Automated construction of realistic lithofacies maps using combinatorial optimization methods

Lithofacies maps display spatial changes in the lithological composition of rocks and the direction of their replacement characteristics for a certain geological time depending on the physical and geographical conditions of their sedimentation. Lithofacies maps are constructed based on the analysis of complexes of genetically related deposits with characteristic material features of lithofacies. The initial data can be either only points on a plane — well coordinates where certain lithofacies occur — or additionally a map of sediment accumulation rates. It is assumed that identical facies should have similar sedimentation rates. The task of constructing a lithofacies map is to determine the boundaries of facies distribution areas. The paper proposes to reduce the map construction problem to the graph coloring problem, which in turn is solved using integer linear programming methods. This approach allows us to automatically construct realistic maps – that is, maps that satisfy expert constraints and rules.