1 Introduction

In September 2022, an earthquake sequence occurred in the Eastern Taiwan. There were four earthquakes with magnitudes greater than 6 in this sequence (Fig. 1a). Among them, the Guanshan earthquake was the first large event with a magnitude of ML 6.4 occurred on September 17, 2022. The biggest Chihshang earthquake with a magnitude of ML 6.8 occurred on September 18, 2022 following. Both events have the intense shocks, causing surface ruptures and multiple disasters. Although the eastern region of Taiwan is prone to earthquakes, the location where this earthquake sequence occurred is situated in an area with relatively low seismic activity (Lee et al. 2023). According to early survey reports (https://fault.gsmma.gov.tw/Reports/More/63cc5a4b2020403d9f79d3c33a7aba0c), the earthquake processes and source rupture behavior of this earthquake sequence are unique. Following a major earthquake, usually, large number of aftershocks are always triggered in the epicentral area within a short period of time. The small earthquakes that occur immediately after the mainshock (for example of the first 30 min) and are located near or within the ruptured area of the earthquake can provide significant information to explore the earthquake source physics and rupture characteristics. In Taiwan, both early warning strong motion network and regional seismic network usually play the role in detecting the aftershocks and monitor earthquake sequence. The early warning strong motion network always reports large event in first time. However, both aftershocks directly masked by the main shock's coda wave or aftershocks with very small magnitudes, are often difficult to be detected by both seismic networks. The events that were missed to report are referred to as "hidden events" in this study and the same as Kiser and Ishii (2013). To retrieve those hidden aftershocks, the deployment of a high-density temporary seismic network, utilizing highly sensitive seismometers and complete coverage of the earthquake source area is expected.

Fig. 1
figure 1

a Schematic geological map of the source region and four major events of this earthquake sequence with magnitude greater than 6 (modified from Lee et al. 2008). Brown circle indicates the Guanshan earthquake, blue circle indicates the Chishang earthquake and two yellow circles indicate other reported events. b The recorded events of the Chishang region by CWNSN from 2022/09/01 to 2022/09/30. The event magnitudes are scaled by the size of event symbols (circle) from magnitude 6 to 1. Event depths are scaled by the color bar listed below. Both Guanshan and Chishang events are indicated as blue star and circle, respectively

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In this study, we aim to investigate the aftershocks of the Guanshan earthquake. As it is the first large event of this earthquake sequence, the identification of aftershocks is not yet affected by other large earthquakes, which greatly reduces the uncertainty of the aftershock study. The earthquake rapid report catalog published by the Central Weather Bureau (CWB) mainly relied the early warning strong motion network for location determination (https://www.cwa.gov.tw/V8/C/E/index.html). The complete event catalog is updated using data from the Central Weather Bureau Seismographic Network (CWBSN), a regional network, and added more small events. The final event catalog of CWBSN will be checked manually and usually delayed several months. However, there was no extra temporary seismic stations set up in the eastern region of Taiwan at the moment of the Guanshan earthquake occurred, it can be expected that smaller aftershocks will not be effectively detected and reported. In the study, we will examine the continuous recordings of the Taiwan Strong Motion Instrumentation Network (TSMIP), a dense seismic network originally designed for earthquake engineering applications, to extract earthquake data for aftershock analysis. We hope to locate all aftershocks of the first 30 min and retrieve small events that were not included in the CWB rapid report catalog (https://scweb.cwa.gov.tw/zh-tw/earthquake/data/). By using newly developed methods to analyze the recorded high spatial-density earthquake data for earthquakes in or near the source area, we are able to locate more hidden aftershocks lost by the CWB rapid report catalog. New messages from these small earthquakes enable us to discuss the source processes of the Guanshan earthquake, as well as to explore characteristics of earthquakes which occurred in an aseismic zone.

