Shallow Slow Slip Events in the Imperial Valley With Along‐Strike Propagation

Shallow creep events provide opportunities to understand the mechanical properties and behavior of faults. However, due to physical limitations observing creep events, the precise spatio‐temporal evolution of slip during creep events is not well understood. In 2023, the Superstition Hills and Imperial faults in California each experienced centimeter‐scale slip events that were captured in unprecedented detail by satellite radar, sub‐daily Global Navigation Satellite Systems, and creepmeters. In both cases, the slip propagated along the fault over 2–3 weeks. The Superstition Hills event propagated bilaterally away from its initiation point at average velocities of ∼9 km/day, but propagation velocities were locally much higher. The ruptures were consistent with slip from tens of meters to ∼2 km depths. These slowly propagating events reveal that the shallow crust of the Imperial Valley does not obey purely velocity‐strengthening or velocity‐weakening rate‐and‐state friction, but instead requires the consideration of fault heterogeneity or fault‐frictional behaviors such as dilatant strengthening.


Introduction
Slow slip, also known as fault creep or aseismic slip, is a key mechanism of seismic moment release on faults (Avouac, 2015;Bürgmann, 2018), occurring either as steady fault slip (e.g., Lindsey et al., 2014), as episodes of slip (Bilham & Behr, 1992;Wei et al., 2013), or as transient afterslip following earthquakes (Jiang et al., 2021).Discrete slow slip events have been observed both on shallow strike-slip faults (Bilham et al., 2016;Jolivet et al., 2013Jolivet et al., , 2023;;Li & Bürgmann, 2021;Rousset et al., 2016;Wei et al., 2013) and on deep subduction zone megathrusts (Schwartz & Rokosky, 2007) around the world.These episodic slip events are significant because they provide a unique opportunity to probe the mechanical properties of fault zones, especially when they are observed at high enough spatial and temporal resolution to capture the slip process.
An important setting for the observational study of slow slip events is the Salton Trough in southern California.A transtensional basin at the southern terminus of the San Andreas fault (SAF), located within the seismically active Brawley Seismic Zone, this area has hosted numerous slip events over the past four decades, either spontaneous (Wei et al., 2009) or dynamically triggered (Donnellan et al., 2014;Wei et al., 2015).Many of these slip events have taken place on the Superstition Hills fault (SHF) (Bilham & Behr, 1992), the Imperial fault (IF) (Goulty et al., 1978), and the southern SAF (Tymofyeyeva et al., 2019) (Figure 1).
In the spring of 2023, two slow slip events occurred on the SHF and IF that were imaged in unprecedented detail by ground-based and space-based geodetic sensors (Vavra et al., 2024).In this work, we further investigate the along-strike propagation of slip, leveraging the complementary temporal resolution from creepmeters and Global Navigation Satellite System (GNSS) measurements with spatial resolution from Interferometric Synthetic Aperture Radar (InSAR).The observations clearly show that both the IF and SHF events propagated along the fault over several weeks; the SHF event in particular included a 20-km-long bilateral rupture.While propagating creep events have been observed with creepmeters for many decades (Evans et al., 1981;Gittins & Hawthorne, 2022;King et al., 1973), these events in the Salton Trough represent, to our knowledge, the first alongstrike propagations of shallow slow slip events directly observed with GNSS and InSAR.We analyze these data toward the generation of a complete spatio-temporal description of creep and we consider their implications for the physics of slow slip.

Superstition Hills and Imperial Fault Creep Events in 2023
Sometime between 3 May 2023 and 15 May 2023 13:49:00 UTC, a large creep event initiated in the north-central part of the SHF as imaged by Sentinel-1 and ALOS-2 InSAR data (Figure 1, interferogram i; Figures S1 and S2; Text S1 in Supporting Information S1 for methods used in data processing).The slip event then ruptured bilaterally to the northwest and southeast, reaching the entire length of the fault by May 27 (interferogram ii).The displacements were 5-25 mm in the line-of-sight (LOS) direction (Text S1, Figure S3 in Supporting Information S1).
GNSS station P503, located 8 km southeast of the initial slip patch, registered initiation of slip around May 16 according to its daily processed time series, and accumulated ∼10 mm of displacement over several days (Figure S4 in Supporting Information S1).More precisely, high-rate GNSS processing by MIT, Central Washington University, and the University of Washington (Figure 1) determined the onset time to be about May 16 18:00:00 ± 3 hr (Figure 1a, Text S2 in Supporting Information S1).About 3 km to the southeast, a creepmeter with one-minute sampling registered a sudden onset of slip on May 16 18:30:00 UTC (Figure 1a).The creepmeter continued to measure a complex and halting pattern of creep consisting of eight sub-events ultimately lasting until May 24.
Between June 8 and June 20, several weeks after this main slip sequence, a small amount of additional slip occurred at the northern terminus of the SHF (Figure S1 in Supporting Information S1, interferogram iii).On July 12, another 5 mm of slip was registered with the creepmeter and in InSAR over the southern end of the fault (Figure S1 in Supporting Information S1, interferogram iv).The total slip at the creepmeter was 40 mm, while the peak cumulative slip captured by InSAR was 47.6 ± 2.2 mm (Figure S5 in Supporting Information S1).
The propagation of slow slip away from the initiation point resembles the migration of a slip pulse during earthquakes in that the duration of slip at one point is shorter than the total duration of the event.The initiation point (Figure 2b) around profile D shows 10 mm of LOS slip in interferogram i but almost no slip in interferogram ii, by which time the slip has propagated to all profiles to the north and south.The slipping region was about 5 km along-strike in interferogram i on May 15; it then propagated to the entire 25-km length of the fault by May 27 (Figure 3).By comparing the timing and location of slip front in the InSAR imagery (15 May 2023) with the largest slip pulse in the GNSS and creepmeter time series (29 hr later), we can calculate average propagation velocities.The average velocity is 6.6-8.9 km/day for the SHF when using the location of the GNSS and the creepmeter, respectively, assuming that the slip process was ongoing when Sentinel-1 imaged the area on May 15.Within resolvable limits, the onset time of the slip pulse is nearly identical between the GNSS station and the creepmeter despite a separation of ∼3 km.This suggests that while the average propagation velocity is on the order of several kilometers per day, the physical slip process occurs haltingly, that is, the rupture may be pulse-like overall, but more crack-like on local scales (Heaton, 1990).
Further south, the IF also experienced aseismic slip in March and April 2023, but this creep event was smaller in slip amplitude and length.Slip initiated on the northern end of the rupture around March 28 (interferogram in Figure 4a), coincident with ∼2 mm of westward motion at GNSS station P744 in late March (Figure 4b).Slip then slowly propagated 8 km southeast to reach a creepmeter on the IF by April 17.The displacement observed in the InSAR peaked at 5 mm in the LOS direction; this is consistent with the 8 mm of right-lateral displacement observed by the creepmeter (Figure 4c).The estimated propagation velocity of this event, as measured between P744 and the creepmeter, is only 0.4 km/day.

