Linearly combined ground motion model using quadratic programming for low- to mid-size seismicity region: South Korea

Abstract

This study suggests a linearly combined ground motion model (GMM) optimized for the within-rock conditions of South Korea. Ground motions recorded by accelerometers positioned in within-rock layers are used as target intensity measures (IMs), and five local GMMs and four global GMMs are used as candidates for combination. Optimization, which seeks to find a weight vector minimizing the uncertainty of the combined model, is performed using the quadratic programming (QP) technique, which provides very fast and solid results for the linear combination problem. This study illustrates how to use the QP technique for the linear combination problems. Also, we suggest optimized weight vectors for GMM combinations for two conditions: 1) the IM prediction of a scenario event without observations and 2) the IM prediction of a past event with observations. Among the local and global GMMs considered, JB03, Eea15, JH21, and BSSA14 are selected as the best four GMMs for the first condition, and Jea02, JB03, JH21, and CB14 are selected as the best four GMMs for the second condition. The combined model reduces the standard deviation of residuals in natural logarithms by 10% and 8% for the first and second conditions, respectively, compared to the best individual GMM at each period. Among the GMMs considered, the prediction by Eea15 is only applicable for magnitudes less than 5. Hence, for large magnitude (Mw ˃ 5) prediction, CB14 is recommended instead of Eea15 for the best four models for the first condition.