Site Amplification Assessment in the East Corinth Gulf Using 3D Finite-Difference Modeling and Local Geophysical Data

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Site Amplification Assessment in the East Corinth Gulf Using 3D Finite-Difference Modeling and Local Geophysical Data

EVANGELOSMOUZAKIOTIS,¹ VASSILIOSKARASTATHIS,¹NIKOLAOSVOULGARIS,²and PANAGIOTISPAPADIMITRIOU²

Abstract—Elastic 3D wave-field simulations were performed in the seismically active region of Eastern Gulf of Corinth, in the area of Loutraki city. A new methodology was tested with the aim of performing multiple simulations for a large variety of realistic sources located around the study area, by employing 3D finite- difference modeling using matrix operations for the calculation of the spatial velocity and stress derivatives. The new methodology was proven to be quite efficient in simulating the near surface 3D site effect of the study area, by greatly minimizing the simulation time, thus allowing the use of 3D finite-difference modeling for a large number of simulations. The complex geological features of the study area were obtained by performing multiple passive MASW surveys within the busy urban area of Loutraki. By processing the acquired geophysical data, a highly inhomogeneous near surface velocity structure in the study area was obtained and was implemented in the 3D wave-field simulations. The near surface amplification that is caused by the 3D subsurface structure was proven to be highly significant for the area of Loutraki, with high spectral amplification compared to the amplification that is caused by an equivalent 1D model in the area. The dominant frequencies of the spectral amplification for the 3D model were also confirmed by Processing HVSR measurements that were also taken in the area. Finally, we also investigated how the propagation direction affects the near surface amplification.

Keywords: Site effect, numerical modeling, 3D wavefield simulation, near surface 3D velocity structure.

1. Introduction

The amplification of the seismic motion at surface due to the local soil conditions is of high importance in seismology and engineering, playing a crucial role in building design and urban development. This phenomenon has been extensively documented in the

literature (Joyner et al. 1981; Bard and Bouchon 1980; Bard and Gariel 1986; Yilmaz et al. 2006;

Karastathis et al. 2010; Novikova et al. 2017) with many reported cases e.g. in the M7.5 earthquake in Mexico in 1985 and the M6.9 earthquake in Kobe, Japan in 1995. In the first case, severe damages were observed in the area of Mexico City which was more than 300 km away from the epicentral area, whereas the observed peak ground acceleration at 20 km from the epicentral area was as low as 0.2 g. This unusual at that time occurrence was related to the presence of a thick soft clay layer, that amplified the seismic motion in the frequency band between 0.3 and 1 Hz by a factor that reached the value of ten (Cha´vez- Garcı´a and Bard 1994). In the case of the Kobe earthquake, despite the moderate magnitude of the event (M6.9), the damage that was caused in the city of Kobe was extreme, with more than 4.000 casu- alties and nearly 400.000 buildings being destroyed whereas the observed ground acceleration reached a value of 0.818 g. The basin morphology of the struck area contributed significantly to the severe ground shaking of this shallow event (Kawase 1996; Moto- saka and Nagano 1996; Pitarka et al. 1996, 1998).

The above cases outlined the effect of the local site conditions in the damage that may be caused by a potential seismic event in areas with complex geological structure and sparked the interest of the scientific community for the investigation and calculation of the local site amplification.

Many methodologies have been proposed in the past for the calculation of site amplification. The most commonly used approaches are based on the calculation of the standard spectral ratio between the site of interest and a reference site (Borcherdt and Gibbs 1976; Tucker et al.1984; Chavez-Garcia et al.1990)

1 Institute of Geodynamics, National Observatory of Athens, Athens, Greece. E-mail: [email protected]

2 Department of Geology, National Kapodistrian University of Athens, Athens, Greece.

Pure Appl. Geophys. 177 (2020), 3871–3889 Ó2020 Springer Nature Switzerland AG

https://doi.org/10.1007/s00024-020-02421-3 Pure and Applied Geophysics

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and the horizontal to vertical spectral ratio (HVSR) (Nakamura 1989) through microtremor measurements (Aki 1957). These cost-effective approaches, however, have distinct limitations when implemented in busy urban environments. In general, HVSR recordings are composed of different combinations of wave phases (e.g. body waves, Rayleigh, Love waves) depending on the characteristics and the spatial distribution of the sources, therefore the results may vary in-between different applications (e.g. Lachetl and Bard1994; Bonnefoy-Claudet et al.

