1 Introduction

On November 14, 2021, at 12:07:04, an earthquake with a magnitude of Mw 6.0 struck at a depth of 19.5 kilometers, approximately 20 kilometers from the city of Fin in Hormozgan Province, which is located in southern Iran. Just ninety-four seconds later, another earthquake, slightly larger in magnitude (Mw 6.1) and at a depth of 10 kilometers, affected the region (Table 1). The epicenter was approximately 10 kilometers away from the location of the first seismic event. These two events resulted in the loss of one life, dozens of injuries, and extensive damage to multiple buildings (https://bhrc.ac.ir/). Fin doublet events occurred in the southern part of the Zagros seismotectonic province, near the western section of the Makran zone. The main geological structures in the study area include folded structures, anticline-syncline sequences, and active faults.

Table 1 Location and origin time of the Fin doublet event derived from the catalog of various seismological centers. Fin(1) and Fin(2) denote the first and second events, respectively
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Usually, earthquakes that occur close in time and space are considered doublet or multiple earthquakes (Lin et al. 2008). In addition to their temporal-spatial proximity, the magnitudes of these events are comparable, making it challenging to determine which event is the mainshock. Doublets can exhibit either similar (e.g. Nakano et al. 2010; Zahradnik et al. 2017; Lay et al. 2010) or different focal mechanisms (e.g. Cesca et al. 2021; Ghods et al. 2015; Liu and Zahradnik 2020; Jia et al. 2020; Wu et al. 2008; Ammon et al. 2008). Studies have shown that doublets occurr in different geological areas, including subduction zones (Astiz and Kanamori 1984; Jia et al. 2020; Nakano et al. 2010; Zahradnik et al. 2017; Lay et al. 2010; Ammon et al. 2008), oceanic microplates (Cesca et al. 2021), and intracontinental (or intraplate) regions (Nissen et al. 2016; Ghods et al. 2015; Niazpour et al. 2020), and even in mining areas, such as injection-induced earthquakes in a salt mines (Liu and Zahradnik 2020).

Among the well-documented studies conducted on multiple earthquakes within the Iranian Plateau, the Varzaghan–Ahar doublet, with magnitudes of Mw 6.5 and 6.4 (Amini et al. 2018), and the Hojedk triplet events, with magnitudes ranging from Mw 5.8 to 6.1 (Niazpour et al. 2020), are particularly notable. It is important to note that these doublet and triplet events were situated within the seismotectonic provinces of Alborz and Central-East Iran, respectively. The recent Fin doublet earthquake, however, occurred within the anticline-syncline sequence in the southern part of the Zagros seismotectonic province. Consequently, an in-depth investigation and analysis of the Fin doublet earthquake has the potential to yield novel insights into this type of seismic event within the Iranian Plateau.

Previous studies on the Fin doublet event suggested that the first and second earthquakes are associated with thick-skinned and thin-skinned tectonic environments, respectively (Golshadi et al. 2023; Toker et al. 2023). These studies also highlighted the role of salt layers in triggering the second event. Specifically, one study employed Interferometric Synthetic Aperture Radar (InSAR) data and Coulomb stress calculations to develop a geodetic model for these events (Golshadi et al. 2023). Another study underscored the influence of the salt decollement layer and rupture decoupling on deformation patterns and displacement models concurrent with earthquakes (Toker et al. 2023). In the discussion section of this article, we compare the key findings from these previous studies with the results of our analysis.

The primary goal of this research is to study the source parameters of the Fin doublet earthquake. For this purpose, we performed an inversion process to retrieve point and extended source modeling using a multistep approach in both the time and frequency domains. In addition, we present the moment tensor decomposition results for these events into double-couple (DC) and non-double-couple (non-DC) components. Finally, utilizing the retrieved parameters, including characteristics related to directivity and rupture geometry, we propose a possible scenario for these events based on the geological and tectonic characteristics of the region.

