in collaboration with Gunther Uhlmann and Hart SmithIn reflection seismology one places sources and receivers on theEarth's surface. The source generates waves in the subsurface that arereflected where the medium properties vary discontinuously; thesereflections are observed in all the receivers. The data thus obtainedare commonly modeled by a s...
Creator:
De Hoop, Maarten (Purdue University)
Created:
2005-10-21
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The Kadomtsev-Petviashvili (KP) equation is a two-dimensional dispersivewave equationwhich was proposed to study the stability of one soliton solution of theKdV equationunder the influence of weak transversal perturbations. It is well knowthat some closed-formsolutions can be obtained by function which have a Wronskian determinantform.It is of...
Creator:
Kao, Chiu-Yen (University of Minnesota, Twin Cities)
Created:
2009-03-23
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Tent-shaped spacetime regions appear to be natural for solving hyperbolic equations. By constraining the height of the tent pole, one can ensure causality. The subject of this talk is a technique to advance the numerical solution of a hyperbolic problem by progressively meshing a spacetime domain by tent shaped objects. Such tent pitching scheme...
Creator:
Gopalakrishnan, Jay (Portland State University)
Created:
2017-06-30
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We will give a brief overview of multiscale modeling for wave equationproblems and then focus on two techniques. One is an energy conservingDG method for time domain and the other is a new a new sweepingpreconditioner for frequency domain simulation. The latter is resultingin a computational procedure that essentially scales linearly even inthe ...
Creator:
Engquist, Bjorn (The University of Texas at Austin)
Created:
2010-11-02
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Joint work with Florence Delprat-Jannaud. Geophysicists are quite aware of the important troubles that can be met whenthe seismic data are contaminated by multiple reflections. The situationthey have in mind is the one where multiple reflections are generated byisolated interfaces associated with high impedance contrasts. We here studya more ins...
Creator:
Lailly, Patrick (Institut Français du Pétrole)
Created:
2005-10-21
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
This presentation is devoted to plane wave methods for approximating the time-harmonic wave equation paying particular attention to the Ultra Weak Variational Formulation (UWVF). This method is essentially an upwind Discontinuous Galerkin (DG) method in which the approximating basis functions are special traces of solutions of the underlying wav...
Created:
2010-11-01
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Joint with R.-E. Plessix.The goal of seismic surveying is the determination of the structure and properties of the subsurface. Oil and gas exploration isrestricted to the upper 5 to 10 kilometers. Seismic data are usually recorded at the earth's surface as a function of time. Creating asubsurface image from these data is called migration.Seismic...
Creator:
Mulder, Wim (The Shell Group)
Created:
2005-10-21
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In this lecture we shall present a survey of recent work on several topics related with numerical approximation of waves.Control Theory is by now and old subject, ubiquitous in many areas of Science and Technology. There is a quite well-established finite-dimensional theory and many progresses have been done also in the context of PDE (Partial D...
Creator:
Zuazua, Enrique (Basque Center for Applied Mathematics)
Created:
2009-03-04
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.