2008; Sa´nchez-Sesma et al. 2011; Molnar et al.

2018). Furthermore, the large amount of artificial noise sources typically cause Rayleigh surface waves that mostly affect the vertical component, often causing incorrect calculations of the HVSR (Naka- mura 1989). In the case of urban environments, the peak of the HVSR can be affected by nearby man- made structures (Castellaro and Mulargia 2009), which are occasionally difficult to avoid when obtaining the field measurements. Additionally, only the dominant frequency, which is linked to simpler subsurface morphologies, may be accurately obtained by the use of this method (Tevez-Costa et al.1996) and therefore, in order to obtain the amplification spectrum in a large frequency band, in regions with complex geology, other methods will have to be implemented. Other approaches can employ numerical modeling in the time or frequency domain such as the finite-difference technique (Virieux1984; Graves 1996; Moczo et al.2000), the finite element method, the finite volume method (Glinsky-Olivier et al.

2006), the boundary element method and the spectral element technique (Faccioli et al. 1996; Komatitsch and Vilotte 1998). Such techniques can incorporate 3D geometries of various complexities in the calculations; in most cases however, the computational cost can be great, thus limiting their use. Each of these methods has also various other inherent limitations such as numerical dispersion in the finite element method (Bonilla 2002) or the limitation to models with weak heterogeneities in the boundary element method (Beskos 1997; Semblat 2010). To overcome the huge computational cost of such 3D techniques, several computational techniques have been proposed in the past (e.g. Olsen et al. 1995;

Graves 1996) and in many cases they have been

successfully employed for the simulation of the wavefield in a 3D medium.

Most applications have been focused on investi- gating the effects of relatively large scale subsurface structures such as basins (e.g. Bard and Gariel1986;

Pitarka et al. 1996; Wang et al.2018) as well as the effect of the local topography. In our study our aim was to investigate the site amplification that is due to the near surface complex 3D structure by performing a large number of simulations using time efficient 3D waveform modeling technique trying to optimize the performance. The purpose behind this optimization was to greatly reduce the computational requirements in order to propose an easy to apply methodology for any possible case.

We tested our proposed methodology at the area of Loutraki, a popular touristic area in the Eastern Corinth Gulf region in Greece (Fig. 1). This area is a typical example of complex near surface structure in a very high seismic risk region. The city of Loutraki has suffered great damages in the past due to local strong earthquakes. Many earthquakes with magnitudes M[6.0 have been recorded since antiquity, with the oldest known case, the earthquake of 420 BC with a proposed magnitude of M6.0 (Papadopoulos 2000; Papazachos and Papazachou 2003). A more contemporary characteristic example is the M6.3 earthquake of 1928, which caused the total destruc- tion of all structures in the city of Loutraki (Papazachos and Papazachou2003). Another case is the earthquake of 1981 with magnitude M6.7 that was followed by large aftershocks with magnitudes ranging from M6.4 to M5.9, which caused wide- spread damages as far as the city of Athens (Jirsa and Brandow 1981; Papazachos and Papazachou 2003).

In both cases, localized damages could be attributed to the local site effect, thus the accurate calculation of site amplification by incorporating all factors that may affect it, in order to mitigate possible damages form future events is highly important.

2. Seismo-Tectonic Setting

The Gulf of Corinth is a WNW-ESE oriented active tectonic graben, or according to others a half- graben with a length of 120 km and a maximum

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width of 20 km. It is divided into two sections with decreasing width towards the west and increasing expansion rate (Avallone et al. 2004). According to the GPS data of Briole et al. (2000) the expansion rate of the eastern part is 10 mm/year whereas that of the western part is 14 mm/year. The Gulf of Corinth is one of the most seismically active regions of Greece, with most of the earthquakes related to normal faulting (Ambraseys and Jackson1990).

The area of interest is located in the easternmost part of the Gulf of Corinth which is dominated by

normal faults, both offshore and onshore, with a general E–W orientation. These faults deform the regional geomorphology by forming successive horsts and grabens. Additional NE–SW trending faults compliment the tectonic features of the region and contribute to some extend to its crustal deformation. A characteristic feature of this complicated structure is the Perachora peninsula, which is bound by normal offshore faults that separate it from the Alkyonides Gulf to the north and the Gulf of Lechaion to the south (Perissoratis et al. 1986;

Figure 1

The Eastern Corinth Gulf region with the most prominent tectonic features and the historical earthquakes with M[6.0 (Papazachos and Papazachou2003). The epicenters and focal mechanism of the M6.3 earthquake of 1928 and the M6.7, M6.4 and M6.3 events of 1981 are also shown (Jackson et al.1982; Taymaz et al.1991). The Loutraki fault that delineates the northern limit of Loutraki city is marked in red. The

location of the study area is also shown in the map

Vol. 177, (2020) Site Amplification Assessment in the East Corinth Gulf Using 3D 3873

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Sakellariou et al. 2007; Charalampakis et al. 2014) and contains multiple faults that form a complex 3D geometry within the Peninsula. The southern part of the region shows evidence of rapid uplift and is characterized by thick (*1 km) sediments linked to the tectonic activity of the area (Doutsos and Pouli- menos 1992). On the contrary, the northern part is mostly devoid of such sediments (Le Pourhiet et al.

2003). The most prominent faults of the region can be seen in Fig.1.

The study area is focused on the city of Loutraki which is situated near the northern border of a basin consisting of alluvial deposits that cover the largest part of the area (Fig.2). Along the coast a narrow zone of recent beach deposits (sands and gravels) extends from the coastal front of the city and south- wards. Near the eastern part of the city, a wide spreading of recent talus cones covers the subtle morphology of the basin. The oldest basin-filling sediments found in the basin area are the pliocene brackish to lacustrine marls which, in the study area, are extensively covered by the recent talus cones and alluvial deposits and only outcrop at the northeastern end of the city (Fig.2). Along the northern limit of the city the mountain-front of Gerania Mts is found which is formed by the fault scarp of the southern branch of the Loutraki Fault. The fault bounds the northern border of the basin and downthrows the city which lies on its hanging-wall. The free-face outcrops locally, but its longest part is covered with colluvial deposits and scree. The footwall mainly consists of mesozoic limestones and shales-chert formation, although in the vicinity of the city only the limestones are met. The general geology of the study area can be seen in Fig.2.

3. Methodology

The staggered-grid 3D finite difference scheme of Graves (1996) was used in order to calculate the seismic wave propagation. The method is based on calculating the three velocity components (Vx, Vy, Vz) and six stress components (txx, tyy, tzz, txy, txz, tyz) in successive time steps. A key factor in these calculations is the calculation of the centered 3D spatial derivatives for the velocity and stress fields in

each consecutive time step. This task usually takes considerable computational time which is a limiting factor in employing this methodology. We implemented a technique in order to greatly reduce the computational time by calculating the partial derivatives of each field in each spatial dimension for all grid nodes simultaneously by matrix operations;

e.g. for the calculation of the first order spatial derivativeDxVx ofVxin thexplane at timet, if we assume a right to left propagation in an orthogonal grid we use the following formula:

DxVx¼Vx^t1_i_ð_2:nx_Þ;j_ð_1:ny_Þ;k_ð_1:nz_ÞVx^t1_i_ð_1:nx1_Þ;j_ð_1:ny_Þ;k_ð_1:nz_Þ

=Dx:

ð1Þ

In the above equation Dxis the node spacing in thexdirection. The termi,j,krepresent the indices of theVxgrid nodes in thex,yandzdirections andnx, ny andnz are the respective number of nodes. Only recursive calculations in time were required in order to calculate the full 4-dimensional problem. Using these matrix operations on the input calculation grids (which in our case had a size of 3009300 9200), the calculation speed for each time step increased by approximately five times. We should further note that all calculations within the simulation scheme are performed by loading all grids directly into system memory. In our case, since all 3D grids (3 velocity components, 6 stress components, Vp, Vs and density) could easily be loaded directly into the system memory, there was no need to store any data on the disk during the simulation. In comparison to Graves’

(1996) cascade scheme, with our method we reached the identical results with a simulation speed for each individual simulated time step about five times faster.

