Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reconstruction of a conformally Euclidean metric from local boundary
  diffraction travel times   We consider a region $M$ in $\mathbb{R}^n$ with boundary $\partial M$ and a
metric $g$ on $M$ conformal to the Euclidean metric. We analyze the inverse
problem, originally formulated by Dix, of reconstructing $g$ from boundary
measurements associated with the single scattering of seismic waves in this
region. In our formulation the measurements determine the shape operator of
wavefronts outside of $M$ originating at diffraction points within $M$. We
develop an explicit reconstruction procedure which consists of two steps. In
the first step we reconstruct the directional curvatures and the metric in what
are essentially Riemmanian normal coordinates; in the second step we develop a
conversion to Cartesian coordinates. We admit the presence of conjugate points.
In dimension $n \geq 3$ both steps involve the solution of a system of ordinary
differential equations. In dimension $n=2$ the same is true for the first step,
but the second step requires the solution of a Cauchy problem for an elliptic
operator which is unstable in general. The first step of the procedure applies
for general metrics.

5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph