Stochastic fracture simulation using pixel-based multiple-point geostatistics by integrating seismic radial anisotropy and well data: applications in two hydrology sites

We propose a pixel-based multiple-point simulation algorithm for stochastic simulation of near surface fractures using seismic radial anisotropy as secondary information. The method borrows information from the training image of the fracture and anchoring within the secondary radial anisotropy data using wavelet-based multiple-point simulation framework. The simulation was performed sequentially, by sampling from the conditional cumulative density function (ccdf) of fracture, conditioning to radial anisotropy. For faster computation, instead of calculating ccdf at each unknown location, a limited number of ccdfs are calculated. The patterns of the multiple-point representation are extracted from the training image and are classified into multiple classes using the wavelet decomposition analysis. Each class is represented by a class prototype and ccdf. During simulation, the conditioning data are compared with the class prototypes, and a random sample is generated from the ccdf of the best match class. We validated the proposed simulation method using a synthetic fracture dataset. A sensitivity analysis was also performed to show the impact of correlation between fracture and radial anisotropy, and the resolution of the radial anisotropy. Results demonstrated that the reproduction of the fracture depends on its correlation with the radial anisotropy. It was also observed that fracture reproduction is proportional to the resolution of the radial anisotropy. We successfully applied our proposed model to two hydrogeological sites in which seismic radial anisotropy was obtained using the dispersion analysis of the surface wave.