# Seismic Ground Response Prediction Based on Multilayer Perceptron
## 2 Analytical Methods and Dataset  
### Earthquake Dataset  
Over 90% of earthquakes worldwide occur in the circum-Pacific orogenic zone, known as the Ring of Fire [16]. In Japan, since the Kobe Earthquake in 1995, the National Research Institute for Earth Science and Disaster Prevention (NIED) has implemented seismometers in boreholes and on the ground surface to record earthquakes throughout the nation. The measured acceleration histories and the information of the sites and earthquake events are presented in the strong-motion seismograph network Kiban Kyoshin Network (KiK-net). From KiK-net, a total of six sites where sufficient data about the earthquakes were available were selected (Figure 1). FKSH17 and FKSH18 represent Kawamata and Miharu in Fukushimaken, IBRH11 and IBRH13 represent Iwase and Takahashi in Ibrakiken, and IWTH21 and IWTH23 represent Yamada and Kamaishi in Iwateken.  
For modeling, 100 sets of acceleration histories measured at the surface and 100 m depth beneath the surface were selected, with 50 earthquake events measured in two directions, east-west and north-south, providing 100 sets of ground motion accelerations in each site. These 100 sets of acceleration histories can be classified as input data (100 ground motions on the surface) and output data (corresponding 100 ground motions at the bedrock). For input data, the velocity and displacement histories were generated from the acceleration  
Figure 1: Six stations selected.  
histories at 100 m depth using the software Seismo Signal 2016 [17]. Then, the acceleration, velocity, and displacement histories at 100 m depth were taken as input data in the MLP model. As output data of the model, the acceleration histories at the surface were employed. Out of 100 sets of seismic motion data, 80 datasets from 40 events were used for training (training dataset), and 20 datasets from 10 events for testing (testing dataset).  
Figure 2 shows the shear wave velocity (\(V_{s}\)) profiles of the selected sites measured by downhole tests and brief classifications of the soil layers. The black triangles in the figure denote the installation locations of the seismometers.  
Figure 2: Soil profiles and shear wave velocities at the sites.  
In the seismic design, the ground stratum can be classified based on the shear wave velocity profile up to 30 m (100 ft) depth beneath the ground [18]. The average shear velocity (\(V_{s,30}\)) is used for the classification and is calculated from Equation (1). The natural period of the soil deposit can theoretically be obtained from Equation (2) when the profile of shear wave velocity is available. The values of average shear velocities and natural periods for six sites are presented in Table 1. The table also includes the depths of the bedrock where the shear wave velocity (\(V_{s}\)) exceeds 1000 and 2000 m/s, respectively.  
\[V_{s,20}=\frac{30}{\sum_{i=1}^{n}\frac{H_{i}}{V_{si}}} \tag{1}\]  
\[T_{G}=4\sum_{i=1}^{n}\frac{H_{i}}{V_{si}} \tag{2}\]  
where \(V_{s,30}\) is the shear wave velocity of the strata from the surface up to 30 m below the surface, \(T_{G}\) is the natural period (s), \(n\) is the number of strata from the surface up to 30 m below the surface, \(H_{i}\) is the thickness of stratum \(i\) (m), and \(V_{si}\) is the shear wave velocity of stratum \(i\) (m/s). It is noted that the natural period can also be evaluated from the field measurements. For example, [PERSON] [19] showed that the fundamental resonance frequency, which corresponds to the lowest amplification frequency, can be successfully determined by the horizontal-to-vertical spectral-ratio (HVSR) method, especially when a sharp velocity contrast is present at depth.  
Based on the National Earthquake Hazard Reduction Program (NEHRP), the sites where \(V_{s,30}\) ranges from 180 to 360 m/s are classified as stiff soil. The sites where \(V_{s,30}\) ranges from 360 to 760 m/s are classified as soft rock, and those with \(V_{s,30}\) over 760 m/s are classified as rock.