2 Tectonic setting

The Iranian Plateau exhibits tectonic complexities as part of the Alpine–Himalayan orogenic belt. The opening of the Red Sea and continental shortening, resulting from the convergence of the Arabia-Eurasia plates, contributes to Iran's reputation as one of the most seismically active regions in the world. According to GPS measurements, the shortening rate of the Iranian Plateau between the Arabian and Eurasian plates is 25 mm per year at 56°E (Vernant et al. 2004). The Zagros Fold and Thrust Belt, one of the five seismotectonic provinces in the Iranian Plateau (Mirzaei et al. 1998), can be geologically subdivided into two regions: the High Zagros (with higher elevation) and the Simple Folded Belt (SFB) (see Fig. 1a). The High Zagros, with sediments from the Mesozoic and Paleozoic eras, features important faults known as the Main Zagros reverse fault (MZRF) and the High Zagros fault (HZF). Outcrops of these faults are partly exposed at the surface (Nissen et al. 2011). The SFB, characterized by a different geological structure than the High Zagros, contains folded sediments (e.g., late Precambrian–Cambrian Hormuz and Miocene Gachsaran evaporites), anticline-syncline sequences, and blind (buried) thrust faulting (e.g., Stocklin 1968; Falcon 1969). The most significant of these faults are the Mountain Front Fault (MFF) and the Zagros Foredeep Fault (ZFF) (Nissen et al. 2011). Previous studies on earthquakes that occurred in SFB have shown that the predominant focal mechanism in this region is reverse faulting, with nearly NW–SE and E–W strikes in the northwestern and southeastern areas, respectively (Roustaei et al. 2010). The centroid depth of most SFB earthquakes is less than 20 km (Talebian and Jackson 2004; Adams et al. 2009). Shallow events in the depth range of 4-8 km are related to the sedimentary cover of the area. However, deep events, with depths of 12-19 km, are associated with crystalline basements (Roustaei et al. 2010).

Fig. 1
figure 1

a Topographic map of Iran, featuring major faults outlined as dark red lines, seismogenic zones (Zagros, Alborz, Kope Dagh, Makran, and Central-East Iran), and subdivisions of the Zagros (Simply Folded Belt and High Zagros). b Historical seismicity (Ambraseys and Melville 1982) and instrumental seismicity (from January 1970 to November 2021, according to Mousavi-Bafrouei et al. 2015 and the IRSC catalog) in the southern part of Iran. The epicenter of the Fin doublet from the IRSC is also marked with stars

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In terms of geological setting, the Fin region, as the southeastern part of the SFB, includes folds parallel to the east‒west trend with conglomerate and limestone sediments that have Hormoz salt in the core of anticline structures. One of the most recent events analyzed in the Fin area was the 2006 March 25 earthquake, Mw 5.7, with reverse faulting and an E–W strike (Roustaei et al. 2010). Figure 1b displays the historical and instrumental seismicity in the southern part of Iran, with magnitudes exceeding Mw 5.0, highlighting the region's high seismic potential. The remarkable aspect of the recent Fin doublet earthquake studied in this paper is its geological location, which is situated to the west of the Khurgu Salt Dome and to the south of the Handun Salt Dome. Both the active Khurgu diapir, also referred to as the Namak diapir in some references (e.g., Molinaro et al. 2004, due to its location at the intersection of the Namak and Siah anticlines), and the inactive Handun diapir have a salt core originating from the Hormuz Formation, with visible outcrops on the surface.

3 Methodology

3.1 Data preprocessing

Epicenter information and waveform data for the Fin double event were obtained from the Iranian Seismological Center (IRSC), which operates more than 130 seismic stations, including 49 short-period and 80 broadband seismometers (further details available at http://irsc.ut.ac.ir). Due to limited station coverage in southern Iran, additional waveform data from two stations, RAYN and UOSS, in the Incorporated Research Institutions for Seismology (IRIS) network (https://ds.iris.edu/wilber3/) were also utilized. To prepare the data for inversion, several signal processing steps were applied. Initially, seismic waveforms were converted into SAC format, and essential data headers—such as earthquake location and time, station information from the IRSC catalog, and pertinent details—were completed. Subsequently, further signal processing included downsampling to achieve a new sampling rate of 0.2 seconds, removal of instrument responses, conversion of velocity seismograms to displacement seismograms, and ultimately conversion of the data format into MiniSEEDs. The inversion process relies on the accurate fitting of observed and synthetic seismograms. A critical component for generating synthetic seismograms is the availability of a suitable Green's function specific to the study region. The velocity model utilized was adapted from Kianimehr et al. (2018) (Fig. 2) and employed in conjunction with the Fomosto tool—a Green’s function creation and management tool within the Pyrocko package (https://pyrocko.org/). Thus, following these comprehensive preprocessing steps, the input data for the inversion process were effectively prepared.

