A 3D complexity-adaptive approach to explore sparsity in elastic wave propagation

We have developed an adaptive approach for seismic modeling by which the computational cost of a 3D simulation can be reduced while retaining the resolution and accuracy. This azimuthal complexity adaptation (ACA) approach relies upon the inherent smoothness of wavefields around the azimuth of a source-centered cylindrical coordinate system. Azimuthal oversampling is thereby detected and eliminated. The ACA method has recently been introduced as part of AxiSEM3D, an open-source solver for global seismology. We use a generalization of this solver that can handle local-scale Cartesian models and that features a combination of an absorbing boundary condition and a sponge boundary with automated parameter tuning. The ACA method is benchmarked against an established 3D method using a model featuring bathymetry and a salt body. We obtain a close fit when the models are implemented equally in both solvers and an expectedly poor fit otherwise, with the ACA method running an order of magnitude faster than the classic 3D method. Furthermore, we evaluate maps of maximum azimuthal wavenumbers that are created to facilitate ACA. We determine how these maps can be interpreted in terms of the 3D complexity of the wavefield and in terms of seismic resolution. The expected performance limits of the ACA method for complex 3D structures are tested on the SEG/EAGE salt model. In this case ACA still reduces the overall degrees of freedom by 92% compared with a complexity-blind AxiSEM3D simulation. In comparison to the reference 3D method, we again find a close fit and a speedup of a factor of 7. We explore how the performance of ACA is affected by model smoothness by subjecting the SEG/EAGE salt model to Gaussian smoothing. This results in a doubling of the speedup. Thus, ACA represents a convergent, versatile, and efficient method for a variety of complex settings and scales.