Abstract: A method and system for generating a model function h(x,y,z) implicitly representing geologic horizons. Geological data representing a fault network and horizons automatically extracted from seismic data may be received. A 3D mesh may be generated and divided into a plurality of fault blocks by the fault network. A discrete function h(x,y,z) may be defined having values of the geological data representing horizons at discrete nodes of the mesh. Constraints may be installed on the discrete function h(x,y,z) defining surfaces representing horizons. Constraints may be installed on the discrete function h(x,y,z) to ensure the uniqueness of the function h(x,y,z). The discrete function h(x,y,z) may be interpolated at the nodes of the mesh to create a piecewise continuous function h (x,y,z) while honoring the constraints. The piecewise continuous horizon function h(x,y,z) may be synchronized across multiple fault blocks. A model of the piecewise continuous horizon function h(x,y,z) may be displayed.

Abstract: A method and system for generating a model function h(x,y,z) implicitly representing geologic horizons. Geological data representing a fault network and horizons automatically extracted from seismic data may be received. A 3D mesh may be generated and divided into a plurality of fault blocks by the fault network. A discrete function h(x,y,z) may be defined having values of the geological data representing horizons at discrete nodes of the mesh. Constraints may be installed on the discrete function h(x,y,z) defining surfaces representing horizons. Constraints may be installed on the discrete function h(x,y,z) to ensure the uniqueness of the function h(x,y,z). The discrete function h(x,y,z) may be interpolated at the nodes of the mesh to create a piecewise continuous function h (x,y,z) while honoring the constraints. The piecewise continuous horizon function h(x,y,z) may be synchronized across multiple fault blocks. A model of the piecewise continuous horizon function h(x,y,z) may be displayed.