Introduction

Simplified, widthless seismogenic faults have long dominated assumptions in earthquake kinematic and dynamic models1,2. However, in most geologically-mapped structures, fault zones are complex structures consisting of two primary units, i.e., the fault core (primary slip plane) and the surrounding damage zone3 (Fig. 1a). During earthquake ruptures, the fault core and damage zone respectively exhibit distinct deformation styles, particularly in the shallow crust near the surface4,5,6 (Fig. 1b). Our understanding of fault deformation styles has significantly improved recently, benefiting from advancements in high-resolution satellite optical geodesy and geological field observations. Such coseismic fault deformation is commonly characterized by (1) highly localized slip along the primary fault planes, generating displaced on-fault displacement where surface rupture typically occurs, and (2) distributed off-fault deformation (OFD) spanning a broad zone of 102–103 m within the fault damage zone7,8,9,10,11 (Fig. 1c). Previous investigations revealed that ~28–88% of fault deformation may be accommodated within off-fault medium surrounding the primary fault, where the deformation manifests as secondary faulting, block rotation, warping, and/or microcracking12,13,14,15,16 (Fig. 1d). This actually illustrates the pervasive occurrence of OFD and its significant role in accommodating coseismic fault deformation. Therefore, quantifying off-fault deformation and characterizing the mechanisms involved are essential both for fully understanding shallow rupture process of fault zone, and accurately assessing near-fault earthquake damage.

Fig. 1: Coseismic deformation style of fault zone and seismotectonic backgrounds of the earthquake doublet.
Fig. 1: Coseismic deformation style of fault zone and seismotectonic backgrounds of the earthquake doublet.The alternative text for this image may have been generated using AI.
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a Structure of fault zone. b Coseismic deformation pattern of earthquake faulting. c Fault-zone’s surface ruptures and deformations. d Different deformation components identified from across-fault displacement profile. e Hill-shaded topography and active faults19. Blue and red lines represent the surface rupture traces of the earthquake doublet18. Focal mechanisms of the initial branch and the main EAFZ (Mw 7.8 event) were plotted as red-and-white beach balls, and focal mechanisms of the northern EAFZ (Mw 7.6 event) as blue-and-white one17.

The universality of OFD in surface-rupturing earthquakes opens a crucial question for studying fault deformation behavior of the 2023 Turkey-Syria earthquake doublet: What proportion of fault deformation presented as OFD style within coseismic fault zone? The earthquake doublet comprises two surface-rupturing earthquakes, with moment magnitude (Mw) of 7.8 and 7.617,18 (Fig. 1e). The causative fault system of them, named the East Anatolian Fault Zone (EAFZ), consists of three sub-fault systems-the Main Strand, Northern Strand, and Karasu Trough19,20. The Mw 7.8 earthquake initially nucleated on the Nurdağı fault, and triggered exceeding 300-km-length surface rupture on the main EAFZ at about 11 s, propagating through the Amanos, Nurdağı-Pazarcık, and Erkenek segments, and their junctions-Demrek restraining stepover (RSS), Islahiye releasing bend (REB), Türkoğlu REB, Gölbaşı releasing stepover (RES), Yarpuzlu restraining doublet bend (RSDB)17,19 (Fig. 1e). The Mw 7.6 earthquake ruptured ~200 km along the northern EAFZ. The initial rupture of the Mw 7.6 event was located at the center of the Çardak fault and propagated bilaterally (Fig. 1e). Its rupture terminated at the western end of the Savrun fault and the eastern end of the Sürgü fault, which bent to the southwest and northeast directions, respectively. The Mw 7.6 event also propagated through a 30-km-length and 7-km-width fault jog-Nurhak fault complexity (FC), which separates the Çardak fault and Sürgü fault. The slip rate of the main EAFZ ranges from ~10 mm/year in the northeast to ~4 mm/year in the southwest19,21; in contrast, the slip rate of the northern EAFZ is relatively slow, with estimate of 2.5 mm/year on the Çardak fault. In addition, the main EAFZ is relatively mature fault system, with cumulative slip of 22.5–26 km on the Erkenek segment and 19–25 km on the Pazarcık segment19. The Çardak fault cuts Ceyhan River valley, forming a 11-km-long left-lateral bend, and hence the bend is considered as the total offset of the fault19.

