# Coseismic Shallow Slip Deficit Accounted for by Diffuse Off-Fault Deformation

Solène L. Antoine, Yann Klinger, Kang Wang, Roland Bürgmann

► To cite this version:

Solène L. Antoine, Yann Klinger, Kang Wang, Roland Bürgmann. Coseismic Shallow Slip Deficit Accounted for by Diffuse Off-Fault Deformation. Geophysical Research Letters, 2024, 51, pp.2024GL110798. 10.1029/2024GL110798 . insu-05081547

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# Geophysical Research Letters®

## RESEARCH LETTER

10.1029/2024GL110798

**Key Points:**

* Refined slip model for the 2019 Ridgecrest earthquake sequence from the inversion of InSAR, optical, and GNSS data

* Shallow slip deficit is partially accounted for by diffuse deformation which likely involves bulk elastoplastic yielding

* A compilation of published data on strike-slip earthquakes highlights possible controlling parameters of the SSD and diffuse deformation

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

S. Antoine,
solene.antoine@hotmail.fr

**Citation:**

Antoine, S. L., Klinger, Y., Wang, K., & Bürgmann, R. (2024). Coseismic shallow slip deficit accounted for by diffuse off-fault deformation. *Geophysical Research Letters*, *51*, e2024GL110798. https://doi.org/10.1029/2024GL110798

Received 24 JUN 2024

Accepted 12 OCT 2024

© 2024. The Author(s).
This is an open access article under the
terms of the Creative Commons
Attribution License, which permits use,
distribution and reproduction in any
medium, provided the original work is
properly cited.

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## Coseismic Shallow Slip Deficit Accounted for by Diffuse Off-Fault Deformation

Solène L. Antoine¹,² ID, Yann Klinger¹ ID, Kang Wang³,⁴, and Roland Bürgmann³ ID

¹Université de Paris Cité, Institut de Physique Du Globe de Paris, CNRS, Paris, France, ²Now at Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA, USA, ³Department of Earth and Planetary Science, University of California, Berkeley, CA, USA, ⁴Now at EarthScope Consortium Inc., Socorro, NM, USA

**Abstract** Earthquake ruptures produce fault slip and kilometer-wide diffuse deformation of the host rocks. However, the origin of the diffuse deformation and its role in the rupture process are debated. We produce a refined slip model for the 2019 Ridgecrest, California, earthquakes, and analyze the relations between down-dip rupture process, and surface diffuse deformation. We show that the decrease in coseismic slip toward the ground surface, also known as shallow slip deficit (SSD), correlates with the occurrence of diffuse deformation at the surface, which is not accounted for by models assuming elastic host rocks. Hence, we suggest that a significant part of the SSD in earthquake source models could be interpreted as a proxy for shallow diffuse inelastic deformation around faults. Revisiting earthquake source models for 28 continental earthquakes, we discuss the controlling parameters of the SSD and diffuse deformation, and propose a conceptual model of the near-field coseismic surface deformation.

**Plain Language Summary** Earthquakes can rupture up to the ground surface, generating displacements along faults and fractures that are visible in the field. This surface deformation can also be accompanied by diffuse deformation that occurs at a wider, >0.5 km, scale around the faults, and is imperceptible from a field perspective. Here, we use numerical modeling combined with detailed surface observations for the 2019 Ridgecrest, California, earthquakes to show that reduction in fault slip near the surface correlates with the occurrence diffuse deformation at the surface. Therefore, the reduction in shallow slip suggested in earthquake rupture models could be interpreted as a proxy for non-elastic diffuse deformation around the faults. Compiling data for worldwide earthquake ruptures, we show that this process occurs similarly for other events, and we analyze the controlling parameters.

