Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eigenrays in 3D heterogeneous anisotropic media: Part I -- Kinematics,
  Variational formulation   We present a new ray bending approach, referred to as the Eigenray method,
for solving two-point boundary-value kinematic and dynamic ray tracing problems
in 3D smooth heterogeneous general anisotropic elastic media. The proposed
Eigenray method is aimed to provide reliable stationary ray path solutions and
their dynamic characteristics, in cases where convergence to the stationary
paths, based on conventional initial-value ray shooting methods, becomes
challenging. The kinematic ray tracing solution corresponds to the vanishing
first traveltime variation, leading to a stationary path, and is governed by
the nonlinear second-order Euler-Lagrange equation (Part I). In Part II we
elaborate on theoretical aspects of the proposed method and validate its
correctness for general anisotropy. In Part III we use a finite-element
approach, applying the weak formulation. In Part IV we propose an efficient
method to compute the geometric spreading of the entire stationary ray path
using the global traveltime Hessian. In Part V we formulate the dynamic ray
tracing, considering the second traveltime variation, which leads to the linear
second-order Jacobi equation, and in Part VI we relate the proposed Lagrangian
approach to the commonly used Hamiltonian approach. The solution is provided in
Part VII, where we implement a similar finite element approach applied for the
kinematic problem. In both kinematic and dynamic problems, in between the
nodes, the values of the ray characteristics are computed with the Hermite
interpolation, which we find most natural for anisotropic media. We distinguish
two types of stationary rays, delivering either a minimum or a saddle-point
traveltime (due to caustics).

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The categories of this paper are: eess
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
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The categories of this paper are: adap-org
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: stat