Geodetic and seismological constraints on fault kinematic and dynamic models of the earthquake doublet illustrate distinct fault rupture behaviors and deformation characteristics over multiple fault segments22,23,24,25,26,27,28,29. However, these models depend on simplifying assumption that faults have no widths, conflicting with geological understanding of fault-zone structure. They also have difficulty resolving distributed OFD, which may account for exceeding 50% of the fault deformation, as observed in other surface-rupturing earthquakes15,16. Of particular interest in the earthquake doublet is whether kinematic and dynamic characteristics of segmented faults result in change in fault deformation style, like proportional variation between on-fault and off-fault deformation. Therefore, characteristic of segmented fault rupture during the earthquake doublet raises another significant question: whether characteristic discrepancy in segmented faulting affects variation of OFD, and what factors control OFD behavior? In this study, we seek to obtain the distribution of both on-fault and total displacements of the earthquake doublet using optical satellite geodesy, and further exploit the difference of the two displacements to reveal OFD. We find that ~17% and 20% of fault deformation is mediated by OFD style. Variations of OFD may be mainly attributed to segmented fault geometry and rupture velocity, improving our understanding for OFD behaviors in surface-rupturing earthquakes.

Results

Distribution of on-fault displacement

The 0.8-m-resolution optical images acquired by the Gaofen-7 satellite were used to measure the dislocated on-fault displacement of the earthquake doublet. We manually identified the displaced surface markers used to measure on-fault displacements through visual inspection of pre- and post-event GF-7 imagery, rather than through image correlation (Fig. 2a, b; Supplementary Fig S1; see “Methods”). We measured a total of 204 on-fault displacements along the Mw 7.8 rupture (Fig. 2c, d; Supplementary Table S2). Our results are highly consistent with the on-fault displacements (a total of 129) that measured from field measurements and drone imagery reported by the previous studies27,28, validating the accuracy and reliability of our measurement (Fig. 2c, d). In total, we collected 333 on-fault displacements to characterize the surface slip distribution of the Mw 7.8 rupture, excluding those beyond the northern (>N60 km) and southern terminations (>S105 km; Fig. 2d). The fault displacement localized on the Mw 7.8 primary fault is predominated by left-lateral strike-slip faulting, with an average slip of 3.31 m. Towards the south of the epicenter, the fault displacement is characterized by several peaks of high displacements, typically ranging from <1 m to 6 m (Fig. 2d). Towards the north of the epicenter, the fault slip varies from 0.5 m to 7.52 m in different locations, with the maximum slip located ~10 km to the epicenter.

Fig. 2: On-fault displacement observations of the earthquake doublet.
Fig. 2: On-fault displacement observations of the earthquake doublet.The alternative text for this image may have been generated using AI.
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a Orthorectified pre- and post-event GF-7 images and post-event Google Earth image (Map data ©2024 Google). b On-fault slip measurements from linear and displaced surface markers in the pre- and post-event images. White lines are used as a reference. c, d Along-strike distribution of on-fault slip related to the 7.8 ruptures. e, f Along-strike distribution of on-fault slip related to the 7.6 ruptures. Colored circles represent slips that we determined; the others were reported in previous investigations27,28,29.

For the Mw 7.6 rupture, we measured on-fault displacements through displaced grass and tree rows from the Gaofen-7 orthorectified image pairs, which cannot often be measured in the field because of lacking comparison of pre-earthquake characteristics29 (Supplementary Fig. S2; see “Methods”). Our on-fault displacement measurements densely cover the western and eastern rupture initiations near the Mw 7.6 epicenter (that is, W20-E20 km), with a total of 133 displacements (Fig. 2e; Supplementary Table S3). Together with the on-fault displacements based on field observations29, we obtained a total of 174 on-fault displacements of the Mw 7.6 rupture. The coseismic displacements localized on the Mw 7.6 primary fault plane are predominantly dominated by left-lateral strike-slip faulting. The Mw 7.6 event exhibited greater on-fault displacements than the Mw 7.8 rupture, with an average value of 5.38 m and a range from <1 m to 8.56 m (Fig. 2f).

Distribution of total displacement

Through sub-pixel image correlation technique, we constructed imaging of coseismic horizontal displacement associated with the earthquake doublet from pre- and post-event Sentinel-2 optical imagery4,30,31 (Fig. 3; Supplementary Figs. S3–S7; see “Methods”). Notably, the pre- and post-event image correlation was implemented using the MicMac software, with a sliding window of 3 × 3 pixels, a step of one pixel and a regularization term of 0.332,33. This results in the surface motion in both the east-west (EW) and north-south (NS) directions with a pixel resolution of 10 m (=the step used in correlation) and independent measurements of every 30 m (=the sliding window size). The output displacement can achieve an accuracy of 1/20 of the input pixel size32. The regularization operation applied moderate smoothing to displacement field, which can effectively suppress correlation noises but do not disrupt complex deformation patterns.

Fig. 3: Total fault displacement observations of the earthquake doublet.
Fig. 3: Total fault displacement observations of the earthquake doublet.The alternative text for this image may have been generated using AI.
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a, b Coseismic displacement fields in the east-west and north-south directions during the earthquake doublet. Note that positive values indicate motion to the east or north and negative to the west or south. Blue and red lines represent the surface rupture traces of the earthquake doublet interpreted from our coseismic displacement fields. c–e Representative examples of measurements of total fault displacement and deformation zone’s width. Fitting lines (red lines) are calculated using the approach proposed by Milliner et al.15.

