Generation of spatially correlated fracture models for seismic simulations

Abstract

SUMMARY The critical geometrical parameters that quantify the spatial distribution of natural fractures are the orientation, length and position of fractures. Knowledge of their spatial distribution is important as they control the movement of subsurface fluids and also influence seismic waves propagating in the subsurface. However, generating realistic models of all of these geometrical parameters to use in forward seismic modelling or inversion applications can become very difficult, especially when constraints are available only at a few sparse well locations. Hence, this provides strong motivation for applying seismic data to estimate these quantities in field settings, and reliable seismic modelling provides important constraints for interpretation and inversion. The Discrete Fracture Network (DFN) approach has been used frequently to generate models with stochastic distributions of fractures based on sparse well and seismic data. However, most of these studies lack any constraint from physical models of the behaviour of fractured media. In this paper, we implement and extend an alternative modelling technique to generate several realizations of a fracture model beginning with theoretical results for the strain energy of a fractured material and propose ways to better incorporate geological field observations. The method utilizes an elastic energy function that sums the interactions of all pairs of fractures present in the model. The energy for each pair depends on the distance between the two fractures, their orientations, lengths and some material properties. This energy function also serves as an objective function for a simulated annealing (SA) algorithm used to obtain multiple realizations of correlated fracture networks. We improve earlier versions of this technique by incorporating periodic boundary conditions, including criteria to limit the maximum range of pair-wise calculations and suggesting methods to constrain models to match field data. Assuming that the host rock is isotropic and homogeneous, this method produces orthogonal sets of fractures, a pattern that is commonly observed during basin formation or subsidence. This shows how the method can be utilized to provide constraints with a physical basis to facilitate the development of fracture models. We also outline how the fracture model can be converted into an anisotropic seismic velocity model to compute synthetic seismograms for reservoir characterization applications.