1 Introduction

On the 6th of February 2023 at 01:17:32 UTC a \(M_{w}=\) 7.7 earthquake hit southeast Türkiye and Syria. The earthquake initiated on the small Nurdağı-Pazarcık Fault (NPF) but then jumped to the East Anatolian Fault (EAF, Survey USG 2023a; Melgar et al. 2023; Okuwaki et al. 2023). Only 9 h after the \(M_{w}=\) 7.7 earthquake the region was hit by another major earthquake with \(M_{w}=\) 7.6 that occurred on the Sürgü Fault (SF, Survey USG 2023b; Melgar et al. 2023; Okuwaki et al. 2023). The result of the two major earthquakes in such a short interval was devastating for the region, with a death toll of around 59000 people (\(\simeq\)51000 in Türkiye and \(\simeq\)8000 in Syria). The region is well known for its high seismic hazard (Akkar et al. 2018) and risk (Crowley et al. 2021) with numerous active faults and historic seismicity (Erdik 2013) and large population (Gunasekera et al. 2023). In fact, the 6th of February earthquakes occurred in a region where the largest ground motions are expected in Türkiye (Fig. 1).

Fig. 1
figure 1

Earthquakes (\(M\ge 3.0\), green dots) and seismic hazard map (Danciu et al. 2021) of south-east Türkiye and Syria. Seismic hazard is for 10 % probability of exceedance in 50 years for soil condition (V\(_{s30}\)) \(=\) 760 ms\(^{-1}\). Blue lines show the active fault lines (Emre et al. 2018), cyan stars show the epicentres of the Kahramanmaras doublet earthquakes, and the black rectangles identify finite fault solutions from (Survey USG 2023a, b)

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Thanks to the dense strong motion station coverage in the near-fault region, a large amount of seismic data was collected during the Kahramanmaraş earthquakes. Near-fault ground motion provides valuable information related to earthquake physics (e.g. directivity effects) and ground deformation (e.g. the fling step effect). If the earthquake rupture propagates towards seismic stations, forward directivity can be observed in stations where the cumulative effect of the rupture arrives in a short window of time with a long period and large amplitude (Somerville et al. 1995). Permanent ground deformation can also be seen in seismic signals (Bolt 2002) and can be identified as impulsive signals. Moreover, site amplification may further amplify impulsive signals (Kobayashi et al. 2019).

Impulsive signals may magnify the destructive effects of earthquakes by creating large seismic demands on structures and infrastructure such as: masonry buildings (Shabani et al. 2023), (i) seismically isolated structures (Bhagat et al. 2021), (ii) reinforced concrete structures (Carocci 2012), (iii) industrial buildings (Zhang et al. 2021), (iv) minarets (Oliveira et al. 2012), (v) bridges (Li et al. 2017; Chen et al. 2022), (vi) wind turbines (Ali et al. 2020), (vii) dams (Gorai and Maity 2021), and (viii) warehouses (Hatayama 2008). Velocity pulses, in general, have high energy at the beginning of the shaking, which may lead to large deformation and damage with respect to non-impulsive signals. Since the impulsive motion concentrates the seismic energy in one or few pulses with a specific period, it may create large inelastic demand on structures with fundamental periods close to the period of the impulsive motion (Kalkan and Kunnath 2006).

In this study, we analyze strong motion records (see Sect. 2) from the Kahramanmaraş earthquakes to detect and analyze the impulsive ground motions. We used the methods of Shahi and Baker (2014), Ertuncay and Costa (2019) as detection algorithms. Shahi and Baker (2014) use the NGA-West 2 database (Ancheta et al. 2014) to define what impulsive motion is and provides the detection algorithm that is explained below. Ertuncay and Costa (2019) use NGA-West 2, GeoNet (GNS Science 2020), the Italian Accelerometric Archive (Pacor et al. 2011), and K-Net databases (Earth Science and Resilience 2019). We also analyze the probability of observing impulsive motion with the models of Shahi and Baker (2014), Ertuncay and Costa (2021), described in Sect. 3. We present individual impulsive motions in Sect. 4 and discuss their features in Sect. 5.

2 Data

Fig. 2
figure 2

Earthquakes and seismic stations used in this study along with their site classes according to Eurocode 8 (EC8, Aucun et al. 2012). Black boxes are the finite fault solutions for the Pazarcık and Elbistan earthquakes as performed by USGS (Survey USG 2023a, b)

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After the first shock of the Kahramanmaraş sequence, there are more than 3057 earthquakes (\(M\ge 3.0\)) registered by Disaster and Emergency Management Authority (AFAD;deprem.afad.gov.tr/event-catalog, last access: 14/06/2023) between 6th of February 2023 and 31st of March 2023. In total, 287879 traces are collected from the Turkish National Seismic Network (52 stations) (Disaster and Emergency Management Authority 1990), the Turkish National Strong Motion Network (143 stations) (Disaster and Emergency Management Authority 1973), and Kandilli Observatory and Earthquake Research Institute (KOERI, 6 stations) (Kandilli Observatory And Earthquake Research Institute 1971; Cambaz et al. 2021), all of which are recorded from accelerometric stations. The location of the earthquakes and stations is presented in Fig. 2 and EC8 site classification of the stations is given in Table 1. In this study, we analyze the traces of 15 earthquakes with a magnitude larger than 5.5 (Table 2).

