Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric theory of inversion and seismic imaging   The goal of inversion is to estimate the model which generates the data of
observations with a specific modeling equation.
  One general approach to inversion is to use optimization methods which are
algebraic in nature to define an objective function. This is the case for
objective functions like minimizing RMS of amplitude, residual traveltime error
in tomography, cross correlation and sometimes mixing different norms (e.g. L1
of model + L2 of RMS error).
  Algebraic objective function assumes that the optimal solution will come up
with the correct geometry. It is sometimes difficult to understand how one
number (error of the fit) could miraculously come up with the detail geometry
of the earth model. If one models the earth as binary rock parameters (only two
values for velocity variation), one could see that the geometry of the rugose
boundaries of the geobodies might not be solvable by inversion using algebraic
objective function.

7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas