A TOPOLOGY OPTIMIZATION APPROACH FOR THE 2D ACOUSTIC INVERSE PROBLEM IN TIME DOMAIN

Resumo

Acoustic Tomography (AT) is a method widely used in the oil and gas industry for the purpose
of finding and/or monitoring sub-sea bed hydrocarbon reservoirs. This approach is based on propagation
and measurement of acoustic waves in order to acquire information about unknown media. As a result,
physical properties of the medium can be identified by solving an inverse problem, which is usually
formulated as the minimization of the difference between the response measured by the receivers, and
a simulated response obtained by a numerical model. An efficient method to solve inverse problems
and to find the distribution of material parameters is the Topology Optimization Method (TOM). This
work proposes a topology optimization approach for the acoustic inverse problem in the time-domain
using finite element method. A material interpolation scheme based on the Solid Isotropic Material
with Penalization (SIMP) is employed to represent the velocity model for the acoustic problem. The
sensitivity analysis is carry out using an automated differentiation tool and the optimization problem is
solved by a Limited-Memory BFGS algorithm. Two examples considering different velocity models are
analyzed and a perturbation is imposed on the measured responses in order to avoid inverse crime.