Anisotropy of fractal dimension of normal faults in northern Rocky Mountains: Implications for the kinematics of Cenozoic extension and Yellowstone hotspot's thermal expansion

•Anisotropy of fractal dimensions provides kinematic information for normal faults.•Extension direction is estimated from the trend of anisotropy ellipse's major axis.•Trajectories of the minor axes form sub-parabolic pattern around eruption centers.•Fractal dimension of normal faults decreases with distance from centers of eruption.

The Basin and Range fault blocks, which were formed by an extensional event around 17 Ma, have continuously been deforming by younger, diachronous system of cross normal faults in southwest Montana and southeastern Idaho since 16.6 Ma. Reactivation of these two mid-Tertiary-Quaternary systems of normal faults, and two older, approximately N-S and E-W sets of regional normal faults, has evolved into a seismically active block faulted terrain. For both fault systems, high fractal dimensions occur in areas characterized by a large number of fault traces, high fault trace linear density, and maximum fault trace azimuthal variation. The major axis of the anisotropy ellipse of the fractal dimensions for each set of the two normal fault systems is sub-perpendicular to the linear directional mean of the faults, and gives an estimate for the direction of extension.Indentations on the point distribution on the anisotropy ellipse of fractal dimensions indicate heterogeneities due to the presence of several fault sets and/or variation in their trend. Domains in which there is only one set of faults produce smooth, well-defined fractal anisotropy ellipses with no indentations. The axial ratio of the anisotropy ellipse provides a measure for the range of variation in the trend of the faults. The trace length, linear density, and fractal dimension of the cross normal faults, decrease, in a direction across and away from the Snake River Plain (SRP), suggesting a diminishing effect of faulting probably due to the attenuation of the Yellowstone hotspot-related thermal doming with distance from centers of eruption. The spatio-temporal distribution of the trajectories of the minor axes of the anisotropy ellipses of fractal dimensions and the linear directional mean of the cross faults define a set of asymmetric, sub-parabolic spatio-temporal pattern about the axis of the SRP, with their apices located on diachronous centers of eruption.