It should be noted however, that the above values may vary, depending on the grid dimensions, as well as the system specifications. Furthermore we should note that for our method, it is assumed that there is enough system memory to directly load all 12 grids (and other miscellaneous variables) on it. In order to further test the validity of our scheme, we performed a test simulation using a simple half-space 3D model (30930930 km, Vp = 4.0 km/s, Vs = 2.4 km/s) and an impulsive source and compared the results with those obtained with the 2D spectral finite element method (e.g. Komatitsch and Vilotte 1998;

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Komatitsch et al. 2001). As seen in the synthetic waveforms for both methodologies (Fig.3), an almost perfect fit was achieved.

Since the implemented grid cannot expand infi- nitely, there are always artificial reflections at the boundaries. To eliminate these artifacts, we implemented a hybrid absorbing boundary condition as proposed by Liu and Sen (2009) based on the first Higdon one way wave equation (Higdon 1991; Liu et al. 2017). In particular, towards the edges of the model grid, we introduced a strip of nodes where the

wave amplitude is gradually diminished by linearly weighting the outgoing wavefield. When this weak- ened wavefield meets the outer boundary, the absorbing boundary condition proposed by Higdon (1991) is then applied. The result is a much greater elimination of artificial reflections compared to the use of a singular absorbing or non-reflecting boundary condition (Madariaga et al. 1998; Jiang et al.

2010). An example showing the result of this application is shown in Fig.4.

Figure 2

General geology in the study region. The formations shown are (in random order):Jm.kLimestones (Middle Jurassic),TRm-Ji.kLimestones (Middle Triassic–Lower Jurassic),Q.scOld talus cones (Quaternary),Pl.mMarls (Pliocene),Q.cn1Recent talus cones (Quaternary),Q.al Alluvial deposits (Quaternary),Q.al2Recent beach deposits (Quaternary),Q.dl1Marine and near-shore deposits (Tyrrhenian) (after IGSR

(1972). The locations where the microtremor array measurements were taken are also shown

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In order to model the effect of topography on the propagating wavefield we implemented a free surface boundary condition based on the formulation of Ohminato and Chouet (1997). Surface morphology was modeled as a set of cubic cells in a way that the center of each surface of a cube represented a node of the original computation grid (Fig.5). The shear stress values were calculated only on the appropriate surfaces and edges (each component was set to zero on surfaces perpendicular to their axes). In order to properly calculate the normal stresses, we increased the stress gradient on the free surface by a factor of two and so, by setting the Lame coefficients to zero in the overlaying nodes, the normal stress on the free surface is zero (Ohminato and Chouet1997).

The source was implemented in the stress components, rather than the velocity components. The double couple source is then represented by a distribution of body forces centered at the normal stress node location that coincides with the actual source location by weighting each adjacent shear and normal

stress node relatively to the moment tensor components. This practice significantly reduces the grid asymmetry (Virieux 1986; Coutant et al. 1995). In order to incorporate the effect of the angle of incidence of the wavefield towards the site of interest, as well as the effect of different source mechanisms in the amplification calculations, we performed the simulations for a large variety of sources, located in the corners of the grid shown in Fig.4, at a depth of 500 m. More specifically we used multiple sources representing normal faults with strikes between 70ô and 110ô and dipping angles between 40ô and 60ô. These source characteristics correspond to the main faults in the region of the Eastern Gulf of Corinth (Sboras et al. 2009; Pavlides et al. 2010). Addition- ally, we set the length of the initial source pulse between 0.1 and 0.25 s. The total number of simulated sources was 48. For all simulations a maximum time step of 0.001 s was found to provide stable results. Thus, for a total simulation time of 5 s, 5000 time steps were simulated.

Figure 3

Comparison of synthetic waveforms calculated with the staggered grid FD scheme that is described in the present work (solid black line) with those obtained by the finite element method (red circles). In this example an impulsive source was used. The results in both cases represent the vertical velocity component. The source time function was a Gaussian pulse with a central frequency of 2 Hz located at a depth of 15 km,

directly under the central receiver

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The 3D velocity model that we implemented was calculated by applying a linear 3D interpolation method in a series of 191D Vs profiles, obtained in several locations within the study area (Fig.2). Each separate profile was calculated with the use of the microtremor array measurement method (Okada and Suto 2003) which is based on the spatial autocorre- lation method (Aki 1957). This methodology was selected for this study due to the fact that it can be applied even in busy urban environments with high cultural noise. In such environments the achievement of a high SNR requires high energy sources

(explosives, large dropping weights, etc.) that cannot be normally hosted in populated areas and cities.

