Аннотация:The article is concerned with the research of methods for solving inverse problems of ultrasonic tomography using mathematical models that take into account wave and absorption effects. The problem of tomographic image reconstruction is posed as a coefficient inverse problem for a wave equation. The effectiveness of the MSM method for solving inverse problems is demonstrated on model problems of ultrasonic tomographic diagnostics. This study demonstrates that the inverse problem of diagnosing soft tissues in medicine must be solved using a model that takes into account absorption. However, this may lead to artifacts in the reconstructed image. Local inclusions in the velocity structure result in artifacts in the absorption image, while local absorbing inclusions have less impact on the reconstructed velocity image. This is due to the fact that the velocity and absorption coefficients correspond to the second and first time derivatives in the wave equation, respectively, and the sounding frequencies are high enough. For the same reason, the quality of velocity reconstruction is higher than that of the absorption factor. In this work, the reasons for the appearance of artifacts and their features are studied at a physical level of rigor. The appearance of artifacts is illustrated by numerical simulations with varying contrast of inclusions.