{
  "id": "1101.4836",
  "version": "v1",
  "published": "2011-01-25T14:57:33.000Z",
  "updated": "2011-01-25T14:57:33.000Z",
  "title": "Solving an inverse problem for the wave equation by using a minimization algorithm and time-reversed measurements",
  "authors": [
    "Lauri Oksanen"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the inverse problem for the wave equation on a compact Riemannian manifold or on a bounded domain of $\\R^n$, and generalize the concept of {\\em domain of influence}. We present an efficient minimization algorithm to compute the volume of a domain of influence using boundary measurements and time-reversed boundary measurements. Moreover, we show that if the manifold is simple, then the volumes of the domains of influence determine the manifold. For a continuous real valued function $\\tau$ on the boundary of the manifold, the domain of influence is the set of those points on the manifold from which the travel time to some boundary point $y$ is less than $\\tau(y)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-25T14:57:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30"
    ],
    "keywords": [
      "wave equation",
      "inverse problem",
      "time-reversed measurements",
      "boundary measurements",
      "compact riemannian manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.4836O"
    }
  }
}