Table 1 EC8 site classes of the stations used in this study
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For the analysis, continuous data from AFAD database (tdvms.afad.gov.tr/continuous_data, last access: 14/06/2023) are downloaded and the traces are cut starting from 5 s before the theoretical P-wave arrival (calculated using the velocity structure of (Kennett and Engdahl 1991)) until 90 s after the theoretical P-wave arrival. We then perform the following processing on the raw data: (i) removal of the instrument response (ii) detrending (ii) 4th order Butterworth band-pass filtering between 0.02 Hz to 10 Hz (iv) Cumulatively integrate (cumtrapz integration) acceleration waveforms to velocity waveforms using the composite trapezoidal rule, (v) detrending (vi) visual inspection to pick and remove signals with visible anomalies (e.g. large data gaps)

Table 2 Events from Kahramanmaraş sequence used in this study
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3 Method

In this study, we use the algorithms of Shahi and Baker (2014) and Ertuncay and Costa (2019) to detect impulsive motions in Kahramanmaraş earthquakes. Pulse detection algorithms are explained in Sect. 3.1. Moreover, the probability of observing impulsive motion is calculated for the events that created at least one impulsive motion are analyzed by using the models developed by Shahi and Baker (2014) and Ertuncay and Costa (2021). The models are explained in Sect. 3.2. Finally, periods of the impulsive motions are compared with magnitude-pulse period relations that are introduced in Sect. 3.3.

3.1 Detection of impulsive signals

To detect impulsive motions methods of Shahi and Baker (2014) and Ertuncay and Costa (2019) are selected. The methods are neither modified nor updated by using the data collected for this study. Shahi and Baker (2014) use wavelet analysis to detect the impulsive motion and the pulse period (\(T_{p}\)) of a given velocity time history using a 4th order Daubechies wavelet. They analyse the frequency characteristics of the signal using the continuous wavelet transform (CWT). CWT coefficients are combined linearly to rotate the signal in arbitrary directions. Depending on the direction, the signal with the most energetic features is determined. PGV, which is also orientation-dependent, is also retrieved. To analyze the signals in a similar manner as Ertuncay and Costa (2019), instead of two orthogonal components a single component is given as an input. However, as given in Sect. 4, orthogonal component analyses are also carried out to find the direction of impulsive motions as a separate analysis. By using the CWT coefficients, the concentration of the seismic energy is defined over a relatively small time and frequency window, one of the indicators of impulsive motion. A wavelet is created by using the largest coefficient, and the fitted Daubechies wavelet is subtracted from the original waveform to calculate the PGV ratio between the original signal and the residual signal. Principal component (PC) analysis between the PGV ratio and the ratio between the squared original signal and the squared residual signal (energy ratio) are performed, and the following relation is developed:

$$\begin{aligned} PC = 0.63 \times (PGV \, ratio) + 0.777 \times (energy \, ratio). \end{aligned}$$
(1)

Support vector classification is introduced by analyzing the PC, and PGV of the signals and pulse indicator (PI) boundary is defined as below:

$$\begin{aligned} PI = 9.384 \times (0.76 - PC - 0.0616PGV) \times (PC + 6.914 \times 10^{-4} PGV - 1.072) - 6.179. \end{aligned}$$
(2)

A given signal is identified as impulsive if PI gets a positive value. For instance, Station 4611 (Fig. 3) has a maximum PGV of \(81.24\,\hbox {cm/section}\) (it is larger than the original PGV of the waveform due to the arbitrary rotation part of the process), PI of 1.28, and PC of 0.85.

Ertuncay and Costa (2019) also use wavelet analysis to detect impulsive motion. The wavelet transformation of a given velocity domain signal is carried out using both Ricker and Morlet wavelets. The concentration of the seismic energy is found in the wavelet domain by computing the wavelet power spectrum (WPS) of the signal, and depending on the location of the maximum energy, two different approaches are used.

If the maximum energy is located where the PGV is observed in the time history of the signal, the algorithm checks if PGV is larger than 30 cms\(^{-1}\). If it is larger than the threshold, then the period of maximum WPS is considered as \(T_{p}\), and it is used for further steps. The starting (\(t_s\)) and ending (\(t_e\)) points of the impulsive part of the waveform are determined using the time instance of PGV as the centre of the impulsive part, and cover the area between \(t_s\) and \(t_e\) (the PGV area). If the mean of WPS energy and the squared velocity time history of the pulse area is larger than 30 % of the entire waveform, then the signal is considered as impulsive.

The alternative pulse location is also considered by Ertuncay and Costa (2019) by allowing the maximum WPS to be different to the PGV position. In this case, the maximum amplitude where WPS is located should be larger than 25 cms\(^{-1}\), and both the WPS and the squared velocity time history of the pulse area must contain at least 10 % more energy than the PGV area. Furthermore, the mean of the WPS energy and the squared velocity time history of the alternative pulse area must be larger than 30 % of the entire waveform. In Fig. 3 the impulsive part of the earthquake carries 67.35 % of the waveform energy and 60.77 % of the WPS energy.

Fig. 3
figure 3

Velocity time history record of the Pazarcık earthquake in the fault-normal component of Station 4611 with impulsive motion extracted using the methods of aShahi and Baker (2014), and b Ertuncay and Costa (2019)

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3.2 Probability of impulsive motion

Shahi and Baker (2014) developed two models to determine the probability of observing impulsive signals for a given earthquake. These models are developed both for impulsive motion due to the directivity effect and for regular impulsive motion. To develop the models, a linear combination of several parameters related to strike-slip and non-strike-slip faults has been used. These parameters are: (i) the length of the fault from the epicentre to the point in which the distance between a site of interest and the fault is minimum (s), (ii) the closest distance from the site of interest to the ruptured fault (R) and (iii) the angle between the lines of the fault plane and the line between the epicentre and the site of interest (\(\theta\)).