1.1 Regional tectonics and seismic activities in the eastern Taiwan

Taiwan is located at the collisional boundary between the Eurasian Plate and the Philippine Sea Plate. The Philippine Sea Plate is moving relative to the Eurasian Plate towards the northwest direction. The fault system in eastern Taiwan is influenced by the oblique collision and strong convergence between two blocks. The dominate fault of this region is named as the Longitudinal Valley fault, it connects the two arc-trench systems of the Ryukyu and Manila trenches. The eastern region of Taiwan is known as a high seismic risk, and has experienced multiple disastrous earthquakes in history (Shyu et al. 2007; Lee et al. 2008; Huang et al. 2009; Mozziconacci 2013a; Wen et al. 2019). The Hualien-Taitung Valley was hit by several strong earthquakes in 1951, with the largest two earthquakes reaching a magnitude of 7.3 on the Richter scale. The 1951 earthquake series have caused serious damage in the source area. Over the past 70 years, this region has several earthquake sequences occurred with damage reports (https://tec.earth.sinica.edu.tw/index.php). On 2022, the Eastern Taiwan earthquake sequence occurred in the southern part of the Hualien-Taitung Valley (Fig. 1a). The source area of this earthquake sequence is located at an active hidden fault zone in the western side of the Hualien-Taitung Valley suture zone near the Central Mountain Range. This fault system is adjacent to the Longitudinal Valley fault in the coastal mountain range, and seismic activities between the two fault systems are often linked (Shyu et al. 2006; Mozziconacci 2013b; Lee et al. 2023). Referring to the distribution of long-term earthquake activity in Taiwan, this earthquake sequence occurred in an area with relatively low seismicity region.

1.2 Seismic observations

On September 17th, 2022, an earthquake occurred at 21:47 local time, with a magnitude of ML 6.4. The epicenter was close to Guanshan in Taitung, at latitude 23.08°N and longitude 121.16°E. On September 18th, 2022, the earthquake occurred at 14:44 local time, with a magnitude of ML 6.8. The epicenter was close to Chishang in Taitung, at latitude 23.14°N and longitude 121.2°E. In Taiwan, the reporting of felt earthquakes and the warning of large earthquakes is carried out by the early warning strong motion network of CWB (https://www.cwa.gov.tw/V8/E/E/index.html). Till the end of September, this earthquake monitoring network detected a total of 207 felt earthquakes during the monitoring of the 2022 Eastern Taiwan earthquake sequence. The temporal distribution of the earthquakes was dominated by the Guanshan (foreshock) and Chishang (mainshock) earthquakes, each showing a clear mainshock-aftershock relationship (Lee et al. 2023). After the Chishang earthquake, aftershocks continued to occur towards the north, eventually extending to the vicinity of Ruisui in Hualien (Fig. 1b). According to the reported moment tensor solutions (https://tecdc.earth.sinica.edu.tw/FM/AutoBATS), the source mechanisms of both events are similar. The possible fault plane is oriented in a north-northeast to south-southwest direction, with a high angle and westward dip, and is dominated by left-lateral slip (Fig. 1). The maximum seismic intensity of the two earthquakes reached level 6 in various parts of Taiwan, and the depth of both earthquakes was only about 7 km, which is considered extremely shallow.

1.3 Data collected from TSMIP

The geological environment in Taiwan is complex and diverse. In order to capture the regional seismic characteristics of large earthquakes, from early 1990, the CWB has continuously installed 737 free-field strong motion sensors in densely populated plain areas and named as TSMIP. Its main mission is for engineering applications, to investigate site effects caused by local geological differences in Taiwan due to earthquake waves, and to establish regulations to achieve the goal of earthquake resistance and disaster reduction. Its secondary mission is for seismological applications, to support earthquake research in related fields by studying path effects of wave propagation and source effects of large earthquakes, including the source size and rupture process. Since 2018, the CWB has upgraded part of TSMIP stations to continuous recording and real-time transmission of data to provide earthquake intensity reports and plan for emergency response needs following future major earthquakes. After the upgrade, a strong motion network with continuous recording has been established. Currently, there are about 400 free-field strong-motion stations, mainly distributed in the Taiwan plain and metropolitan areas (https://gdmsn.cwa.gov.tw/network_tsmip.php).

During the 2022 eastern Taiwan earthquake sequence, the TSMIP stations continuously recorded the events and the network was fully operational. Figure 2 displays the seismic stations surrounding the epicenter of the Guanshan earthquake and the vertical component seismograms for seismic stations within 100 km epicenter distances. The high spatial density of stations near the source region and the resulting high-resolution seismograms enable a detailed examination of the Guanshan earthquake and its aftershocks. This study focuses on enhancing aftershock signals and relocating events using an array stacking approach, which eliminates the need for phase picking of emergent first arrivals of small events. The methods of analysis proposed will be explained in the next section.

Fig. 2
figure 2

a The selected stations of TSMIP recorded the Guanshan earthquake with epicentral distance less than 100 km. b Vertical array waveforms plotted by epicentral distances

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2 Methods

2.1 Automatic gain control: signal enhancement for low amplitude aftershocks

Automatic gain control (AGC) is one of the most common gain recovery methods used in seismic signal processing. In this study, the concept of AGC will be applied to process earthquake multiple event seismograms, increase the strength of aftershock signals to identify the timing of aftershocks and perform location estimation. AGC is a type of limited output that uses a combination of linear amplification and compression amplification to adjust the output of the original signal. When a weak signal is input, the seismic signal is linearly amplified to ensure the output signal strength. When the input signal reaches a certain strength, the compression of the seismic signal is activated, causing the output amplitude to decrease.

In this study, we proposed the Root mean square (rms) amplitude automatic gain control (or named as rms amplitude AGC) for signal enhance. This method is one of the most commonly used types of gain control (Gadallah and Fisher 2005, 2009). The rms amplitude AGC gain function is based on the rms amplitude of the input signal within a specified time window. The gain function is calculated as follows: first, the input seismic waveform is divided into fixed time windows, and the square of the amplitude of each sample in the time window is calculated. Second, the average of these values is calculated, and the square root is taken. This is defined as the rms amplitude of the time window. The ratio of the desired rms amplitude (for example, a value of 2000) to the actual rms value is specified as the value of the gain function at the center of the time window. Therefore, the scaling function g(t) at the center of the time window is given by the following equation:

$$g\left(t\right)=\frac{\mathrm{desired\,rms}}{\sqrt{\frac{1}{N}{\sum }_{i=1}^{N}{x}_{i}^{2}}},$$
(1)

where xi is the amplitude of the input signal at time point i, and N is the number of samples within the window.

To demonstrate the effectiveness of our processing method, this study used the Guanshan earthquake and its aftershock data for the following 300 s as an example, as shown in Fig. 2. The seismic records from the near-source station did not show any clear aftershock signals, and the earthquake catalog from the Central Weather Bureau did not list any located aftershocks also within this 300-s time window. However, after applying the Automatic Gain Control (AGC) method proposed in this study to enhance the aftershock signals, the obtained results are shown in Fig. 3. Comparing the two figures, it is evident that multiple aftershocks near the Guanshan earthquake source occurred within this 300-s time window after the main earthquake, which were not visible in the seismic records without the AGC processing. This example highlights the potential application of the AGC method in detecting hidden aftershocks within a short time window following a major earthquake.

Fig. 3
figure 3

The same seismic waveforms of Fig. 2b processed by the AGC algorism to enhance aftershocks. Each trace is scaled to the same size in this record section

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2.2 Back-projection (BP) method: application for earthquake location

The BP method uses a grid search approach to consider all grid points within the model as possible earthquake source locations. The seismic wave travel time differences between each grid point and all seismic stations are calculated using an appropriate velocity model (Ishii et al. 2005). By moving all grid points appropriately to match the seismic wave travel times recorded by the seismic stations, the earthquake wave energies are shifted in time and overlaid to obtain the corresponding peak values. The grid point that produces the highest peak value is identified as the earthquake source through evaluation. The calculation steps can be represented by the following formula:

$${{\text{Stack}}}_{i}\left(t\right)=\frac{1}{N}\sum_{k=1}^{N}{S}_{k}\left(t-{t}_{ik}\right),$$
(2)

where Stacki(t) represents the time series of earthquake waveform energy summed over all seismic stations, N is the number of seismic stations, k is the index of the kth seismic station, Sk(t) is the seismic wave amplitude time series of the kth seismic station, and tik is the theoretical travel time between index grid point i of the model and the kth seismic station (Ishii et al. 2007). The theoretical travel time used for stacking can be either the travel time of P-waves or S-waves.

To locate an earthquake using the BP method, we need to discretize the earth model into a three-dimensional (3-D) grid. Assuming the true location of the earthquake source is within the 3-D grid. As a sample, we calculate the predicted travel times from location of a selected grid point within the model to each seismic station. We then time-shift the seismic records based on predicted travel times, and stack all seismic records for this grid point. Each grid point within the model is considered a potential earthquake source and the same calculations are repeated for each point of the model. If the grid point is the true hypocenter, the arrival times will align after time shifting, resulting in a constructive stack on the seismic record. For other non-source grid points, they will not align, and the stack out of phase. This repetitive process generates a 4-D BP image that includes the time history of the stack amplitude at each potential hypocenter within the search 3-D volume. Finally, the earthquake hypocenter location and origin time are represented by the time point of maximum amplitude at the corresponding grid point. A unique feature of the BP method is that there is no need to pick arrival times for the seismic records during the earthquake location process.

In this study, we have developed a suitable program based on above procedure. The earthquake location calculation is performed by directly stacking seismic records from the TSMIP network with a dense array configuration. A 1-D regional model of Taiwan (Roecker et al. 1987) and a lateral homogeneous raytracing method (Huang 1996) are selected for the predicted travel times used in this study. Example for a medium magnitude event in the eastern Taiwan is shown in Fig. 4 (left panel), and the corresponding resolution (stacked energy) checks on the right.

Fig. 4
figure 4

Comparison of event locations reported by the CWB (indicated as circle) and BP (symbol: +). The spatial variation of epicenter in the EW, NS and Vertical components are shown in right panels following the BP method. This is a selected event on eastern Taiwan from CWB rapid catalog (event time: 2023/06/15/03:19:8.5) as an example. Total of 150 TSMIP waveforms with epicentral distances less than 150 km are selected by BP to locate events. The data has been previously processed by 1 Hz low pass filterer to remove incoherence signals

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2.3 Analysis and results

To effectively locate earthquakes, we selected data with a high signal-to-noise ratio from nearby stations of the Guanshan earthquake epicenter (as shown in Fig. 2) for analysis. In this study, we selected data from TSMIP seismic station within 60 km of epicentral distance. In total, 87 vertical component seismograms have been selected to use in this study. For each station, a total of 30-min time trace (including the Guanshan earthquake) was extracted and plotted on a figure based on the epicentral distance of the Guanshan earthquake, as shown in Fig. 5a. Although several low-amplitude aftershock signals have showed in selected stations, however, the CWB fast report catalogue only identified and marked five aftershocks during this time period on their rapid report website.

Fig. 5
figure 5

a 30-min vertical component continuous data after the ML 6.4, Guanshan earthquake collected from the TSMIP stations with epicentral distances less than 60 km. Vertical dashed lines (red) denote original time of aftershocks reported by the CWB rapid catalog. b The same network vertical-component waveforms on upper panel processed by AGC (10 s time window) to modulate aftershock amplitudes. Small events with similar alinement of mainshock are seen in this profile. It indicates all events near the epicenter and considered as near source aftershocks

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In this study, AGC is used in data processing to improve the visibility of aftershocks in which attenuation or spherical divergence has caused amplitude decay. The rms AGC is used for amplitude equalization. It gives a measurement of the overall absolute amplitude in the window, both as positive and as negative values. To perform the automatic detection, a fixed gate length is necessary. After several trying, we selected 10 s for this case. Corresponded to Fig. 5a, the processed AGC Plots of seismograms is shown in Fig. 5b. It shows that each trace has similar time moveout, it indicates those events are closer to the epicenter of Guanshan earthquake. In total, 80 events have identified in this plot as events near the ML 6.4 Guanshan event. The counted event number with time (N-T plot) have been summarized as Fig. 6.