### 1. Introduction

In numerical models, earthquake ruptures are most often approximated as fault slip occurring on one or several 2D or 3D planar faults embedded in an elastic half-space, possibly layered (Ragon & Simons, 2020). However, the increasing number of high-resolution observations for earthquake ruptures begs for a change of paradigm: Instead of considering only the well-documented localized fault slip, one should also consider that a significant part of the near-surface deformation could be accommodated through bulk elastoplastic deformation (Kaneko & Fialko, 2011; Mia et al., 2023; Nevitt et al., 2020; Roten et al., 2017). Bulk elasto-plastic deformation can be inferred from surface observations of off-fault fracturing (Rodríguez Padilla et al., 2022) and/or km-wide continuous gradients of off-fault displacement (Fialko et al., 2005), also sometimes referred to as diffuse deformation (Antoine et al., 2021, 2022; Provost et al., 2024). Because the diffuse deformation occurs at an intermediate scale between the localized fault slip and the large-scale elastic deformation (0.5–2 km; Antoine et al., 2022, 2021; Provost et al., 2024), it is generally poorly documented using common observational methods such as field, GNSS and InSAR. Therefore, the mechanisms involved in the diffuse deformation, including the relative elastic and/or plastic contributions, are poorly constrained.

In fact, due to limited spatial coverage and loss of coherence close to the faults, GNSS and InSAR data are, for most cases, not able to image the coseismic deformation in first ~1 km around the ground ruptures (e.g., Tung et al., 2021; Yue et al., 2021). When inverting for coseismic slip at depth, limited constraints on the surface fault displacements added to intrinsic simplifications embedded in the elastic modeling assumptions together lead to large uncertainties on the shallow parts of rupture models (Marchandon et al., 2021; Ragon & Simons, 2020; Xu et al., 2016). Consequently, the inference that coseismic slip in the models often decreases toward the surface (in
upper 3–4 km), referred to as the shallow slip deficit (SSD; Fialko et al., 2005), remains debated. Considering the SSD as a true feature of the rupture process, and not a modeling artifact, implies that either the missing slip is accommodated by creep on the fault during the postseismic or interseismic phases (Milliner et al., 2020; L. Wang et al., 2014), or that slip is accommodated away from the faults through diffuse deformation (Antoine et al., 2021; Fialko et al., 2005; Simons et al., 2002; Zhao et al., 2023). However, observations show that postseismic slip or interseismic creep at the surface is, for most earthquakes, not large enough to balance the SSD resulting from models (Brooks et al., 2017; Fialko et al., 2005; Pousse-Beltran et al., 2020; K. Wang and Bürgmann, 2020), hence calling for diffuse deformation around the faults. Therefore, determining how much deformation occurs in the shallow crust during an earthquake compared to deformation at depth, and through which mechanisms, is an outstanding problem to understanding the earthquake rupture process.

Here, taking advantage of the exceptional dataset available for the 2019 Ridgecrest earthquake sequence (i.e., Antoine et al., 2021; DuRoss et al., 2020; Ross et al., 2019; K. Wang et al., 2020), we assess the possibility that diffuse deformation accounts for the SSD arising in kinematic slip models. The Ridgecrest ruptures present, on average, 33% of surface displacement in the form of diffuse deformation at the surface (Figure 1a; Antoine et al., 2021), and a possible SSD ranging between 2% and 45% depending on the models which are considered (Jin & Fialko, 2020; K. Wang et al., 2020). Because of the large variety of rupture models that exist for this earthquake sequence (i.e., Jin & Fialko, 2020; Liu et al., 2019; Magen et al., 2020; Milliner and Donnellan, 2020; Ross et al., 2019; Tung et al., 2021; K. Wang et al., 2020; Yue et al., 2021), and given the uncertainties affecting the models' shallower part, we could not directly compare the surface observations with the SSD found in existing rupture models. Hence, we invert for the source parameters of the 2019 Ridgecrest earthquakes using GNSS, InSAR, and fault offsets derived from optical image correlation (OIC) on a complex-geometry fault model. Incorporating the surface slip measurements at the faults, and especially those derived from optical data with centimeter-level uncertainty and homogeneous sampling, imposes a strong constraint on the shallow slip distribution, and allows us to build a high-resolution slip model of the earthquake sequence with well-quantified SSD estimates for both the $M_w$6.4 foreshock and the $M_w$7.1 mainshock events. The output of this model is then compared to direct measurement of off-fault surface deformation to analyze the relation between diffuse deformation and the SSD derived from our model.