The models are as in below:

$$\begin{aligned} \begin{aligned} P(directivity|R,s,\theta ,strike-slip)&= \frac{1}{1+e^{0.7897+0.1378R-0.3533\sqrt{s}+0.020\theta }}\\ P(pulse|R,s,\theta ,strike-slip)&= \frac{1}{1+e^{0.4570+0.1260R-0.2440\sqrt{s}+0.013\theta }} \end{aligned} \end{aligned}$$
(3)

Ertuncay and Costa (2021) also develop two models for strike-slip and non-strike-slip faults using a multivariate naïve Bayes classifier. They use parameters: (i) \(M_{w}\), (ii) Joyner-Boore distance (the shortest distance from a site to the surface projection of the rupture plane), (\(R_{jb}\)), and (iii) source-to-site azimuth (Kaklamanos et al. 2011).

The strike-slip model dataset in Ertuncay and Costa (2021) contains earthquakes with magnitudes between 5.7 to 7.9, which covers the magnitude of earthquakes analysed in this paper.

3.3 Pulse period comparison

Periods of the impulsive motions that are determined by the methods explained in Sect. 3.1 are compared with the pulse period estimation algorithms. There are various approaches to detect the longest period. These approaches include the earthquake magnitude (Somerville 2003; Bray and Rodriguez-Marek 2004; Shahi and Baker 2014; Ertuncay 2020) and parameters related to the earthquake kinematics (e.g. rise time, rupture speed); earthquake and station relations (e.g. the distance between the ruptured fault and a site of interest); and the velocity structure of the earthquake area (Fayjaloun et al. 2017; Scala et al. 2018). In this study, we focus only on the algorithms that provide a relation between \(M_{w}\) and \(T_{p}\), since studies related to these parameters are not in agreement in terms of earthquake kinematics, and these parameters are the most likely to vary during rupture (Melgar et al. 2023; Barbot et al. 2023). A comparison between the calculated pulse periods and predictions from previously developed equations is presented in Table 3.

Table 3 Relations between \(M_{w}\) and \(T_{p}\) used in this study
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4 Results

In total we detect 72 impulsive signals using the Shahi and Baker (2014) algorithm and 62 impulsive signals using the Ertuncay and Costa (2019) algorithm. Those signals are observed in 3 earthquakes, the Pazarcık (Kahramanmaraş), Nurdağı (Gaziantep), and Elbistan (Kahramanmaraş) events.

4.1 Pazarcık earthquake (\(M_{w}=7.7\))

Fig. 4
figure 4

Impulsive signals detected by aShahi and Baker (2014) b Ertuncay and Costa (2019) from the Pazarcık earthquake. The red star is the epicentre of the event retrieved from the AFAD catalogue, and the black boxes are the ruptured segments as defined by USGS (2023a)

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The Pazarcık earthquake (Event ID: 1) initiated in the relatively small NPF (Segment 1), which intersects with EAF). EAF, then, bilaterally ruptured in two different segments. The first segment ruptured towards the North-East (Segment 2), and the second segment ruptured towards the South-West (Segment 3, Survey USG 2023a; Melgar et al. 2023; Okuwaki et al. 2023). A large number of impulsive signals have been detected from this earthquake thanks to the dense station coverage along Segment 3 (Fig. 4). Even though most of the impulsive motions are recorded in the very near-fault stations, pulse-shaped signals are recorded at distances of up to \(R_{jb}\simeq\)78 km from the fault (Fig. 5). The first impulsive motion detected in Station 4615 has the closest epicentral distance, \(R_{epi}\), and most of the seismic energy arrives at the station in a single pulse. Due to the multi-segment nature of the earthquake, some of the stations have \(R_{jb}=\)0 km despite having \(R_{epi}\simeq\)150 km (e.g. Station 3124). As a result of the complex rupture, some stations, such as Station 4620 and Station 3115, show impulsive motion whilst having waveforms that are energetic for almost 60 s, which is unusual as impulsive motion tends to result in rather simple seismic traces (Somerville 2003).

Fig. 5
figure 5

Velocity time histories of impulsive signals recorded from the Pazarcık earthquake. In the case of impulsive motion in more than one orientation for a given station, the velocity time history of the channel with the largest \(T_{p}\) is selected. FN, FP, and Ver. represent fault-normal, fault-parallel, and vertical components, respectively

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To detect impulsive motions, stations are rotated from East–West and North-South orthogonal components to fault-normal and fault-parallel components using the strike angles of each segment, which are 28 \({}^{\circ }\), 60 \({}^{\circ }\), and 25 \({}^{\circ }\) for Segments 1–3, respectively. The strike angle of the closest segment to each station is used for the rotation. The same method is applied for the Elbistan earthquake. In total we find 40 impulsive signals using the Shahi and Baker (2014) method and 55 impulsive signals using the Ertuncay and Costa (2019) method. Among the impulsive motions, 17 and 25 of them are in the fault-parallel direction, 14 and 18 of them are in the fault-normal direction, and 9 and 12 of them are in the vertical component for Shahi and Baker (2014) and Ertuncay and Costa (2019) methods, respectively (Table 4). The maximum pulse period of the impulsive motion is up to 15.6 s in Station 0120 (Fig. 6). In the velocity response spectra of this station, there are two distinctive peaks around \(\simeq\)7 s and \(\ge\)10 s and the Shahi and Baker (2014) method effectively detects the latter one as impulsive, as in the response spectra of the residual waveform the second peak vanishes and the spectral amplitudes of the wavelet fitted by Shahi and Baker (2014) and the recorded signal match.

