Random boundary condition for low-frequency wave propagation

Broadband modeling application

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Figure 4. Time-domain and frequency-domain broadband source with a peak frequency of $25$ Hz: a) Time-domain wavelet; b) Frequency-domain amplitude spectrum. [ER]

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Figure 5. Time domain wavefield snapshots for a broadband point source with a peak frequency of $25$ Hz, in velocity fields with different random boundary conditions. The top row shows one realization of velocity with a) constant velocity, b) cubic grains with $20$ m side length, c) cubic grains with $200$ m side length, and d) randomly shaped grains with effective length $200$ m. The bottom row shows average wavefields using $16$ realizations of velocity with e) constant velocity, f) cubic grains with $20$ m side length, g) cubic grains with $200$ m length, and h) randomly shaped grains with effective length $200$ m. [CR]

In this section, we test a broadband point source with a peak frequency of $25$ Hz, using the same boundary as in the previous example. Figure 4 shows the amplitude spectrum of the point source used, which contains non-trivial high- and low-frequency components. Figure 5 (top row) shows 2D slices of the wavefield using one realization of each velocity. In this case, the proposed random boundaries still work quite well. A random boundary with a small grain size is effective at high frequency, but has difficulty eliminating low-frequency components of the source. This is more obvious in the bottom row of Figure 5, which is the stacked wavefield of the same source and record time, using $16$ different realizations of random boundaries.

Random boundary condition for low-frequency wave propagation