Methods and algorithms of computational mathematics and their applications

Structure-oriented smoothing for wave propagation modelling by beam method with frequency dependence

A. D. Stein, M. I. Protasov

Trofimuk Institute of Petroleum-Gas Geology and Geophysics SB RAS

Abstract: This paper considers an empirical method for obtaining a frequency-dependent velocity model using structure-oriented smoothing. Smoothing is performed depending on the source position, frequency, and time field. Three smoothing methods are implemented: smoothing along a locally flat wavefront, smoothing by anisotropic diffusion and volumetric smoothing in the Fresnel zone. Anisotropic diffusion smoothing time is compared with the frequency of the smoothing in the Fresnel zone. A comparison of smoothing methods is carried out, showing that volumetric smoothing in the Fresnel zone provides the most stable solution.

Keywords: structure–oriented smoothing, frequency dependence, smoothing, Lomax smoothing, anisotropic diffusion, Fresnel zone, Gauss smoothing.

UDC: 519.688

Received: 14.07.2025
Accepted: 15.08.2025

DOI: 10.26089/NumMet.v26r321