Can large strains be accommodated by small faults: “Brittle flow of rocks

Brittle deformation in the upper crust is thought to occur primarily via faulting. The fault length‐ frequency distribution determines how much deformation is accommodated by numerous small faults versus a few large ones. To evaluate the amount of deformation due to small faults, we analyze the fault length distribution using high‐quality fault maps spanning a wide range of spatial scales from a laboratory sample to an outcrop to a tectonic domain. We find that the cumulative fault length distribution is well approximated by a power law with a negative exponent close to 2. This is in agreement with the earthquake magnitude‐frequency distribution (the Gutenberg‐Richter law with b‐value of 1), at least for faults smaller than the thickness of the seismogenic zone. It follows that faulting is a self‐similar process, and a substantial fraction of tectonic strain can be accommodated by faults that don't cut through the entire seismogenic zone, consistent with inferences of “hidden strain” from natural and laboratory observations. A continued accumulation of tectonic strain may eventually result in a transition from distributed fault networks to localized mature faults. Plain Language Summary The Earth's crust is pervasively damaged, and contains faults, fractures, and joints of various sizes and orientations. We use mapped fault traces from multiple data sets spanning a wide range of scales to investigate how much deformation is accommodated by small versus large faults. The fault length distribution is often assumed to be fractal, that is, following a power law. The power‐law exponent α quantifies the relative contributions of many small faults relative to a few large ones. For α ≤ 1, the contribution of small faults is negligible, while for α ≥ 2, strains accommodated by small faults become significant. We find that the cumulative fault length distribution approximately follows a power law with an exponent α ≥ 2. This implies that small faults in developing shear zones can accommodate a substantial fraction of tectonic strain.