We address the basic theoretical and algorithmic aspects of memory-efficient implementation of realistic attenuation in the staggered-grid finite-difference modeling of seismic-wave propagation in media with material discontinuities. We show that if averaging is applied to viscoelastic moduli in the frequency domain, it is possible to determine anelastic coefficients of the averaged medium representing a material discontinuity. We define (1) the anelastic functions in a new way, as being independent of anelastic coefficients, and (2) a new coarse spatial distribution of the anelastic functions in order to properly account for material discontinuities and, at the same time, to have it memory efficient. Numerical tests demonstrate that our approach enables more accurate viscoelastic modeling than other approaches.

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