Fig. 2
figure 2

The adopted velocity model based on Kianimehr et al. (2018). The thin and thick lines denote the S-wave and P-wave depth profiles, respectively

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3.2 KIWI multistep inversion approach

The retrieval of source parameters is crucial, because it can help elucidate the characteristics of earthquakes. This study utilized the KIWI (KInematic Waveform Inversion) tool (http://kinherd.org; Cesca et al. 2010) for stable parameter retrieval using the eikonal model in sequential steps. The eikonal source model is defined by 13 parameters. Among these factors, some are related to the point source, which determines the location and time of the centroid point, as well as parameters that influence the radiation pattern, such as strike, dip and rake. The remaining parameters describe the extended source and geometry of the rupture, including the rupture radius and coordinates of the nucleation point (Cesca et al. 2010; Heimann 2011).

3.2.1 Retrieving point source parameters

In the first step, the focus is on retrieving point source parameters by applying a bandpass filter below the corner frequency. For example, the second event of the Fin doublet earthquake, the inversion process was performed by applying a filter in the frequency range of 0.04 to 0.07 Hz and using 10 stations with an azimuthal gap of less than 90° (as shown in Fig. 3a). The inversion input data include earthquake location, origin time, waveforms from selected stations, and synthetic seismograms generated for different starting source models. Characteristics such as fault plane parameters (strike, dip and rake) for two possible fault planes, scalar moment, and centroid depth are estimated by fitting the amplitude spectra of the observed and synthetic seismograms using a non-linear inversion scheme. In this step, the flatness of the relative misfit curves indicates the stability of the results obtained from the retrieval of point source parameters (Cesca et al. 2010). In other words, the solutions are more accurate if the misfit curves for strike, dip, rake, and depth are sharper at the minimum point compared to when the curves are flat at the minimum point. Furthermore, rapid directivity detection is conducted using the method described by Cesca et al. (2011), which relies on the azimuthal variation of the apparent duration observed at each station. Figure 3b shows the apparent duration obtained from the first inversion step as a function of each station's azimuth relative to the epicenter.

Fig. 3
figure 3

a Triangles (with name labels) represent the seismic stations used during the inversion for the second event. The color indicates the apparent duration obtained for each station during the first step of inversion. b The apparent duration plot is based on the azimuthal distribution of stations and the best-fitting model, indicating a pure unilateral rupture. c An example of the waveforms recorded for this doublet event at four stations

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In the second step, with the purpose of resolving the polarity ambiguity of the focal mechanism and retrieving the location and time offset of the centroid, the fitting of observed and synthetic seismograms in the time domain is performed. Simultaneously, in both the first and second steps, a full moment tensor (MT) inversion is conducted. The misfit for full MT solutions is generally less than or equal to that for pure double couple (DC) solutions because DC sources form a subset of the full moment tensor (Cesca et al. 2013). The full moment tensor inversion involves retrieving the moment tensor components and decomposing them into DC and non-DC (isotropic (ISO) and compensated linear vector dipole (CLVD)) parts.

3.2.2 Retrieving extended source parameters

In contrast to the previous two steps, the final step assumes an extended source and involves the use of a bandpass filter that includes frequencies higher than the corner frequency, in addition to the low frequencies. The fitting of the observed and synthetic amplitude spectra is performed in the frequency domain. In the third step, the rupture geometry is retrieved, which includes the area and radius of the circular rupture, as well as the coordinates of the nucleation point—a location within the rupture surface where the rupture process initiates toward the centroid point. In the KIWI inversion tool, it is assumed that rupture propagates in a circular form on the fault plane, with two main constraints affecting its propagation. Firstly, the Moho discontinuity can flatten the lower part of the circle if the rupture dimensions extend to this discontinuity. Secondly, the free surface of the Earth can flatten the upper part of the circle, indicating that the rupture reached to the surface. Therefore, these two constraints affect the rupture geometry (Cesca et al. 2010). Additionally, the main fault plane is distinguished from the auxiliary plane in this step. Here, one of the two possible fault planes is assumed, and the inversion by fitting of amplitude spectra is conducted. The fault plane demonstrating the lower misfit is identified as the main fault plane.