Table 4 Parameters of impulsive signals in Pazarcık earthquake
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To calculate the probabilities of occurrence of impulsive motions we use the Shahi and Baker (2014), Ertuncay and Costa (2021) methods. The Shahi and Baker (2014) method works only for a single fault rupture. To use the model for multiple segments, we move the epicentre position to the edges of the segments that are closer to the epicentre for Segments 2 and 3 (personal communication with J. W. Baker). Finite source models of Pazarcık (Survey USG 2023a) and Elbistan (Survey USG 2023b) earthquakes show that the dip angle of the ruptured faults are not 90 \({}^{\circ }\), hence the surfuce projection of the faults cover an area instead of a line. To calculate the probabilities of observing impulsive motions with the model of Shahi and Baker (2014) as given in Eq. 3, upper edge of the ruptured fault is considered as the rupture line.

Most of the impulsive signals are detected in areas with a large probability of observing impulsive motion, as determined by both models (Fig. 7). However, several non-impulsive signals in the near-fault region are close to the impulsive stations. For instance, there are 7 stations without impulsive motions in the area where Segment 2 and Segment 3 meet. Some of these stations, however, did not record the entire earthquake due to data transmission problems. Station 0213, on the other hand, recorded an impulsive motion even though it only recorded the first 20 s of the event. In this regard, non-impulsive stations in this area can be ignored for the evaluation of the pulse occurrence models. Outliers such as Stations 0120 (\(R_{jb}=\)65.16 km), 2308 (\(R_{jb}=\)75.25 km), and 0125 (\(R_{jb}=\)78.40 km) are located in the low probability zones for impulsive motion.

Fig. 6
figure 6

a Velocity time history of Station 0120 in Pazarcık earthquake (black) and the wavelet fitted by the Shahi and Baker (2014) method, and b velocity response spectra of the station, the wavelet, and residuals between the velocity waveform and the wavelet. Grey area defines the contribution of the impulsive part of the signal on the velocity response spectra

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Fig. 7
figure 7

Probability of observing impulsive motion from aShahi and Baker (2014) and b Ertuncay and Costa (2021) methods for the Pazarcık earthquake. The blue star is the epicentre of the event, and black and turquoise triangles are the non-impulsive and impulsive stations, respectively

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4.2 Nurdağı earthquake (\(M_{w}=6.6\))

Fig. 8
figure 8

Velocity time histories of impulsive signals recorded in Nurdağı earthquake

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Nurdağı earthquake (Event ID: 3) is the largest aftershock of the Kahramanmaraş earthquakes with \(M_{w}=6.6\). It occurred 11 minutes after the main shock and in between the second and third segments of the Pazarcık earthquake. Most of the impulsive signals are located near the epicentre with \(R_{epi}\) less than 50 km (Fig. 8). Velocity time histories of the impulsive motions are simpler than the Pazarcık earthquake, and most of their seismic energy is concentrated at the beginning of the waveform as epicentral distances are short. Unlike the Pazarcık and Elbistan earthquakes, no finite fault model has been developed for this earthquake yet. Hence \(R_{jb}\), and fault-normal & fault-parallel information are not retrieved for the earthquake. They can be developed using relations such as Wells and Coppersmith (1994), but the complex ruptures of the Pazarcık and Elbistan earthquakes show that the rupture area of the Nurdağı could have a complex structure too. The point source approach has been implemented to prevent incorrect interpretation of the impulsive motion of the earthquake.

Fig. 9
figure 9

Impulsive signals detected by aShahi and Baker (2014) b Ertuncay and Costa (2019) in Nurdağı earthquake. The red star is the epicenter of the event. Both the epicenter and the focal mechanism are retrieved from the AFAD catalogue

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Table 5 Parameters of impulsive signals in Nurdağı earthquake
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To detect impulsive motions, stations are rotated from East–West and North-South orthogonal components to fault-normal and fault-parallel using the strike angle of the event with the assumption that the Nurdağı earthquake ruptured a single segment. The focal plane solution of AFAD (https://deprem.afad.gov.tr/event-detail/408329, last access: 30/11/2023) estimates the strike angles as 300 \({}^{\circ }\) and 187 \({}^{\circ }\). Between these, we believe that 300 \({}^{\circ }\) is the strike angle of the fault plane since it is in agreement with the seismicity of the Kahramanmaraş sequence, whereas 187 \({}^{\circ }\) is the strike angle of the auxiliary plane. In total Shahi and Baker (2014) and Ertuncay and Costa (2019) found 5 and 2 impulsive signals, respectively (Fig. 9). Among the impulsive motions, (Shahi and Baker 2014) detected 2 impulsive motions in the fault-parallel and another 2 impulsive motions in the fault-normal components, whereas (Ertuncay and Costa 2019) detected only 2 impulsive motions in the fault-normal component. Moreover, a vertical component impulsive motion is also detected by Shahi and Baker (2014) (Table 5). Pulse periods of the impulsive motions in the earthquake are rather short, up to 2.5 s (Fig. 10). The Ertuncay and Costa (2019) method fits a Ricker wavelet to the impulsive motion and, by nature of the wavelet, there are two valleys on each side of the central lobe that fit into the PGV on the time domain. However, in the recorded signal, there is no such motion, which creates unexpectedly large spectral periods in the fitted wavelet. Apart from the larger spectral periods of the fitted wavelet, the pulse period is captured as spectral periods of the residual signal have no features in periods around 2.1 s.

