Two-level uncertainty assessment in stochastic seismic inversion based on the gradual deformation method

Abstract

Geostatistical seismic inversion can combine seismic data, well data, and spatial continuity of the property of interest to obtain high-resolution reservoir models and evaluate uncertainties. Some workflows estimate global geostatistical parameters, such as correlation length, and keep them fixed in all simulations and inversions. This can introduce biases due to the sparsity of available well data and underestimate the uncertainty of inversion. A better approach is to incorporate the uncertainty in these global parameters. Lateral correlation length is one of the most difficult parameters to estimate. We have developed a seismic inversion method based on local gradual deformation method, which incorporates the uncertainty of lateral correlation length and provides a two-level uncertainty evaluation. We first estimate a uniform prior distribution of lateral correlation length from well data and additional geologic expert knowledge. After using fast Fourier transform (FFT) moving average simulations and local gradual deformation optimization, we obtain multiple realizations from which we could extract the lateral correlation lengths and calculate their posterior distribution. The FFT moving average method generates reservoir models by a convolution between a filter operator and a random noise field. The filter operator does not change during inversion, and the correlation structure of the random noise field could be changed by the local gradual deformation method to match the seismic data. A synthetic model test shows that the correlation lengths and the global probability distribution of the inverted results tend to the true geostatistical characteristics. The posterior distribution of the lateral correlation length narrows after inversion. Compared with conventional geostatistical seismic inversion techniques, uncertainties in the results increase because we incorporate the uncertainty in the global parameters. A real case also demonstrated that by modifying the random noise field locally, thin layers in a thick formation are well restored, even if they are not interpreted in advance.