At each site, after transforming the data to phase velocity-frequency domain, we obtained the funda- mental mode Rayleigh wave dispersion curve. As a last step, we calculated the Vs profile by the use of inversion on the dispersion curve (Xia et al.

1999,2004). We used arrays with11-receiver layouts inL-shape and 10 m receiver interval. The arrays had a maximum aperture for each linear component of 50 m. The geophones used were of 4.5 Hz natural frequency. As seen in Fig.6, such an arrangement

Figure 4

Seismic records on the surface for an impulsive source, applied on the input 3D model for the study area (shown in Figs.6,7). The receivers are located on a N–S direction (shown in Fig.5a) and the source is located in the middle of the receiver line with an offset of 500 m to the west.aThe recordings without the implementation of any boundary conditions,bafter implementing the one way wave equation boundary condition of Higdon andcafter implementing the Hybrid absorbing boundary condition of Higdon with an additional strip of ten nodes at each

boundary are shown

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provided a clear picture of the dispersion curve in the study area, for frequencies as low as 4 Hz, which in turn resulted in Vs profiles of down to 40 m of depth.

The minimum investigation depth of our survey was estimated to be at between 3 m (Park et al. 2002).

In order to obtain the Vp velocity values at shallow depths, we were based on the first arrivals of seismic refraction data (site L2 shown in Fig.2). In this case, a 24 geophone spread of 72 m (geophone spacing of 3 m) was used, with an accelerating dropping weight as an active source. Using the results of this survey (shown in Fig.7), in combinations with the results of the Vs profile at the same site, we obtained an average Poisson ratio of 0.4, which we used in the rest of the model space. For the purpose of modelling the structure at larger depths, we employed a smooth interpolation scheme between the velocity values in the bottom layers of our profiles and the maximum depth of the model space (set at 1500 m).

In this case a Vp value of 5.3 km/s (Zelt et al.2004) and a Vp/Vs ratio of 1.80 (Le Meur et al.1997) was used for the basin bedrock. The density values that were used in this work were approximated based on the above Vp values, based on Gardner’s formula (Gardner et al.1974).

The final calculated near-surface 3D velocity model can be seen in Figs.8and9. As seen in these figures the velocity distribution that was calculated is compatible with the topography and the geology of the study area. More specifically, we obtained the highest Vs values in the Northern parts of the area, which is characterized by consolidated old scree formations related to the Gerania mountain region.

Consequently, the lowest Vs values were obtained in the Western part of the area, over alluvial deposits adjacent to the sea.

The final input grid consisted of 300 nodes in the east–west, 300 nodes in the north–south and 200 in the vertical directions. The dimensions of the grid are 2.492.491.5 km. The node spacing is 8 m in the horizontal plane. We used variable node spacing in the vertical direction, since our aim was to achieve fine grid spacing near the surface for accurately modeling the topography and at the same time obtain higher frequency results, without greatly increasing the total number of nodes, thus increasing the memory requirements and computation time (Mikumo and Miyatake 1987; Moczo 1989). This smaller node spacing compensates for the decrease in velocities in shallow depths and thus the frequency content of the

Figure 5

The 3D simulation domain showing the 3D morphology as a set of cubic cells (89895 m on the surface level) and the Vs velocity values, up to the depth of 200 m with different color in each cell. The vertical axis is exaggerated by a factor of 3

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Figure 6

Phase velocity spectrum obtained in L19 site (Fig.2). The dotted line delineates the picked dispersion curve

Figure 7

Example record from the seismic refraction data

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simulated wavefield is preserved. It also allows the simulation of effects caused by the detailed velocity structure at shallow depths and the topography. The minimum node spacing that was achieved using such a grid is 5 m on the surface level. The discrete partial derivatives with respect to the vertical direction were consequently calculated by taking into account this variable node spacing. The digital elevation model

that was used for this study has an accuracy of 5 m.