Our horizontal displacement accurately reproduces a spatially complex deformation patterns of the earthquake doublet, where slipping on the primary surface ruptures and anastomosing fault branches were well mapped (Fig. 3a, b). The Mw 7.8 rupture generates predominated left-lateral slip on the Amanos, Pazarcık, and Erkenek segments, with southwest-northeast trending. The Mw 7.6 rupture extends with a west-east trending left-lateral slip on the Çardak fault, transitions to a southwest-northeast trending on the Sürgü fault, and to a northeast-southwest trending on the Savrun fault. Furthermore, we used the across-fault displacement profiles (Fig. 3c–e) to finely illustrate the distribution of total fault displacement and deformation zone’s width along the Mw 7.8 and Mw 7.6 ruptures and their branches, respectively (Figs. 4 and 5; Supplementary Tables S4, S5; see “Methods”). For the Mw 7.8 primary rupture, the total fault displacements range from 0.50 ± 0.29 m (1σ) to 7.34 ± 0.84 m, with an average slip of 3.93 ± 0.77 m (Fig. 4a, b); the Mw 7.6 earthquake produced average total slip of 4.50 ± 0.39 m, varying from 0.92 ± 0.65 m to 8.34 ± 0.44 m (Fig. 5a, b). In deformation-zone width, the Mw 7.6 rupture exhibited an average width of 350 m, ranging from 20 m to 1860 m (Fig. 5a, c), while the width of the Mw 7.8 rupture ranges from 40 m to 2440 m, with an average value of 300 m (Fig. 4a, c). Considering that the displacements were resolved at 30 m scale with moderate regularization, we emphasize that (i) fault zones with a width of less than 30 m carry significant uncertainty, as they fall below the resolution at which the data can be reliably resolved, and (ii) the widths reported in the main text are rounded to the nearest 10 m, aligning with the resolution of both the input image and displacement field.

Fig. 4: Distribution of total fault displacement along the Mw 7.8 earthquake rupture.
Fig. 4: Distribution of total fault displacement along the Mw 7.8 earthquake rupture.The alternative text for this image may have been generated using AI.
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a Total fault slip and fault-zone’s width along the Mw 7.8 rupture that is determined in this study. b Magnitude of total fault slip along the Mw 7.8 rupture. c Coseismic deformation-zone width along the Mw 7.8 rupture. The histogram and kernel density estimation (KDE) display the statistical characteristics of the total fault displacement.

Fig. 5: Distribution of total fault displacement along the Mw 7.6 earthquake rupture.
Fig. 5: Distribution of total fault displacement along the Mw 7.6 earthquake rupture.The alternative text for this image may have been generated using AI.
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a Total fault slip and fault-zone’s width along the Mw 7.6 rupture that is determined in this study. b Magnitude of total fault slip along the Mw 7.6 rupture. c Coseismic deformation-zone width along the Mw 7.6 rupture. The histogram and KDE display the statistical characteristics of the total fault displacement.

The amount of total fault slip and deformation-zone width are heterogeneous, with smaller fault slip and wider deformation zone at the coseismic rupture terminus, junction of fault segments, and structurally complex fault strands (that is, Demrek RSS, Islahiye REB, Gölbaşı RES, Yarpuzlu RSDB, Nurhak FC, and fault splays). For instance, as the Mw 7.6 event extends towards the southwest-northeast trending Sürgü fault (E35–E66 km; Fig. 1e), there was a significant decrease in total slip and an increase in width. Similar characteristics were observed at the western terminus (W55–W40 km) along the Savrun fault, and at the northern and southern terminus of the Mw 7.8 rupture. In addition, at the conjunctions of fault segments and geometrically complex strands, we identified that the fault deformation is distributed over a wide region spanning 0.5 to 2 km in width (Figs. 5 and 5). This implies substantial variations of coseismic deformation styles across these regions, like proportional adjustment between localized on primary fault and distributed within the surrounding fault zone26.

