We consider a nonlinear ordinary differential equation associated with a number of inverse scattering problems in acoustic and seismic sounding in which acoustic impedance and an impedance-dependent unknown damping coefficient are the unknown function. We prove that the Cauchy problem is uniquely solvable when the derivative is treated as a generalized function. It is established that the inverse scattering problem in a layered dissipative medium simultaneously determines the acoustic impedance and the damping coefficient. A regularized numerical algorithm is proposed and numerical results are reported.
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Translated from Prikladnaya Matematika i Informatika, No. 54, 2017, pp. 57–74.
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Baev, A. Numerical Solution of the Inverse Scattering Problem for the Acoustic Equation in an Absorptive Layered Medium. Comput Math Model 29, 83–95 (2018). https://doi.org/10.1007/s10598-018-9390-9
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DOI: https://doi.org/10.1007/s10598-018-9390-9