Such high accuracy was required, since the computation grid that was used for the finite difference calculations encompasses the rather small region of the city of Loutraki, with an area of *1.5 km².

4. Results

The results clearly show that the wavefield is strongly affected by the velocity structure throughout its propagation to the north as it approaches the region with the higher velocity values, near the highlands, in the northern part of the model region shown in Fig.8. In Fig.10we present snapshots of a simulated seismic wave calculated using the 3D model as well as an equivalent 1D model, as it propagates within the study region, represented by the simulation space shown in Fig.5. This particular 1D model was calculated by the average velocity values at different depth levels of the 3D model. For this case, the source was located in the southwestern area acting as a normal fault with a strike of 90^oand a dip of 50^o. It is obvious that a strong effect of the 3D velocity structure on the simulated amplitudes exists, particularly at the area adjacent to the coast the western area of the simulation space, whereas in the 1D average velocity model case the values seem to be unaffected. Having established the shallow 3D velocity structure effect on the wavefield as it propagates, we proceed with the assessment of the spectral amplification due to this 3D structure.

Therefore, we performed the large number of simulations for both the average 1D and 3D models in order to compare the spectral amplitudes at the surface. In that way we isolated and calculated the relative amplification due to the 3D structure, compared to that of a layered 1D model, by calculating the spectral ratios of the mean velocity components of the obtained synthetic waveforms between the 3D and 1D cases. The results are shown in Fig. 11.

We can notice from this figure that in the southwestern part of the area, the relative 3D ground amplification generally exceeds the value of two at the frequency of 2 Hz and is higher than 1 for the frequencies of 3 and 4 Hz. The northern part of the region, which is characterized by an increase in the

Figure 8

Horizontal slices of the 3D Vs model in the study area. The coastline and the location of the vertical slices of Fig.6are also shown in solid black lines. The vertical black line in the first panel

also denotes the receiver spread for Fig.4

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velocity values, shows no attenuation due to the 3D site effect at the same frequencies. The highest relative amplification values (*3) were observed in the coastal region, in the area that coincides with the lowest velocity values (shown in Fig.8).

By examining the spectral ratios for the sites with the highest attenuation values, we found that two main spectral peaks exist at the frequencies of 2 and 3.1 Hz and a minor one at 4.5 Hz (Fig.12). The existence of multiple peaks can be explained by the 3D velocity variations, especially for sites A and B (see Fig.11). At sites C and D (see Fig.11) the attenuation values are much lower, but still the peaks at 2 and 3.5 Hz exist. It is worth mentioning, however, that the source location and consequently the direction of propagation can affect significantly the surface attenuation (Fig.13). More specifically, the spectral peak at 2 Hz is mostly attributed to the simulated wavefields propagating towards NE direction (source located at the SW). The peak at 3.5 Hz is related to both NE and SW propagating directions (sources at SW and NE corners of the area). The

small peak at 4.5 Hz is due to the SW direction of propagation.

5. Discussion

By utilizing our proposed methodology, we were able to prove that the near surface 3D velocity model can describe significant amplifications of the ground motion in contrast to an average 1D layered model that is usually used in seismic hazard studies and therefore can underestimate the seismic risk of a specific area.

However, the velocity profiles that we obtained reached up to a depth of*40 m. In order to accurately simulate a real seismic event and obtain the real peak ground acceleration/velocity the actual velocity structure for much greater depths (e.g. 8 km for a typical large event in the eastern Gulf of Cor- inth) and consequently covering a larger area would be required. Our aim however, was to prove that a complex, realistic 3D structure could cause

Figure 9

Vertical cross sections of the 3D model with W–E (top) and S–N (bottom) orientation. The locations of the cross sections can be seen in Fig.8. The depth scale is exaggerated by a factor of 10

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significant amplification, a factor that is very important in seismic hazard studies within urban environments.

In order to validate our results we also used HVSR measurements at selected locations. As can be seen in Fig.14, the dominant frequency is approximately 2.05±0.15 Hz at the coastal area, in the frequency range of 1–7 Hz, where the most of the energy of the simulated waveforms is contained. This value is in good agreement with the value of the first spectral peak for the simulated results of Fig.12a and b. In contrast, no significant peak can be observed on the HVSR spectrums in Fig.14b and c, that correspond to sites in the southern part of the study area, just as in the case of the synthetic spectra of Figs.11 and14c, d.

The validity of our calculations can be further proven by the actual recorded damages of the 1981 M6.6 event. This event caused the collapse of several

buildings within the city, with most of them being adjacent to the coastal area. One notable example is the Contis hotel, which was a seven-story building with a reinforced concrete frame that collapsed completely. It should be noted however, that the collapse was caused not only by the unfavorable soil conditions, but also due to some irregularities in the building plan (National Research Council 1982).

6. Conclusions

The amplification has been proven as highly variable in space due to the inhomogeneities in the near surface velocity structure. The results of our analysis point out to a general increase in amplification values in regions of lower velocity values, as well as the existence of numerous spectral peaks, that are mainly related on the 3D effect. The highest

Figure 10

Snapshots of the velocity field propagating from an E–W striking source with a dip of 50^oto the north for the 1D model (top panels) and the 3D model (middle panels)

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A B

D C

(a) (b)

(c) (d)

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Figure 11

3D/1D Spectral attenuation distribution for the area for the frequencies ofa0–1 Hz,b1–2 Hzc2–3 Hz,d3–4 Hz ande4–5 Hz

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attenuation values, reaching up to the value of three were calculated for sites where an abrupt decrease in the velocity values was observed. Thus, we can

conclude that the 3D velocity structure may amplify the input motion, compared to a 1D layered model up to several times. Furthermore, we observed that the

Figure 12

Spectral attenuation for sites a–d shown in Fig.11. The left panels show the amplitude spectrums of the simulated waveforms for the 3D (red) and the 1D (blue) models. The right panels show the spectral ratios for each simulated event and the mean spectral ratio (solid black line) for

each site

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direction of propagation of the wavefield heavily influences the calculated attenuation values which, for some simulated sources, reached the value of ten (within the energy bandwidth that was simulated, 1–5 Hz). These results point out to the significance of assessing the 3D site effect in local seismic hazard studies, especially in regions with complex geological features, since the routine seismic hazard studies do not typically take into account the 3D site effect.

We provide a new methodology that allows the simulation of this 3D site effect in a relatively fast and efficient way by implementing a 3D finite difference modelling algorithm that takes advantage of matrix operations in order to decrease the simulation time and at the same time uses a spatially varying grid spacing in order to decrease memory requirements for a dense grid. Therefore, we were able to perform a large number of simulations for a variety of double couple sources located around the study region and thus we accurately simulated the surface spectral amplification in the area up to the frequency of 5 Hz. Furthermore, it was possible to observe and

assess the effect of the direction of propagation and thus the angle of incidence on every point of the surface.

The subsurface structure derived by detailed geophysical investigation covering all the investigation area. By acquiring array microtremor measurements, we were able to obtain efficiently and at a low cost numerous 1D Vs velocity profiles, within a busy urban environment such as the city of Loutraki. Using these profiles we were able to syn- thesize a 3D velocity model for the area and utilize it in order to calculate the real amplification effect that a realistic, shallow 3D structure would cause.

In the highly destructive earthquake of 1981 there were specific sites with considerably higher damage distribution. We have proven that a contributing reason to this phenomenon can be the inhomogeneous subsurface structure. More specifically the abrupt rise of the bedrock relative the coastal sediments contributed to the creation of complex wavefield forms that resulted in an amplification of the total seismic energy in specific areas.

Figure 13

Spectral Attenuation for the sites a and b (Fig.11). Simulated spectra from different source locations are shown with different colors

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Acknowledgements

This research was supported by the ‘‘Development of Infrastructure and Services through Actions of Excel- lence for the Mitigation of the Geodynamic Hazard Effects (GEORISK)’’ project and partially by the

‘‘Integrated early warning system and seismic risk mitigation at industrial sites (ARES)’’ project, through which funding and equipment were provided

in order to carry out all the field work. The authors would also like to thank Liakopoulos S. and Kontakos K. for their help in the fieldwork. Thanks are also due to Dr. Sboras S. for his helpful insight about the geology of the study area.

Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figure 14

Horizontal to vertical spectral ratios for sites a, c and d (Fig.11)

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(Received July 11, 2019, revised January 7, 2020, accepted January 8, 2020, Published online January 17, 2020)