Fig. 6
figure 6

The counted number with time plot (The N-T chart) of the first 30 minters minutes aftershocks of the 2022 September 17, ML 6.4, Guanshan earthquake

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In this study, the method to locate aftershock for this ML 6.4 Guanshan earthquake will be the BP method proposed in this study. It will be carried out through the energy superposition of seismograms without individual picking the arrival times of seismic waves. The total aftershock location processes will be based on 30-min seismic data and processed with AGC to enhance weak signals (Fig. 5b). We extract the common time window of seismograms containing aftershock signals for further earthquake location. Taking Fig. 7 as an example, we selected the waveform data from 300 to 380 s in Fig. 5b (as shown in Fig. 7a) for the following earthquake location determination. To ensure the stability of the superposition results, we converted the selected waveform data into its envelope forms to provide time traces as shown in Fig. 7b. By performing the energy superposition computation using Eq. (2) of this study, we ultimately obtained the spatial coordinates and origin time of the located aftershock, as shown in Fig. 7c. The same procedure will be applied to all distinguishable time windows of aftershocks within this 30-min period. However, most of the time windows of aftershocks are too short to complete stable image superposition. In the end, a total of 29 aftershocks have located and are all plotted in Fig. 8, with their corresponding source parameters listed in Table 1. The results show that major aftershocks are distributed on the north and south sides of the epicenter, with a small number of them distributed in the eastern side.

Fig. 7
figure 7

a AGC enhanced waveforms of event 4 (Table 1), (b) enveloped waveforms and (c). the BP location report of this study. NST: the number of stations (vertical component waveforms) selected to relocate this event

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Fig. 8
figure 8

The located events of this study (small blue circle symbols), CWB reported events (medium gray circle symbols) and source rupture slip distribution (colored contours in unit of centimeter) of the Guanshan earthquake reported by Lee et al. (2023). The CWB reported Guanshan earthquake is plotted as the symbol of big red star

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Table 1 Relocated events of this study (#01 is the ML 6.4 Guanshan earthquake)
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3 Discussion and conclusions

As shown in Fig. 8, the aftershocks determined in this study (29 events) presents more detailed spatial distribution than that determined by CWB (5 events) within the same time period. It indicated that the ML 6.4 Guanshan earthquake has triggered a series of aftershocks in the source region. The earthquake locating process of CWB primarily involves extracting the arrival times of seismic waves to simplify the seismic data. It then goes through validated and widely used computer locating programs such as HYPO71 (Lee and Lahr 1975; Lee et al. 2003), HYPOINVERSE (Klein 1978, 2003), HYPOELLIPSE (Lahr 1989, 2003), etc., to perform data inversion and confirm the epicenter location. Although the locating system of CWB adapts to regional variations and optimizes rapid reporting operations by moderately modifying existing computer locating programs, the fundamental approach still requests picking the arrival times of seismic waves and then locating the earthquake. Above earthquake location methods relying on first arrival picking is challenging for small events with low signal-to-noise ratio or multiple events occurred in a short time period.

To address this issue, we used an alternative procedure to explore, it based on the idea of migrating the energy of an earthquake back into its source position by stacking along theoretical travel-time curves. We selected also the TSMIP data which is a dense seismic array designed for seismic hazard assessment purposes and does not used for event location. In this study, employed the BP method which is a technique commonly used to image seismic sources (Ishii et al. 2005; Meng et al. 2011; Beskardes et al. 2018). This method utilizes the recorded seismic waveforms from multiple stations and calculates the correlation between each station and potential source locations. By scanning the entire study area, this method is able to identify hidden aftershocks that may have been missed by conventional methods. In this study, we revised this method with AGC to enhance buried signals to retrieve the early aftershocks of the 2022 September 17, Guanshan Taiwan earthquake. The findings of the study reveal that the BP method successfully detects and locates a significant number of hidden aftershocks that were not previously identified. The identified aftershocks provide valuable insights into the fault geometries and seismic activity in the region following the main earthquake. It provides an opportunity to view the evolution this earthquake sequence.

