Rain and small earthquakes maintain a slow-moving landslide in a persistent critical state

Large and shallow earthquakes (Mw > 5.5) commonly trigger widespread landsliding via dynamic loading that elevates shear stress and weakens soils through fracturing. Multiple mechanisms may act, including undrained loading that elevates pore pressure, especially when rain increases water content. Observations show a range of time lags between shaking and slope failures—from immediate to days, months, or years—often linked to precipitation and damage-induced permeability changes that enhance infiltration. Slow-moving landslides can accelerate for years after moderate earthquakes due to reduced rock strength and increased preferential infiltration paths. Despite qualitative hypotheses linking shaking, precipitation, material damage, and permeability, quantitative landslide-scale observations have been lacking. This study aims to quantify how earthquakes and rainfall jointly control the mechanics and kinematics of a slow-moving landslide by monitoring surface displacement and bulk material rigidity (via relative seismic velocity changes, dv/v) at the actively deforming Maca landslide (Peru), where seasonal rainfall and frequent local earthquakes coexist.

Prior work established that earthquakes trigger landslides regionally, with patterns related to ground motion and site effects, and that undrained cyclic loading can rapidly reduce shear resistance in fine-grained soils and rock. Delayed landslide responses have been attributed to earthquake-induced microfracturing that modifies groundwater flow and permeability, leading to enhanced infiltration. Transient post-earthquake increases in landslide rates have been documented for months to years after large events (Mw > 6.6), and slow-moving landslides can also show long-lived acceleration after moderate earthquakes (e.g., Mw 5.4). Seasonal control by rainfall and threshold behavior are well recognized in slow-moving landslides, including in lacustrine deposits similar to Maca. Ambient seismic noise interferometry has been used to track near-surface rigidity changes and damage-healing processes in diverse settings, with dv/v often showing co-seismic drops and logarithmic recovery. However, quantitative in situ coupling of dv/v, rainfall, and displacement on an active landslide—and the role of small earthquakes in modulating recovery—had not been documented.

Study site and instrumentation: The Maca slow- to very slow-moving landslide (~60 million m³) in the Colca Valley, southern Peru, comprises a permeable 8–12 m-thick debris avalanche layer overlying >50 m of fine lacustrine deposits; the sliding surface is ≥40 m depth within lacustrine material. Seasonal rainfall occurs December–May; the area is seismically active. A hut on the fastest-moving zone hosted a continuous GPS and a three-component broadband Noemax seismometer (natural frequency 4.5 Hz; flat response ~0.1–50 Hz) from December 2015 onward. Quarterly GPS campaigns since 2013 provided displacement context prior to continuous monitoring.

Geodetic processing: Fifty-five continuous GPS stations from regional networks were processed with GAMIT 10.6 using double-difference, ionosphere-free combinations, precise orbits/EOPs, antenna phase centers, ocean/atmospheric loading, and VMF1 mapping functions. Zenith delays were estimated every 2 h; horizontal gradients once per day. Daily solutions were framed to ITRF2008 and the South American plate using PYACS. Landslide velocity at the Maca station was computed from daily displacement with a 5-day moving average, except immediately after the August 2016 earthquake.

Seismic ambient noise processing and dv/v: Single-station cross-correlations were computed for NE, ZE, and ZN component pairs from hour-long recordings. Signals were spectrally whitened (0.2–35 Hz) and amplitude-clipped (SNR ≤ 3σ) to suppress transient large events. Hourly correlograms were obtained and denoised using an SVD-based Wiener filter (K=7, L=7, N=30 singular values), then averaged daily. Relative velocity changes dv/v were estimated via the stretching method over 3–8 Hz using coda windows [-2.8:-0.4] and [0.4:2.8] s relative to zero lag to avoid source autocorrelation. Daily dv/v were averaged across component pairs; uncertainties were derived from stretching correlation coefficients. Elevated seismicity can increase dv/v uncertainties by ~30% due to decorrelation. Gaps reflect missing or saturated records.

