Statistical analysis of the relationships between faults attributes

摘要

The statistical analysis of fault attributes scaling relationships is discussed. Dependences of length, width of damage zone and thickness of fault core on displacement were studied assuming power law relations. The approximation forms a piecewise-linear function with few slopes in log-log scale. The Bayesian Information Criterion (BIC) was used to find the best fit for an optimal number of parameters. Numerical tests show that the best fit was obtained when using power law relations with two slopes. Bayesian analysis of model parameters' probability distribution was performed. For length-displacement relation (L-D), the slope decreases from one scale of faults to another. This change occurs at ～1 m displacement for reverse and normal faults in siliciclastic rocks, at ～1500 m displacement for strike slip and at ～300 m displacement for normal faults in non-siliciclastic rocks. The slope of the damage zone width-displacement (W-D) relation decreases at ～10 m, while it slightly increases for fault core thickness-displacement (T-D) relation at ～10 cm. The result of the probability density of changepoints confirms the calculated changepoints, which correspond to maximal BIC in most cases. We propose an evolutionary growth pattern of faults based on the statistical results, in which faults lengthen during the initial stage. During subsequent overlapping and linkage between the faults, mainly displacement accumulates. Fault damage zone and fault core form early in the process of faulting. In mature faults, the development of damage zone would be slower than for small faults, whereas fault core slightly thickens with further localization.