## 2. Modeling of the Foreshock and Mainshock Ruptures

We use fault displacement discontinuities, referred to as offsets, extracted from high-resolution (0.5 m) optical image displacement maps (Antoine et al., 2021, 2024b) to constrain slip at the surface of the rupture model for the 2019 Ridgecrest earthquake sequence (Text S1 in Supporting Information S1). These offset data present homogeneous sampling and centimeter-scale uncertainties across the study area, and hence, provide a strong constraint on fault slip near the surface. To limit epistemic uncertainties associated with the distributed near-fault inelastic deformation that cannot be reproduced by elastic modeling, we use only the fault offsets, and not the entire displacement field from OIC. Thus, the difference between the elastic model prediction and the data is likely to reflect the near-fault inelastic deformation. We complement this dataset with GNSS and InSAR data that better constrain the slip distribution at depth (K. Wang et al., 2020; Text S1 in Supporting Information S1). Datasets include both the foreshock and the mainshock events and some postseismic deformation (Text S1 in Supporting Information S1), and are inverted together to produce the slip model. The along-strike model geometry (Figure 1b and Figure S1 in Supporting Information S1, and Text S2 in Supporting Information S1) is defined by the trace of the well-documented ground ruptures (Antoine et al., 2021; DuRoss et al., 2020). The along-dip model geometry is considered vertical, although seismic data suggest slight variations in fault geometry at depth (Jin & Fialko, 2020; Plesch et al., 2020; Ross et al., 2019). Meshing is done such that the surface of the fault model has similar resolution as the near-fault displacement data (~0.5 km; see Text S1 in Supporting Information S1). It is the high-spatial resolution in the fault model and the displacement data that allows for retrieving the complex and high-amplitude variations in the shallow slip distribution, and therefore to refine the SSD estimate. The joint inversion is performed in a homogeneous elastic half-space, with the Green's functions calculated for each dataset (Text S3 in Supporting Information S1). The data are combined using weight matrices that reflect the data uncertainty, either uniformly in the case of InSAR and offsets data, or for each data point in the case of GNSS. Different data weights (Figure S2 in Supporting Information S1) and regularization values (Figures S3 and S4 in Supporting Information S1) are tested. To minimize the influence of the model regularization on the amplitude of shallow slip (Causse et al., 2010; Ortega-Culaciati et al., 2021), and hence on the SSD,
<figure><img src="image_3.png" /><figcaption>**Figure 1.** (a) Surface right-lateral displacement along the mainshock rupture. Black line and gray area are, respectively, the total surface displacement, and the diffuse deformation (Antoine et al., 2021). Red, green and blue crosses are the surface offset on faults F1, F2 and F3, respectively, measured using 500 m wide across-fault displacement profiles in the optical maps of Antoine et al. (2021). (b) Map view of the mainshock fault model (Figure S1 in Supporting Information S1). Segments S1-S3 correspond to the mainshock rupture. Segment S4 corresponds to the foreshock rupture. (c) Mainshock slip (m) model in the fault-parallel component (Figures S5 and S6 in Supporting Information S1). Blue star is the mainshock epicenter. (d) Average slip versus depth profile for the foreshock (pink), the mainshock (black), and the three segments of the mainshock slip model (S1 in dark blue, S2 in red, and S3 in green). Average surface slip from optical data is indicated for each segment using the markers of the corresponding color (Table S1 in Supporting Information S1, and Text S8 in Supporting Information S1). Diffuse deformation is not predicted by the model.</figcaption></figure>

we opted for a low degree of regularization in our model (Figures S3 and S4 in Supporting Information S1, and Text S4 in Supporting Information S1). We chose the model (Figure 1c, Figure S5 and S6, and Text S5 in Supporting Information S1; Antoine et al., 2024c) that best balances the fit to the different datasets (Figures S7–S10 in Supporting Information S1, and Text S6 in Supporting Information S1). This model, including the down-dip slip distribution, is stable against variations in the down-dip fault geometry (Figure S11 in Supporting Information S1, and Text S7 in Supporting Information S1).