Fig. 10
figure 10

a Velocity time history of Station 2718 in Nurdağı earthquake (black) and the fitted wavelet (red) by the Ertuncay and Costa (2019) method and b velocity response spectra of the station, the wavelet, and the residuals between the velocity waveform and the wavelet. Grey area defines the contribution of the impulsive part of the signal on the velocity response spectra

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4.3 Elbistan earthquake (\(M_{w}=7.6\))

Fig. 11
figure 11

Impulsive signals detected by a the Shahi and Baker (2014) method and b the Ertuncay and Costa (2019) method for the Elbistan earthquake. The red star is the epicenter of the event retrieved from AFAD catalog and black boxes are the ruptured segments as defined by USGS (2023b)

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Elbistan earthquake (Event ID: 6) is the second destructive earthquake of the Kahramanmaraş earthquakes, which happened only nine hours after the Pazarcık earthquake. The earthquake was initiated on the SF fault, and the rupture was bilateral with 3 ruptured segments (Survey USG 2023b; Melgar et al. 2023; Okuwaki et al. 2023). The earthquake initiated in the first segment and ruptured bilaterally to the west and northeast segments.

Fig. 12
figure 12

Velocity time histories of impulsive signals recorded for the Elbistan earthquake. In case of impulsive motions in more than one orientation for a given station, the velocity time history of the channel with the largest \(T_{p}\) is selected

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Even though the number of impulsive signals is lower than for the Pazarcık earthquake, there are a significant number of impulsive signals recorded for the Elbistan earthquake (Fig. 11). Station coverage around the fault plane is not as good as the Pazarcık earthquake, with only one station on top of the fault (\(R_{jb}=\)0 km). Impulsive motions for the Elbistan earthquake also reached up to \(R_{jb}\simeq\)150 km (Fig. 12). Keep in mind that the epicentre of the earthquake is not located on the ruptured fault, since epicentre information is retrieved from AFAD, whereas the finite fault model is retrieved from Survey USG (2023b), which creates differences in the distances given in Fig. 12. However, it does not create significant changes, and has no bearing on the results of this study. Due to the proximity of Station 4611 to the ruptured fault, most of the seismic energy is concentrated at the beginning of the signals, whereas in other impulsive stations, there are various trends. In stations such as NAR and Station 0131, seismic energy is concentrated into a single long-period waveform, whereas stations such as Station 2703 and Station 0118 show more complex seismic traces with seismic traces that are energetic over longer time spans.

Table 6 Parameters of impulsive signals for the Elbistan earthquake
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To detect impulsive motion, stations are rotated from East–West and North-South orthogonal components to fault-normal and fault-parallel components by using the strike angles of each segment, which are 276 \({}^{\circ }\), 60 \({}^{\circ }\), and 250 \({}^{\circ }\). In total Shahi and Baker (2014) and Ertuncay and Costa (2019) found 26 and 5 impulsive signals, respectively. Among the impulsive motions, 9 and 1 of them are in fault-parallel, 11 and 3 of them are in fault-normal, and finally, 6 and 1 of them are in vertical components for Shahi and Baker (2014) and Ertuncay and Costa (2019) methods, respectively (Table 6). The pulse period of impulsive motions in the earthquake can reach up to 11 s in Station 0133 (Fig. 13). In Station 0133, seismic energy is concentrated into a single pulse that excites the spectral energies between 6 and 11 s. The wavelet fitted by the Shahi and Baker (2014) method represents the impulsive behaviour of the station as the spectral energies of the residual waveform have no such distinctive peaks at these periods.

Fig. 13
figure 13

a Velocity time history of Station 0133 in Elbistan earthquake (black) and fitted wavelet (blue) by the Shahi and Baker (2014) method and b velocity response spectra of the station, the wavelet, and residuals between the velocity waveform and the wavelet. The grey area defines the contribution of the impulsive part of the signal on the velocity response spectra

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The probability of occurrence is calculated as in Sect. 4.3. In Elbistan, earthquake probability results differ from one another (Fig. 14). There are widespread impulsive signals at longer distances to the South and South-West of the fault rupture, which provides a considerable amount of the total impulsive motions identified for the earthquake. The Shahi and Baker (2014) model underestimates impulsive motion at long distances. Due to the fixed PGV threshold of the Ertuncay and Costa (2019) method, the NAR station is the only station in the area with 0 % probability.

Fig. 14
figure 14

Probability of observing impulsive motions a the Shahi and Baker (2014) method and b the Ertuncay and Costa (2021) method for the Elbistan earthquake. The blue star is the event epicentre, and black and turquoise triangles are the non-impulsive and impulsive stations, respectively

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5 Discussion

For the Pazarcık earthquake, a very complex multi-segment fault rupture occurred, and the rupture’s features may have influenced the impulsive motion. Melgar et al. (2023) found that in the EAF section of the Pazarcık earthquake, a sub-shear rupture occurred, whereas the results of Okuwaki et al. (2023) indicate a super-shear rupture in Segment 3. The number of impulsive signals in Segment 3 agrees with Okuwaki et al. (2023) due to the large number of impulsive motions found by both Shahi and Baker (2014) and Ertuncay and Costa (2019) methods.