Distribution of off-fault deformation

Finally, by comparing the total displacement with the on-fault displacement, we calculated the distribution of OFD in percentage (OFD%) associated with the earthquake doublet, which effectively defines the ratio between fault total and off-fault deformations5,6 (Fig. 6; Supplementary Fig. S8; see “Methods”). Generally, 80% of the fault displacement is localized on the primary fault plane of the Mw 7.8 earthquake, whereas the remaining 20% is distributed over the 200-m-width deformation zone surrounding it (Fig. 6a, b). The OFD% along the bilateral rupture of the Mw 7.8 earthquake exhibits a notable disparity: the average OFD% along the southern rupture (strand S9–S140 km) is 23%, larger than the 15% observed along the northern rupture (strand N3–N98 km), with average width of 200 m and 210 m, respectively. This suggests that the southern rupture manifest more fault deformation as OFD. Especially, the fault deformation is more localized throughout the Pazarcık segment, where an average of OFD% is just 16% and 11% distributed over mean widths of 180 m and 220 m along the southern (S9–S24 km) and northern (N3–N34 km) sides of it, respectively. Towards south, as the rupture traverses the Türkoğlu REB (S30-S41 km), the estimated OFD% significantly increased to 25%, with a mean width of 180 m. Within the Türkoğlu REB (Fig. 4a), the OFD% at numerous measurement sites surpass 50%, indicating that OFD is a primary mechanism for accommodating fault deformation in the region. Subsequently, along the Amanos segment, the estimated OFD% is 19% at strand S50–S65 km, 26% at S74–S111 km, and 39% at S130–S140 km (i.e., southern termination), with respective average deformation zone widths of 230 m, 380 m, and 260 m. On the Erkenek segment (N49–N100 km), the relatively distributed deformation was observed at two regions, with estimates of 41% and 27%, respectively.

Fig. 6: Distribution of OFD% along the earthquake doublet.
Fig. 6: Distribution of OFD% along the earthquake doublet.The alternative text for this image may have been generated using AI.
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a, b OFD% and deformation-zone width along the Mw 7.8 rupture. c, d OFD% and width along the Mw 7.6 rupture. The rupture velocity of multiple fault segments was reported by Ren et al.17. The histogram and KDE display the statistical characteristics of OFD and width.

For the Mw 7.6 rupture, an average of 17% of fault deformation is accommodated as OFD, spanning a mean deformation zone width of 140 m (Fig. 6c, d). Similar to the Mw 7.8 rupture, the Mw 7.6 rupture is also characterized by bilateral rupture; as expected, the OFD% exhibits a bilateral variability: the average OFD% along the eastern rupture (strand E6–E62 km) is 25%, larger than the 11% observed along the western rupture (strand W2–W55 km), with average width of 120 m and 180 m, respectively. Specifically, on the western side of the epicenter, we measured a comparatively low OFD% (an average of 10% and 8%) and narrower deformation zone (an average of 110 m and 70 m) at strands W2–W6 and W8–W17 km; conversely, on the eastern side, the OFD% significantly increases to 28% and 20%, distributed over a broader deformation zone of 120 m and 130 m at strands E6–E11 and E13–E18 km. As the rupture propagated bilaterally towards the eastern and western terminations (E51–E62 km and W52–W55 km, respectively), the OFD escalates to 49% and 36%, distributed within a 510- and 540-m-width zone, respectively. In addition, we observed a poor correlation between the magnitude of the OFD% and width in the two earthquake ruptures, suggesting that width of the zone has almost no impact on the OFD% (Supplementary Fig. S9). Overall, segmented variations of OFD% align well with geometric segmentations, jogs of preexisting fault structures, and dynamic rupture behaviors associated with the earthquake doublet17,22,23,24,25. Our results highlight that, for the earthquake doublet, the previous studies in principle lack consideration of OFD, as they usually consider fault slip estimated from elastic kinematic models or on-fault displacement from geological measurements as the shallow fault deformation. This frequently results in an oversight of complex deformation patterns of faults and an underestimation of total fault slip at the surface.

Discussion

Increasing distributed deformation induced by complex fault geometry

Fault geometrical complexity, including features such as fault morphology (e.g., bends, stepovers, dense fractures or cracks) and interactions between different faults (e.g., overlaps, connections, splays, or branches), is thought to control on fault OFD, with larger OFD% observed in geometrically complex fault segments4,5,13. The earthquake doublet confirms that in regions where the macroscopic fault geometry is straightforward-for example strands N3–N43 km and W17–E18 km of the Mw 7.8 and Mw 7.6 ruptures, fault deformation is predominantly localized on the primary fault planes, with relatively less OFD% (Fig. 7a, d). Conversely, despite the lack of dense measurements, the OFD% significantly increased at the fault terminations of the Mw 7.6 and 7.8 ruptures, respectively, which is highly consistent with previous findings4,5,13,15 (Fig. 6). Fault terminations often give rise to complex rupture structures (e.g., wing cracks, splaying, horsetailing, antithetic shear fracture), which promotes distributed fault deformation and influences rupture propagation2,3,6,34. Similarly, (i) in the Islahiye REB, the OFD% reached up to 43% but decreased to 13% on the adjacent strand with a simpler geometry (Fig. 7b); (ii) the fault deformation in the Türkoğlu REB becomes more distributed than adjacent geometrical simple strands S50–S65 km and S19–S24 km, respectively (Fig. 7c). These results are compatible with the previous findings, showing that fault segments with sampler geometries are more favorable for deformation localization.