The preferred model (Figure 1c, Figures S5 and S6 in Supporting Information S1) presents maximum slip between 3 and 6 km depth close to the mainshock epicenter (cumulative contribution of F1 and F2; Figures S5 and S6 in Supporting Information S1), and a SSD that varies from ~0% (e.g., km 17.5 to 18.5) to ~100% (e.g., 0 to 9 km) along the rupture strike. Here, we assume that the mainshock event occurred on NW-SE-trending faults, and the foreshock event occurred on SW-NE-trending faults (Milliner & Donnellan, 2020; Ross et al., 2019). Comparing the peak average slip at depth to the average surface slip measured in optical data, we obtain an average SSD of 56% for the foreshock, and 33% for the mainshock (Figure 2b). Previous studies focused on resolving the SSD showed that modeling assumptions and lack of data close to the faults could lead to an artificial SSD of 5%–25% (Marchandon et al., 2021; Ragon & Simons, 2020; Xu et al., 2016). The values of SSD that result from our inversion are above this uncertainty range. Thus, the SSD observed in our model should, at least in part, represent an actual decrease of localized fault slip at shallow depth that is accompanied by other deformation processes in the shallow crust. The only exception is S2 for which we measure an average SSD of –8%, value which falls into the ±5%–25% range of potentially artificial SSD due to modeling bias (Marchandon et al., 2021; Ragon & Simons, 2020; Xu et al., 2016). Apart from this segment S2, we suggest that substantial inelastic
<figure><img src="image_4.png" /><figcaption>**Figure 2.** (a) Modeled peak average slip at depth ($\bar{s}_{max}$; Table S2 in Supporting Information S1, and Text S9 in Supporting Information S1) versus average total surface displacement from optical imagery data ($\bar{D}$ (m), including the diffuse deformation; Table S1 in Supporting Information S1). Mainshock includes segments S1, S2, and S3. Segment S1 is not included in the linear regression $x = y$. Color scale is the average surface slip along each segment from optical data ($\bar{s}_{surface}$; Table S1 in Supporting Information S1). (b) Comparison between average down-dip slip distribution from the model (solid lines; Figure 1d), and surface displacement data. The dotted lines interpolate the displacement profiles in regions where we suppose diffuse deformation accommodates deformation. (c) Average percentages of SSD (Table S2 in Supporting Information S1) versus diffuse deformation ($\bar{d}$; Table S1 in Supporting Information S1), with added points for the 2021 Maduo, and the 2013 Baluchistan earthquakes (Antoine et al., 2022, 2024a; Lauer et al., 2020; Jin & Fialko, 2021; Vallage et al., 2015). Color scale for symbols is the same as in (a). (d) Simplified model of fault zone deformation including the area of surface fracturing (~10–100 m wide), and the ~2 km-wide diffuse deformation zone.</figcaption></figure>

yielding of the off-fault medium through diffuse deformation should account for the large SSD inferred in the kinematic model, as evidenced by geodetic studies (Antoine et al., 2021, 2022; Fialko et al., 2005; Li et al., 2022; Zhao et al., 2023) and suggested by forward rupture modeling (Cappa et al., 2014; Dalguer et al., 2003; Kaneko & Fialko, 2011; Mia et al., 2023; Roten et al., 2017; Taufiqurrahman et al., 2023).

