The Plane-Wave Detection Problem
Symes, William W.
We study in some detail a simple nonlinear estimation problem, which shares several important features with some inverse problems in wave propagation. We consider the estimation of waveforms and incidence angles of transient plane waves from measurements along a line segment. We formulate this estimation problem as a nonlinear least-squares problem in several ways. We show that the "natural" formulation, output least squares, is severely ill-posed because of the extreme nonlinearity of the model/data relation. We suggest an alternate formulation, the penalized coherency method, and show that this alternative optimization problem is well-posed. We use throughout as our main analytical tool G. Chavent's theory of quasi convex sets.
Citable link to this pagehttps://hdl.handle.net/1911/101667
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