The overlaid beneath Fig. 8 is the coseismic slip distribution of the Guanshan earthquake inferred through joint inversion of multiple geophysical data by Lee et al. (2023). The hidden earthquake distribution determined in this study is consistent with the main slip distribution of the Guanshan earthquake. According to the study by Lee et al. (2023), the main rupture of this earthquake sequence mainly occurred on a west-dipping fault and its slip originated from the hypocenter and propagated toward the north. The Guanshan earthquake is considered as a foreshock in the earthquake sequence, understanding its detailed aftershock activity may provide an opportunity to insight the subsequent earthquake development. By examining the spatial and temporal distribution of these aftershocks, it may identify statistical patterns that can be used for forecasting purposes (Zhang et al. 2021) and the size distribution, and short-term forecasting of large aftershocks. It has important implications for evaluating seismic hazards (Gulia et al. 2018). However, it is beyond the scope of the initial research of this study.

To validate the performance of the BP method of this study, we compared our results with new location event catalog of this earthquake sequence by Sun et al. (2023) based on an independent dataset of this earthquake sequence. For monitoring micro-seismicity on the creeping Chihshang Fault system and due to the sparse distribution of seismic stations in eastern Taiwan, NTU and IES deployed five broadband stations (red triangles in Fig. 9), the Chihshang seismic network (CSN), in early November 2021 to increase the station coverage. From September to October 2022, SeisBlue (Huang et al. 2023; Kuo-Chen et al. 2022), a deep learning-based seismological data processing platform, detects 6924 earthquakes by using the continuous seismic data from the 9 BATS stations without the CSN data but 14,454 earthquakes by combining the CSN and BATS data. Particularly on 17 September 2022 when the strong Mw 6.5 foreshock occurred, SeisBlue detects about 100 events without the CSN data but over 800 events with it. The earthquake detection ability is greatly improved by the CSN data. The details of the two-month (September to October 2022) deep learning-based SeisBlue earthquake catalog of the 2022 Mw 2022 Chihshang earthquake sequence would be described in Sun et al. (2023) included in this special issue. The SeisBlue earthquake catalog contains 43 aftershocks that occurred within 30 min after the Mw 6.5 Guanshan foreshock struck (Fig. 9; Table 2). Those events are located by the program HYPOCENTER (Lienert and Havskov 1995) with a 1-D velocity model by Central Weather Bureau, Taiwan (Chen and Shin 1998). Comparison of the located event number and distribution of epicenter are similar from both BP and the deep learning (DL) location methods. However, it shows some differences in detail. The original times for commonly located events showed several second variations and epicenters from BP method showed lower spatial resolutions than DL method. Both differences can be explained as different earth models are used by BP and DL methods, and the BP method used rough grids to search its epicenter. Furthermore, two events are located on western side of source region as deep events by BP method (Table 1) and do not identified by the DL method (Fig. 9). After checking array observations, it is found that multiple small events are identified on selected seismograms and both hypocenters are mislocated by BP stacking approach.

Fig. 9
figure 9

The 30-min aftershock seismicity right after the 2022-09-17 Guanshan earthquake occurred. The colored circles and starts are events detected by SeisBlue (Sun et al. 2023) and this study, respectively. Red triangles and squares are broadband stations. Gray squares indicated the locations of city or county. Red traces are active faults identified by Central Geological Survey, Taiwan (Lin et al. 2021) and the names of regional faults are referred to Fig. 1a

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Table 2 Earthquakes detected by SeisBlue using 14 permanent broadband stations for the first 30 min after the Mw 6.5 Guanshan foreshock occurred
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In conclusion, results of this study indicate the importance of utilizing advanced imaging techniques like BP method to enhance the understanding of aftershock sequences and improve seismic hazard assessments. The results contribute to the knowledge of post-earthquake processes and can assist in refining seismic monitoring strategies for large events in the future.