multi-scale geometrical representation of (seismic) waves via a decomposition into wave packets. Wave packets can be thought of as certain localized “fat” plane waves. As a starting point we take the frame of continuous “curvelets” and associated transform. Different discretizations, and approximations, of this transform lead to different discrete wave packets. One such discretizat...

Seismology and engineering seismology have been dramatically affected by the emergence of high-performance computing. A recent report by the National Research Council's Committee on Seismology (NRC, 1996) is entirely devoted to surveying the status and potential of high-performance computing activities in this field. Here we summarize several applications and focus on one particular problem, th...