CONVERGENCE OF POINT PROCESS INTENSITY IN A TWO-DIMENSIONAL PARAMETER SPACE
A point process is one of the fundamental concepts in probability theory and statistics, used to model random events scattered in space or time. A point process with a two-dimensional parameter space is denoted by {????(????)???????2}. In this study, ???? represents the observation area of earthquak...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/85832 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | A point process is one of the fundamental concepts in probability theory and statistics, used to model random events scattered in space or time. A point process with a two-dimensional parameter space is denoted by {????(????)???????2}. In this study, ???? represents the observation area of earthquake occurrences in West Java from 2014 to 2023, thus ????(????) denotes the number of earthquake events in the region ??????2. A successful event is defined as an earthquake occurring in West Java between 2014-2023 with a magnitude ?4.0 on the Richter scale and a hypocenter depth ?[0,300] km. The area ???? is partitioned using a polar partitioning approach that utilizes polar coordinates (?, r). Three partitioning models are: model A, B, and C. Model A is a polar partitioning technique where ????????=???????? and ?????????????????, for |????????|=|????????|,?????????. In model B, the condition is ????????=???????? and ????????=????????. Meanwhile, model C has the condition ????????????????? and ?????????????????. The condition ????????????????? and ????????=???????? does not satisfy |????????|=|????????|,?????????, thus cannot be considered a valid polar partitioning model. The models applied to ???? are model A, B, and a mixed model (A and B). Models A or B are used to determine the minimum number of partitions such that each partition contains at most one successful event. The mixed model is used to observe and classify areas based on the distribution of earthquakes. These three partitioning models yield different calculated values of ?. Additionally, ? is estimated using the Kernel Estimation Intensity (KEI) based on model A. Convergence of intensity refers to the approximation of a sequence of ? values toward a specific value as r and/or ? change. The earthquake intensity in the point process will approach a constant or stable value for certain r and/or ?. |
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