Surrogate combining harmonic decomposition and polynomial chaos for seismic shear waves in uncertain media

A polynomial chaos (PC) surrogate is proposed to reconstruct seismic time series in one-dimensional (1D) uncertain media. Our approach overcomes the deterioration of the PC convergence rate during long time integration. It is based on a double decomposition of the signal: a damped harmonic decomposition combined with a polynomial chaos expansion of the four coefficients of each harmonic term (amplitude, decay constant, pulsation, and phase). These PC expansions are obtained through the least squares method which requires the solution of nonlinear least squares problems for each sample point of the stochastic domain. The use of the surrogate is illustrated on vertically incident plane waves traveling in 1D layered, vertically stratified, isotropic, viscoelastic soil structure with uncertainties in the geological data (geometry, wave velocities, quality factors). Computational tests show that the stochastic coefficients can be efficiently represented with a low-order PC expansion involving few evaluations of the direct model. For the test cases, a global sensitivity analysis is performed in time and frequency domains to investigate the relative impact of the random parameters.