## 4.1 *Vs* to depth profile from PSO inversion result

The HVSR curve can be used to reconstruct a 1D shear wave velocity (*Vs*) model at the station's location by assuming a 1D structure. The curve provides information about the amplification of seismic waves at different frequencies, which the subsurface structure influences. By analyzing the HVSR curve and comparing it to theoretical models or empirical relationships, it is possible to estimate the shear wave velocity profile at the station's location. This condition allows for the reconstruction of a simplified 1D model of the subsurface, providing insights into the geological layers and their properties.

The results of the 1D inversion modelling that carried out can be seen in Figs. 3 and 4. Figure 3 shows the HVSR observation curve and calculations resulting from the inversion process. The two curves show an excellent correlation. It is characterized by a relatively good fit between the observation curve and calculations. From several HVSR curve samples, it was found that the dominant \({f}_{o}\) is at a frequency of 10–20 Hz. The relatively high \({f}_{o}\) value indicates that the sediment layer in the study area is not very thick (not very deep). The HVSR curve also shows a low H/V (amplification) value (the majority is below 3). It means the research area is relatively safe when seismic activity occurs because there is no significant amplification of seismic waves. Areas that are vulnerable when an earthquake occurs have a high amplification value. This is because the seismic vulnerability index is proportional to the square of the amplification.

Figure 4 displays the subsurface layer model obtained from the HVSR curve inversion. Overall, the inversion results provide a maximum depth profile of up to 120 meters, with an average depth of 100 meters. Within the top 5 meters of the model, the estimated Vs values range from 200 to 300 m/s, suggesting the presence of a soil layer at this depth. Then, at depth > 5 meters, it shows a significant increase in *Vs* value. This velocity increase reaches 800–900 m/s. Then, the third layer to the last layer shows an increase in velocity ranging from 1000 m/s to 2000 m/s. Specifically, at point M76 in the fifth layer, the velocity in that particular layer can exceed 2000 m/s. Overall, it is assumed that the bedrock layer can be found in the third layer, starting at a depth of 20 meters.

The black lines in Fig. 4 represent the best model obtained during the inversion process. From this figure, it is clear that the PSO algorithm is quickly converging. This is marked by black lines that continue to coincide so that in inversion using PSO, significant iterations are unnecessary. To assess the uncertainty in the model, standard deviation values were calculated for both the thickness and *Vs* velocity values. These standard deviations were obtained by considering all the models generated during the inversion process. The results obtained show a relatively small standard deviation value. This shows that the model is collected in a point area relatively close to the best model globally.

Overall, the inversion results using the PSO algorithm have provided excellent results. The fast convergence of the PSO algorithm is shown by the overlapping black lines in Fig. 4, indicating that the algorithm quickly finds the optimal solution. It shows there is no need for many iterations when using the PSO inversion method. In addition, the relatively small standard deviation values for thickness and velocity *Vs* indicate that the models generated in the inversion process cluster closely around the best global model. This shows a high level of confidence in the results obtained. Therefore, it can be said that the PSO inversion results provide outstanding and reliable results.

To understand how local sites are in the Bakauheni area, we modeled the average HVSR curve over the entire measurement area. We modelled the mean Vs profile to the depth. These results can be seen in Fig. 5(a-b). However, it should be noted that this mean model only provides general information and does not consider local variations in the Bakauheni area.

