Fractal nature and scaling of normal faults in the Española Basin, Rio Grande rift, New Mexico: implications for fault growth and brittle strain

Quaternary faults in the western Española Basin of the Rio Grande rift show a power-law size (displacement) distribution suggesting that faulting in this region is scale invariant, and that faults are self similar. The power law, or fractal, distribution is characterized by fractal dimension of 0.66 to 0.79 and represents a young, immature, active fault population in a continental extensional regime. Based on this distribution, it is estimated that unobserved faults with very small displacements account for up to 6% of the total strain. Since 1.2 Ma. total extension in this part of the basin has been at least 5%. A direct correlation exists between maximum displacement and length of faults in this area suggesting that they obey a scaling relationship in which the ratio of log d_max/log L is 5 × 10^-3. This ratio is nearly constant for faults whose lengths span three-orders of magnitude, indicating that there is no difference in the scaling relationship of displacement and length between faults of all sizes. Considering previous models, these fault characteristics suggest that, in the western Española Basin: (1) host rock shear strengths are low; (2) remote shear stresses were probably high: and (3) most faults do not extend throughout the brittle crust. Finally, displacement profiles on five of the largest faults arc asymmetric and show a rapid decrease in displacement from the point of maximum displacement toward the fault tip. The fractal nature, scaling relationship and distribution of displacement on faults are used to suggest that faults grew by nearly proportional increases in displacement and length, perhaps by mechanisms dominated by propagating shear fractures rather than by linkage of pre-existing joints or faults.