Fast Computation of Uncertainty Quantification Problems for Viscoacoustic Wave Equation

This paper is concerned with the fast computation of uncertainty quantification problems for viscoacoustic wave equation. Waves propagating through real geology are subject to large uncertainties due to the complex structure, non-uniformity, and porosity of the geology, where the uncertainty in wave speed has the greatest impact on wave propagation. We use a probabilistic collocation method based on the Karhunen-Loève expansion to study the effect of wave velocity uncertainty on the wave field in the viscoacoustic wave equation. Meanwhile, in the process of calculating stochastic viscoacoustic wave equations, for the difficult problem of large data storage and high arithmetic complexity, we combine the short-memory operator splitting method and the sparse mesh scheme based on Smolyak's algorithm to solve this problem. The short-memory operator splitting method reduces the amount of data storage for the numerical simulation of a single sample from <Formula format="inline"><TexMath><?TeX $\mathcal{O}( {{N}_T{N}_X} )$ ?></TexMath><File name="a00--inline1" type="gif"/></Formula> to <Formula format="inline"><TexMath><?TeX $\mathcal{O}( {{N}_X{N}_{step}} )$ ?></TexMath><File name="a00--inline2" type="gif"/></Formula>, which dramatically reduces the computation time. Moreover, the sparse grid scheme can greatly reduce the number of required sample points. The research results in this paper help to improve the imaging resolution and accuracy of seismic surveys, which lays the foundation for the evaluation and optimization of geological models, resource development, and other aspects of research.