Somerville et al. (1997) and Burks and Baker (2016) link impulsive motion in near-fault stations to S-wave polarization. Horizontally polarized S-waves (SH) are the main reason for the two-sided impulsive motions in the fault-normal component, which is present in more than half of the impulsive motions found by the Shahi and Baker (2014) method for the Pazarcık earthquake, and vertically polarized S-waves (SV) may be linked to the Gaussian-like pulses. There are 25 and 17 fault-parallel impulsive motions at present in the Pazarcık earthquake detected by Ertuncay and Costa (2019) and Shahi and Baker (2014), respectively. However, not all of the velocity time histories are Gaussian-like and have impulsive motions that are more complex than a simple Gasussian-like wavelet.

Stations NAR, KHMN, and 4615 are located next to the NPF fault where the rupture initiated and only a small portion of the seismic moment was released (3 %, Okuwaki et al. 2023). These stations, however, recorded impulsive motions between \(T_{p}\simeq\)3.5 s–5.0 s, which can be linked to the super shear rupture velocity around the tip of the NPF (Rosakis et al. 2023). Satoh (2023) also points out the significance of local super shear rupture on NAR and Station 4615.

The distribution of impulsive signals shows the transition between S-wave-driven and surface wave-driven impulsive signals. For the Pazarcık earthquake (Fig. 5), Station 4615 is very close to the epicenter and Segment 1 of the earthquake, and \(R_{jb}\) distances are close to 0 km, and most of the seismic energy is concentrated between 10 s and 15 s after the origin time. For Station 4615 and Station 3115, impulsive motions are caused by the S-waves, but in Station 0120 a more complex seismic trace is observed, and the impulsive motion is located more toward the end of the S-wave. It is possible that surface waves played a part in the impulsive motion. Station 3124 and other nearby impulsive motions in Hatay are located on top of Segment 3. It is important to point out that complex, multi-segment rupture enriched the seismic waveforms differently. In Station 4615, the rupture of Segment 1 is the main contributor to the seismic trace; in Station 3125 the effect of Segment 1 and even Segment 2 are significantly smaller. Hence for this station there are small ground motions between 50 s and 75 s after the origin time, and the effect of Segment 3 is visible after 75 s. Satoh (2023) also finds that in the northern part of Segment 3, various areas in the ruptured zone are responsible for the strong ground motion. This can be linked to widespread impulsive motion in the upper and central part of Segment 3 and its surroundings. For the Elbistan earthquake (Fig. 12), a similar trend can be identified. Impulsive signals up to 150 km \(R_{jb}\) distance are located in the S-wave, with the exception of Station 2703 where the \(R_{jb}\) distance is more than two times larger than the others. For stations with \(R_{jb}\) distances larger than 100 km, impulsive motions are located toward the later stages of the seismic waves.

The probability calculation method of Shahi and Baker (2014) calculates the probability of observing an impulsive signal around the epicentral area of the Pazarcık earthquake as being over 90 % whereas the Ertuncay and Costa (2021) method gives a maximum value of 85 %. For the Shahi and Baker (2014) method, the width of the high percentage zone is related to the fault length, wherethe widest area with the largest percentages is Segment 3 of the Pazarcık earthquake. Super-shear rupture on Segment 2 of the earthquake produced a large amount of impulsive motion even though the width of the impulsive motion is narrower than Segment 2 due to the shorter length of the segment. The Ertuncay and Costa (2021) method does not affect the fault length as \(M_{w}\) is the main source of the impulsive motions. Even though the maximum percentage of the model is lower than the Shahi and Baker (2014) method, also having non-impulsive motions around the \(R_{jb}\) area lowers the actual percentage of impulsive signals around the fault lines (Fig. 15).

Fig. 15
figure 15

Spatial distribution of the percentage of impulsive motions detected by a, c the (Shahi and Baker 2014) method, and b, d the (Ertuncay and Costa 2019) method, along with the average probability of pulse occurrence predicted for the a, b Pazarcık and c, d Elbistan earthquakes

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For the Elbistan earthquake the Shahi and Baker (2014) method underestimates the probability of observing impulsive motion due to a large amount of impulsive motions detected to the south and southwest of the ruptured faults. The percentage of impulsive motions increases with distance, unlike the expected descending trend. It must be taken into consideration, however, that seismic stations are not evenly distributed, and this may amplify the apparent impulsive motion percentage. Widespread impulsive motion over long distances is an unexpected finding, which makes it hard to predict long-period signals. Moreover, impulsive motion on the western part of the ruptured fault can be linked to super shear rupture features of the earthquake (Melgar et al. 2023). Since the length of the fault is the driving force of the impulsive motion for the Shahi and Baker (2014) method, Segment 2 has the highest probability of generating impulsive motion. The Ertuncay and Costa (2021) method successfully predicts the impulsive motion at Station 4612, whereas the other three impulsive motions that are identified by the Ertuncay and Costa (2019) method are located in the areas with low probability of occurrence.