Fig. 7: Geometrical complexity and sediment facilitating OFD%.
Fig. 7: Geometrical complexity and sediment facilitating OFD%.The alternative text for this image may have been generated using AI.
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a Surface distribution of OFD% along strand N3–N43 km with simple geometry. b, c Variation of OFD% at geometrically complex segment and adjacent geometrically simple segment along the strand S74–S95 km and S19–S65 km. d, e Along-strike distribution of OFD% and deformation-zone width near the Mw 7.6 epicenter (W17–E18 km). f, g Variation of OFD% through bedrock (W8–W17 km) and sedimentary terrain (E6–E11 km).

In addition, the increased OFD% in the Islahiye and Türkoğlu REBs enough to demonstrate that OFD behavior is the dominant style of fault deformation in structurally complex fault strands. Despite direct observations of OFD were unavailable in other complex strands-like Demrek RSS, Gölbaşı RES, Nurhak FC, and fault splays, we deduced that distributed deformation within a wider zone is a predominated style (Figs. 4c, 5c). The across-fault displacement profiles illustrate the high distributed deformation patterns at Nurhak FC along the Mw 7.6 rupture (Fig. 3d) and fault splay along the Mw 7.8 rupture (Fig. 3e), thereby validating the rationality of our deduction. Notably, fault geometric complexity also manifests in variations in depth, such as depth-varying fault dipping angles and directions, which can result in variation of OFD and width. For example, the fault flattening upon reaching the free surface promotes extension in the hanging wall observed in the 2013 Balochistan earthquake, and in turn generated the distributed set of surface tensile cracks to accommodate OFD35. However, due to lack of depth-varying comprehensive constraints, we emphasized that in our studies, we only considered controls of surficial fault geometrical complexity on OFD, excluding any depth-varying complexity.

As mentioned above, the presence of high OFD, particularly in areas with complex fault geometry, can be seen as a mechanism for accommodating the imposed strain. This suggests that the fault cores in these regions have not fully developed to accommodate high coseismic strain, necessitating that the surrounding damage zones absorb a portion of strain to facilitate rupture propagation4,5,6 (Fig. 1a–e). In the context of long-term strain accommodation and multiple earthquake ruptures, these geometrically complex regions of the EAFZ gradually form specially developed fault cores (similar to the present geometrically simple fault strands), with gradually decreased fault OFD. Furthermore, on geological timescales, these geometrically complex regions may experience enhanced strain localization, eventually leading to the extinction of the complexity and the development of a more thoroughly connected and homogenized fault system along the EAFZ. This feedback between fault geometry and OFD offers valuable insights into the long-term structural evolution and strain release of the EAFZ.

Facilitation of coseismic rupture speed on OFD

Stress concentrations at a propagating rupture tip are believed to narrow as the rupture velocity increases towards the limiting Rayleigh wave velocity36,37,38,39. For example, as an earthquake goes to supershear ruptures, it manifests Mach fronts that produce considerable ground motion at distances far from the fault and more localized rupture within the coseismic damage zone40,41,42. Rupture speed also governs the spatial extent of off-fault damage zone, due to a Lorentz-like contraction of the spatial extent of stress field around a rupture tip36,37,39,43,44,45. For instance, fracture mechanics numerical models revealed that the location of the transition from subshear to supershear speed is characterized by a decrease in the width of the coseismic off-fault damage zone39. Such signature was validated with optical satellite geodesy observations of fault zone width, together with early aftershock distributions in the 2001 Mw 7.8 Kunlun (China) earthquake. The theoretical consideration is that variations in rupture speed influence fault OFD, with at least distinct differences in OFD between fault segments propagating in subshear and supershear domains. Interestingly, our observations revealed the segmented variation of OFD% is correlated with the segmented change of rupture speed in the earthquake doublet. For the Mw 7.8 primary rupture, the rupture speed was determined to be 2.0–3.5 km/s in the southern rupture and 4.0–4.5 km/s in the northern rupture, with corresponding OFD% estimate of 23% and 15%, respectively (Fig. 6a). Likewise, for the Mw 7.6 primary rupture, the OFD increases as the rupture speed decreases: from 11% at 4.0–4.5 km/s along the western rupture to 25% at 3.0–3.5 km/s along the eastern rupture (Fig. 6c). However, we noticed, except for the speed change at the strands W8–W17 km (speed of 4.0–4.5 km/s) and E6–E10 km (speed of 3.0–3.5 km/s), the former propagates through the bedrock terrain, with OFD% estimate of 8% (Fig. 7d–f); conversely, the later propagates through the soil in farmlands that are classified as unconsolidated sediment terrain, with estimate of 28% (Fig. 7d, e, g).

Compared to bedrock terrain, surficial unconsolidated sediments generally exhibit lower stiffness and frictional slip between particles2. The properties allow them to absorb and disperse coseismic stress, thereby promoting distributed strain and accommodating more fault deformation as off-fault deformation5,46,47,48,49. Considering that the rupture speed difference of the two strands is unlikely not the only factor that contributes to OFD% reduction of 20%. Therefore, we believe that the substantial increase in OFD% can be partially attributed to the presence of surficial unconsolidated sediments. Interestingly, this notion of rupture velocity facilitating OFD finds additional supports in observations from various natural earthquakes16,50 (Fig. 8a): the 2018 Palu (an average of 20% OFD at 4.1–4.3 km/s51,52), 2013 Balochistan (28% OFD at 3.0–4.0 km/s6,53), 1992 Landers (46 ± 10% OFD at 2.5–2.9 km/s5,54), 2016 Norcia earthquake (50% OFD at 2.0–3.2 km/s55,56), and 2018 Hualien earthquake (60% OFD at 1.94 km/s57,58). The fault OFD and rupture speed of these earthquakes define a clear negative correlation together, with a Pearson correlation coefficient (PCC) of −0.63, which indicates that fault OFD is negatively influenced by rupture speed (Fig. 8a). Besides the strand S9–S65 km, the strands that ruptured at subshear speed of 3.0–3.5 km/s (eastern rupture of the Mw 7.6 event, and S74–S140 km) is higher OFD compared to those that ruptured at supershear speed of 4.0–4.5 km/s (western rupture of the Mw 7.6 event, as well as N3–N34 km and N49–N98 km), completely consistent with theoretical understanding and numerical simulation results36,37,39,43,44,45 (Figs. 6, 8a). Thus, theoretical considerations and our results indicate that faster rupture speed encourages coseismic deformation to localize on the primary fault plane, thereby leaving a minor amount available for the generation of OFD during the dynamic rupture process.

Fig. 8: Correlations between rupture velocity, cumulative fault offset and OFD%.
Fig. 8: Correlations between rupture velocity, cumulative fault offset and OFD%.The alternative text for this image may have been generated using AI.
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a Linear relationship between OFD% and rupture velocity during multiple earthquakes, showing lower OFD% with faster rupture velocity. b Linear relationship between OFD% and cumulative fault displacement, showing lower OFD% with increasing cumulative fault displacement (higher structural maturity). PCC (Pearson correlation coefficient) can evaluate the strength and direction of the linear relationship between two variables.

Limited influence of fault maturity on segmented variation of OFD

With the cumulation of fault displacement, the fault geometry evolves or ‘matures’ from a network of disconnected and disorganized segments to a structurally simplified, continuous geometry, with strain progressively localizing on the fault core34,59,60,61,62,63,64. Consequently, OFD is expected to decrease with increasing fault structural maturity5,6,10,15,16,58,65,66. Fault deformation along relatively immature strike-slip faults often tend to produce a larger OFD%, averaging between 28% and 64% for events like the Landers (3.5 km of cumulative fault offset), Hector Mine (3.4 km), Kumamoto (0.8–1.4 km), and Ridgecrest (0.25–0.6 km and 1.6 km) earthquakes (Fig. 8b). In contrast, the main and northern strands of the EAFZ, i.e., the causative faults of the earthquake doublet, were determined to be ~19–26 km and ~11 km cumulative displacements, suggesting that they are more mature fault systems than the causative faults of these earthquakes above19 (Fig. 8b). As expected, the Mw 7.8 and Mw 7.6 ruptures accommodated OFD% of 20% and 17%, respectively, lower than those of other strike-slip earthquakes (Figs. 7, 8b). A well-defined correlation between OFD% and fault structural maturity is revealed from multiple earthquake ruptures, where OFD% is inversely correlated with fault structural maturity (PCC = −0.61; Fig. 8b). However, our results, in agreement with previous observations26, both suggest that the average OFD% of the Mw 7.8 rupture was larger than the Mw 7.6 rupture, contradicting the aforementioned correlation (Fig. 6). Actually, compared to the Mw 7.6 rupture, the Mw 7.8 rupture propagated at a relatively slow rupture speed through more sediment terrains and more geometrically complex segments which involve longer, structurally complicated, poorly linked fault segments19,26,67 (Figs. 3, 4, 5). These scenarios are not conductive to fault strain localization, thereby resulting in more distributed fault deformation. The result contrasts with previous view that those earthquakes rupturing on more mature fault segments generate more localized on-fault deformation; instead, during the earthquake doublet, fault geometrical complexity and rupture speed can exert a more important control than fault maturity on first-order variation of off-fault deformation. Our results also highlight that fault maturity typically controls extent of OFD, but has a limited influence on first-order variation of OFD.

Conclusions

Our high-resolution satellite optical geodesy observations revealed that the Mw 7.8 and 7.6 earthquakes generated 20% and 17% off-fault deformation, respectively. Such fault behavior and complex deformation patterns were not captured by fault kinematic models or geological observations. We found that the variation in OFD during the earthquake doublet was primarily controlled by fault geometrical complexity and segmented changes in rupture speed. More significantly, multiple natural earthquakes collectively confirm that fault OFD is negatively correlated with rupture speed, which aligns closely with numerical simulation results and theoretical understandings. In addition, our observations showed that factors previously thought to influence fault OFD-such as unconsolidated sediments and fault maturity-played a limited role in the earthquake doublet.

Methods

Measuring on-fault displacement

Based on field measurements and drone mapping after the earthquake doublet, a total of 170 horizontal displacements were collected to characterize the fault surface slip of the earthquake doublet27,28,29 (Fig. 2). Since these slips were reported by three studies (Meng et al.57; Karabacak et al.28; Softa et al.29), some fault slips at the same location were measured repeatedly. We calculated the average of the repeated measurements to represent the fault slip at that location. While these displacements provide insights into the displaced slips localized on the primary faults, i.e., on-fault displacement, they lack sufficient detail, particularly along the Mw 7.6 rupture. More detailed on-fault displacement is required to obtain the along-strike variation of on-fault displacement distribution associated with the earthquake doublet. To characterize the displacement localized on the primary fault, we further collected the optical images with a high spatial resolution of 0.8 m acquired from the Gaofen-7 satellite before and after the earthquake doublet. These high-quality pre- and post-event Gaofen-7 images cover the surface rupture of the earthquake doublet, with lower cloud coverage. We implemented a standard optical satellite image pre-processing chain in the PIE-Engine platform (Pixel Information Expert Engine)68. These images, including panchromatic and multispectral bands, are orthorectified using the satellite ancillary information that includes the exterior orientation (i.e., look angle, attitude, and satellite position) and a 12.5-m pre-earthquake ALOS (Advanced Land Observing Satellite) DEM to correct for topographic distortions69. Furthermore, to identify displaced surface markers later used to measure on-fault displacement, we fused panchromatic and multispectral orthorectified images, resulting in 1.0-m-resolution pre- and post-earthquake fusion images (Fig. 2a). For accurate co-registration of the displaced surface markers, we selected the pre-event orthorectified images as a reference and co-registered the post-earthquake images. In addition, to enhance our dataset, we also collected some orthorectified post-earthquake images from Google Earth, with a high spatial resolution of 0.5 m (Fig. 2a).

After obtaining the pre- and post-event images, we initially mapped the primary surface ruptures, and secondary ruptures and fractures, which enabled us to accurately quantify the small coseismic fault slip. By comparing the pre- and post-event images, we identified the surface rupture passes through the linear cultural markers (e.g., field borders and ridges, fences, roads, and railways, grass and tree rows, and channels), and verified the continuity and geometry of these features using the pre-earthquake images (Fig. 2b; Supplementary Figs. S1, S2). These displaced features in the post-seismic scenes were digitized at the maximum possible resolution and projected the features into the fault, thus allowing us to measure displacements reflect lateral (fault parallel) displacement only. The projection of the feature into the fault zone is estimated using its orientation over a range of distances (5–30 m) from the fault with consideration of the feature’s orientation on both sides of the fault6. The Mw 7.8 rupture passed through residential areas, where farmlands and roads recorded significant on-fault displacements; conversely, the Mw 7.6 rupture occurred in mountainous areas, particularly along the western fault segment, resulting in few measurable displaced surface markers. This leads to the limited measurement of the on-fault displacement from field geological observations29. Interestingly, we tracked many on-fault displacements through displaced grass and tree rows, which are often challenging to measure in the field due to a lack of pre-earthquake comparison (Supplementary Fig. S2). Note that the on-fault slip data is not available in areas lacking cultural markers and displaced geomorphic features, or where the scale of the on-fault slip is below our image resolution (~1.0 m).

Measuring total fault displacement

The sub-pixel image correlation technique, widely used to reconstruct horizontal displacements from pre- and post-earthquake satellite images, provides unique insights into fine deformations occurring within several tens to hundreds of meters around the primary fault plane4,15,30,31. To retrieve horizontal displacements later used for measuring fault total displacement, we employed the sub-pixel image correlation technique on multiple Sentinel-2 optical images (pixel size = 10 m). Initially, we collected 8 Sentinel-2 orthoimages covering the surface ruptures related to the earthquake doublets through the Google Earth Engine platform70 (Supplementary Table S1). These images, acquired during the same or similar season and with minimal cloud, snow, and ice coverage (<5%), were specifically chosen to minimize decorrelation and potential correlation noises arising from landscape features. Among these, 4 and 4 images were captured before and after the earthquake doublet, respectively. The pre- and post-event image correlation was implemented using the MicMac software, with consistent settings applied to detect surface displacements. This includes a sliding window of 3 × 3 pixels, a step of one pixel, and a regularization term of 0.3, resulting in east-west (EW) and north-south (NS) correlation maps with 10 m pixel resolution32,33 (Supplementary Figs. S3, S4). These correlation maps unveil the EW and NS components of horizontal motion induced by the earthquake ruptures, respectively.

In addition, we observed some systematic correlation errors (resulting from translation and rotation between input images) and stripe artifacts (originating from the orbital uncertainty) in our raw displacement field (Supplementary Figs. S3, S4). To reduce the false detection of fault displacement, we employed the de-ramping and de-striping corrections to remove the systematic errors71 (Supplementary Figs. S5, S6). After applying the aforementioned corrections, however, it is quite often that there are still residual errors in the data. The remaining errors, together with unknown image distortions, and random image noises derived from thermomechanical and electronic effects, could still contaminate the displacement signals31. In the pre- and post-event images, the presence of illumination intensity changes (e.g., low contrast, blurring, and different positions of light source), apparent movement caused by specular reflectance features, and strong soil surface state changes can also amplify the correlated noises. To address these issues, we applied a stacking denoising method to nine EW and NS displacement fields from multiple-pairwise Sentinel-2 image correlation, respectively51,72, as illustrated in Figs. S5 and S6. This stacking denoising method further removed the remaining correlation noises, resulting in cleaner displacement fields. Consequently, our high-quality EW and NS displacement fields can reveal the detailed surface motions and damage-zone deformations induced by the earthquake doublet (Fig. 3; Supplementary Fig. S7).

Following fine reconstruction of the coseismic displacement fields related to the earthquake doublet, we utilized across-fault profiles oriented perpendicular to the fault rupture strike to meticulously quantify the total fault deformation encompassed within the coseismic damage zone. Considering the geometrically structural complexities of the coseismic ruptures, we carefully delineated detailed traces of the main faults and branches from the coseismic displacement fields (Fig. 3a, b). These ruptures were then systematically divided into a total of 1884 profiles, each characterized by a distinct local strike angle and an along-strike length of 200 m. The perpendicular length of all displacement profiles, set at 4000 m, was designed to traverse the entire deformation zone, encompassing both on-fault displacement localized on the primary fault and any off-fault deformation distributed within the surrounding deformation zone. The EW and NS displacements were extracted separately using the across-fault profiles, and each was subsequently projected onto fault-parallel and fault-perpendicular directions using corresponding local fault strikes (Fig. 3c). The total fault displacements of each coseismic damage zone were calculated from each fault-parallel displacement profile using a pixel template alignment stacking method15 (Fig. 3c). Error estimates represent the standard deviation (one-sigma) calculated from a trend that visually best fits the displacement on each side of the fault. The deformation-zone widths are defined as the fault-perpendicular extent of detectable pixel motion on either side of the earthquake fault zone. Besides from calculating total fault displacement, the fitting line in the same stacked profiles serves as a reference to stably identify inflection points that mark the boundaries of the fault zone (Fig. 3c–e), after which we manually measured the width of each profile individually. In addition, in structurally complex fault segments, such as fault splays and stepovers, the total fault displacement and width of the damage zone (Fig. 3d, e) were determined to include slip on both primary and secondary faults, as well as highly distributed deformation between them, thereby resulting in a kilometers-scale-width deformation zone.

Quantifying OFD and OFD%

As mentioned above, OFD consists of distributed fracturing and diffuse deformation of the bulk volume, occurring over scales of hundreds of meters to kilometers around the primary faults4,5. Unlike localized, on-fault displacement, quantifying OFD is often challenging due to the absence of macroscopically visible surface deformation indicators, potentially biasing estimates of the earthquake displacement budget. OFD is commonly quantified relative to the total and on-fault displacements as follows5,6: OFD [m] = total displacement [m] – on-fault displacement [m]. In addition, OFD is expressed as a percentage of deformation that occurs off the main fault, donated as OFD%: OFD% = (OFD [m]/total displacement [m]) × 100%. The physical significance of the OFD% represents the relative magnitude and amount of the deformation accommodated within the damage zone compared to what is localized on the discrete primary fault plane. To unveil off-fault deformation along the earthquake doublet, we conducted a direct calculation of OFD at those locations where both the on-fault slip (Fig. 2c, e) and the total fault displacement (Figs. 4a, 5a) were available, excluding those where the on-fault slips were unavailable (Supplementary Fig. S8). Although the total slip is measured from a spatial-filed profile with a width of 200 m while the on-fault slip is measured from point-field geomorphic features, the point-to-point calculation introduces some biases in OFD but is unlikely to significantly influence its first-order distribution pattern (Supplementary Fig. S10).