Effects of errors and biases on the scaling of earthquake spatial pattern: application to the 2004 Sumatra-Andaman sequence

This study discusses the scaling properties of the spatial distribution of the December 26, 2004, Sumatra aftershocks. We estimate the spatial correlation dimension D-2 of the epicentral distribution of aftershocks recorded by a local network operated by Geological Survey of India. We estimate the value of D-2 for five blocks in the source area by using generalized correlation integral approach. We assess its bias due to finite data points, scaling range, effects of location errors, and boundary effects theoretically and apply it to real data sets. The correlation dimension was computed both for real as well as synthetic data sets that include randomly generated point sets obtained using uniform distributions and mimicking the number of events and outlines of the effective areas filled with epicenters. On comparing the results from the real data and random point sets from simulations, we found the lower limit of bias in D-2 estimates from limited data sets to be 0.26. Thus, the spatial variation in correlation dimensions among different blocks using local data sets cannot be directly compared unless the influence of bias in the real aftershock data set is taken into account. They cannot also be used to infer the geometry of the faults. We also discuss the results in order to add constraints on the use of synthetic data and of different approaches for uncertainty analysis on spatial variation of D-2. A difference in D-2 values, rather than their absolute values, among small blocks is of interest to local data sets, which are correlated with their seismic b values. Taking into account the possible errors and biases, the average D-2 values vary from 1.05 to 1.57 in the Andaman-Nicobar region. The relative change in D-2 values can be interpreted in terms of clustering and diffuse seismic activity associated with the low and high D-2 values, respectively. Overall, a relatively high D-2 and low b value is consistent with high-magnitude, diffuse activity in space in the source region of the 2004 Sumatra earthquake.