For the Pazarcık and Elbistan earthquakes, longer period pulses agree with the Shahi and Baker (2014); Ertuncay (2020) methods and short periods pulses are in agreement with the Somerville (2003), Bray and Rodriguez-Marek (2004) methods (Fig. 16). Standard deviations (STDs) generated by the Shahi and Baker (2014), Ertuncay (2020) methods covered all long-period signals but failed to capture the short-period ones. Predictions of Somerville (2003) for rock sites are almost entirely covered thanks to their large standard deviation, but none of the stations are located in rock sites (Table 1), and the model for soil sites also failed to cover the short period signals. The prediction by the Bray and Rodriguez-Marek (2004) methods are similar to the prediction of the Somerville (2003) methods. The models for soil and rock sites converge around magnitude 7.7, and both models underestimate long-period impulsive motion. The importance of impulsive motion, however, is in the long-period features, and the methods of Shahi and Baker (2014), Ertuncay (2020) performed well over long periods and Somerville (2003) covers the long periods due to its \(\sigma\). Models developed by Bray and Rodriguez-Marek (2004) perform relatively badly at long periods.

Fig. 16
figure 16

Periods of impulsive motions determined by a the Shahi and Baker (2014) method, and b the Ertuncay and Costa (2019) method along with pulse periods determined by the Somerville (2003), Bray and Rodriguez-Marek (2004), Shahi and Baker (2014), Ertuncay (2020) models. Dashed lines define the standard deviations of the models

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Even though impulsive motions are more dominant in FP and FN components, previous studies show that they are not the only orientation in which the maximum pulse may be observed (Shahi and Baker 2011, 2014). Shahi and Baker (2011) try to find pulses by rotating the given signal in all possible directions to maximize finding impulsive motion, which may lead to finding false-positive impulsive motion (Shahi and Baker 2014). Shahi and Baker (2014) overcome this problem by rotating the 2 orthogonal components to find the maximum pulse with its direction as explained in Sect. 3. To find impulsive motions with the largest pulse direction, we provide the horizontal components of the signals (Fig. 17). As expected in both earthquakes, near-fault pulses mostly agree with the fault plane (FN) or its orthogonal (FP) direction. There are several stations, however, that do not follow this general trend. For instance, several stations in Hatay have their maximum pulse direction at \(\approx\)45 \({}^{\circ }\). In Hatay city, the impulsive motions are positioned in the later stages of the seismic waveform (Fig. 5), and the Vs30 values at the stations are relatively low. Both complex rupture features and local soil conditions may affect the ground motion and create impulsive motion in this direction. Several stations where Segment 1 and Segment 3 meet also have maximum pulse direction at \(\approx\)45 \({}^{\circ }\), and again, this peculiar direction can be linked to the rupture features. Since revealing their behaviour is not the topic of this study, we do not carry out further investigation into the forces that played a role in the direction of the impulsive motions, but we nonetheless prefer to report the observations that we retrieve. For the Elbistan earthquake Station 4612 and stations on the South-West of Segment 2 are in agreement with the FN direction of the segment. Other stations, however, are in different directions with respect to the others. Those stations are located away from the near-fault area, and surface waves may be the dominant force on the East–West orientation of the impulsive motion. Moreover, a number of impulsive signals and stations with impulsive features presented for both the Pazarcık and Elbistan earthquakes are different in Fig. 17. It is due to the fact that, to find the direction of the pulse, orthogonal components are given as inputs, whereas in the previous section the components are given individually. Those differences are considered as "false-positives" by Shahi and Baker (2014). Our main idea, however, is to find impulsive motions in the 3 fundamental components, namely FN, FP, and vertical. Thus we do not consider them as "false positives" but as actual impulsive signals.

Fig. 17
figure 17

Direction of the strongest pulses in the a Pazarcık and b Elbistan earthquakes detected by the Shahi and Baker (2014) method. The red star is the epicentre of the event; black triangles are non-impulsive stations, and black circles with coloured lines are impulsive stations. The color of the lines represents the pulse period

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Long-period signals may create large seismic loads on structures (Kalkan and Kunnath 2006). When the pulse period of the impulsive motion is similar to the fundamental period of a given structure, it can be the main source of the building response and may create a resonance effect (Archila et al. 2017; Takewaki et al. 2011). For this purpose, finding the dominant periods of the ground motion is important. In both the Pazarcık and Elbistan earthquakes, a wide range of pulse periods are found (Fig. 16); some of them have periods even longer than 10 s. Stations such as NAR, 4611, and 4615 recorded impulsive motion in two of the three earthquakes (Fig. 18). In the town of Narlı, where the station NAR is located, there are most of the buildings have 2–3 stories buildings with relatively low damage. On the other hand, numerous tall buildings collapsed on the 6th of February in the cities of Hatay, Kahramanmaraş, and Adana. Construction flaws, insufficient building design principles, and/or the cumulative effects of several earthquakes may have played a role in their collapse (Vuran et al. 2024), but investigation of the collapsed buildings is not in the scope of this study. In some of the stations with impulsive motions, however, the response spectra of the ground motion exceeds the current building design code of Türkiye (Fig. 19 Akkar et al. 2018).

Fig. 18
figure 18

a Seismic records of the Pazarcık, Nurdağı, and Elbistan earthquakes for Station 4615 and b their pseudo-spectral velocities (Sv.)

