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Description

We construct a frame of wave-atom-like multi-scale Gaussian beams following the dyadic parabolic decomposition of phase space. With this frame we generate a parametrix for the wave equation and study the approximate solution of the Cauchy initial value problem. We provide a natural estimate in terms of the scale parameter which is of order $-\sfrac{1}{2}$. We then introduce the notion of well-spread families of multi-scale Gaussian beam parameters. These families enable the generation of approximate solutions to boundary value problems with the natural error estimate. We show an application of this result in reverse-time-migration type imaging with wavefield reconstruction of seismic array data. joint work with Michele Berra and Jos\'{e}-Luis Romero