# The prediction of seismic amplification effect in three-dimensional sedimentary basins and its application

*Dis Prev Res*2023;2:19.

## Abstract

Numerous studies have shown that the basin amplification effect is influenced by characteristic parameters such as basin geometry and media impedance contrast, but quantitative analysis of the effect for three-dimensional (3D) basins is still rare. In this paper, the basin amplification effect is quantified through an aggravation factor *AGF*),

## Keywords

*,*seismic motion

*,*characteristic parameters

*,*amplification effect

*,*aggravation factors

## INTRODUCTION

As a typical complex site, the significant amplification of ground motion in sedimentary basins has been confirmed in multiple seismic surveys and strong earthquake observations^{[1-4]}. Many large cities (e.g., Tokyo, Beijing, Los Angeles, Mexico City, *etc*.) are built on the basins. Once a destructive earthquake occurs, it would cause terrible loss of life and property. In recent years, in the background of frequent global earthquakes and the development of the “resilient city”, it is important to conduct research on the seismic effects of sedimentary basins and quantitatively evaluate the seismic ground motions, aiming to ensure engineering seismic safety and promote the construction of resilient cities.

Due to the special geometry of the basin and the impedance difference between the media inside and outside the basin, the seismic waves are entrapped by the basin to generate complex wavefields, leading to various basin effects: (1) basin-edge effect^{[5-7]}; (2) focusing effect^{[8-10]}; and (3) resonance effect^{[11,12]}. The determination of seismic fortification parameters in the Seismic Ground Motion Parameter Zonation Map of China (GB18306-2015)^{[13]} and Code for Seismic Design of Buildings (GB50011-2010)^{[14]} are based on 1D horizontally layered sites. However, the simplified 1D seismic response analysis cannot involve the propagation of surface waves and other basin effects in the basin. Furthermore, Eurocode 8^{[15]} in Europe and the International Existing Building Code^{[16]} in America make allowance implicitly for 1D sites but overlook complex 2D or three-dimensional (3D) site effects due to irregular subsurface geometry. Therefore, it is necessary to conduct 2D or 3D research on the basin effects. The main content of this necessity of conducting 2D or 3D research on the basin effects focuses on irregular subsurface geometry and surface topography. The irregular underground geometric shape mainly affects the propagation of seismic waves within the soil, including reflection and refraction at the interface of the medium, while the surface topography mainly affects the propagation and attenuation of seismic waves on the surface.

At present, research approaches for basin effects include observation, analytical, and numerical methods. Although an observation method^{[17-19]} can provide the most realistic seismic records, it relies on a dense and extensive station distribution and is costly to collect huge amounts of data. The advantage of the analytical method^{[20,21]} is to analyze and explain the site ground motion characteristics essentially, but it is difficult to give the corresponding analytical solutions in heterogeneous media with irregular subsurface configurations. In recent years, the rapid development of computing technology has facilitated the progress of numerical methods for modeling complex geological structures in two or three dimensions, including finite-difference methods (FDM)^{[6,22,23]}, finite-element methods (FEM)^{[24-26]}, boundary element methods (BEM)^{[27-29]}, spectral element methods (SEM)^{[30,31]}, *etc*.

Based on the above-mentioned numerical approaches, numerous studies have been conducted on the influence of basin characteristic parameters on basin effects. Semblat *et al.* analyzed the amplification of seismic motion in terms of level^{[28]}, occurring frequency, and location in 2D alluvial basins at different depths using the BEM. Lee *et al.* used the SEM to simulate strong ground motion throughout the Taipei metropolitan area and concluded that the amplification of ground motion was mainly controlled by basin depth and shallow shear wave velocity^{[31]}. Vessia *et al*. investigated the effect of basin shape ratios and sediment impedance contrasts on the amplification effect of 2D trapezoidal valleys using the FEM^{[24]}. *et al*.^{[22]}. Moczo *et al*. performed 3D, 2D, and 1D simulations for six typical sedimentary valleys of various widths and depths and investigated the sensitivity of earthquake ground motion characteristics to impedance contrast^{[23]}, attenuation, velocity gradient, and geometry. Qiang *et al*. investigated the effects of structural parameters on seismic aggravation of two-dimensional sedimentary valleys using the FEM^{[26]}. Due to the limitation of computational effort and calculation methods, 2D simplified models are mostly used to study the influence of basin characteristics parameters on the basin amplification effect in existing studies, while 3D models are often applied to simulate the actual basin under scenario earthquake, and few people have used 3D simplified models to analyze the basin amplification effect. Since the actual sedimentary basin is in 3D space, compared with the 2D model, the 3D model can consider a variety of basin effects more comprehensively and realistically and give a more accurate and reliable quantitative relationship between basin aggravation factors and characteristic parameters. Tong *et al*. pointed out in their study of seismic amplification in the Santa Monica region that considering the concentration of damage and the patterns of high amplification, the proper treatment of the problem must take 3D subsurface structures into account^{[12]}. For all these reasons, 3D basin models are established in this study.

In this paper, we investigate the sensitivity of aggravation factors to inclination angles, shape ratios, sediment thicknesses, and impedance contrasts by establishing 78 3D trapezoidal sedimentary basin models with different characteristic parameters. First of all, we qualitatively analyze the influence of basin characteristic parameters on the aggravation factor of the 3D basin. Then, the basins are divided into several regions, and the aggravation factors of each region are quantitatively analyzed to provide prediction formulas for aggravation factors. Finally, the prediction formulas are applied to the Euroseistest basin and the Shidian basin in order to provide a reference for local seismic motion estimation.

## MODELING AND METHODOLOGY

To discuss the effects of different geometric and media parameters on the seismic response of the basins, we establish 3D trapezoidal sedimentary basin models located in a semi-infinite space, as shown in Figure 1. A total of 78 basin models are formed by combining different basin widths *W*, sediment thicknesses *H*, inclination angles *A,* and sediments shear wave velocity *V*_{s}, while the media parameters of bedrock of all models are the same. Due to the fact that the sediment density, bedrock density, and bedrock wave velocity remain constant, different sediment wave velocities represent different impedance contrasts. The sediment-bedrock impedance contrast *α* defined as the ratio between the seismic impedance (that is, the multiplication of density and shear wave velocity) of the sediments and the bedrock. The media parameters, including shear wave velocity *V*_{s}, compression wave velocity *V*_{p}, density *ρ*, and Poisson's ratio *v* of the media inside and outside the basin, are listed in Table 1. Each model is encoded under a unique ID in the form _{i}H_{j}V_{sl}A_{k}*Sr* is defined as the ratio between the maximum thickness of the sedimentary layer and the half of basin width, *Sr* = 2*H*/*W*, and *T*_{0} is the 1D fundamental period at the center of the basin, *T*_{0} = 4*H*/*V*_{s}.

Properties of the simulation model

Category | ID code | ρ (kg/m^{3}) | V_{S} (m/s) | V_{P} (m/s) | Q_{S} | Q_{P} | v |

Basin | Vs_{1} | 1,800 | 300 | 600 | 30 | 60 | 0.33 |

Vs_{2} | 1,800 | 400 | 800 | 40 | 80 | 0.33 | |

Vs_{3} | 1,800 | 500 | 1,000 | 50 | 100 | 0.33 | |

Rock | - | 2,200 | 1,500 | 3,000 | 9,999 | 9,999 | 0.33 |

Nomenclature of the ID code for each model

i, j, k, l | W_{i} (m) | H_{j} (m) | A_{k} (°) | Vs_{l} (m/s) |

1 | 2,000 | 100 | 20 | 300 |

2 | 3,000 | 200 | 45 | 400 |

3 | 4,000 | 400 | 65 | 500 |

Geometrical and dynamic properties of all models

Model ID | W | H | A | Vs | Sr | T_{0} | Model ID | Wm | H | A | Vs | Sr | T_{0} |

W_{1}H_{1}Vs_{1}A_{1} | 2,000 | 100 | 20 | 300 | 0.10 | 1.33 | W_{2}H_{2}Vs_{3}A_{1} | 3,000 | 200 | 20 | 500 | 0.13 | 1.60 |

W_{1}H_{1}Vs_{1}A_{2} | 2,000 | 100 | 45 | 300 | 0.10 | 1.33 | W_{2}H_{2}Vs_{3}A_{2} | 3,000 | 200 | 45 | 500 | 0.13 | 1.60 |

W_{1}H_{1}Vs_{1}A_{3} | 2,000 | 100 | 65 | 300 | 0.10 | 1.33 | W_{2}H_{2}Vs_{3}A_{3} | 3,000 | 200 | 65 | 500 | 0.13 | 1.60 |

W_{1}H_{1}Vs_{2}A_{1} | 2,000 | 100 | 20 | 400 | 0.10 | 1.00 | W_{2}H_{3}Vs_{1}A_{1} | 3,000 | 400 | 20 | 300 | 0.27 | 5.33 |

W_{1}H_{1}Vs_{2}A_{2} | 2,000 | 100 | 45 | 400 | 0.10 | 1.00 | W_{2}H_{3}Vs_{1}A_{2} | 3,000 | 400 | 45 | 300 | 0.27 | 5.33 |

W_{1}H_{1}Vs_{2}A_{3} | 2,000 | 100 | 65 | 400 | 0.10 | 1.00 | W_{2}H_{3}Vs_{1}A_{3} | 3,000 | 400 | 65 | 300 | 0.27 | 5.33 |

W_{1}H_{1}Vs_{3}A_{1} | 2,000 | 100 | 20 | 500 | 0.10 | 0.80 | W_{2}H_{3}Vs_{2}A_{1} | 3,000 | 400 | 20 | 400 | 0.27 | 4.00 |

W_{1}H_{1}Vs_{3}A_{2} | 2,000 | 100 | 45 | 500 | 0.10 | 0.80 | W_{2}H_{3}Vs_{2}A_{2} | 3,000 | 400 | 45 | 400 | 0.27 | 4.00 |

W_{1}H_{1}Vs_{3}A_{3} | 2,000 | 100 | 65 | 500 | 0.10 | 0.80 | W_{2}H_{3}Vs_{2}A_{3} | 3,000 | 400 | 65 | 400 | 0.27 | 4.00 |

W_{1}H_{2}Vs_{1}A_{1} | 2,000 | 200 | 20 | 300 | 0.20 | 2.67 | W_{2}H_{3}Vs_{3}A_{1} | 3,000 | 400 | 20 | 500 | 0.27 | 3.20 |

W_{1}H_{2}Vs_{1}A_{2} | 2,000 | 200 | 45 | 300 | 0.20 | 2.67 | W_{2}H_{3}Vs_{3}A_{2} | 3,000 | 400 | 45 | 500 | 0.27 | 3.20 |

W_{1}H_{2}Vs_{1}A_{3} | 2,000 | 200 | 65 | 300 | 0.20 | 2.67 | W_{2}H_{3}Vs_{3}A_{3} | 3,000 | 400 | 65 | 500 | 0.27 | 3.20 |

W_{1}H_{2}Vs_{2}A_{1} | 2,000 | 200 | 20 | 400 | 0.20 | 2.00 | W_{3}H_{1}Vs_{1}A_{1} | 4,000 | 100 | 20 | 300 | 0.05 | 1.33 |

W_{1}H_{2}Vs_{2}A_{2} | 2,000 | 200 | 45 | 400 | 0.20 | 2.00 | W_{3}H_{1}Vs_{1}A_{2} | 4,000 | 100 | 45 | 300 | 0.05 | 1.33 |

W_{1}H_{2}Vs_{2}A_{3} | 2,000 | 200 | 65 | 400 | 0.20 | 2.00 | W_{3}H_{1}Vs_{1}A_{3} | 4,000 | 100 | 65 | 300 | 0.05 | 1.33 |

W_{1}H_{2}Vs_{3}A_{1} | 2,000 | 200 | 20 | 500 | 0.20 | 1.60 | W_{3}H_{1}Vs_{2}A_{1} | 4,000 | 100 | 20 | 400 | 0.05 | 1.00 |

W_{1}H_{2}Vs_{3}A_{2} | 2,000 | 200 | 45 | 500 | 0.20 | 1.60 | W_{3}H_{1}Vs_{2}A_{2} | 4,000 | 100 | 45 | 400 | 0.05 | 1.00 |

W_{1}H_{2}Vs_{3}A_{3} | 2,000 | 200 | 65 | 500 | 0.20 | 1.60 | W_{3}H_{1}Vs_{2}A_{3} | 4,000 | 100 | 65 | 400 | 0.05 | 1.00 |

W_{1}H_{3}Vs_{1}A_{2} | 2,000 | 400 | 45 | 300 | 0.40 | 5.33 | W_{3}H_{1}Vs_{3}A_{1} | 4,000 | 100 | 20 | 500 | 0.05 | 0.80 |

W_{1}H_{3}Vs_{1}A_{3} | 2,000 | 400 | 65 | 300 | 0.40 | 5.33 | W_{3}H_{1}Vs_{3}A_{2} | 4,000 | 100 | 45 | 500 | 0.05 | 0.80 |

W_{1}H_{3}Vs_{2}A_{2} | 2,000 | 400 | 45 | 400 | 0.40 | 4.00 | W_{3}H_{1}Vs_{3}A_{3} | 4,000 | 100 | 65 | 500 | 0.05 | 0.80 |

W_{1}H_{3}Vs_{2}A_{3} | 2,000 | 400 | 65 | 400 | 0.40 | 4.00 | W_{3}H_{2}Vs_{1}A_{1} | 4,000 | 200 | 20 | 300 | 0.10 | 2.67 |

W_{1}H_{3}Vs_{3}A_{2} | 2,000 | 400 | 45 | 500 | 0.40 | 3.20 | W_{3}H_{2}Vs_{1}A_{2} | 4,000 | 200 | 45 | 300 | 0.10 | 2.67 |

W_{1}H_{3}Vs_{3}A_{3} | 2,000 | 400 | 65 | 500 | 0.40 | 3.20 | W_{3}H_{2}Vs_{1}A_{3} | 4,000 | 200 | 65 | 300 | 0.10 | 2.67 |

W_{2}H_{1}Vs_{1}A_{1} | 3,000 | 100 | 20 | 300 | 0.07 | 1.33 | W_{3}H_{2}Vs_{2}A_{1} | 4,000 | 200 | 20 | 400 | 0.10 | 2.00 |

W_{2}H_{1}Vs_{1}A_{2} | 3,000 | 100 | 45 | 300 | 0.07 | 1.33 | W_{3}H_{2}Vs_{2}A_{2} | 4,000 | 200 | 45 | 400 | 0.10 | 2.00 |

W_{2}H_{1}Vs_{1}A_{3} | 3,000 | 100 | 65 | 300 | 0.07 | 1.33 | W_{3}H_{2}Vs_{2}A_{3} | 4,000 | 200 | 65 | 400 | 0.10 | 2.00 |

W_{2}H_{1}Vs_{2}A_{1} | 3,000 | 100 | 20 | 400 | 0.07 | 1.00 | W_{3}H_{2}Vs_{3}A_{1} | 4,000 | 200 | 20 | 500 | 0.10 | 1.60 |

W_{2}H_{1}Vs_{2}A_{2} | 3,000 | 100 | 45 | 400 | 0.07 | 1.00 | W_{3}H_{2}Vs_{3}A_{2} | 4,000 | 200 | 45 | 500 | 0.10 | 1.60 |

W_{2}H_{1}Vs_{2}A_{3} | 3,000 | 100 | 65 | 400 | 0.07 | 1.00 | W_{3}H_{2}Vs_{3}A_{3} | 4,000 | 200 | 65 | 500 | 0.10 | 1.60 |

W_{2}H_{1}Vs_{3}A_{1} | 3,000 | 100 | 20 | 500 | 0.07 | 0.80 | W_{3}H_{3}Vs_{1}A_{1} | 4,000 | 400 | 20 | 300 | 0.20 | 5.33 |

W_{2}H_{1}Vs_{3}A_{2} | 3,000 | 100 | 45 | 500 | 0.07 | 0.80 | W_{3}H_{3}Vs_{1}A_{2} | 4,000 | 400 | 45 | 300 | 0.20 | 5.33 |

W_{2}H_{1}Vs_{3}A_{3} | 3,000 | 100 | 65 | 500 | 0.07 | 0.80 | W_{3}H_{3}Vs_{1}A_{3} | 4,000 | 400 | 65 | 300 | 0.20 | 5.33 |

W_{2}H_{2}Vs_{1}A_{1} | 3,000 | 200 | 20 | 300 | 0.13 | 2.67 | W_{3}H_{3}Vs_{2}A_{1} | 4,000 | 400 | 20 | 400 | 0.20 | 4.00 |

W_{2}H_{2}Vs_{1}A_{2} | 3,000 | 200 | 45 | 300 | 0.13 | 2.67 | W_{3}H_{3}Vs_{2}A_{2} | 4,000 | 400 | 45 | 400 | 0.20 | 4.00 |

W_{2}H_{2}Vs_{1}A_{3} | 3,000 | 200 | 65 | 300 | 0.13 | 2.67 | W_{3}H_{3}Vs_{2}A_{3} | 4,000 | 400 | 65 | 400 | 0.20 | 4.00 |

W_{2}H_{2}Vs_{2}A_{1} | 3,000 | 200 | 20 | 400 | 0.13 | 2.00 | W_{3}H_{3}Vs_{3}A_{1} | 4,000 | 400 | 20 | 500 | 0.20 | 3.20 |

W_{2}H_{2}Vs_{2}A_{2} | 3,000 | 200 | 45 | 400 | 0.13 | 2.00 | W_{3}H_{3}Vs_{3}A_{2} | 4,000 | 400 | 45 | 500 | 0.20 | 3.20 |

W_{2}H_{2}Vs_{2}A_{3} | 3,000 | 200 | 65 | 400 | 0.13 | 2.00 | W_{3}H_{3}Vs_{3}A_{3} | 4,000 | 400 | 65 | 500 | 0.20 | 3.20 |

To simulate the effects of sedimentary basins on seismic wave propagation and scattering, the FK-SE method, which combines the frequency-wavenumber domain^{[32]} and the SEM^{[33]}, is used to analyze the basin ground motion amplification effects. First, the semi-infinite space free-field response under the incident plane wave is calculated by the FK method, and then the equivalent nodal force input at the boundary of the spectral element is calculated; finally, the 3D complex wavefield is solved by the high-precision SEM. The wavefield at the combination of FK and SEM is determined according to the reference^{[34]}; i.e., the wavefield *U*_{total} at the boundary position is composed of two parts, the incident wavefield *U*_{FK} calculated by the FK method and the scattered wavefield *U*_{SC} in the region, when the scattered wave propagates outward from the calculation area and passes through the boundary, as shown in Equation (1). At the boundary of the SEM calculation region, the incident wavefield is subtracted from the total wavefield at the outer edge of the calculation domain, and only the absorption boundary condition is applied to the remaining scattered wavefield.

To ensure the accuracy of the SEM, it is required that the seismic wave contains at least five GLL nodes per wavelength. This means that the size of the elements *d* and the polynomial order *N* are both constrained by the shortest wavelength *λ*_{min} propagated in the media, and they should satisfy Equation (2)^{[33]}.

The grid size of the sedimentary part is 30 m, and the maximum grid size outside the basin is 80 m. The total number of spectral elements in the model is 870,829, and the maximum frequency of simulation is

A profile of the 3D model is cut along the *xOz* plane, and 101 receivers are evenly arranged from left to right along the basin surface. The 3D numerical simulations of the seismic response of all models, along with the corresponding 1D analyses of the isolated soil columns, are performed using as input acceleration the Gaussian pulse, as shown in Figure 2 in both frequency and time domains, as vertically incident plane SV waves. The bandwidth of the Gaussian pulse is 0~5 Hz. Then, the acceleration time history of the response of each receiver is obtained with the Gaussian pulse as input motion, which is further used to calculate the transfer functions of each receiver. In the end, the transfer functions are convolved with actual seismic waves to form a synthetic set of acceleration time histories.

## INPUT GROUND MOTIONS

The selection of the input ground motion record should be based on several criteria: (1) motion recorded on rock or stiff soil sites; (2) magnitude range; (3) wide distribution of peak frequencies of the peak acceleration response spectrum within the considered frequency range; and (4) sufficient number of records for a meaningful statistical analysis. Based on the above standards, ten seismic acceleration records are selected from the Pacific Earthquake Engineering Research Center (PEER Available from: https://ngawest2.berkeley.edu/) as the input motion, which are recorded at rock or stiff soil sites with a wide distribution of peak frequencies of the peak acceleration response spectrum within the considered frequency range, involving different magnitudes, fault types, epicentral distances, and peak accelerations (PGA). The detailed parameters of the selected ten acceleration records are shown in Table 4. The selected acceleration records are low-pass filtered at 5 Hz, and the ten acceleration records and the normalized acceleration response spectra (*ζ* = 0.05) after the filtering process are shown in Figure 3. The curve of the CSDB-II is the seismic design response spectra for Class II Sites of Code for Seismic Design of Buildings.

Figure 3. (A) Acceleration time histories of input seismic records and (B) corresponding normalized response spectra with respect to CSDB-II design spectra. CSDB-II: Class-II site of Code for Seismic Design of Buildings.

Description of input seismic records

ID | Record number | Earthquake | Station | Magnitude | Fault type | R_{rup}(km) | PGA(cm/s^{2}) | V_{30}(m/s) |

In1 | 59 | San Fernando | Cedar Springs_ Allen Ranch | 6.61 | Reverse | 89.72 | 17.5 | 813.48 |

In2 | 765 | Loma Prieta | Gilroy Array #1 | 6.93 | Reverse oblique | 9.64 | 154.5 | 1,428.14 |

In3 | 1,050 | Northridge-01 | Pacoima Dam (downstr) | 6.69 | Reverse | 4.92 | 187.2 | 2,016.13 |

In4 | 1,108 | Kobe_ Japan | Kobe University | 6.9 | Strike-slip | 0.9 | 275.8 | 1,043 |

In5 | 1,161 | Kocaeli_Turkey | Gebze | 7.51 | Strike-slip | 7.57 | 257.6 | 792 |

In6 | 1,943 | Anza-02 | Idyllwild-Keenwild Fire Sta. | 4.92 | Normal oblique | 32.12 | 16.8 | 845.41 |

In7 | 3,325 | ChiChi_Taiwan-06 | HWA003 | 6.3 | Reverse | 56.02 | 38.0 | 1,525.85 |

In8 | 4,097 | Parkfield-02_CA | Slack Canyon | 6.0 | Strike-slip | 2.99 | 206.7 | 648.09 |

In9 | 4,483 | L'Aquila_Italy | L'Aquila - Parking | 6.3 | Normal | 5.38 | 304.2 | 717 |

In10 | 8,165 | Duzce_Turkey | IRIGM 496 | 7.14 | Strike-slip | 4.21 | 738.5 | 760 |

## AGGRAVATION FACTOR

The aggravation factor is used to characterize the basin amplification effect, which is widely adopted in many studies^{[23,27,35-39]}. It is defined as the ratio between the acceleration response spectra of the 3D basin model and the corresponding 1D model surface observation points. The 78 3D basin models and the corresponding 1D models in Table 3 are numerically simulated; 101 observation points are evenly located on the basin surface, and ten actual acceleration records are input for each, as shown in Figure 3. A total of 78 × 2 × 101 × 10 = 157,560 ground acceleration time courses is synthesized by numerical simulations. Due to the symmetry of basin models, the seismic response of one-half of the receivers is analyzed in the following. The acceleration response spectra are obtained from the simulated acceleration time series, and the 3D results are compared with the 1D results to obtain the aggravation factor *AGF*_{m} as follows:

where *m* is the input motion number; *T/T*_{0} is the ratio of the period *T* to the fundamental period *T*_{0} of the 1D soil column in the middle of the basin; *X/W* is the ratio of the distance *X* from the basin surface receiver to the basin bedrock junction to the basin width *W*; *SA*_{3D,m}(*T/T*_{0}, *X/W*) and *SA*_{1D,m}(*T/T*_{0}, *X/W*) represent the 5% damped acceleration response spectra for 3D and 1D results at each input motion, respectively. Therefore, *AGF*_{m}(*T/T*_{0}, *X/W*) represents the aggravation factor dependent on the dimensionless period *T/T*_{0} and the location parameter *X/W* at each input motion. To reduce the influence of the uncertainty of the input ground motions with different characteristics on the aggravation factors, the arithmetic mean of the basin aggravation factor *AGF*(*T/T*_{0}, *X/W*) is calculated according to Equation (4) over the ten aggravation factors.

### Qualitative analysis of aggravation factor

Figure 4 shows the effect of inclination angles, thicknesses, widths, and impedance contrasts on the *AGF**T/T*_{0}, *X/W*)*AGF*. The aggravation factors present a significantly variant behavior in its spatial distribution accompanied by a change in inclination angle, as shown in Figure 4A. Comparing the results of W_{1}H_{2}Vs_{2}A_{2} and W_{1}H_{2}Vs_{2}A_{3} models, we can see that the effect of inclination angle on the *AGF* is mainly concentrated in the edge part, and the effect on the central part is not obvious. It is noteworthy that a large amplification phenomenon still occurs in the central part of W_{1}H_{2}Vs_{2}A_{1}. The possible reason is that the inclination angle and width of this model are small, and the surface waves excited in the wide edge part propagate a short distance to the central part, resulting in obvious amplification phenomena with a maximum aggravation factor of 2.84. In addition, the *AGF* is less than 1.0 in some areas of the edge part, showing the characteristic of reduction; i.e., the 3D response is smaller than the corresponding 1D response, and the larger the inclination angle, the smaller the *AGF*, and the more obvious the characteristic of reduction. The reason may be that in the 1D analysis, due to the difference in media impedance contrast, the incident body wave is reflected back and forth within the sedimentary media several times, resulting in a larger site response, while in the 3D models, the incident wave is refracted at the slope of the basin edge and part of the energy is transmitted to the interior of the basin, and the larger inclination angle, the more energy is transmitted to the interior of the basin after refraction, and the site response is, thus, reduced.

Figure 4. Aggravation factor *AGF* (*X/W*, *T/T _{0}*) affected by (A) inclination angles, (B) widths, (C) thicknesses, (D) impedance contrasts along the half-width of the basin surface for selected symmetrical models.

It can be seen that the period and location distribution of the aggravation factor *AGF* for different basin widths is in Figure 4B. In wide basins, the maximum value of *AGF* occurs close to the change in sediment thickness at the basin edge (*X/W* = 0.2), and in narrow basins, the maximum value of *AGF* is closer to the middle region of the basin (*X/W* = 0.4). The *AGF* in the narrow basin model reaches a maximum value of 2.34, which is significantly higher than the results for the larger width basins. The reason is that the surface waves excited by the edge of the basin propagate toward the center of the basin and continuously decay with the propagation distance. In models with larger widths, the aggravation factor in the central part is close to 1.0. In addition, as the width increases, the proportion of the significant amplification area decreases, and its location gradually concentrates at the edge part of the basin.

Figure 4C indicates that there is a significant increase in *AGF* in the central region of the basin with increasing sediment thicknesses. Moreover, the reduction range in the basin edge part also expands with increasing sediment thickness; e.g., the reduction range (*AGF* < 1) is less than 0.1 W in W_{1}H_{1}Vs_{2}A_{2} and _{1}H_{2}Vs_{2}A_{2},_{1}H_{3}Vs_{2}A_{2}. The larger the sediment thickness at the same inclination angle, the larger the surface projection of the basin edge part, and the reduction phenomenon occurs in the projection range. In general, basin widths and sediment thicknesses (both can be attributed to shape ratio) mainly affect the response of the central part, and the amplification effect is stronger in the central part of the basin with a high shape ratio. It cannot be ignored that the thickness of the sediment also influences the response of the basin edge part.

The period and location distribution of the aggravation factor *AGF* for different impedance contrasts can be seen in Figure 4D. For the low impedance contrast basins, such as W_{1}H_{2}Vs_{1}A_{2}, the amplification is obvious only where the sediment thickness changes, while in higher impedance contrast basins, amplification is present in all central parts of the basin. The reason for this phenomenon is that seismic waves are slow to attenuate in soils with high wave velocities, and the surface waves excited at the basin edge spread to the middle of the high wave velocity basin, causing ground motions to amplify. Meanwhile, as the impedance contrast increases, the level of reduction gradually decreases. Because the high impedance contrast media has a weaker ability to capture the wave, the incident wave is reflected by the ground surface and transmits out at the media interface, resulting in a reduced 1D response.

### Quantitative analysis of aggravation factor

The above-mentioned studies and the actual seismic damage indicate that there are significant differences in the amplification effects of ground motions in different regions in the basin. Therefore, dividing the basin into several regions and statistically analyzing the aggravation factors within each region can avoid overestimating or underestimating the amplification effect of certain regions of the basin to a certain extent. The half-width of the symmetrical basin surface is divided into five regions (*a*, *b*, *c*, *d*, and *e*) with two equal-width regions (*a* and *b*) over the edge part of the basin and three equal-width regions (*c*, *d*, and *e*) over the central part of the basin [Figure 5]. The best-fit curves expressing the correlation of max *AGF* with the characteristics parameters for each region are estimated through regression analyses using the least squares method. Additionally, considering the poor fit of the data for certain parameters, a mean value of max *AGF* of each partition is further examined for each region. Additionally, the standard deviation (SD) is calculated, and the mean value ±1 times the SD is used to measure the dispersion of the data.

The fitted relationship between inclination angles and max *AGF* is shown in Figure 6. In the basin edge part, max *AGF* decreases with increasing inclination angle and can be as low as 0.7 at *A* = 65°, indicating that ground motion is significantly suppressed. The boxplot [Figure 6C] shows that the data dispersion at *A* = 65°*R*^{2}, which are used to characterize the degree of interpretation of the best-fit curves to the data, of the best-fit curves in regions *a* and *b* are 0.525 and 0.615, respectively. The max *AGF* exhibits a significant negative correlation with the inclination angle in regions *a* and *b*. While in the central part of the basin (Regions *c*, *d*, and *e*), the correlation between max *AGF* and the inclination angle is weakened, as the corresponding best-fit curves tend to be flat. However, it should be pointed out that our results differ from the findings of Riga^{[22]}, whose study revealed that the aggravation factor of Region *a* is not significantly affected by inclination angles. The difference may be explained by the fact that the other characteristic parameters of the selected basin models are different, further reflecting the fact that the basin amplification effect is influenced by various factors.

Figure 6. Influence of inclination angle on max *AGF* for five regions: (A) best-fit curves for regions *a*, *b*; (B) best-fit curves for regions *c*, *d*, *e*; (C) boxplot of max *AGF* for regions *a*, *b*; (D) boxplot of max *AGF* for regions *c*, *d*, *e*.

The effect of shape ratios on max *AGF* is illustrated in Figure 7, and max *AGF* shows a tendency to increase with the increase of shape ratio throughout the basin surface. It should be noted that when fitting the max *AGF* curves in Regions *a* and *b*, the case of *Sr* = 0.4 is not involved because there is a lack of data with *A* = 20°*Sr* = 0.4. As discussed in the previous section, the inclination angle has a significant impact on max *AGF* in regions *a* and *b*. To avoid missing data interfering with the results, the case of *Sr* = 0.4*AGF* is more affected by the inclination angle in the edge part of the basin, while max *AGF* is more affected by shape ratio in the central part.

Figure 7. Influence of shape ratio on max *AGF* for five regions: (A) best-fit curves for regions *a*, *b*; (B) best-fit curves for regions *c*, *d*, *e*; (C) boxplot of max *AGF* for regions *a*, *b*; (D) boxplot of max *AGF* for regions *c*, *d*, *e*.

The effect of impedance contrast on max *AGF* is illustrated in Figure 8. The best-fit curves of max *AGF* in all regions of the basin are relatively flat. The 95% confidence bands for max *AGF* lie between 0.9 and 1.2 in the edge part (regions *a*, *b*), while the 95% confidence bands for max *AGF* lie between 1.2 and 1.7 in the central part (regions *c*, *d*, *e*). The amplification effect in the central part is usually higher than that in the edge part, which is also shown in the previous discussions on inclination angle and shape ratio. As can be seen from the boxplots, the max *AGF* shows a poor correlation with the impedance contrast because the same impedance contrast is used in the 3D model and the corresponding 1D model.

### Difference in aggravation factors between 2D and 3D

The fitting results based on 3D simulations are compared with the 2D results of Riga^{[22]}, as shown in Figure 9. Except for Region *a*, 3D results are larger than 2D results in other regions. Given that the basins with higher shape ratios are modeled (*Sr* = 0.2~0.4) in our research and that higher shape ratio basins tend to have larger max *AGF*, it is bound to have an impact on the comparison. Therefore, when comparing the differences in the influence of inclination angle on max *AGF* between 2D and 3D, more attention should be paid to the changing trend. In the central part of the basin (regions *c*, *d*, *e*), the 3D results show a certain decreasing trend, but the 2D results suggest that max *AGF* basically does not vary with inclination angles. Probably, Riga adopted larger basin widths, resulting in the surface waves excited at the basin slope not reaching the central part of the basin. The curves of the effect of shape ratios on max *AGF* demonstrate that max *AGF* increases with the increase of shape ratios for both 2D and 3D results. In Region *a*, 2D results are higher than 3D results at low shape ratios, and 3D results are higher than 2D results at high shape ratios. Yet, the situation in Region *e* is the opposite of Region *a*.

## APPLICATION OF AGGRAVATION FACTOR PREDICTION FORMULA

The best-fit formulas for basin aggravation factors in different regions with respect to each parameter (inclination angles, shape ratios, and impedance contrasts) are listed in Table 5. The influence weight *w* of each parameter on max *AGF* is calculated based on the coefficient of determination *R*^{2} of each best-fit curve, and the prediction equation for max *AGF* in each region containing three parameters is obtained according to Equation (5):

Fitting formulas for the maximum aggravation factor in each region

Parameters | Regions ID | Best-fit formulas | R^{2} | w |

Inclination angle | a | ln(max AGF) = 1.764 - 0.480 ln(A) | 0.525 | 0.791 |

b | ln(max AGF) = 1.435 - 0.375 ln(A) | 0.615 | 0.902 | |

c | ln(max AGF) = 0.677 - 0.077 ln(A) | 0.030 | 0.186 | |

d | ln(max AGF) = 0.757 - 0.099 ln(A) | 0.038 | 0.224 | |

e | ln(max AGF) = 1.028 - 0.175 ln(A) | 0.114 | 0.538 | |

Shape ratio | a | ln(max AGF) = 0.467 + 0.209 ln(Sr) | 0.138 | 0.208 |

b | ln(max AGF) = 0.262 + 0.062 ln(Sr) | 0.043 | 0.063 | |

c | ln(max AGF) = 0.621 + 0.114 ln(Sr) | 0.124 | 0.770 | |

d | ln(max AGF) = 0.651 + 0.131 ln(Sr) | 0.125 | 0.735 | |

e | ln(max AGF) = 0.539 + 0.076 ln(Sr) | 0.040 | 0.189 | |

Impedance contrast | a | ln(max AGF) = 0.114 + 0.014 ln(α) | 0.001 | 0.001 |

b | ln(max AGF) = 0.363 + 0.174 ln(α) | 0.024 | 0.035 | |

c | ln(max AGF) = 0.522 + 0.086 ln(α) | 0.007 | 0.044 | |

d | ln(max AGF) = 0.535 + 0.096 ln(α) | 0.007 | 0.041 | |

e | ln(max AGF) = 0.830 + 0.289 ln(α) | 0.058 | 0.273 |

where *w*(*A*), *w*(*Sr*), and *w*(*α*) are the influence weight of inclination angles, shape ratios, and impedance contrasts, respectively. Based on the above prediction equations, after determining the inclination angle, shape ratio, and impedance contrast, the predicted values of the corresponding aggravation factors can be calculated to predict the amplification effect of the basin.

### Prediction of aggravation factors in the Euroseistest basin

The Euroseistest basin is an approximately symmetrical cross-section of the Mygdonian basin, a sedimentary basin located in Thessaloniki, Northern Greece, which was established in 1993 as a test site for seismological and earthquake engineering research. Zhu *et al*. developed a simplified 2D model of the Euroseistest basin and simulated the distribution of aggravation factors within the surface area of the basin^{[40]}, as shown in Figure 10. According to the simplified model, it is known that inclination angle *A* = 8°, shape ratio *Sr* = 0.08, impedance contrast *α* = 0.177, and the comparative analysis of the predicted values of the aggravation factor and the results of Zhu are shown in Figure 10. It can be seen that the distribution pattern of the aggravation factor along the surface is basically consistent. However, except for Region *a*, the prediction values of the remaining four regions are overestimated, probably because the surface receivers of the 3D model are additionally influenced by waves coming from outside the plane where the profile is located. Other possible reasons need an in-depth discussion, such as attempting to eliminate interference from waves in other directions in the 3D model.

### Prediction of aggravation factors in the Shidian basin

The Shidian basin is located in the western region of Yunnan Province, China, and has occurred high intensity anomalies numerous times during historically strong earthquakes. The 1976 Longling earthquake, the 1988 Lancang-Gengma earthquake, and the 2001 Shidian earthquake have caused serious damage in this basin, although the epicenters of these earthquakes are located tens to hundreds of kilometers from the basin^{[41]}. Based on the soil samples and wave velocity measuring results from 24 boreholes in the basin, *et al*.^{[42]}. According to the 3D velocity structure model, three typical profiles are selected in order from north to south. The first profile is located in the transition area from shallow to deep sediment thickness in the basin, and the second and third profiles are located deeper inside the basin. The second profile is more symmetrical on both sides, and the third profile is asymmetrical. The position and bedrock shape of each profile are shown in Figure 11. The irregular bedrock shapes are simplified to trapezoids, and the inclination angle and shape ratio of the simplified model are recorded. On the other hand, the multi-layer soil with different wave velocities in the basin is simplified to single-layer soil, and the simplified shear wave velocity is calculated according to Equation (6).

The simplified basin characteristics parameters are shown in Table 6, which are applied to the aggravation factor prediction equation to predict the amplification effect of the Shidian basin. It should be noted that for the asymmetric basin, both half-widths need to be partitioned into regions, with the region numbers *a*_{1}~*e*_{1} and *a*_{2}~*e*_{2}, respectively, and the partitioning rules are the same as those for the symmetric basin. The predicted values of max *AGF* for different regions of each profile are shown in Table 7 and Figure 12. The bold represents the maximum aggravation factor in each region of the corresponding profile model in Table 7. For profile 1, the maximum value of max *AGF* (around 2.155) occurs in Region *a*_{2}; for profiles 2 and 3, the maximum value of max *AGF* occurs in Region *e*_{2} with 1.630 and 1.597, respectively. The difference between the max *AGF* of the edge part and the central part is not significant in profile 2, while the max *AGF* of the central part is significantly higher than that of the edge part in profile 3. It can be concluded that the basin with a small inclination angle has a larger aggravation factor in the edge part and even exceeds the central part. When the inclination angle increases to a certain degree, the aggravation factor in the central region is higher than that in the edge region.

Simplified profile characteristics parameters

Profiles number | Inclination angle (°) | Shape ratio | Impedance contrast | |

Left | Right | |||

Profile 1 | 11 | 6 | 0.09 | 0.176 |

Profile 2 | 12 | 12 | 0.10 | 0.185 |

Profile 3 | 35 | 15 | 0.11 | 0.188 |

Predicted values of max *AGF* for different regions of each profile

Regions ID | max AGF | ||

Profile 1 | Profile 2 | Profile 3 | |

a_{1} | 1.662 | 1.607 | 1.048 |

a_{2} | 2.155 | 1.468 | |

b_{1} | 1.647 | 1.599 | 1.106 |

b_{2} | 2.041 | 1.479 | |

c_{1} | 1.457 | 1.468 | 1.457 |

c_{2} | 1.472 | 1.475 | |

d_{1} | 1.464 | 1.475 | 1.451 |

d_{2} | 1.487 | 1.480 | |

e_{1} | 1.637 | 1.630 | 1.467 |

e_{2} | 1.748 | 1.597 |

## CONCLUSION

Currently, research on the impact of basin characteristic parameters on basin effects generally adopts simplified two-dimensional models or 3D models of specific basins, and few people have used 3D simplified models to analyze the basin amplification effect. Compared with the 2D model, the 3D model can more comprehensively investigate basin effects. Therefore, we established 78 3D sedimentary basin models to study the amplification effect of basins with different geometric and physical parameters. Basin-induced amplification is quantified through a period-dependent and location-dependent aggravation factor (*AGF*), defined as the ratio between 3D and 1D acceleration response spectra at some points on the basin surface. The basins are divided into several regions, and the aggravation factors of each region are quantitatively analyzed to provide prediction formulas for aggravation factors, which are applied to the Euroseistest basin and the Shidian basin. The main conclusions are as follows:

(1) The effect of inclination angles on the *AGF* is mainly concentrated in the edge part, and max *AGF* increases with decreasing inclination angles.

(2) The seismic motion in the edge part of the basin with a small inclination angle is significantly amplified. The reason is that when the inclination angle is small, the incident wave excites a more complex wave field over a wider range of the edge slope, and the refraction of the body wave caught in the sediments is more complicated between the media partition interface and the ground surface.

(3) The seismic motion in the edge part of the basin with a large inclination angle is obviously suppressed. The reason may be that some of the incident waves are refracted at a large angle in a steep basin slope and then propagate toward the interior of the basin, leading to the reduction of the surface response in the edge part.

(4) Basin width and sediment thickness (both can be attributed to shape ratios) mainly affect the response of the central part, and the amplification effect is stronger in the central part of the basin with a high shape ratio.

(5) The poor fitting of the aggravation factor curve regarding the impedance contrast indicates that the amplification effect does not correlate well with the impedance contrast. The aggravation factor, as the ratio between the 3D response and the 1D response, is not significantly affected by the impedance contrast because the same impedance contrast is used in the 3D model and the corresponding 1D model.

(6) From the prediction results for the Euroseistest basin, the distribution pattern of the aggravation factor along the surface is basically similar. Nevertheless, the aggravation factor of the 3D model is higher than that of the 2D model because the surface observation points are additionally influenced by waves coming from outside the plane of the 2D model.

(7) The predicted results for the Shidian basin show that the basin with a small inclination angle has a larger aggravation factor in the edge part and even exceeds the central part; when the inclination angle increases to a certain degree, the aggravation factor in the central region is higher than that in the edge region.

The prediction formula we proposed involves four parameters, including inclination angles, widths, sediment thicknesses, and impedance contrasts, which can be easily obtained through geological structure exploration, making it convenient to serve as a reference indicator for evaluating basin effects in practical engineering. However, it is necessary to point out some limitations of this study. On the one hand, the nonlinearity of the soil was not considered in this study. As mentioned above, more than 100,000 ground motions were obtained by using the convolution method based on the linear constitutive model of the soil. If the nonlinearity is considered, it would require large computational efforts to obtain such a large amount of ground motion data. In addition, the nonlinearity will affect both 1D and 3D results, so the effect on the aggravation factor may not be significant. However, there is no doubt that considering the nonlinearity of soil in studying seismic motion in future research is more reasonable, especially in soft soil sites. On the other hand, in order to appropriately reduce the number of computational models, only three different scenarios were considered for inclination angles, depths, widths, and impedance contrasts. It should be acknowledged that setting more scenarios can make the prediction formula more accurate, but the conclusions of this study are correct. Finally, this study only considers ideal trapezoidal sedimentary basins under incident plane waves. However, the actual bedrock shape, topography, and incident wave field are usually more complex. In the future, further research will be conducted on more complex conditions.

## DECLARATIONS

Authors’ contributionsConceptualization, methodology, validation, formal analysis, resources, supervision, project administration: Ba Z

Software, investigation, data curation: Mu S, Zhao J

Methodology, writing - original draft, visualization: Mu S, Zhang Y, Chen S

Availability of data and materialsNot applicable.

Financial support and sponsorshipFinancial support from the National Natural Science Foundation of China (Grant #52178495) is gratefully acknowledged.

Conflicts of interestAll authors declared that there are no conflicts of interest.

Ethical approval and consent to participateNot applicable.

Consent for publicationNot applicable.

Copyright© The Author(s) 2023.

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## Cite This Article

## How to Cite

Ba, Z.; Mu S.; Zhao J.; Zhang Y.; Chen S. The prediction of seismic amplification effect in three-dimensional sedimentary basins and its application. *Dis. Prev. Res.* **2023**, *2*, 19. http://dx.doi.org/10.20517/dpr.2023.22

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