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Fig. 19
figure 19

a Spectral acceleration (Sa) of the fault-normal channel for Station 3145 along with the 2018 Turkish design code for 10 % probability of exceedance in 50 years for different soil classes, b pseudo-spectral velocity (Sv)

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Impulsive signals are known for their large PGV values (Moustafa and Takewaki 2010). In both the Pazarcık and Elbistan earthquakes, large PGV values are observed (Fig. 20). To compare the PGVs with the ground motion prediction equation (GMPE), we use the Kale et al. (2015) (KALE15) model, since it was created for Türkiye and Iran using earthquakes and seismic records from these regions. As seen in Fig. 20, the Kahramanmaraş earthquakes produced a large number of ground motion records that surpass the prediction of the KALE15 model. For impulsive motions detected by the Shahi and Baker (2014) method there is only one station (in Pazarcık) that is within and close to the border of the \(+1\) STD of the prediction. Both of the earthquakes produced PGVs larger than the predicted values independent from being impulsive, which can be linked to the directivity effect (Bray and Rodriguez-Marek 2004). In the residual analysis of the PGVs, stations located on top of the rupture zone (\(R_{jb}=\)0 km) have a very large difference from the median values of the GMPEs, and the difference diminishes around 100 km for the Pazarcık earthquake. In the rupture area (\(R_{jb}=\)0 km), it is expected to have an underestimation of the GMPE model due to the complex physics of large magnitude earthquakes and lack of observed waveforms from near-fault stations. On the other hand, the Elbistan earthquake created larger ground motions than expected by the KALE15 model, even at longer distances. Extensive stress accumulated around the region after the Pazarcık earthquake may be linked to the unexpectedly large ground motion as there is a correlation between stress drop and ground motion variability (Oth et al. 2017). All impulsive motions have larger amplitudes compared to predictions from the KALE15 method.

Fig. 20
figure 20

Observed PGVs of the a Pazarcık, b Elbistan earthquakes for horizontal components compared to the GMPE model of Kale et al. (2015) and the residuals of the observed and predicted PGVs for the c Pazarcık, and d Elbistan earthquakes. Turquoise and black circles are PGVs of impulsive and non-impulsive signals determined by the Shahi and Baker (2014) method, respectively. Stations located on top of the fault (\(R_{jb}=\)0 km) are moved to 0.1 km for visualization

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Unusually, the Pazarcık earthquake produced a large number of vertical component impulsive motions. Historically, horizontal ground motions are generally stronger than vertical ones. In fact, vertical ground motions attenuate faster than horizontal motions in the far-field (Campbell 1997). Recent studies reveal, however, that in near-fault regions, vertical ground motion can also have large amplitude and have significant effects on structures (Bozorgnia and Campbell 2004). The Kahramanmaraş earthquakes are in agreement with recent studies with PGVs up to 100 cms\(^{-1}\) (Fig. 21). The largest PGV in the vertical component is a spike-like waveform in Station 3138, which can be linked to the flapping effect that can be observed when the base of the station is not well connected to the ground and bounced during ground shaking (Goto et al. 2019), meaning that impulsive motions detected at this station are not trustworthy. Other vertical component impulsive signals, however, do not have this anomaly, and they are produced by real ground motion (Fig. 22).

Fig. 21
figure 21

a Acceleration and b velocity time histories recorded for the Pazarcık earthquake on the vertical component of Station 3138

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Fig. 22
figure 22

a Acceleration and b velocity time history along with the extracted pulses by the Shahi and Baker (2014), Ertuncay and Costa (2019) methods for the Station KHMN record in for the Pazarcık earthquake

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6 Conclusion

In this study we find that during the Kahramanmaraş earthquakes 3 earthquakes produced, in total, 72 and 62 impulsive motions according to the methods of Shahi and Baker (2014), Ertuncay and Costa (2019), respectively. The periods of the impulsive signals reach up to 15.5 s for the Pazarcık earthquake, which has the largest magnitude out of the Kahramanmaraş earthquakes. For the Pazarcık and Elbistan earthquakes, previous studies detected super-shear ruptures, which may be the reason for the abundance of impulsive motions. For the Elbistan earthquake, impulsive motions were observed up to 150 km distance from the fault (Fig. 11), which exceeds the expectation of impulsive signal probability derived from the Shahi and Baker (2014), Ertuncay and Costa (2021) methods. The models do not necessarily perform badly, however, since stations are not evenly distributed around the region, which may amplify the presence of impulsive motion over a certain distance range. The direction of the most energetic impulsive motions is also analyzed with the Shahi and Baker (2014) method. In both earthquakes, the directions are mostly in alignment with the fault-normal and fault-parallel directions. The direction of the predominant pulses in Hatay, on the other hand, is slightly different from the other impulsive stations in which local soil conditions and earthquake rupture may play a role. Long-period impulsive motions exceed the current design codes of Türkiye, which may create unexpected damage even in newly built high-rise buildings. PGV values are also higher than the GMPE model of Kale et al. (2015), which is produced for the region. Surprisingly, numerous impulsive motions are located in the vertical component. Strike-slip faults are known to have relatively low amplitude vertical ground motion, but for the Kahramanmaraş earthquakes, this assumption is falsified. The Kahramanmaraş earthquakes and the dense near-fault seismic network provided crucial information about the near-fault effects of large-magnitude earthquakes. This study show how previous models of impulsive motion performed for the Kahramanmaraş earthquake, and future studies may initiate by analyzing our results to understand long-period ground motion and its possible effects on structures and infrastructure better.