Amplitude behavior in low-rank acoustic modeling

The numerical simulation of wave propagation can be represented by a propagator matrix applied to previous instances of the wavefield. Using the sparsity of the propagator matrix to approximate it by a low-rank representation, one can increment the wavefield’s phase from one time instance to another. Though this procedure does not pay attention to the amplitudes of the seismic waves, it is important to understand its dynamic properties. Here, we evaluate the amplitudes obtained by the low-rank method in the simulation of 2D acoustic wave propagation. In homogeneous media, where theoretical expressions for the wavefield are available, the method provides not only an excellent kinematic approximation, but also reliable amplitudes. For a single horizontal reflector below a homogeneous overburden, the reflection coefficients approximated by the low-rank method are of the same quality or slightly superior to those obtained by a second-order finite-difference (FD) method (implementation from SU). However, in more generally inhomogeneous media, our tests showed larger discrepancies between FD and low-rank modeling results. While comparing unfavorably with FD regarding computation time for small models, its quasi-linear scaling with model size makes the low-rank method superior for large models. Moreover, a generalization to more complex, e.g., anisotropic, media is straightforward.