Reply to “The Correspondence of Earthquakes and Faults” by C. Scholz

Zou and Fialko (2024a), https://doi.org/10.1029/2024ea003824 analyzed the fault length statistics using several data sets spanning a wide range of length scales from millimeters to tens of kilometers, and concluded that the cumulative fault length distribution follows a universal power law with an exponent close to −2, implying that small faults can accommodate an appreciable fraction of tectonic strain. C. Scholz wrote a Comment in which he agrees with the main conclusions of our study, but questions the methodology that “fortuitously” gave rise to a correct answer. In particular, Scholz suggests that there is a spurious correlation in our estimation of the slope of a composite data set, which cancels out due to a lower-dimensional sampling bias. Here we show that our estimated absolute value of the power law exponent of $\sim 2$ is not a result of normalizing the fault length-frequency distribution by the map area, as suggested by Scholz. We also maintain that the lower-dimensional bias is likely to decrease the estimated value of the power law exponent, but not by as much as 1 unit, so that the strain energy in the crust hosting the fault population remains finite. Estimating the magnitude of the lower dimensional bias for realistic fault distributions is important for distinguishing between the “inclusive correspondence” between faults and earthquakes, as proposed by Scholz in his Comment, and similar but distinct distributions of active and inactive faults, as proposed by Zou and Fialko (2024a), https://doi.org/10.1029/2024ea003824. This issue also directly bears on the amount of inelastic strain absorbed by small faults in developing shear zones.