### 3. Comparison Between Shallow Slip Deficit, and Surface Diffuse Deformation

Total surface displacement measurements derived from the optical displacement maps (Antoine et al., 2021) are averaged along the length of the four rupture segments considered in our model (Table S1 in Supporting Information S1), and are compared with the slip distribution resulting from this model (Figure 2). We observe that, along most of the individual ruptured segments, the total measured surface displacement, including the localized and diffuse components, is comparable with the amplitude of the maximum average slip modeled along the fault
at depth (Figure 2a). In particular, there is a close agreement between the estimated average diffuse deformation and the amplitude of SSD along the mainshock rupture (Figures 2a and 2b). We also observe a correlation between the average percentages of SSD and diffuse deformation, especially along the mainshock rupture (Figures S1–S4 in Supporting Information S1; Figure 2c). Estimations of SSD and diffuse deformation for case studies, including the 2013 Baluchistan (Antoine et al., 2022; Lauer et al., 2020; Vallage et al., 2015) and the 2021 Maduo (Antoine et al., 2024a; Jin & Fialko, 2021) earthquakes also support the observed correlation between SSD and diffuse deformation (Figure 2c). Hence, from an observational perspective, once we consider diffuse deformation away from the primary surface ruptures there is no significant SSD for this event. This suggests that the SSD mostly reflects the inability of elastic earthquake source models relying on discrete dislocations to account for the diffuse component of the shallow deformation.

This observation, however, does not apply to segment S1 of the mainshock rupture for which peak average slip at depth is much larger than the average total surface displacement (Figure 2a). In this case, surface displacements are likely under-estimated since slip on multiple small left-lateral cross faults is not included in the right-lateral coseismic slip budget (Antoine et al., 2021). It is also possible that the surface diffuse deformation includes a component of block rotation within the northwest portion of the mainshock rupture that involves densely spaced northeast-striking “bookshelf” faulting (Milliner et al., 2021), which is then partially reproduced by the elastic modeling. The correlation between SSD and diffuse deformation does not apply either to the case of the foreshock rupture, where the diffuse deformation only accounts for 36% of the inferred SSD. This observation suggests that the foreshock event ruptured only partially to the surface, in agreement with its smaller magnitude, and that part of the modeled SSD actually represents a deficit in coseismic surface inelastic deformation.

As a consequence of the contribution of the diffuse deformation to the coseismic displacement budget along most of the foreshock and mainshock ruptures, the area affected by coseismic deformation should be considered wider than the width of the ruptures described in the field (Figure 2d; Perrin et al., 2021; Rodriguez Padilla et al., 2022). For the Ridgecrest mainshock, the average total surface deformation zone width is ~2 km (Antoine et al., 2021), including the diffuse deformation, while it only averages 69 m wide when considering solely the primary ruptures (Milliner and Donnellan, 2020). For the foreshock, the width of the total surface deformation zone is ~680 m, and only ~59 m considering only the ruptures. Based on the down-dip slip distribution derived from our model, the diffuse deformation zone likely starts at depth where the SSD initiates, so about 4 km (Figures 1d and 2c). The diffuse deformation zone likely widens upwards as slip on the primary faults decreases (Figure 2d), as suggested by dynamic rupture models (Kaneko & Fialko, 2011; Roten et al., 2017; Taufiqurrahman et al., 2023). Such a wide deformation zone is also consistent with seismic observations that reveal a sub-surface Ridgecrest fault zone featuring a 1–2 km wide seismic low-velocity region (Qiu et al., 2021). This wide low-velocity zone includes an even slower inner core, averaging 300 m in width, that may correspond to the localized deformation region. It is also consistent with the width of the local aftershock zone along the Ridgecrest earthquake rupture (Rodriguez Padilla et al., 2022). Finally, kilometer-wide inelastic deformation zones were also evidenced along other earthquake ruptures (Li et al., 2022; Liu et al., 2003; Perrin et al., 2021; Provost et al., 2024) and fault zones (Powers & Jordan, 2010; Rodriguez Padilla & Oskin, 2023), suggesting that the wide diffuse deformation could be a common characteristic of continental strike-slip ruptures.