Figure 5(a) shows the mean model HVSR curve over the entire measurement area in the Bakauheni area. In this model, the mean value of the HVSR curve is measured at each frequency and then plotted as a function of frequency. This model creation refers to Nelson & McBride (2019) and Trichandi et al. (2023), who created an average spectrum model of the HVSR curve. The subsurface layers, sediment or weathered layers, and bedrock can be separated from this curve. The boundary between layers is located at the top of the HVSR curve obtained, so it can be said that the location of the \({f}_{o}\) value marks the layer boundary between the sediment or bedrock. In this mean HVSR curve, the \({f}_{o}\) value is obtained at 15.12 Hz. The bedrock layer is characterized by low frequency towards \({f}_{o}\), while the sedimentary layer (weathering zone) is at \({f}_{o}\) to high frequency. By knowing the \({f}_{o}\) value, the depth of the sediment layer (including the weathered layer) can be determined using the following equation:

$${f}_{o}=\frac{{V}_{s}}{4d}$$

3

where \({f}_{o}\) = natural frequency associated with sediment layer/bedrock, *Vs* = the mean *Vs* (shear wave velocity) of sediment, and d = sediment layer thickness.

In Eq. (3), the thickness value of the sediment layer can be known if the mean *Vs* value in the sediment layer is known. It can be estimated based on the mean Vs profile against depth in Fig. 5(b) to determine the mean Vs value. The figure shows the model of the mean *Vs* profile against depth in the Bakauheni area. In this model, the mean value of velocity *Vs* is measured at each depth and then plotted as a function of depth.

Based on the mean *Vs* curve obtained, it can be seen that the mean *Vs* curve shows exciting changes in seismic wave velocity in the Bakauheni area. At a depth of up to 5 meters, the mean *Vs* value obtained is around 600 m/s, which is assumed to be the mean *Vs* value in the sediment layer. This shows that the material below the surface consists of sedimentary layers with relatively low seismic wave velocities at this depth. Thus, if it is assumed that the mean *Vs* in the sediment layer is ~ 600 m/s, then based on Eq. (3), the thickness of the sediment layer is 9.92 meters. It shows that the Bakauheni area has a thin sediment layer.

However, at depths > 5 meters, there is a significant increase in the mean *Vs* value, reaching around ~ 900 m/s at a depth of 20 meters. This indicates significant geological changes beneath the sediment layer, and perhaps a denser or harder rock layer exists in this area. Furthermore, the mean Vs increases slowly at a depth of 20 meters to 70 meters. This suggests a gradual change in the geological properties of the area, perhaps a transition from sedimentary layers to denser rock. The mean Vs appears constant at depths of more than 70 meters to 120 meters. This shows that the subsurface material tends to be homogeneous in this area with relatively stable seismic wave velocities.

Figure 6(a) shows a natural frequency map in the research area, showing the contrast of high and low anomalies. Overall, the study area is dominated by high frequencies, indicating that this area has relatively shallow sediment thickness. The sediment thickness map in Fig. 5b confirms this, which shows low anomalies (blue < 20 meters). High *f**o* anomaly > 15 Hz is distributed in the SW-middle-NE and southern parts. While low *f**o* anomalies < 15 Hz dominate in the central, eastern, and NW parts. In general, the *f**o* anomaly map does not clearly show the existence of a caldera in the research area. However, in areas B-2, B-4, B-5, and B-6, there is a low *f**o* anomaly in the caldera, indicating that this area has a thick layer of sediment.

Table 1

Statistic of the sediment thickness

min | max | mean | median |

4.39 | 103.57 | 18.22 | 10.55 |

Based on Fig. 6(b), it is obvious that the B-2, B-4, B-5, and B-6 caldera areas have a thickness of > 30 meters (yellow to red). Based on statistics on the thickness of the sediment layer in the research area (Table 1), overall, Bakauheni has an average thickness of 18.22 meters with a median value of 10.55 meters. The median value correlates very well with the average thickness value calculated from the average HVSR curve. On the other hand, the average value calculated at each point shows a more considerable value. The data has a high thickness value (data has a wide range), making the average value more extensive than the median value.

The minimum thickness is 4.39, and the maximum thickness reaches 103.57 meters. This very thick area is located in the eastern part, which is an area with low topography and near the beach (alluvium formation). This result also matches the morphological form of Bakauheni (Fig. 2), which shows that the area with a thick layer of sediment is located at low topography. This shows that areas B-2, B-4, B-5 and B-6 have a lot of sedimentary material.