Double Penalty Approach for Cauchy Cluster Process with Log-Additive Intensity (Case Study: Earthquake Risk Modeling in Sumatra)

Susanto, Tabita Yuni (2023) Double Penalty Approach for Cauchy Cluster Process with Log-Additive Intensity (Case Study: Earthquake Risk Modeling in Sumatra). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Earthquake distribution modeling in Sumatra has been carried out using various cluster point processes assuming a log-linear intensity model. However, the log-linear assumption could be unrealistic in a real case especially when the form of the intensity is different from the log-linear model. In this study, we consider modeling the distribution of earthquakes in Sumatra by using Cauchy cluster process with a log-additive intensity function. The estimation procedure consists of two steps. The first step is considering penalized iteratively reweighted least squares (PIRLS) with double penalties to estimate the first-order parameter. We employ cubic, cyclic, and thin plate regression spline as smooth functions. To select the optimum smooth function, the number of basis sizes, and smoothing parameters, we use the smallest Generalized Cross Validation (GCV) value. Next, the second step employs the second-order composite likelihood to estimate cluster parameters. The covariates used are the geological variables (volcano, fault, subduction zone) and the geometry of the subduction plate (dip, strike, depth). For the earthquake analysis in Sumatra, the log-additive intensity shows more flexibility to determine the contribution of each covariate, especially to capture the effect of the nearest distance to the fault and volcano which is far from log-linear. The optimum log-additive model uses a cubic regression spline (for distance to the subduction zone and volcano, dip, depth, strike), and a thin plate regression spline (for distance to fault with an optimum basis size of 13. The optimum basis size for distance to subduction zone, dip, and strike is 15, while for distance to the volcano and depth is 14. Cauchy cluster process model with the log-additive intensity gives better performance than the log-linear in terms of AIC value and intensity prediction maps. The double penalty approach does not improve the model significantly (only decreases AIC values of 1.141). The estimated number of mainshocks is around 71 with aftershocks spread by 10.7 km around the mainshocks. We detect two hotspots for the major earthquake in Sumatra: the northern part and the western part (Mentawai, Nias, Simeulue)

Item Type: Thesis (Masters)
Uncontrolled Keywords: Earthquake, GCV, Geometry, Smooth Function, Spatial Point Process.
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
Q Science > QA Mathematics > QA401 Mathematical models.
Divisions: Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User: Tabita Yuni Susanto
Date Deposited: 17 Feb 2023 08:37
Last Modified: 17 Feb 2023 08:37

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