4. Nature of the Diffuse Deformation

Based on the observations of (a) the lack of shallow afterslip and creep (K. Wang and Bürgmann, 2020), and (b) the inability of the elastic model to reproduce the diffuse deformation (Figure S10 in Supporting Information S1), we proposed that the shallow diffuse deformation is dominantly permanent, and therefore an inelastic process. Similar arguments were raised by Fialko et al. (2005), Nevitt et al. (2020), and Scott et al. (2019) for the 2005 Bam, the 2016 Napa, and the 2016 Kumamoto earthquakes, respectively. In the case of the 2019 Ridgecrest mainshock rupture, residuals between the elastic model prediction and the near-fault surface displacement maps present similar patterns and amplitudes as the diffuse deformation around the faults (Figure S10 in Supporting Information S1), supporting our interpretation. Models developed at a local scale along the bookshelf faulting region (NW of S1) of the mainshock Ridgecrest rupture also show that diffuse deformation cannot be fully reproduced using pure-elastic modeling (Milliner et al., 2021). Eventually, it is consistent with the seismic observations of a kilometer-wide low-velocity zone (Qiu et al., 2021) and the surface observations of distributed fractures (Adachi et al., 2023; DuRoss et al., 2020; Rodriguez Padilla et al., 2022; Xu et al., 2020), showing that inelastic deformation can be triggered at more than 1 km around the primary faults.
There exists no direct inference of the diffuse deformation in the field. However, small-scale diffuse deformation is commonly observed in laboratory experiments when rock samples are loaded through peak stress, including diffuse microfracturing that occurs for stresses approaching 80% of the failure stress (Lockner, 1998; McBeck et al., 2022). Through a similar process, also possibly including plastic deformation (Aben et al., 2017; Baud et al., 2021; Fossen et al., 2007; Micarelli et al., 2006), we suggest that upper crustal rocks would deform inelastically at distances one order of magnitude greater than what is generally inferred in the field from mapping fractures, which is a few meters to a few hundreds of meters off the primary faults (Mitchell & Faulkner, 2009; Rockwell et al., 2002; Savage & Brodsky, 2011). Physical formulations of this process that include brittle crack propagation (Bhat et al., 2012; Petit et al., 2024) and plastic deformation (Nicolas et al., 2017) are proposed in micromechanical models, and support our interpretation of the diffuse deformation mechanism.

The spatial correlation of the diffuse microfracturing with aftershock activity, however, remains unclear. Shelly (2020) documents shallow aftershocks at both rupture ends, including the bookshelf faulting area, and at the junctions between the mainshock and foreshock ruptures, and faults F1 and F3 (~37–38 km in Figures 1a–1c). Tsuchiyama et al. (2022) also document low-frequency aftershocks within the top 5 km of the crust, with the lowest-frequency events occurring in the top 1 km. These low-frequency aftershocks, however, do not show a clear spatial correlation with the diffuse deformation regions. This suggests that either seismic magnitudes associated with microcrack failures are too small to be detected or that the deformation is aseismic. In fact, aseismic deformations, including plastic processes, is favored at shallow crustal conditions (Lockner & Bee-ler, 2002; Nicolas et al., 2017). Moreover, whether the diffuse deformation occurred coseismically or during the postseismic phase (Brooks et al., 2017; Milliner et al., 2020) cannot be determined based the InSAR and optical data that do not have the necessary temporal resolution. Near-fault (±100 m) GNSS observations made just after the earthquake along a section where we measured ~0.5 m diffuse deformation report only a few centimeters of post-seismic deformation (Brooks et al., 2020), suggesting that diffuse deformation occurred either coseismically or within the first hours after the event.

Finally, in the case of the Ridgecrest foreshock, the diffuse deformation does not account for all the SSD observed in the model (Figure 2b). This suggests that the Ridgecrest foreshock ruptured only partially through the shallow crust. Similar type of events includes for example, the 2014 M<sub>w</sub>6.0 Napa earthquake, for which some SSD is still found after considering the diffuse part of the surface deformation as well as the early afterslip (Brooks et al., 2017). Hence, it is possible that high values of SSD associated with smaller events (M < 7, Figure 3a) may be simply due to a decrease in slip toward the rupture tips, as expected for partial ruptures that do not saturate the entire seismogenic layer. In this case, elastic energy that remains in the shallow crust could be released by shallow aseismic slip, especially in the case of known creeping faults (Bilham, 1989; L. Wang et al., 2014), or during future coseismic events (Thakur & Huang, 2021).

**5. Controlling Parameters of the SSD, and Diffuse Deformation**

Fault instability in the shallow crust is controlled by the stress change due to the downdip earthquake rupture, and the shallow fault strength (Ikari et al., 2011; King et al., 1994). The stress change depends upon parameters such as the amplitude of coseismic slip, the rupture speed, and their spatial and temporal variations (Bruhat et al., 2020; Fryer et al., 2022; Jara et al., 2021). The fault strength depends on the fault cohesion and friction, where the latter involves a static coefficient and an evolution law (Barbot, 2019; Kaneko et al., 2016). Fault strength is controlled by the lithology (Barbot, 2019; Ikari et al., 2011), the fault geometry and roughness (Fryer et al., 2022), and the fluid content (Baud et al., 2000; Noël et al., 2024). Together, all these parameters control the amount of shallow slip that can occur during a given earthquake, and thus the potential SSD and associated diffuse bulk yielding. However, there is no consensus on the dominant processes and parameters, primarily because of (a) the inherent complexity and diversity of earthquake ruptures due varying geologic, tectonic and seismic contexts, and (b) the uncertainties in observations and models. Here, we compile published rupture models for 28 continental dominantly strike-slip earthquakes including the 2019 Ridgecrest sequence (Figure 3, Table S3 in Supporting Information S1, and Text S10 in Supporting Information S1). All models use near-fault data in the inversion, or are validated against near-fault data if not directly included in the inversion. We evaluate the correlation of the SSD with (a) the earthquake magnitude as a proxy for the coseismic displacement and rupture width, (b) the depth of maximum slip, and (c) the fault cumulative displacement which reflects the structural maturity of the fault (Manighetti et al., 2021; Perrin et al., 2016). In this compilation, we consider only strike-slip events that produced inelastic ground surface deformation, highlighted by the presence of surface fractures. We exclude fully blind
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Evolution of SSD with (a) earthquake magnitude, (b) depth of peak average slip, and (c) fault cumulative displacement (Table S3 in Supporting Information S1; see Text S10 in Supporting Information S1 for detail on each event). One event can be represented by more than one point if different values or a range of values were selected from in the literature (see Table S3 in Supporting Information S1). (d) Conceptual model of fault zone surface deformation evolution with increasing SSD. Primary slip zones are in red, damage zones in orange, and the diffuse deformation zone in gray. Below are possible controlling parameters including, primarily, the coseismic slip amplitude and the earthquake magnitude, and secondary, the fault zone lithology, geometrical complexity and roughness.</figcaption></figure>

earthquakes that generate mainly elastic surface deformation and are well reproduced using elastic dislocation models. Fully blind ruptures on continental faults are more likely for events of magnitudes below ~$M_w$6-6.5, whose rupture width is often smaller than the thickness of the seismogenic crust (~10 km; Wells & Coppersmith, 1994). This compilation also excludes shallow small-magnitude ($M_w$ < 6) earthquakes that directly nucleate within the shallow crust (e.g., 2019 $M_w$4.9 Le Teil and 2021 $M_w$5.2 Baicheng earthquakes; Marconato et al., 2022; Di et al., 2023, respectively). The details of the analysis of the coseismic and postseismic surface displacements for each event of the compilation, including surface observations, rupture models, and derived SSD values, are described in Table S3 in Supporting Information S1 and Text S10 in Supporting Information S1.

The earthquake model compilation highlights an apparent correlation of the SSD with the earthquake magnitude (Figure 3a), a low correlation with the maximum slip centroid depth (Figure 3b), and no correlation with the fault maturity (Figure 3c). These results are consistent with previous results from Sethanant et al. (2023) who performed a similar SSD compilation including a greater number of events. More specifically, our results show that SSD decreases with increasing earthquake magnitude, with $a > 45\%$ SSD for $M_w \le 6.8$ events, and a 0%-45% SSD for $M_w > 6.8$ events. Starting from $M_w \ge 7.5$, majority of the reported events show a ~0% SSD which suggests that, for this magnitude, slip tends to saturate entirely the seismogenic crust from ~15 to 20 km depth up to the surface. This is consistent with the scaling laws of earthquakes, which imply larger displacement and rupture area for larger earthquakes (Kanamori & Brodsky, 2004; Wells & Coppersmith, 1994). Consequently, larger-magnitude events would tend to have larger surface slip and lower to no SSD. Other parameters such as the earthquake centroid depth (Figure 3b), the bulk rheology (Barbot et al., 2008), and the fault structural maturity (Figure 3c) would then have only secondary effects on the shallow slip distribution and the occurrence of SSD.
Based on the observation that the SSD can reflect shallow bulk yielding (Figure 2), we propose a conceptual model of evolution of the shallow fault zone deformation with the SSD per event (Figure 3d). This conceptual model is supported by existing field and geodetic observations, when available (Text S11 in Supporting Information S1). In this model, earthquakes that do not present any SSD would, at the surface, localize all the coseismic deformation along a primary fault offset and a few tens-to hundreds-meters-wide off-fault damage zone (Jara et al., 2021; Rockwell et al., 2002). This would usually occur for the largest events, of magnitude above ~7. Ruptures that present some SSD (~10%~60%) would present, at the surface, more discontinuous primary slip zones and lesser off-fault damage, both surrounded by regions of diffuse deformation (e.g., Antoine et al., 2021; Scott et al., 2018). Finally, for earthquakes that present a large SSD (~60%–100%), the surface deformation would dominantly consist of a wide and continuous diffuse deformation zone, and possibly some distributed cracks (e.g., Brooks et al., 2017; Koehler et al., 2021, Fialko et al., 2005). For such events, it is not excluded that the surface diffuse deformation includes an elastic component, and reflects partially inelastic and permanent deformation. This conceptual model highlights the complementarity between fault slip and bulk yielding such that the total amount of surface displacement is equal to the displacement occurring at depth. It does not mean that smaller earthquakes produce larger off-fault inelastic deformation than large ones since the net fault displacement differs by orders of magnitude. This model is complementary to those that describe the evolution of off-fault damage (Jara et al., 2021; Okubo et al., 2019), and should be modulated by the effects of fault geometrical complexity (Antoine et al., 2022; Klinger et al., 2018).

## Data Availability Statement

Static Global Navigation Satellite System (GNSS) coseismic displacements are available at http://sopac-csrc.ucsd.edu/index.php/ridgecrestjuly2019 (last accessed June 2024). InSAR coseismic displacement data used in this study are available at K. Wang and Bürgmann (2019) (last accessed June 2024; see also K. Wang & Bürgmann, 2020). High-resolution optical displacement maps are available at Antoine et al., 2024b (last accessed June 2024; see also Antoine et al., 2021). Fault offsets extracted from high-resolution optical image correlation results, and slip model derived are available at Antoine et al., 2024c (last accessed June 2024).

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## Acknowledgments

This work was partly supported by TOSCA CNES and the ANR-18-CE31-0012 projects. Yann Klinger was supported by the Miller Foundation at UC Berkeley during his visit at UC Berkeley. Roland Bürgmann and Kang Wang acknowledge support by the Southern California Earthquake Center (SCEC). This study contributed to the IdEx Université de Paris ANR-18-IDEX-0001.
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