Distributed deformation and block rotation in three dimensions

Abstract

The focus of this paper is to understand distributed deformation, in particular the relationship between fault slip and rotation of faults and blocks in a three dimensional stress field. Regions of distributed deformation, such as Southern California, are organized in complex arrays of contemporaneously active block‐faulted domains. We believe that the present day orientation of faults in many domains is due to the contemporaneous slip and rotation of the faults and of the blocks they bound. Traditional friction models cannot explain active unfavorably oriented faults and do not consider how faults become unfavorably oriented. To solve this problem, we propose a three dimensional block rotation model that tracks the orientation of blocks and their bounding faults during rotation. Mechanically, we consider Coulomb criteria for rock fracture as an upper bound, and slippage on a frictional surface as a lower bound. The key parameter in our model is the value of ϕ = (σ2 – σ3)/(σ1 – σ3). Principal stress directions are assumed irrotational through time. This model predicts up to 75° of vertical axis rotation along a single set of faults. During rotation, fault slip may change, sometimes dramatically, giving rise to mixed vertical as well as horizontal axis of rotation of blocks and faults. For very unfavorably oriented faults the model predicts rotations about a vertical axis in both the normal and reverse stress regimes, and about a horizontal axis in the strike‐slip stress regime. Therefore paleomagnetically inferred rotations may not always be directly related back to a specific stress regime. Combining frictional constraints of the block rotation model with paleomagnetic, structural and geological data, we show how only one set of faults, preexisting and rotating in an irrotational strike‐slip stress field, can account for the three major phases of deformation observed in the Western Transverse Range domain, Southern California: preexisting north‐northeast faults were reactivated as normal faults, rotated and became strike‐slip, and subsequent rotations of faults resulted in their present east‐west high angle reverse orientation. This example demonstrates that it is not necessary to invoke complex regional and local changes in the stress regime or erratic changes in plate motion to account for alternate periods of compression and extension.