11:45 AM - 12:00 PM
[SSS11-16] A surrogate model for long-period seismic simulation of the Nankai Trough Earthquake using a sequentially additive Gaussian Process Regression
Keywords:surrogate model, Gaussian process regression, Nankai Trough earthquake, seismic ground motion simulation
Simulations for long-duration seismic motion for Nankai Trough earthquake have been studied, especially the wave propagation simulations using the finite difference method are often conducted so far. However, such theoretical methods require a lot of effort, resources, and time to obtain results for one specific earthquake scenario, and therefore, in order to use them for probabilistic seismic hazard assessment, where results for a large number of arbitrary earthquake scenarios are required, it is necessary to develop regression equations for seismic wave propagation simulation. On the other hand, previous studies have gradually accumulated simulation results calculated for a set of earthquake scenarios that take into account the diversity of Nankai Trough earthquakes.
The objective of this study is to construct a surrogate model for long-period seismic motion simulation that uses the areal results of seismic wave propagation simulations for many source scenarios accumulated so far to predict seismic motion for an arbitrarily specified virtual source scenario. This surrogate model is intended to be applied to probabilistic seismic hazard assessment, and its function is not only to obtain predictions from deterministic regression equations, but also to generate a sample of predictions from a probability distribution of uncertainties. Therefore, in this study, Gaussian process regression (GP regression) is used to develop a surrogate model for simulating the seismic hazard of Nankai Trough earthquakes. In particular, a multi-hot representation of the source region is adopted as input variable (explanatory variable) for the GP regression so that the diversity of the source model can be taken into account. In this way, it is expected to be able to predict earthquake ground motions for source regions with shapes that are not included in the accumulated results; GP regression is characterized not only by the regression equation for prediction, but also by the ability to generate sample paths considering correlations between input variables, since the covariance of the variability is obtained. Therefore, the process of generating sample paths that take into account spatial correlations between stations when the earthquake scenario is fixed is also discussed.
As a preparation for this report, a standard GP regression is performed on the PGV and period 3s velocity response Sv data sets with both station and source information as explanatory input variables. As a result, it is confirmed that a certain degree of prediction accuracy is obtained for PGV, but not sufficient for Sv. Therefore, the main outcome of this study is to apply a sequentially additive GP regression to the Sv data set. In the sequentially additive GP regression, the residuals obtained by subtracting the mean function of the posterior distribution obtained in the first GP regression from the original data set are used as the data set for the second GP regression, the residuals obtained by subtracting the mean function of the posterior distribution obtained in the second GP regression from that data set are used as the data set for the third GP regression, and the operation is repeated recursively thereafter. By setting factor-specific input variables for GP regression in each step according to the objective, it is expected to extract a mean function from the original data set in the form of the sum of factor-specific functions in a sequential manner, thereby gradually reducing the variance of the error. In this report, we show that a certain degree of prediction accuracy can be achieved for Sv by using sequentially additive GP regression.
Acknowledgments: This study is part of ' Research Project for Disaster Prevention on the great Earthquakes along the Nankai Trough' funded by Ministry of Education, Culture, Sports, Science and Technology, Japan.
The objective of this study is to construct a surrogate model for long-period seismic motion simulation that uses the areal results of seismic wave propagation simulations for many source scenarios accumulated so far to predict seismic motion for an arbitrarily specified virtual source scenario. This surrogate model is intended to be applied to probabilistic seismic hazard assessment, and its function is not only to obtain predictions from deterministic regression equations, but also to generate a sample of predictions from a probability distribution of uncertainties. Therefore, in this study, Gaussian process regression (GP regression) is used to develop a surrogate model for simulating the seismic hazard of Nankai Trough earthquakes. In particular, a multi-hot representation of the source region is adopted as input variable (explanatory variable) for the GP regression so that the diversity of the source model can be taken into account. In this way, it is expected to be able to predict earthquake ground motions for source regions with shapes that are not included in the accumulated results; GP regression is characterized not only by the regression equation for prediction, but also by the ability to generate sample paths considering correlations between input variables, since the covariance of the variability is obtained. Therefore, the process of generating sample paths that take into account spatial correlations between stations when the earthquake scenario is fixed is also discussed.
As a preparation for this report, a standard GP regression is performed on the PGV and period 3s velocity response Sv data sets with both station and source information as explanatory input variables. As a result, it is confirmed that a certain degree of prediction accuracy is obtained for PGV, but not sufficient for Sv. Therefore, the main outcome of this study is to apply a sequentially additive GP regression to the Sv data set. In the sequentially additive GP regression, the residuals obtained by subtracting the mean function of the posterior distribution obtained in the first GP regression from the original data set are used as the data set for the second GP regression, the residuals obtained by subtracting the mean function of the posterior distribution obtained in the second GP regression from that data set are used as the data set for the third GP regression, and the operation is repeated recursively thereafter. By setting factor-specific input variables for GP regression in each step according to the objective, it is expected to extract a mean function from the original data set in the form of the sum of factor-specific functions in a sequential manner, thereby gradually reducing the variance of the error. In this report, we show that a certain degree of prediction accuracy can be achieved for Sv by using sequentially additive GP regression.
Acknowledgments: This study is part of ' Research Project for Disaster Prevention on the great Earthquakes along the Nankai Trough' funded by Ministry of Education, Culture, Sports, Science and Technology, Japan.