Determination of internal structure of geomedium using ABCD matrices and shadow method

The article briefly reviews and analyzes the methods to determine internal structure of a geomedium, such as X-ray tomography, acoustic microscopy and laser ultrasonic structural imaging. The relevance of the acoustic shadowing of the internal structure of a geomedium is justified. The method to solve this task with regard to diffraction, phase-velocity dispersion and frequency-dependent attenuation is proposed. The mechanism of the acoustic wave propagation in a heterogeneous medium is examined. The theory of modeling of acoustic signal propagation in such media is described. It is analyzed how diffraction phenomena influence the signal, and the method of including them in modeling using ABCD matrices is presented. The analysis of the phase-velocity dispersion and frequency-dependent attenuation, as well as their connection with the Kramers–Kronig relations is performed, and the method to include these characteristics in modeling is described. A special layered specimen with embedded heterogeneity is manufactured for testing using the proposed method. The restored profile of the specimen is presented with characterization of each layer. The comparison of the results with the conventionally obtained data proves applicability of the developed method to determining internal structure of geomedia in the shadow mode.

Keywords: laser optoacoustic method, ultrasonic control, layered media, nondestructive testing, modeling methods, ABCD matrices, structural imaging, acoustic pulse propagation.
For citation:

Pashkin A. I., Vinnikov V. A., Cherepetskaya E. B. Determination of internal structure of geomedium using ABCD matrices and shadow method. MIAB. Mining Inf. Anal. Bull. 2022;(8):14-26. [In Russ]. DOI: 10.25018/0236_1493_2022_8_0_14.


The study was supported by the Russian Foundation for Basic Research, Project No. 20-35-90044.

Issue number: 8
Year: 2022
Page number: 14-26
ISBN: 0236-1493
UDK: 550.3
DOI: 10.25018/0236_1493_2022_8_0_14
Article receipt date: 23.06.2022
Date of review receipt: 28.06.2022
Date of the editorial board′s decision on the article′s publishing: 10.07.2022
About authors:

A.I. Pashkin1, Engineer, e-mail:, ORCID ID: 0000-0002-8774-5982,
V.A. Vinnikov1, Dr. Sci. (Phys. Mathem.), Assistant Professor, Head of Chair, e-mail:,
E.B. Cherepetskaya1, Dr. Sci. (Eng.), Professor, e-mail:, ORCID ID: 0000-0002-9642-2149,
1 National University of Science and Technology «MISiS», 119049, Moscow, Russia.


For contacts:

A.I. Pashkin, e-mail:


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