The uncertainty analysis of seismic reflection coefficient estimation based on polynomial chaos expansion

To estimate the seismic reflection coefficients, using deterministic computational methods, the velocities and density of a layer are assumed to be constant; this assumption is not required when using statistical analysis, such as the polynomial chaos expansion. If we let the input parameters of a layer to vary, the determination of the reflection coefficient will have uncertainty. Accurate determination of the reflection coefficient is valuable for the correct modelling of wave propagation amplitude. The standard deviation is an indicator of our data distribution. To reduce the uncertainty of the reflection coefficient estimated using the Zoeppritz equations, standard deviations are considered for the input parameters. In this paper, the following steps are taken to investigate the changes of the reflection coefficient curve of layer with depth: 1) the P-, and S-wave velocities, and density, are used in the Zoeppritz equations to determine the reflection coefficients in the polynomial chaos expansion; 2) the accuracy of the estimated reflection coefficients is better, while the standard deviations for the input parameters is low. Using the lower standard deviations for the input parameters resulted highly accurate in estimating reflection coefficients and critical angle.