Statistical Analysis on Background Seismicity of Southern California Region: Application of Nearest Neighbour Declustering and Network Analysis

The Nearest Neighbour declustering technique is utilized to differentiate dependent events, such as aftershocks and foreshocks from independent events, such as isolated and mainshocks events . The estimated background field could either be stationary or non-stationary over time and may exhibit patterns that depend on both space and time. Any residual deviations from a time-stationary and spatiotemporally-independent Poisson point field could offer insights into regional loading processes and merit further investigation (Zaliapin and Ben-Zion, 2020). We apply the adopted technique on the Southern California region, an area that includes four significant events with magnitudes greater than 7, over the years 1981- 2021 and the catalog's completeness ranges between magnitudes 2 to 3 (Zaliapin and Benzion, 2020). For generating the complete background set, both outdegree and closeness centrality yielded nearly identical mainshock node counts for background detection in our study region, highlighting the robustness of these centrality measures.   In a tree network, hierarchy identification might not be straightforward, but utilizing centrality can aid in placing elements accurately. Higher centrality values indicate a simpler structure compared to lower centrality values. Although the traditional highest magnitude method produces results almost similar to those of the centrality measure from network analysis, the network-based approach offers new possibilities for future research in the study of earthquake sequences and their evolution. In a spatially inhomogeneous, temporally homogeneous Poisson process (SITHP), there is a strictly positive probability that two events may occur arbitrarily close to each other  and NN method works better for declustering with this condition (Luen and Stark, 2012). In this study, three temporal statistical tests have been conducted: the Conditional Chi square(CC) test, the Brown-Zhao(BZ) test, and the Kolmogorov smirnov (KS) test on the complete background set. It was found that the KS test, which assumes the time series follows a uniform distribution and does not require any adjusting parameters, is more reliable than the other two tests(requires more tuning constants). For almost all magnitude cut-offs, the temporal tests fail the null hypothesis; however, for a magnitude of 3.4, the temporal test is satisfied, but the space time test ( Luen and Stark test) fails the null hypothesis. For the nearest neighbour (NN) method, the null hypothesis is rejected for all magnitude ranges in our study region. Consequently, it can be concluded that NN declustering is not effective for this dataset or the number of data points is low. Notably, the Luen and Stark space time test yielded a value of 0 for most magnitudes, except for magnitudes 4 and 4.2. This suggests two potential scenarios: either the earthquakes are inadequately declustered, leading to some background events being overlooked or there is another possibility that this model is not fit for the Poisson process and suggesting a need for an alternate conditional model.

References:

Luen, B., & Stark, P. B. (2012). Poisson tests of declustered catalogues. Geophysical journal international, 189(1), 691-700. https://doi.org/10.1111/j.1365-246X.2012.05400.x.

Zaliapin, I., & Ben‐Zion, Y. (2020). Earthquake declustering using the nearest‐neighbour approach in space‐time‐magnitude domain. Journal of Geophysical Research: Solid Earth, 125(4), e2018JB017120. https://doi.org/10.1029/2018JB017120.