Was the Slip Surface-Rupturing?
We analyzed fault-crossing InSAR profiles to determine how close the slip came to the surface at various locations along the strike of the SHF and IF creep events.The lateral profiles (Figure 2 and Figure S6 in Supporting Information S1) suggest that creep broke the surface in the regions of maximum slip on the SHF (Profiles I and H), but did not break the surface elsewhere.If the slip was buried, elastic dislocation modeling suggests the uppermost extent of slip must have been between 10 and 40 m depth for both the SHF and IF (Text S1, Table S1 in Supporting Information S1), leaving a thin shell of the uppermost crust unruptured (Brooks et al., 2017;Evans et al., 1981).One possible explanation for this shallow locking depth is that it corresponds to the local water table (Survey, 2001), implying that a fluid-saturated medium is required for the nucleation and propagation of slow slip events.Alternately, the deformation could have been distributed over a wider zone in the non-surface-breaking profiles instead of a single fault trace.A third hypothesis is that the large shear strains in the shallowest layer could have produced inelastic yielding.We estimated the peak shear strain from model fitting of the profiles (Text S1 in Supporting Information S1) to be 4 × 10 5 -4 × 10 4 .This is below the 1 × 10 3 strain suggested to be a general elastic yield limit of Earth's crustal materials (Lockner, 1998), so this explanation is unlikely.
Comparing Profile D in interferograms i and ii on the SHF, we find that the apparent locking depth, assuming an elastic medium, was deeper in the earlier interferogram but shallower (49 ± 2 m vs. 40 ± 2 m) at the later time (Table S1 in Supporting Information S1).This suggests that slip initiated at depth and rose closer to the surface as the creep event progressed, as other documented creep events have done (B.Y. P. L. Williams et al., 1988).

Slip Distribution, Stress, and Strength
The inferred distribution of creep of the SHF along strike is not uniform (Figure 3).The northern half of the fault experienced 10-20 mm of creep, while the southern half experienced approximately twice as much.The maximum creep of 40 mm is co-located with the SHF creepmeter (Figure S5 in Supporting Information S1), suggesting that large surface slip is a persistent feature in that location (Bilham & Behr, 1992).The larger surface slip in the south is also a feature of the shallow afterslip following the 1987 SHF earthquake, which seems spatially overlapping with the 2023 creep event (Bilham, 1989;Sharp et al., 1989;P. Williams & Magistrale, 1989).
A first-order estimate of the shear stress drop of the SHF event can be obtained from the slip distribution by estimating the depth-extent of slip, the amplitude of slip, and the shear modulus (Text S3 in Supporting Information S1, Equation 2 in Supporting Information S1).Previous work suggests that slip in SHF creep events typically extends from 2 to 3 km depth to near the surface (Bilham & Behr, 1992;Wei et al., 2009) and similar depth values are estimated for the 2023 SHF event (Vavra et al., 2024, and Figure S7 in Supporting Information S1).Assuming slip occurs above 2 km depth with a typical amplitude of 20 mm and a shear modulus of 4 GPa (Shaw et al., 2015), we find a stress drop for the overall slip event of 80 kPa, similar to inferred stress drops on the order of 10-100 kPa for both Cascadia Episodic Tremor and Slip (ETS) events (Schmidt & Gao, 2010) and for shallow, episodic slip events along the Calaveras fault (Evans et al., 1981).
We also examine the two smaller episodes of creep on the SHF several weeks after the main slip sequence (Figure 1a) for clues into the fault's strength.These triggered slow slip events occur in regions where the slip of the main sequence has strong gradients (Figure 3), thereby creating positive Coulomb Failure Stress (King et al., 1994).The slip gradients in the northern and southern parts of interferogram ii (i.e., 12 mm over 2 km, 40 mm over 5 km from the left and right sides of Figure 3) can be converted into along-strike shear strains of about 3-4 × 10 6 .Assuming this region has a shear modulus of 4 GPa to depths of ∼2 km (Shaw et al., 2015), this slip gradient implies that the aseismic slip was triggered by a "coseismic" shear stress change of about 12-16 kPa.These stresses imply a fault interface that is either very weak or very close to failure, consistent with other observations of triggered aseismic slip (Xu et al., 2018) and tectonic tremor (Rubinstein et al., 2007).The three-tosix-week delay in slip may be a response to time-dependent processes like pore pressure diffusion (Hudnut et al., 1989).

Propagation and Mechanics
One of the most striking features of both 2023 events is their along-strike propagation.The propagation velocities for the SHF (6-9 km/day) seem to be quite similar to other aseismic slip events on strike slip faults.For example, creep events on the central San Andreas and Calaveras faults show typical propagation velocities of 7-24 km/day  (Evans et al., 1981;King et al., 1973;Mortensen et al., 1977).The velocities on the SHF are also remarkably similar to the propagation speeds of subduction zone ETS events, which appear to be ∼10 km/day (Bartlow et al., 2011;Hirose & Obara, 2010;Rousset et al., 2019).
We note that unlike the SHF, the propagation speed on the IF was only 0.4 km/day.While this is much slower than most previously observed creep events, it is consistent with ∼1 km/day propagation speeds recorded on the IF for creep events in April 1977 (Goulty et al., 1978).Whether IF creep events typically propagate slower than other faults, and the physical reasons that might occur, would be an interesting subject of future work.
The shallow depths and dense observational coverage of the 2023 events allow opportunities to further investigate the kinematics and dynamics of slow ruptures.SSEs such as the SHF and IF events appear to be instabilities with bounded, ribbon-like rupture areas.Much work has posited that for such events, whose rupture is dominated by along-strike propagation, the moment is expected to scale linearly with event duration (Gomberg et al., 2016;Ide et al., 2007) rather than the M ∝ T 3 expected from normal earthquakes with circular crack-like ruptures.In that context (Figure 5), both the SHF and IF events have much longer durations than would be expected for events of their size relative to other observations.Strangely, the IF event has half the length of the SHF event but takes about twice as long (Figure 5).Recent updates (Ide & Beroza, 2023) to the scaling relationship from Ide et al. (2007) suggest that the dominantly observed scaling may in fact be an upper bound on the propagation velocity, and slower events may exist but are typically hidden from observation because of signal-to-noise limitations at low frequencies and amplitudes.The 2023 SHF and IF events seem consistent with the revised interpretation, displaying a low rupture velocity and plotting within the "hidden" region of Figure 5.They are likely observable due to their very shallow depths.
Other observational (Frank & Brodsky, 2019;Michel et al., 2019) and numerical modeling work has suggested that slow slip events could instead share similar scaling with regular earthquakes.Some models (Dal Zilio et al., 2020) appeal to specific magnitude/rupture-velocity relationships in faults with rate-and-state friction and dilatant-strengthening effects (Segall et al., 2010), while other models (Weng & Ampuero, 2022) appeal to various configurations of stress heterogeneities along the interface.These models reproduce both the along-strike propagation and bounded pulse-like ruptures that we observe in the SHF and IF events.The models of Dal Zilio What processes create a dynamic-like rupture that moves at such a slow speed?For dynamic events, pulse-like ruptures often require physical healing mechanisms like strongly velocity-dependent friction (Beeler & Tullis, 1996) or trapped waves within strong velocity contrasts (Huang & Ampuero, 2011).However, aseismic creep is too slow to generate seismic sliding velocities, dynamic waves, or healing processes such as shear heating.Dilatant strengthening (Segall et al., 2010) is potentially implied because the SHF event had halting sub-events.Poroelasticity, dilatant strengthening, or a combination of both, may help produce pulse-like slow slip rupture behavior in numerical models (Heimisson et al., 2019).However, opportunities exist to test these hypotheses explicitly from the Imperial Valley events of 2023 and from similar slip episodes we can expect on the SHF and IF in the future.Because the SHF and IF slip events are shallow and relatively accessible, fault samples could be tested in drained and undrained conditions to determine their physical properties, relate them to the presently observed slow slip behavior, and better understand the propagation of slow slip events.This future research would have possible implications for slow slip events on both shallow strike-slip faults and subduction zone systems.

Conclusions
We analyze space-based and ground-based geodetic data associated with two creep events in southern California's Imperial Valley using creepmeters, satellite radar, and GNSS.These events allow for some of the most detailed spatio-temporal description to date of shallow creep event propagation.Both creep events had clear along-strike propagation at average velocities consistent with previously observed slow slip events (∼1-10 km/day), but propagation velocities may have been locally much higher or lower as the slip events evolved in space and time.The SHF event had bilateral propagation and two triggered slip events delayed by 1-2 months.Both shallow slip events occurred over considerably longer times than similar-sized slow slip events in subduction zones, filling a "hidden" region in the global population of slow slip events.They underscore the need for continued dense instrumentation and remote-sensing analyses to better understand the dynamics of episodic aseismic creep on strike slip faults.Ide and Beroza (2023).Both Superstition Hills fault and Imperial fault creep events plot in the region identified as "Hidden" (gray region) due to limitations of seismological and geodetic instruments across frequencies.In this case, they are identifiable in the observational data due to their extremely shallow depth.Figures were created using GMT6 (Wessel et al., 2019).The authors are grateful to Ellis Vavra, Jerry Svarc, Andrew Barbour, Josie Nevitt, Kang Wang, and Paul Segall for helpful discussions.The authors are also grateful to the associate editor and three anonymous reviewers for their reviews that greatly improved the manuscript.The authors declare no competing interests.

Figure 1 .
Figure 1.(a) May 2023 fault-parallel time series from a creepmeter and from Global Navigation Satellite Systems station P503 using four processing techniques.The timeseries of the creepmeter at one-minute intervals is shown in blue.(b) Two subsequent Sentinel-1 interferograms over the Superstition Hills fault (SHF).Sharp discontinuities, including the one indicated by the white arrow, represent aseismic creep on the SHF.The locations of P503 and the creepmeter are shown as a triangle and a square respectively.(c) Tectonic setting of southern California, with the SHF in red.

Figure 2 .
Figure 2. (a) Locations of 10 profiles along the Superstition Hills fault.The color shows the unwrapped line-of-sight (LOS) displacement from May 3 to May 27.(b) LOS displacement profiles from each interferogram in Figure 1.Profiles without discernible slip are shown in gray.Only profiles H and I have sharp discontinuities, indicating surface breaking.In the right panel, we only show the northernmost and southernmost profiles from interferograms iii and iv, respectively, because slip was only observed along short sections of the fault during those intervals.(c) The near-fault region of several profiles from (b), with model fits in red (Text S1, Equation 1 in Supporting Information S1) and the modeled locking depths d, assuming only elastic deformation, indicated in red text.

Figure 3 .
Figure 3.Estimated fault-parallel slip amounts on the Superstition Hills fault as a function of distance along the fault for each sequential Sentinel-1 interferogram.The pulse-like rupture is evident, propagating from approximately km 7 outward in both directions.The locations of the Global Navigation Satellite Systems station P503, the creepmeter, and two releasing fault steps are marked.The gray bar represents the root-mean-square noise level of the interferograms without a creep signal (2.2 mm).The delayed triggered slow slip events (interferograms iii and iv) occur in regions of maximum slip gradients during the initial slow slip event.See Figure S5 in Supporting Information S1 for a cumulative-slip version of this plot.

Figure 4 .
Figure 4. (a) Sequential Sentinel-1 interferograms along the Imperial fault (IF).Slip begins in the northern part of the fault in late March and propagates to the southern part by mid-April.The maximum line-of-sight (LOS) displacement is about 5 mm.The inset map shows the setting with the IF highlighted in red.(b) Time series of Global Navigation Satellite Systems station P744 (black triangle in panel (a)) and creepmeter on IF (black square in panel (a)) during early 2023.(c) Zoomed-in version of panel (b) (see dashed box in panel (b) for time range).

Figure 5 .
Figure 5. Modified moment-duration scaling plot fromIde and Beroza (2023).Both Superstition Hills fault and Imperial fault creep events plot in the region identified as "Hidden" (gray region) due to limitations of seismological and geodetic instruments across frequencies.In this case, they are identifiable in the observational data due to their extremely shallow depth.