Calculating normal fault geometries at depth: theory and examples

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Abstract
In recent years, a large number of methods relating the shape of a normal fault at depth to the shape of a sedimentary horizon in its hangingwall have been described. Such methods are best used in areas where it can be assumed that the footwall remains relatively undeformed during extension. This assumption may not always be valid, especially in the case of large-scale, basement-extending normal faults. Conservation of area (or solid area when compaction occurs) must be the fundamental constraint. The advantages and disadvantages of the various methods are briefly outlined. A general model which assumes that hangingwall deforms by arbitrarily inclined simple shear and differential compaction is discussed. Fault geometry, the inclination of simple shear, and compaction parameters may all be determined from N beds using a simple inversion scheme based on this general method. The algorithm has previously been tested on synthetic data using a range of fault geometries. Such testing indicates that all unknown parameters including fault geometry can, in general, be uniquely determined provided that the geometries of two or more beds within the hangingwall are known. It is important that hangingwall and footwall stratigraphies are accurately known, though uncertainty in either could be included as a bounded variable within a formal inversion scheme. In this paper, the method is applied to laboratory-modelled normal faulting and to depth-converted seismic reflection data. Results suggest that hangingwalls deform by bulk, antithetically inclined, simple shear. Differential compaction of hangingwall sediments is often important and should be taken into account.

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