Throughout each step, the misfit between the observed and synthetic seismograms is calculated as a criterion to assess the quality of the results. Moreover, inversion is conducted using different station configurations, such as removing or adding seismic traces and repeating the inversion process, to evaluate the stability of the solutions.

4 Results

In this section, we elucidate the outcomes derived from the inversion analysis of the Fin doublet earthquake, providing a comprehensive presentation of the retrieved parameters at each step of the inversion process.

A summary of the results from three inversion steps is presented in Table 2. First, we describe the results related to the point source parameters retrieved in the first and second steps. The scalar moment and moment magnitude during the first step of inversion are estimated to be 1.06×1018 Nm and 5.9 for the first event, and 2.21×1018 Nm and 6.1 for the second event, respectively. Fault planes with east-west strike for both events are retrieved in the first step. The centroid depth determined for the first earthquake is 7.9 km, which is shallower than the hypocenter depth of 19.5 km. The centroid depth of the second earthquake is 11.5 km, which is not much different from the hypocenter depth. Figure 4 presents the results of the first step inversion for the second event, depicting two possible fault plane orientations, the scalar moment and centroid depth. At the bottom of Figure 4, a remarkable fit between the observed and synthetic amplitude spectra of waveforms is evident. Generally, a misfit below 0.4 in the first step indicates an excellent solution quality (Cesca et al. 2010). For the second event, better stability is observed in the depth and dip misfit curves as compared to rake and strike parameters (refer to Fig. 4). In addition, in the first inversion step of the second event, rapid directivity detection indicates unilateral directivity propagating towards the west of the epicenter which can be confirmed by comparing the waveforms of the stations located to the west and east of the epicenter (Figs. 3b and 3c). In the second step, by resolving polarity ambiguity, the thrust faulting mechanism with an east‒west strike is identified for this doublet event. The centroid location for the first and second earthquakes is estimated 21 km east of the epicenter and 20 km northeast of the epicenter, respectively. The centroid time is 8 seconds for the first event and 7 seconds for the second event. Figure 5 displays the results of the second step of the inversion process for the second event, along with the observed and synthetic waveform fitting in time domain. It is noteworthy that the RAYN station exhibits the lowest correlation among the fits. However, due to data unavailability in the southwestern azimuth, substituting this station was impractical, justifying a higher misfit in this step (Fig. 5).

Table 2 Summary of point and extended source parameters for the Fin doublet earthquake*
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Fig. 4
figure 4

(Top) Inversion first step results of point source parameters and misfit curves (depth, dip, strike, and rake) for 14 November 2021, second event. (Bottom) Amplitude spectra fitting for observed (gray areas) and synthetic (black lines) data

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Fig. 5
figure 5

(Top) Inversion second step results including focal mechanism, location and time centroid (increasing the size of the gray points indicates an increase in the fit quality) for 14 November 2021, the second event. (Bottom) S‐wave fitting for observed (gray lines) and synthetic (black lines) data

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The full moment tensor decomposition of the first earthquake reveals 87% DC, 8% CLVD, and 5% isotropic components. The decomposition of the second earthquake shows 64% DC, 23% CLVD, and 13% isotropic components. The misfit values for both earthquakes are equal between the full moment tensor and pure DC solutions. Specifically, the misfits for the first earthquake in the first and second inversion steps are 0.40 and 0.78, respectively. Similarly, for the second earthquake, the misfits in the first and second steps are 0.34 and 0.64, respectively.

In the third inversion step for finite source modeling, the rupture radius and area are determined for the first event to be 10 km and 286 km2, respectively (see Table 1). The second event is characterized by a rupture radius of 5 km and a rupture area of 78 km2 (Fig. 6). The rupture for the first earthquake reached to the surface of the Earth, whereas the rupture for the second earthquake did not (Fig. 7d). Additionally, the coordinates of the nucleation point, situated within the rupture plane where the rupture process initiates toward the centroid, is obtained. For instance, the first earthquake exhibits symmetric bilateral directivity based on the location of the nucleation point. In the case of the second event, the nucleation location reveals unilateral directivity effects of the rupture from east to west. Furthermore, the fault plane is identified from the auxiliary plane in the third step, indicating thrust faulting with E–W strike and northward dip for both earthquakes (Fig. 7). The strike, dip, and rake angles are retrieved 254°, 64°, and 76° for the first earthquake, and 269°, 62°, and 96° for the second earthquake, respectively. It is important to note that we assessed the stability of our solutions by performing inversions using different subset of stations. For example, we removed one trace or added a new one and then repeated the inversion. Our findings indicate that the first earthquake consistently provided a stable solution across all three inversion steps. In contrast, while the second earthquake yielded stable solutions in the first and second steps of the inversion process, the third step failed to reliably identify the main fault plane. Consequently, due to this uncertainty in recognizing the main fault plane, the characteristics of a fault with a strike of 76°, a dip of 29°, and a rake of 79° should be considered probable for the second earthquake. For a comprehensive visualization of the inversion outcomes, Figure 7 illustrates the cross-section of the doublet events and their aftershocks, the projection of the rupture plane on the surface, as well as the epicenter, centroid, and nucleation coordinates.

Fig. 6
figure 6

(Top) Retrieval extended source parameters in the third inversion step, including the focal mechanism (true fault plane discrimination with a thick line), rupture geometry, and misfit curves (source radius and relative rupture velocity) for 14 November 2021, second event. (Bottom) Amplitude spectra fitting for observed (gray areas) and synthetic (black lines) data

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Fig. 7
figure 7

a The epicenter of Fin doublet events with aftershocks, according to the IRSC catalog. b The earthquakes and topographic elevation of the region along the AB cross-section. c The results of the earthquakes inversion include the centroid, the focal mechanism (step 2), the nucleation point, and the rupture geometry (step 3). d Rupturing process resulting from third step inversion for the Fin doublet event

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Two additional datasets related to the second earthquake are presented in Fig. 8. The first dataset includes recordings from 25 stations of the Building and Housing Research Center (BHRC) acceleration network. The peak ground acceleration (PGA) values at these stations range from 0.1 to 57%g, with the highest recorded at the Siyahoo (SIH) station, which is located 29 km northeast of the epicenter (see Fig. 8). The second dataset comprises intensity maps (ShakeMap) provided by the United States Geological Survey (USGS). These maps combine seismic and macroseismic observations via interpolation to depict potential hazards and damage in all directions following an earthquake (Wald et al. 2011). Figure 8 displays the PGA and Modified Mercalli Intensity (MMI) results derived from ShakeMap for the second earthquake.

Fig. 8
figure 8

(Top) MMI polygons and PGA contours (dashed lines labeled with PGA values in %g) according to USGS ShakeMap for the second event. The circles represent acceleration stations (with name labels), colored by the PGA (%g) values reported by the BHRC for the second earthquake. (Bottom) The second event's epicenter (from the IRSC report) and centroid locations (from step 2 inversion) are shown

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In the next section, we will attempt to summarize the possible scenarios for the occurrence of these doublet earthquakes using the relationship between these results.

5 Discussion

5.1 Interpretation of findings

To evaluate the directivity of these earthquakes, we first review some retrieved parameters of these two events. The epicenter of the first earthquake, according to the IRSC report, was located less than 10 km south of the Handun Salt Dome and approximately 20 km west of the Khurgu Salt Dome (see Fig. 7c). Approximately 90 seconds later than the origin time of the first event, the second earthquake occurred less than 10 km from the Khurgu Salt Dome. The centroid location of the first earthquake, determined using KIWI inversion, was situated 21 km east of its epicenter, with a depth of 7.9 km shallower than hypocentral depth. Figure 7 shows that this location is near the Khurgu Salt Dome outcrop. Additionally, based on the nucleation points identified in this study, bilateral directivity was identified for this event, resulting in a rupture area of 286 km2. Due to the shallow centroid depth and the large rupture area for this event, the rupture extended to the Earth's surface. The epicenter of the second event was located near the western edge of the rupture zone of the first event. The centroid location of the second event was retrieved at a depth of 11.5 km and a distance of 20 km east‒northeast of its epicenter. In the third step of the inversion for the second event, a rupture with an area of 78 km2 was obtained in the northeast of the rupture area of the first event. According to the location of the nucleation point, the rupture directivity for the second event propagated unilaterally from east to west. This result was consistent with the directivity results obtained in the first step of inversion (Fig. 3). Note the resolution of a clear directivity pattern, which is independently but consistently resolved both in the azimuthal variation of apparent durations (Fig. 3) and in finite source modeling (Fig. 6).

Figure 3c shows waveform examples from four selected stations for the doublet event, which were chosen based on their geographic positions. Two stations lie to the east and northeast, and the other two lie to the west and northwest of the events, facilitating a comparative analysis considering their relatively similar spatial distances. In these waveforms, the P-wave for the first event arrives at approximately 40 seconds, and for the second event, it arrives at approximately 130 seconds in the time series. Given the determined westward directivity of the second event, notable differences in waveform amplitude are evident. West of the events, at the JHRM and LMD1 stations, the waveform amplitude during the second event was significantly greater than that during the first event. Conversely, at KBAM and CHMN, which are located east of the events, there is minimal difference in the waveform amplitudes between the first and second events (Fig. 3c). This provides additional evidence demonstrating the unilateral westward directivity of the second event.

Furthermore, the highest acceleration recorded for the second event was at the Siyahoo (SIH) station, which is located near the earthquake centroid. However, due to the absence of an acceleration station in the west direction of the event at a distance similar to that of the Siyahoo, it was not possible to perform a correct analysis of the directivity using acceleration records. It can be concluded that the highest acceleration was recorded in the direction where the centroid of the earthquakes was estimated. In this sense, the results are consistent.

However, this westward directivity possibly influenced by regional geological complexities, such as the presence of evaporite layers and salt domes. These factors are crucial for comprehensive seismic hazard analysis in the region.

The retrieved focal mechanisms and fault planes for both events align with the geological structures. Consequently, these earthquakes can be attributed to the MFF, which is characterized by an east‒west strike and a northward dip. Furthermore, our results are in good agreement with the focal mechanism solutions provided by IRSC, GCMT, GFZ, and, to a lesser extent, the USGS for this doublet event (see Table 1). Although our findings diverge from the focal mechanism presented by ISC, we assign greater validity to our results based on the consistency with geological features and various reliability tests conducted in this study. The misfit obtained at each inversion step indicates that the solutions are robust. Additionally, during the inversion process, we assessed the stability of our solutions by performing repeated inversions with different subset of traces. With these stability tests, the reliability of the retrieved parameters was confirmed, particularly for the first event. According to the conducted stability tests, in the case of the second earthquake, there remains uncertainty about the distinguishing of the fault plane and the auxiliary plane. This dip could either be northward or southward; however, if it dips toward the south, it would be inconsistent with the characteristic northward dip of the MFF.

The full moment tensor decomposition for the first and second earthquakes revealed DC components of 87% and 64%, respectively. Comparative analysis of moment tensor solutions from other reports, such as GCMT, also indicated higher non-DC values for the second event compared to the first (Table 1). It is important to note that while our study employs the full moment tensor method using the KIWI, other reports may utilize the deviatoric method. Despite this difference in calculation methodologies, the results remain comparable in terms of DC and non-DC values.

In our investigation, a pertinent question emerged regarding the possibility of attributing the existence of large non-DC components obtained for the second event to non-shear processes. We could consider this scenario plausible only if there was a significant misfit improvement in our results. Cesca et al. (2013) proposed misfit improvement as a criterion for identifying induced earthquakes, suggesting that if the misfit of the moment tensor model shows a significant improvement compared to the misfit of the DC source model, the event can be considered induced. Otherwise, even with high values of non-DC components, the event cannot be classified as induced because the non-DC part is not well resolved. As indicated in the results section, our findings show that the misfit of the DC source model was equal to the misfit of the moment tensor model, without any misfit improvement. Therefore, the presence of non-DC values in the second earthquake can be attributed to the coda waves of the first earthquake affecting the waveform of the second earthquake, reflecting the inherent complexity of studying doublet earthquakes.

5.2 Comparison with previous studies

To evaluate consistencies and discrepancies, we compared the findings of this study with those reported in prior research. Using InSAR data, Coulomb failure function analysis, and the depth distribution of aftershocks, Golshadi et al. (2023) identified blind thrust structures as the causative faults for the Fin doublet event. They characterized the causative fault for the first earthquake with a strike of 284 degrees and a northward dip of 53 degrees, which aligns somewhat with our findings for the first event. However, their results for the second earthquake, which indicate an 85° strike and southward dip, are consistent with our results if we assume a south-dipping plane as the main fault plane. Notably, there remains a discrepancy regarding the dip of the fault; Golshadi et al. (2023) reported a dip of 6 degrees for the fault of the second earthquake, whereas our results, considering the uncertainty in distinguishing the two planes for the second event, estimate the dip to be 29 degrees toward the south.

The study conducted by Toker et al. (2023) used the finite-fault inversion method to analyze the characteristics of the thrust fault plane for two earthquakes. They estimated that the strike, dip, and rake for the first earthquake were 114°, 32°, and 91°, respectively, and those for the second earthquake were 49°, 24°, and 27°, respectively. According to their findings, a bilateral rupture occurred for both events, with the presence of a salt layer causing stress decoupling. The mobilization of this salt layer after the first earthquake is suggested to have triggered the second event and influenced the change in the focal mechanism between the two earthquakes.

In contrast, our study identified different fault characteristics. We identified a fault with an east‒west strike and a northward dip, which aligns with the regional tectonic setting. While Toker et al. (2023) estimated bilateral rupture for both events, our findings indicate bilateral rupture for the first event and westward unilateral rupture for the second event. It is important to highlight that our methodology involved using waveforms recorded at local and regional distances to determine the source parameters, whereas Toker et al. (2023) relied on teleseismic broadband waveforms, and thus lower frequency data, to estimate the coseismic slip distributions.

Although our findings exhibit significant differences in fault plane characteristics for both events compared to other studies (Table 3), we assessed the stability of the results. Additionally, our results are consistent with the tectonic structure of southern Iran. Furthermore, the unilateral directivity retrieved for the second event in our results aligns with the waveforms recorded at the stations. Moreover, our approach involved utilizing local and regional data encompassing a broader frequency range, thereby enhancing the robustness of our findings as compared to data recorded at teleseismic distances. While we do not intend to dismiss the findings of prior research, the fact that each of these studies identified distinct fault planes, coupled with varying methodologies, underscores the complexity of seismotectonic investigations in southern Iran. Moreover, limitations in station coverage across southern Iran amplify the challenges inherent in our analysis.

Table 3 Comparison of fault plane characteristics for the doublet event: current study vs. previous studies
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6 Conclusion

In this study, we investigated the source parameters and directivity of the Fin doublet earthquake using a multistep inversion approach. Reliable solutions for the source parameters were obtained, particularly for the first event, aligning well with the tectonic setting of the MFF.

For the second event, two scenarios are plausible: (1) it occurred due to MFF activity, with waveform complexity and overlap with the first event causing instability in the solutions, and (2) it was triggered by a blind thrust fault with a southward dip, as suggested by previous studies. The uncertainty in analyzing this event arises from the small time offset between the doublet earthquakes and the tectonic intricacies of the area, including the presence of salt layers.

Directivity analysis revealed that the first earthquake exhibited bilateral directivity, resulting in a significant rupture area that reached the Earth's surface. The second earthquake showed a unilateral westward directivity, supported by waveform amplitude differences and apparent duration results.

Moment tensor decomposition indicated DC components of 87% for the first earthquake and 64% for the second earthquake. The lack of misfit improvement in the moment tensor solutions indicates that the high non-DC value for the second event is not linked to induced earthquakes. This is because the presence of coda waves from the first event made its solution less stable and well-resolved.

In conclusion, this study advances our understanding of the source parameters of the Fin doublet earthquakes, emphasizing the critical role of directivity analysis in assessing seismic hazards. The findings underscore the need for future research to enhance methodologies for studying multiple earthquakes and mitigating the complexities posed by their waveforms. The main limitation of this study was the poor coverage of seismic stations in southern Iran, which needs improvement for further research.