The purpose of our first example is to investigate the accuracy of the solution of the constant- wave equation using the proposed low-rank scheme, in the presence of a sharp contrast in both velocity and
. We use an isotropic two-layer model with
in the top layer and
in the bottom layer. The model is discretized on a
grid, with a spatial sampling of
along both
and
directions. An explosive source with a peak frequency of
is located at the center. The reference frequency is
. Wavefield snapshots are taken at
. Figure 1a shows the acoustic case, in which the model has the velocity discontinuity but no attenuation (
). For comparison, Figure 1b demonstrates the effect of homogeneous attenuation where
. Both velocity dispersion and amplitude loss can be observed. In Figure 1c, we set
in the top layer and
in the bottom layer. The transmitted arrival exhibits less attenuation compared with that in Figure 1b. In Figure 1d, both velocity and
remain the same as those in Figure 1c; however, the fractional power of Laplacians,
, is taken to be the averaged value, which corresponds to the original implementation by Zhu and Harris (2014). To compare the results modeled by the two strategies, a middle trace at
is extracted from both wavefield snapshots (Figures 1c and 1d). Figure 2 shows the two traces, along with their difference. Errors caused by using a constant
instead of a spatially varying
can be easily observed.
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snap-0,snap-1,snap-3,snap-4
Figure 1. Viscoacoustic wave propagation in a two-layer model: (a) acoustic modeling with ![]() ![]() ![]() ![]() ![]() ![]() |
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cross
Figure 2. Traces at ![]() ![]() ![]() |
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