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- Frédéric Hérau, Johannes Sjöstrand, Christiaan C Stolk
- 2004

Onétudie des estimations semiclassiques sur la résolvente d'opérateurs qui ne sont ni ellip-tiques ni autoadjoints, que l'on utilise pourétudier leprobì eme de Cauchy. En particulier on obtient une description précise du spectre pres de l'axe imaginaire, et des estimations de résolventè a l'intérieur du pseudo-spectre. On applique ensuite les résultatsà… (More)

Seismic data are commonly modeled by a high-frequency single scattering approximation. This amounts to a linearization in the medium coefficient about a smooth background. The discontinuities are contained in the medium perturbation. The high-frequency part of the wavefield in the background medium is described by a geometrical optics representation. It can… (More)

Strong refraction of waves in the migration velocity model introduces kinematic artifacts-coherent events not corresponding to actual reflectors-into the image volumes produced by prestack depth migration applied to individual data bins. Because individual bins are migrated independently, the migration has no access to the bin component of slowness. This… (More)

Microlocal analysis of a seismic linearized inverse problem. Abstract: The seismic inverse problem is to determine the wavespeed c(x) in the interior of a medium from measurements at the boundary. In this paper we analyze the linearized inverse problem in general acoustic media. The problem is to nd a left inverse of the linearized forward map F, or,… (More)

- Felix J Herrmann, Peyman Moghaddam, Christiaan C Stolk
- 2008

A nonlinear singularity-preserving solution to seismic image recovery with sparseness and continuity constraints is proposed. We observe that curvelets, as a directional frame expansion, lead to sparsity of seismic images and exhibit invariance under the normal operator of the linearized imaging problem. Based on this observation we derive a method for… (More)

- Christiaan C Stolk, Maarten V De Hoop, William W Symes
- 2005

In contrast to prestack migration methods based on data binning, common image gathers produced by shot-geophone migration exhibit the appropriate semblance property in either offset domain (focussing at zero offset) or angle domain (focussing at zero slope), when the migration velocity is kinematically correct and when events to be migrated arrive in the… (More)

- Christiaan C Stolk, Maarten V De Hoop, Tim J P M Op, T Root, Doi
- 2011

In this paper, we revisit the reverse-time imaging procedure. We discuss an inverse scattering transform derived from reverse-time migration (RTM), and establish its relation with generalized Radon transform inversion. In the process, the explicit evaluation of the so-called normal operator is avoided, at the cost of introducing other pseudodifferential… (More)

Prestack wave equation migration using the double square root equation produces prestack image volumes free of artifacts, even in the presence of multipathing due to complex structure. In particular image gathers in angle or offset ray parameter are flat at correct velocity, and gathers in offset are concentrated at zero offset. Differential semblance… (More)