Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamic inverse problem in a weakly laterally inhomogeneous medium   An inverse problem of wave propagation into a weakly laterally inhomogeneous
medium occupying a half-space is considered in the acoustic approximation. The
half-space consists of an upper layer and a semi-infinite bottom separated with
an interface. An assumption of a weak lateral inhomogeneity means that the
velocity of wave propagation and the shape of the interface depend weakly on
the horizontal coordinates, $x=(x_1,x_2)$, in comparison with the strong
dependence on the vertical coordinate, $z$, giving rise to a small parameter
$\e <<1$. Expanding the velocity in power series with respect to $\e$, we
obtain a recurrent system of 1D inverse problems. We provide algorithms to
solve these problems for the zero and first-order approximations. In the
zero-order approximation, the corresponding 1D inverse problem is reduced to a
system of non-linear Volterra-type integral equations. In the first-order
approximation, the corresponding 1D inverse problem is reduced to a system of
coupled linear Volterra integral equations. These equations are used for the
numerical reconstruction of the velocity in both layers and the interface up to
$O(\e^2)$.

30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat