Analysis of Peak Ground Acceleration Attenuation Characteristics in the Pazarcik Earthquake, Türkiye

Abstract

This study collected acceleration records and station reports from 379 strong-motion stations triggered by the M_w7.7 earthquake in Pazarcik, Türkiye, on 6 February 2023. A total of 451 horizontal and 194 vertical strong-motion acceleration records with complete waveforms and reasonable data were selected to establish appropriate equations for predicting seismic parameters. Two iterative algorithms, specifically the optimization algorithm and orthogonal distance regression, were employed to formulate prediction equations for PGA and EPA in the NS (north–south), EW (east–west), and vertical directions. Furthermore, a comparative analysis of the attenuation curves for PGA and EPA was conducted within the vertical and horizontal directions. The results indicated that the observed and predicted values of vertical PGA and EPA at the same fault distance were approximately 0.577–0.673 times those of horizontal PGA and EPA. The ratio range calculated in our study aligns closely with previous research results, slightly more than 2/3 only in the vicinity of fault zones. The analysis demonstrated that the horizontal PGA value of the soil site at the same fault distance was approximately 1.46 times that of the bedrock site, while the vertical PGA value was only 1.12 times. The comparison of attenuation relationships revealed that within the fault distance range of 20 km to 100 km, the horizontal PGA of the Wenchuan earthquake was approximately 1.26–2.16 times that of the Pazarcik earthquake, and the ratio increased with an increasing fault distance.

1. Introduction

Providing seismic action predictions for earthquake-resistant design is the main objective of engineering seismology in civil engineering [1]. The attenuation relationship of ground motion, which also has been referred to as the ground motion prediction equation in recent years, is the most commonly used method in engineering seismology to estimate the seismic impact or to predict seismic action [2]. Research on ground motion attenuation began in the 1940s when Gutenberg and Richter established statistical relationships between epicentral acceleration and the earthquake magnitude and attenuation relationships between epicentral acceleration and distance based on seismic intensity and strong-motion observation data in the California region of the United States [3]. Since then, the study of ground motion attenuation has been one of the most important topics in engineering seismology research, and the progress of the related research strongly relies on the collection of strong-motion observation data. In the early stage, Türkiye mainly used ground motion prediction equations from North America and Europe because of the lack of strong-motion records [4]. After the Izmit (1999, M_S 7.4) and Bolu (1999, M_W7.1) earthquakes in Türkiye, with the continuous construction of strong-motion observation stations and the improvement of strong-motion networks, Türkiye has gradually gathered a sufficient number of strong-motion observation records. Some researchers developed regional ground motion attenuation models for Türkiye and fitted ground motion prediction equations using various parameters [5,6,7,8].

To establish prediction equations for the horizontal peak ground acceleration (PGA) and acceleration response spectrum (Sa) for different site categories, Gulkan and Kalkan utilized strong-motion records of earthquakes with magnitudes greater than 5 that occurred in Türkiye between 1976 and 1999 [5]. They found that the PGA and Sa values were overestimated for distances of approximately 15–20 km compared to the research results of Boore et al. [4]. Rathje et al. employed strong-motion records from 22 stations triggered by the Izmit earthquake to fit the attenuation relationships of PGA and Sa values at periods of 0.3, 1.0, and 2.0 s and established ground motion prediction equations for three different site categories: rock, stiff soil, and soft soil [9]. They analyzed the influence of site classification on ground motion attenuation relationships. Kalkan and Gülkan collected 100 vertical strong-motion records from earthquakes within Türkiye between 1976 and 2002 and established a set of vertical ground motion prediction equations to predict vertical PGA and vertical Sa values [10]. Through strong-motion data, Akkar and Cagnan developed a new set of regional ground motion prediction models for Türkiye [8]. They fitted attenuation relationships for horizontal PGA, peak ground velocity (PGV), and Sa values and compared them with the prediction equations of European and global ground motion models, which led to the identification of the differences between the Turkish models and global prediction models [11]. Gulerce and Akyuz optimized the NGA-W1 model using strong-motion network data in Türkiye and calculated spectral ratios of vertical-to-horizontal acceleration attenuation curves to better estimate vertical response spectrum values [12]. Askan et al. carried out a comprehensive study on strong-motion characteristics using a dataset of 77 strong ground motion records within a 200 km range of the epicenter of the M_w7.0 earthquake that occurred on the Samos Island in the Aegean Sea on 30 October 2020, which affected Türkiye and Greece [13].

On 6 February 2023, at 04:17 local time in Türkiye, an M_w7.7 magnitude earthquake occurred in the southern part of Kahramanmaras Province, with a surface wave magnitude (M_s) of 7.8 according to the China Earthquake Networks Center. The epicenter was located in Pazarcik, which is 34 km south of Gaziantep, at a latitude of 37.288 degrees north and a longitude of 37.043 degrees east. According to Türkiye’s Disaster and Emergency Management Authority, the focal depth was 8.6 km, and nine hours later at 13:24 local time, a M_w7.6 earthquake took place in the central part of Kahramanmaras Province, with the epicenter in Eibistan. The Pazarcik earthquake occurred on the main branch fault of the East Anatolian Fault Zone (EAFZ), with a deformation zone exceeding 200 km. The successive occurrence of earthquakes caused an increase in the loss of both lives and property. More than 500,000 structures suffered structural damage at different levels, while more than 50,000 people died [14]. Both earthquakes significantly affected 11 different provinces, such as Hatay, Kahramanmaras, Adıyaman, Malatya, Adana, Osmaniye, Kilis, Sanlıurfa, Gaziantep, Osmaniye, and Diyarbakır [14].

The strong seismic network in Türkiye obtained a large number of strong-motion records during the Pazarcik earthquake (2023, M_w7.7), and many strong-motion stations had detailed site information, providing valuable basic data for investigating the attenuation characteristics of PGA and EPA in Türkiye. PGA stands for Peak Ground Acceleration, which is the maximum absolute value of ground motion duration during an earthquake. PGA is predominantly controlled by the high-frequency components of seismic motion and can exhibit significant instability due to the influence of complex factors. EPA, short for Effective Peak Acceleration, denotes the peak ground acceleration associated with the mean value of the acceleration response spectrum Sa(T) within the high-frequency range (0.1 to 0.5 s) when considering a damping ratio of 5%. It is important to note that the seismic response of a structure is not solely reliant on individual peak ground acceleration values. As a result, it is meaningful to introduce EPA values that are relevant to the structural seismic response based on these response spectra. We selected appropriate attenuation models, adopted reasonable regression statistical methods, established prediction equations for PGA and EPA, and investigated the differences in attenuation characteristics for different site classifications. This paper presents seismic PGA and EPA prediction equations specifically developed for the East Anatolian Fault Zone in Türkiye, utilizing the most recent data from significant and powerful earthquakes. Furthermore, this paper pioneers a comparative analysis of attenuation characteristics between the Pazarcik Earthquake and the Wenchuan Earthquake. It quantifies soil site amplification factors in relation to bedrock, leading to noteworthy conclusions.

2. Methods and Data

2.1. Attenuation Model

Ground motion is influenced by factors, such as the seismic source, propagation medium, and site conditions. The attenuation relationship simplifies the expression of these three main influencing factors [2]. The attenuation model refers to the functional form of the attenuation relationship of ground motion, and the ground motion prediction equation represents the functional relationship between ground motion parameters and factors, such as the magnitude, distance, and site conditions. For nonlinear fitting of the strong motion observation data and for obtaining the coefficients of the attenuation model, the selection of an appropriate attenuation model is the key step in establishing a ground motion prediction equation. The quality and quantity of the samples used for regression analysis primarily determine the advantages and disadvantages of establishing prediction equations based on empirical methods.

Duke introduced the linear term of “R” in the attenuation model to quantitatively represent the energy attenuation attributed to absorption, providing a comprehensive model that accounts for geometric attenuation factors associated with source characteristics, propagation distance, and inelastic attenuation effects [15]. This Duke model has since become the predominant choice for attenuation modeling in subsequent regression analyses within the field, as follows:

$$\lg \left(Y\right)=A_1+B_{1}R+C_1\mathit{lg}(R+R_0)+D_{1}M+\epsilon$$

(1)

In this study, the surface wave magnitude (MS) was used as the magnitude parameter, and since the research was limited to the attenuation characteristics of the mainshock in Pazarcik, Türkiye, the source parameter was set as a constant term, namely 7.8. Regarding the distance factor, both geometric attenuation and non-elastic attenuation were considered. The following attenuation model was used in this research:

$$\lg \left(Y\right)=A_1+B_{1}R+C_1\mathit{lg}(R+R_0)+\epsilon$$

(2)

where Y represents the ground motion parameter, which refers to the relevant variable, specifically the peak ground motion parameter that reflects the intensity characteristics of ground motion. R stands for the fault distance, representing the independent variable. A₁, B₁, and C₁ are unknown constants obtained through fitting, and ε denotes the random error. The term R₀ is introduced to control the near-field ground motion and needs to be determined through a trial calculation. After determining the attenuation model, the least squares method is often employed to perform regression fitting on the seismic record data to determine the coefficients in the functional relationship.

Referring to previous research results, R₀ is usually selected within the range of 0 to 45 with intervals of 5. In this study, east–west PGA data were fitted using R₀ = 25, which provided the best fitting effect after the comparative analysis. Owing to limitations in length, the trial calculation process is not further described. During the regression analysis, the value range for A1 was 0 to 20, and for B1, it was −1 to 0. If B1 is determined to be 0 after the trial calculation, the B1R term in Model 2 is removed, and the model is adjusted to Model 3, represented by Equation (3), for further data fitting. The value range for C₁ was −5 to −0.1.

$$\lg \left(Y\right)=A_2+C_2\lg (R+R_0)+\epsilon$$

(3)

The meanings of the parameters in Equation (2) are the same as those in Equation (1). In the following, prediction equations are presented for PGA and EPA parameters for the bedrock site and soil site, without considering site classification, for both horizontal and vertical directions.

2.2. Fitting Method

The attenuation relationship was acquired using a nonlinear fitting process. The goodness of fit of the model is evaluated based on the adjusted R-squared, which is the sample R-squared adjusted for the number of observations and degrees of freedom. The adjusted R-squared, which is equivalent to the ratio of the sum of squares of regression to the total sum of squares, represents the proportion of the total variation in the dependent variable (y) that can be explained by the independent variables in the regression model. It is one of the indicators used to assess the effectiveness of the established model. An adjusted R-squared value close to 1 indicates a better fit of the regression model to the observed values, while a value close to 0 demonstrates a poor fit of the regression model to the observed values. The fitting function expression is chosen based on the attenuation model, and initial values, parameter bounds, and fitting convergence constraints for each fitting parameter are set. We used two iterative algorithms, namely the Levenberg–Marquardt optimization algorithm and the orthogonal distance regression method, for fitting the data. Each set of data was fitted using both methods, and the result with higher goodness of fit was selected as the final attenuation relationship. The optimization algorithm is an optimization technique rooted in the least squares problem. Its primary goal is to minimize the sum of squared residuals, which represents the squared differences between observed values and model predictions. On the other hand, the orthogonal distance fitting method aims to determine the curve or model that best fits a given dataset. Its fundamental principle involves minimizing the sum of squared orthogonal distances between observed data points and the fitted curve. This approach not only considers residuals that are perpendicular to the fitted curve but also residuals orthogonal to the tangent direction of the curve.

2.3. Data Selection

The strong-motion data used in this research were obtained from the Türkiye Strong-Motion Acceleration Records Database and Analysis System (website: https://tadas.afad.gov.tr/ (accessed on 4 April 2023)). The Pazarcik earthquake triggered 379 strong-motion stations across Türkiye and Cyprus, with the farthest station located 635 km from the epicenter. The epicenter location and the distribution of triggered stations are shown in Figure 1. Each station’s records of two horizontal components from the same set were treated as two separate records and were collectively referred to as horizontal records. In total, 1137 acceleration time histories were collected from 379 stations in the east–west, north–south, and vertical directions. After carefully examining the waveforms, 169 records with incomplete time histories or recording errors were removed. Because records with very small peak accelerations have limited practical significance for engineering seismic research, a further 323 records with peak accelerations of less than 3 gal were excluded. As a result, a total of 451 horizontal strong-motion records and 194 vertical strong-motion records were employed for statistical analysis.

To investigate the attenuation characteristics of different site categories, we collected the foundation reports of relevant stations. According to the values of the equivalent shear wave velocity (Vs30) obtained from some reports and the associated site information descriptions, they were converted into commonly used site categories in engineering practice in China. Referring to the literature [17], the Vs30 values were converted into the following site categories in China: Class I (Vs30 > 550 m/s), Class II (265 < Vs30 ≤ 550), Class III (165 < Vs30 ≤ 265), and Class IV (Vs30 ≤ 165), with Class II having a wide range of Vs30 values. The data of 144 stations with site category information are presented in

Table 1. Compilation table of seismic recording data.

Station No.	Fault Distance (km)	PGA /gal	Vs30	Station No.	Fault Distance (km)	PGA /gal	Vs30
3139	0.06	493.15	272	5805	181.97	13.25	1072
3142	0.11	745.01	539	2412	182.15	8.44	955
3131	0.16	366.66	567	3304	183.50	19.31	297
3132	0.38	523.94	377	3801	190.14	23.99	407
3137	0.39	843.07	688	2401	190.54	10.12	314
3143	1.02	356.52	444	2414	193.24	10.37	372
3123	1.72	601.79	470	2404	195.10	9.55	567
3124	2.10	647.58	283	99008	200.61	18.43	263
3129	2.42	1218.06	447	4701	201.27	27.65	709
2708	2.53	1113.36	523	5102	201.66	19.07	678
3144	2.86	771.07	485	5811	205.67	15.55	207
3138	2.88	748.46	618	5804	208.48	20.01	392
3145	3.59	692.63	533	5802	209.95	12.35	282
3126	3.78	1021.03	350	3302	211.04	7.12	1007
3141	3.80	875.29	338	5814	212.36	5.62	804
3125	5.15	1131.11	448	5812	217.19	14.23	426
4616	5.42	503.64	390	2413	218.01	63.99	435
3140	7.36	211.76	210	7201	218.35	36.85	450
4625	9.94	486.92	346	99006	219.88	7.97	679
3136	10.55	398.22	344	5803	220.36	9.90	659
4615	11.28	581.50	484	1211	224.84	27.60	463
4624	12.25	318.48	280	2902	228.51	13.36	594
8002	14.19	204.79	430	2904	229.53	8.53	521
3115	16.53	242.21	424	5801	229.77	7.93	413
4404	16.94	139.02	1380	2411	232.61	111.47	284
4620	17.85	323.53	484	4206	233.53	13.36	458
4611	18.61	314.93	731	3306	234.46	8.52	490
3116	18.77	174.17	870	5001	238.24	5.84	369
4617	21.29	113.09	574	2803	239.23	6.14	425
4408	22.11	138.78	654	2802	242.32	7.67	309
3134	28.98	199.41	374	99005	243.03	7.22	457
3133	31.03	143.64	377	2903	243.38	10.54	367
8003	32.75	182.78	350	5808	246.75	4.13	691
3135	33.43	1373.13	460	5813	249.72	4.06	978
4406	44.07	129.32	815	5806	250.11	5.42	320
0120	58.15	120.39	439	2516	256.52	22.16	373
8004	60.10	182.64	426	2506	261.21	7.52	365
2308	63.73	185.37	450	6901	268.77	12.59	519
0125	70.61	86.66	208	6004	274.65	5.00	376
6303	71.48	115.03	986	7001	275.73	4.56	538
2309	72.13	34.99	860	3307	276.30	2.82	855
6304	74.40	236.84	376	6008	286.76	17.59	248
4612	78.63	121.24	246	2508	289.00	9.27	195
4407	79.19	33.21	735	2509	291.08	5.77	495
0119	80.99	50.80	485	99001	292.69	6.63	473
4628	81.63	81.99	186	2513	294.71	6.49	303
0122	84.61	52.57	501	6001	294.99	3.75	324
2302	90.38	238.76	907	2501	295.79	6.27	375
4405	91.71	129.44	579	6006	308.09	4.30	417
0127	99.94	51.07	583	4001	311.19	2.23	460
0123	105.51	38.37	519	6603	315.44	6.97	361
5807	108.25	35.93	445	6007	317.97	5.16	313
0118	109.48	37.57	946	5201	320.59	8.19	199
0129	113.75	41.81	965	0718	324.85	3.24	344
2304	120.47	48.69	489	5202	326.44	2.85	1024
3802	121.96	84.19	305	6005	331.48	12.21	327
2307	124.28	38.51	329	0604	344.63	4.64	291
2409	126.70	17.68	875	0509	346.85	6.08	373
2101	135.06	71.37	519	AMSY	352.25	3.57	942
3305	135.91	18.24	362	0506	354.16	2.87	284
6302	138.19	51.08	936	0713	356.65	3.61	540
0128	140.42	14.13	494	0714	358.44	2.88	607
2305	141.26	54.39	907	5502	376.53	2.81	422
5810	144.29	17.37	528	5506	388.44	2.43	1510
2415	146.00	21.53	444	0507	391.43	2.82	368
3301	149.23	45.58	366	5504	391.63	6.43	404
3804	151.12	18.22	637	7101	402.68	3.36	421
5809	155.09	24.68	340	0511	402.97	2.74	415
3805	158.89	23.51	384	0510	403.18	3.48	363
0124	160.84	8.35	583	5508	403.79	4.20	450
99007	162.98	8.30	575	5503	415.92	4.79	246

, which includes the fault distance, east–west-corrected horizontal PGA, and Vs30 for each station. A total of 451 horizontal ground motion records were selected, out of which 280 records had known site conditions. Among these, there were 76 horizontal records from Class I sites, 186 records from Class II sites, and 18 records from Class III sites. No records from Class IV sites were included.

When fitting the attenuation relationship, the fault distance was used as a distance parameter. The calculation method of the fault distance was as follows: the surface rupture zone of the Pazarcik earthquake in Türkiye was taken as the projection of the causative fault on the Earth’s surface. The latitude and longitude coordinates of multiple survey points of the surface rupture zone were connected to form a surface rupture line. The distance between each station and the segments of the surface rupture line was calculated based on their respective latitude and longitude coordinates, and the minimum value was taken as the fault distance, denoted as Rrup (km). The strong-motion records were grouped according to the site conditions and fault distance. The distribution of strong-motion records is presented in

Table 2. Statistical summary of strong-motion records grouped by site conditions and fault distances.

Fault Distance (km)	Horizontal	Class I	Class II	Class III	Uncertain Site Category
<3	28 (14)	6 (3)	18 (9)	0 (0)	4 (2)
3–9.9	18 (9)	0 (3)	12 (6)	2 (1)	4 (2)
10–29.9	30 (15)	10 (5)	14 (7)	0 (0)	6 (3)
30–59.9	16 (8)	2 (1)	8 (4)	0 (0)	6 (3)
60–99.9	46 (23)	12 (6)	10 (5)	6 (3)	18 (9)
100–199.9	106 (53)	22 (11)	38 (19)	0 (0)	46 (23)
200–299.9	127 (58)	19 (8)	56 (26)	6 (3)	46 (21)
>300	80 (14)	5 (0)	30 (3)	4 (2)	41 (9)
Total	451 (194)	76 (37)	186 (79)	18 (9)	171 (72)

. From Table 2, it can be observed that within the fault distance range of less than 60 km, 92 horizontal and 46 vertical strong-motion records were obtained. Among them, there were only two horizontal and one vertical strong-motion records for Class III sites. The distribution of samples in different distance ranges was uneven because of the limited number of strong-motion records in Class III sites. Fitting attenuation relationships specifically for Class III sites resulted in significant errors. To mitigate this issue, we combined Class II and Class III sites in the site category analysis and referred to them collectively as “soil sites,” while Class I sites were referred to as “bedrock sites.”

In Table 2, the values outside the parentheses denote the quantity of horizontal strong-motion records, whereas the values inside the parentheses indicate the quantity of vertical strong-motion records. The term “uncertain site category” refers to the number of stations for which VS30 information has not yet been acquired.

The strong-motion records were obtained from the Pazarcik earthquake in Türkiye. Therefore, our research results are highly specific and mostly reflect the seismic attenuation characteristics of the southeastern region of Türkiye, where the East Anatolian Fault Zone is located.

2.4. Data Processing

The raw records suffer from baseline drift, background noise, and errors caused by sensor tilt. Hence, direct usage of the raw records is not appropriate. It is necessary to perform baseline correction and filtering on the selected data and then calculate the acceleration response spectrum and extract the PGA and EPA values. Baofeng compared causal and non-causal filters and then compared the results obtained using four different filters at different orders [18]. It was found that non-causal filtering not only maintained phase integrity but also decreased the loss of useful information. Among the different orders, the Butterworth filter exhibited the best stability. Thus, we also adopted a fourth-order non-causal Butterworth high-pass filter with a cutoff frequency of 0.1 Hz (for more details refer to Converse et al. [19] and Baofeng et al. [18]).

3. Empirical Results and Analysis

3.1. Establishment of Prediction Equations of Peak Ground Motion

3.1.1. PGA Prediction Equation

Peak ground acceleration (PGA) represents the maximum value of inertial forces caused by ground motion and is measured based on cm/s² (also known as gal) or ^m/s2 or in terms of gravitational acceleration (g). In this study, gal was used as the unit of PGA. PGA reflects the high-frequency characteristics of ground motion. It is important to note that the PGA attenuation relationships presented in this section are derived from the fitting of data without distinguishing different site conditions. Through a comparative analysis, we found that the orthogonal distance fitting method outperformed the optimization algorithm in fitting the PGA attenuation relationship. The results of the fitting using Model 2 are presented in

Table 3. Coefficients of PGA prediction equations.

Type	A + σ	B + σ	C + σ	Adjusted R-Square
East–West PGA	5.488 ± 0.525	0 ± 0.00109	−1.813 ± 0.307	0.994
North–South PGA	5.704 ± 0.564	0 ± 0.00118	−1.912 ± 0.330	0.994
Horizontal PGA	5.617 ± 0.385	0 ± 0.000797	−1.870 ± 0.225	0.994
Vertical PGA	5.212 ± 0.563	0 ± 0.00146	−1.788 ± 0.342	0.994

, which exhibits high goodness of fit values for each direction. However, coefficient B is zero, and coefficients A and C have large standard deviations, indicating the need for further fitting. BR represents the non-elastic attenuation term within the medium. It arises from the energy absorption in the propagation medium, leading to the energy attenuation of seismic waves. Given the relatively limited impact of the non-elastic attenuation, it is often simplified in engineering applications by amalgamating its effects into geometric attenuation, thereby omitting the BR term.

To achieve better fitting results, the data of PGA in each direction were refitted using Model 3. The obtained coefficient values are presented in

Table 4. Modified coefficient table of PGA prediction equation.

Type	A + σ	B	C + σ	Adjusted R-Square
East–West PGA	5.709 ± 0.232	/	−1.913 ± 0.113	0.994
North–South PGA	5.750 ± 0.233	/	−1.927 ± 0.114	0.994
Horizontal PGA	5.730 ± 0.164	/	−1.920 ± 0.0800	0.994
Vertical PGA	5.691 ± 0.274	/	−2.011 ± 0.139	0.994

. The goodness of fit for the horizontal PGA attenuation relationship improved to 0.99411, and the standard deviation of coefficient A decreased from 0.38454 to 0.16406. The standard deviations of the fitting parameters for all four prediction equations also decreased, demonstrating a better fitting performance that could reflect the attenuation trend of the original data.

The PGA values and attenuation curves for the east–west (EW) and north–south (NS) components of each station’s records are shown in Figure 2a. For the same fault distance, the calculated values of the NS PGA equation were slightly larger than those of the EW PGA equation. Based on the analysis of 194 strong-motion records, the NS PGA was on average 1.0057 times the EW PGA. The ratio of the NS PGA to EW PGA ranged from 0.44 to 1.82, with 91 stations having ratios greater than one and 103 stations having ratios smaller than one. The PGA values and attenuation curves for the horizontal and vertical components of each station’s records are displayed in Figure 2b. Overall, both the recorded and calculated values of the horizontal PGA were larger than those of the vertical PGA. The attenuation rates for horizontal and vertical components were generally similar, with a slightly faster decay observed in the vertical direction.

3.1.2. EPA Prediction Equation

Effective peak acceleration (EPA) is a measure of peak acceleration with average significance, calculated using the acceleration response spectrum. It has the unit of gal and is calculated based on the following formula:

$$\mathrm{EPA}=R_a/2.5$$

(4)

where Ra represents the smoothed average of the 5% damped acceleration response spectrum within the frequency range of 2 to 10 Hz, divided by 2.5 to obtain the EPA [2].

Due to the influence of high-frequency components and various complex factors, PGA is highly unstable, as it is controlled by high-frequency ground motion. The seismic response of a structure does not solely depend on individual PGA values. For example, decreasing the peak values that are above the structural natural frequency does not substantially affect the structural response because the response is influenced by the contributions of all harmonic components within a certain frequency band [20,21]. The use of response spectra for the measurement of the seismic response of structures is an appropriate and broadly accepted method. Considering the typical natural frequency range of general building structures, the frequency range of 2 to 10 Hz is commonly selected. Dividing the average value of the smoothed response spectra with a damping of 5% by 2.5 yields the equivalent value of EPA [2]. In this research, Model 3 was utilized to fit the EPA prediction equation. The coefficients are presented in

Table 5. Coefficients of EPA prediction equations.

Type	A + σ	B	C + σ	Adjusted R-Square
Horizontal EPA	5.415 ± 0.167	/	−1.818 ± 0.0826	0.992
Vertical EPA	4.797 ± 0.165	/	−1.644 ± 0.0854	0.995

, and the EPA attenuation curves shown in Figure 3 suggest that the vertical EPA exhibits a slightly slower decay rate compared to the horizontal EPA.

3.1.3. Comparison between PGA and EPA

EPA represents the average value of ground motion in a frequency range, while PGA only represents the value at a specific frequency point, which is the maximum absolute value of the ground acceleration time history. Owing to the difference in the physical interpretation of PGA and EPA, their attenuation characteristics also differ. Figure 4a displays the distribution of the PGA-to-EPA ratio, and Figure 4 compares the attenuation curves of PGA and EPA. From Figure 4a, it can be observed that the majority of station records have higher PGA values compared to EPA values. The average ratio of horizontal PGA to horizontal EPA was approximately 1.476, with a range of 0.76 to 3.22. The average ratio of vertical PGA to vertical EPA was roughly 1.543, with a range of 0.88 to 4.268. Figure 4b reveals that PGA has a slightly faster attenuation rate compared to EPA, which is evident in both horizontal and vertical directions. Near the fault (with a fault distance smaller than 10 km), the horizontal EPA and vertical PGA values were very close. As the fault distance exceeded 100 km, the attenuation curves of the vertical PGA and vertical EPA became increasingly similar.

3.2. Comparison of Vertical and Horizontal Peak Ground Motion Attenuation

3.2.1. Comparison of Vertical PGA and Horizontal PGA

The analysis showed that the PGA of vertical strong-motion records was 0.673 times that of the horizontal PGA. Because of the randomness and variability of PGA values in strong-motion records, there were 20 stations where the vertical PGA exceeded the recorded PGA in the NS direction, and also there were 15 stations where the vertical PGA exceeded the recorded PGA in the EW direction. This demonstrated that the probability of a vertical acceleration peak exceeding the horizontal acceleration peak was approximately 13.3%.

In engineering practice, it is generally considered that the vertical peak is 1/2 to 2/3 times the horizontal peak. For instance, the seismic coefficient for the vertical direction in seismic design codes can be considered to be 65% of that for the horizontal direction. Therefore, the reference value of the 2/3 ratio was introduced in Figure 5. Figure 5 displays the distribution of the ratio between the vertical PGA and horizontal PGA. The green dotted line represents the computed ratio of the vertical PGA divided by the horizontal PGA, which both were predicted using different equations, and it exhibits the trend of the V/H (vertical/horizontal) PGA fitting values with respect to the fault distance. By inputting different fault distances into the PGA prediction equation at 1 km intervals, the predicted PGA values for vertical and horizontal directions were calculated. The calculated vertical PGA was almost 0.577 times that of the horizontal PGA.

According to Figure 5, the ratio between the computed values of the vertical and horizontal PGA predicted using the equations was greater than 1/2. The ratio between the vertical and horizontal PGA decreased gradually with an increasing fault distance and was slightly greater than 2/3 in the range of fault distances from 0 to 7 km. This suggests that vertical seismic action has a significant impact on the seismic resistance of engineering structures in the near-fault area. From a statistical perspective, although there were a few cases in the near-fault range of large-magnitude earthquakes where the ratio exceeded 2/3, the difference with 2/3 did not go beyond 5%. Considering the redundancy in structural seismic design, estimating the vertical seismic action using a ratio of 2/3 in the near-fault range of large-magnitude earthquakes is still safe and feasible. This estimation scheme for vertical seismic action has also been validated based on a single earthquake event in Türkiye (Pazarcik earthquake), which further confirms its reasonableness.

3.2.2. Comparison of Vertical EPA and Horizontal EPA

The average ratio of the vertical EPA to NS EPA for all strong-motion records was 0.6075, while the average ratio of the vertical EPA to EW EPA was 0.6029. The NS EPA was roughly 1.0089 times the EW EPA. The computed values of the vertical EPA from the prediction equation were 0.590 times the computed values of the horizontal EPA. Figure 6 suggests that within a fault distance of 0–300 km, the V/H ratio of the computed values from the EPA prediction equation is consistently below 2/3, ranging from 0.42 to 0.69. The V/H values of EPA in the strong-ground-motion records at each station exhibited a substantial dispersion, with a maximum value of 1.37 and a minimum value of 0.25. Records with V/H ratios smaller than 2/3 accounted for over 68% of the total records. It is evident from the comparison of Figure 5 and Figure 6 that the V/H curves for PGA and EPA computed from the prediction equations differ significantly. The V/H curve for EPA gradually increased with an increasing fault distance, while the PGA exhibited a pronounced vertical effect near the fault. Further research is required to scrutinize the influence of near-field vertical effects on structural damage in Turkish earthquakes.

3.3. The Attenuation Characteristics of Bedrock Sites and Soil Sites

Site conditions are one of the most important factors that influence seismic attenuation. Owing to the influence of the site effects, ground motion can exhibit considerable variations within a small range. Hence, it is necessary to establish ground motion prediction equations for different site types. In this study, the PGA attenuation relationships for bedrock and soil sites were fitted separately according to Model 2. The fittings included both horizontal and vertical components. For the vertical attenuation fitting of soil sites, Model 3 was employed, allocating a zero value for B. The fitting processes were carried out using the orthogonal distance regression method, and the values of the parameters are presented in

Table 6. Coefficients of horizontal PGA prediction equations.

Type	A + σ	B + σ	C + σ	Adjusted R-Square
Bedrock Horizontal	5.204 ± 0.978	−0.00113 ± 0.00234	−1.646 ± 0.585	0.992
Soil Horizontal	5.323 ± 0.363	−0.000627 ± 0.000815	−1.671 ± 0.217	0.998
Bedrock Vertical	4.778 ± 1.339	−0.000907 ± 0.00359	−1.537 ± 0.818	0.996
Soil Vertical	5.683 ± 0.215	/	−1.994 ± 0.111	0.999

.

The PGA attenuation fitting curves for horizontal bedrock sites and soil sites, along with the PGA records from strong motion events on these sites, are shown in Figure 7a. The dataset for horizontal soil sites consisted of 204 samples, while the dataset for horizontal bedrock sites consisted of 76 samples. The PGA attenuation fitting curves for vertical rock and soil sites are exhibited in Figure 7b, based on a dataset of 88 records from soil sites and 34 records from rock sites. Figure 7a indicates that the attenuation fitting curves for bedrock and soil sites match well with the original data, reflecting the attenuation trend of the original data. However, the horizontal attenuation relationship fitting for bedrock sites had slightly larger errors due to the limited number and discrete distribution of near-field effective records obtained from bedrock sites.

An analysis of Figure 7 reveals that under the same fault distance conditions, the horizontal PGA for soil sites is greater than that for bedrock sites. This is attributed to the stronger ground-motion-amplification effect in softer soil layers. The vertical characteristics exhibited some differences compared to the horizontal characteristics, with significant amplification effects in the vertical soil layers observed only within the fault distance range of 0 to 100 km. Beyond 100 km, the vertical PGAs for both bedrock and soil sites were almost similar. To quantitatively represent the ground-motion-amplification effect of soil sites, we calculated site amplification factors based on the fault distance (

Table 7. Table of site amplification factors for different soil types.

Site Type	Bedrock Site		Soil Site
Fault Distance (km)	Horizontal	Vertical	Horizontal	Vertical
0–50	1	1	1.23	1.45
51–100	1	1	1.28	1.15
101–150	1	1	1.34	1.06
151–200	1	1	1.41	1.03
201–250	1	1	1.48	1.03
251–300	1	1	1.56	1.05
301–350	1	1	1.65	1.09
351–400	1	1	1.74	1.13
Average Value	1	1	1.46	1.12

). The site amplification factor is the ratio of the PGA calculated using the soil site PGA prediction equation to the PGA calculated using the bedrock site PGA prediction equation at the corresponding distance point [22]. Overall, using the bedrock site PGA as a reference, the average amplification factor for horizontal site effects was 1.46, while that for vertical soil site effects was 1.12, indicating a substantially stronger seismic effect in soil layers compared to bedrock. This helps us to explain the more severe seismic damage to structures on soil sites compared to those on bedrock sites at the same fault distance. It is worth mentioning that the seismic-motion-amplification effect of soil was largely manifested in the horizontal direction, while no significant seismic-motion-amplification effect was observed in the vertical direction. As the fault distance increased, the horizontal amplification effect of soil became increasingly prominent.

4. Discussion

It is constructive to analyze and compare the attenuation characteristics between the Pazarcık earthquake (M_s 7.8) in Türkiye and the Wenchuan earthquake (M_s 8.0) that occurred on May 12, 2008, in China. The strong-motion records of the Wenchuan earthquake were provided by the China Earthquake Networks Center. A total of 337 horizontal strong-motion records from 174 stations were collected for regression analysis [22]. Among them, there were 33 records from bedrock sites and 304 records from soil sites, including Class II and Class III sites. The distribution of PGA values with respect to the fault distance for the Wenchuan and Pazarcık earthquakes is shown in Figure 8a. Comparatively, the Pazarcık earthquake had a richer set of bedrock site strong-motion records compared to the Wenchuan earthquake. Multiple sets of near-fault strong-motion records were obtained for the Pazarcık earthquake, including 34 horizontal acceleration records within a fault distance of smaller than 5 km, while only three records were obtained for the Wenchuan earthquake. This highlights the invaluable nature of the abundant strong-motion records obtained from the Pazarcık earthquake, particularly for the study of attenuation relationships and near-field seismic characteristics for different site categories.

The values of the parameters of the horizontal PGA attenuation equation for the Wenchuan earthquake are presented in

Table 8. Coefficients of horizontal PGA prediction equation.

Type	A	B	C	Adjusted R-Square
Wenchuan Earthquake	4.842 ± 0.345	−0.000329 ± 0.00441	−1.3204 ± 0.186	0.99074

, and the attenuation curves for the Wenchuan and Pazarcık earthquakes are displayed in Figure 8b. Figure 8b reveals that for distances greater than 5 km, under the same fault distance conditions, the attenuation values of the Wenchuan earthquake are larger than those of the Pazarcık earthquake, and the difference between the two increases with an increasing distance. At a fault distance of 20 km, the PGA of the Wenchuan earthquake was approximately 1.26 times that of the Pazarcık earthquake; at 50 km, it was roughly 1.66 times; at 100 km, it was almost 2.16 times; at 200 km, it was approximately 2.86 times; and at 300 km, it was roughly 3.3 times. This was chiefly due to the higher magnitude of the Wenchuan earthquake compared to the Pazarcık earthquake, which resulted in a significantly greater release of energy. In addition, the PGA attenuation rate of the Wenchuan earthquake was slower than that of the Pazarcık earthquake, which was predominantly attributed to the differences in regional geological and tectonic settings, as well as variations in quality factors. For fault distances smaller than 5 km, the PGA attenuation curves of the Wenchuan and Pazarcık earthquakes were very close. This was attributed to two factors: first, the saturation phenomenon of seismic parameters during large earthquakes, and second, the lack of near-fault strong-motion records for the Wenchuan earthquake, which likely led to the underestimation of the PGA values near the fault.

5. Conclusions

This paper provides seismic peak ground acceleration prediction equations tailored to the East Anatolian Fault Zone. These results can be valuable for seismic hazard assessments, the seismic-resistant design of significant engineering projects, and seismic risk evaluation in the southeastern region of Türkiye. The PGA and EPA prediction equations and attenuation characteristics of the Pazarcik M_w7.7 earthquake in Türkiye were investigated and the following conclusions were drawn:

(1)

The PGA values were higher than the EPA values for the same fault distance, both in the vertical and horizontal directions. On average, the PGA was approximately 1.4 to 1.5 times larger than the EPA. When considering the impact of seismic parameters on damage assessment, it is recommended to use EPA values to reduce PGA variability and to improve reliability.

(2)

The PGA exhibited certain vertical effects near the fault, while the EPA did not show this phenomenon. Through the comparison of multiple sets of vertical and horizontal data, we found that the estimation of vertical seismic action as two-thirds of the horizontal seismic action was reasonable. Based on the analysis of Pazarcik earthquake data, this estimation had a reliability of over 85%. For engineering design considerations, the vertical seismic action can also be estimated as half of the horizontal seismic action for far-field cases.

(3)

There were significant differences in the attenuation relationship between the PGA and EPA for different site types. The amplification effect of PGA in soil sites compared to that in bedrock sites was more pronounced horizontally than vertically. Taking PGA in bedrock sites as a reference, the average amplification factor for horizontal soil sites was 1.46, while for vertical soil sites, it was 1.12. The soil amplification effect was related to the fault distance, with a greater amplification effect observed in the horizontal PGA as the fault distance increased, while the vertical effect exhibited the opposite trend.

(4)

For fault distances greater than 5 km, the PGA of the Wenchuan earthquake was consistently larger than that of the Pazarcik earthquake for the same fault distance. As the fault distance increased, the ratio between the PGA predicted values of the Wenchuan and Pazarcik earthquakes gradually increased from 1.0 to 3.60. For fault distances smaller than 5 km, the PGA attenuation curves of the Wenchuan and Pazarcik earthquakes were almost similar. This comparison indicated that the seismic damage range caused by the Wenchuan earthquake was much larger than that caused by the Pazarcik earthquake.

(5)

Due to the concentration of strong motion data in Class II sites, there was a limited amount of available data for Class I and Class III sites. Specifically, the distribution of bedrock data within a fault distance of 0–50 km was uneven. Therefore, further data verification and in-depth research are needed to examine the influence of site types on attenuation characteristics. This study focused on a single seismic event, and thus, the developed ground motion prediction equations have a limited range of applicability. Future research should make full use of the strong-motion records from multiple seismic events in the Turkish strong-motion network. This should be achieved through the inclusion of the earthquake magnitude as a variable in regression fitting to establish ground motion prediction equations by incorporating source parameters, distance parameters, and site parameters.