Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Waveform inversion via reduced order modeling   We introduce a novel approach to waveform inversion, based on a data driven
reduced order model (ROM) of the wave operator. The presentation is for the
acoustic wave equation, but the approach can be extended to elastic or
electromagnetic waves. The data are time resolved measurements of the pressure
wave at the sensors in an active array, which probe the unknown medium with
pulses and measure the generated waves. The ROM depends nonlinearly on the data
but it can be constructed from them using numerical linear algebra methods. We
show that the ROM can be used for the inverse problem of velocity estimation.
While the full-waveform inversion approach of {nonlinear least-squares} data
fitting is challenging without low frequency information, due to multiple
minima of the objective function, the minimization of the ROM misfit function
has a better behavior, even for a poor initial guess. In fact, the ROM misfit
function is demonstrably a convex function for low-dimensional parametrizations
of the unknown velocity. We give the construction of the ROM, introduce the
inversion approach based on the ROM misfit and assess its performance with
numerical simulations.

29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin