GRAPHICAL METHOD TO RELATE KINEMATIC VORTICITY, VELOCITY, AND INCREMENTAL STRAIN WITHIN PLANE AND NONPLANE CONDITIONS: EXAMPLE FROM THE TRANSTENSIONAL WALKER LANE BELT, WESTERN GREAT BASIN

Divergence between velocity trajectories calculated from regional GPS networks and incremental strain trajectories determined from earthquake focal mechanisms and fault-slip inversion studies are best reconciled as the predicted consequence of nonplane rotational strain deformation. The observations are consistent with theoretical models connecting kinematic vorticity, particle velocity paths, and incremental strain (eg. Tikoff & Teyssier, 1994), especially for deforming zones associated with oblique plate motions. Producing analytical or numerical solutions that directly relate incremental strain and velocity trajectories via kinematic vorticity of the resultant strain field, however, is not as visually straight forward as a graphical solution. A 2D Mohr circle graphical solution exists that allows rapid calculation and easy visualization of physical relations. The Mohr circle modification for strain derived by De Paor (Simpson & De Paor, 1993) uses stretch and rotation, originally devised for rotated porphyroclasts in ductile shear zones, is ideal for the analysis of modern geodynamic data. This construction provides a link between GPS velocities and the instantaneous strain. Alternatively, the orientation of the velocity vector corresponding to the flow apophysis can be determined if the incremental strain axes are known, for instance from earthquake data. The vorticity number (W_K) can then be calculated. Forward strain modeling is also possible because this construction can be integrated over different lengths of time. To complete this construction the boundary parallel displacement rate, GPS velocity vector (and / or plate convergence vector) and width of the deforming zone are needed. This construction is applied to different domains of strain within the Walker Lane, Nevada. The regional northwest translation of the Sierra Nevada microplate produces a transtensional regional strain. This strain is partitioned into wrench dominated and pure shear dominated domains. The construction is able to successfully predict both the incremental strain axes and G.P.S. velocity field for both domains. The construction has also been successfully applied to the transpressional Aleutian Island Arc and the transtensional Reykjanes Peninsula, Southern Iceland.