Depth sensitivity: Active seismic tests (80-kg mass drop) and surface-wave inversion (Geopsy) yielded Vs ≈ 110 m/s for the upper 8–12 m and Vs ≈ 350 m/s for underlying lacustrine deposits. Rayleigh-wave sensitivity analyses (gpdc) indicated 3–8 Hz surface waves are sensitive down to ~40 m depth, sampling the unstable mass.

Mechanistic modeling of dv/v: Three mechanisms were evaluated: (1) undrained cyclic loading (liquefaction-like Vs reduction near a 38–40 m sliding surface), (2) water table elevation in a perched aquifer at 10 m depth, and (3) shaking-induced damage. Rock physics modeling used Biot–Gassmann relations with porosity 35% and compaction coefficient 120, calibrated to VP ~1900 m/s and VS ~350 m/s for saturated lacustrine deposits. Bulk and shear moduli inputs were set from plagioclase feldspar (Ks=75.6 MPa, Gs=25.6 GPa). Predicted Rayleigh-velocity variations versus frequency were obtained (gpdc) for each mechanism.

Ground motion and PGV: Peak ground velocity (PGV) on the landslide was taken from recorded unsaturated seismograms (vector sum of horizontal components PGV_N + PGV_E). When the on-site seismometer saturated (common for ML 3.5–7.1 events) or data were missing, PGV was estimated using GMPEs; comparison favored Akkar & Bommer (2010) over Boore & Atkinson (2007) for this dataset. Validation employed 348 events (Feb 2016–Nov 2018) up to 400 km distance and ML 3.5–8. GMPE-based PGV estimates carry a relative standard error of ~56%.

Meteorology and effective precipitation: Daily precipitation and temperatures were from the SENAMHI Madrigal station (5 km from Maca, similar elevation). Effective precipitation was defined as daily precipitation minus evapotranspiration (ET) computed with the Hargreaves method, scaled by crop coefficient Kc = 0.3 to obtain ETc for sparsely vegetated soil. Effective rainfall was accumulated seasonally (Dec to mid-August) for interannual comparisons.

Seismicity dataset: Over the monitoring period, 165 local earthquakes with ML 3.1–5.5 occurred within 50 km. Events with PGV ≥ 0.01 cm/s at the landslide were cataloged; seismometer saturation flagged major events. Analytical focus included two key earthquakes in 2016 (ML 5.0 in February during wet season; ML 5.5 in August during dry season) and low-PGV sequences in 2017–2018 to assess small-event effects.

• Combined forcing effect: The February 20, 2016 ML 5.0 earthquake during the rainy season resulted in ~80 cm of co- and post-seismic displacement over 5 months, despite a lower estimated shaking (PGVapp ~3.5 cm/s) than the August 15, 2016 ML 5.5 dry-season earthquake (PGVapp ~5.3 cm/s), which produced only ~1 cm co-seismic slip followed by ~11 cm relaxation over 30–40 days.
• Rain alone insufficient: The 2014 rainy season experienced similar precipitation to 2016 but far fewer earthquakes (44 events with PGV > 0.01 cm/s vs 99 in 2016) and produced almost no displacement. In 2017, rainfall exceeded 2016 by more than a factor of two, yet displacement was only about half of 2016 due to lower seismicity, confirming rainfall and earthquakes act synergistically to enhance motion.
• Material rigidity changes: After the August 2016 ML 5.5 event, dv/v in the 3–8 Hz band dropped co-seismically by >2%, sampling depths to ~40 m within the landslide body. dv/v recovered approximately logarithmically, returning to pre-event levels in ~1.5 months during the dry season.
• Mechanism discrimination: Modeling showed (i) undrained loading localized near the sliding surface should yield a dv/v minimum near ~3 Hz and smaller drops at higher frequencies, inconsistent with observed spectra; (ii) a 1 m rise in a perched water table at 10 m depth would cause only ~0.04% dv/v change, two orders of magnitude smaller than observed; thus, the dv/v drop is best explained by shaking-induced damage (opening of cracks, reduced rigidity) followed by viscoelastic healing.
• Wet-season behavior: For the February 2016 ML 5.0 event, dv/v continued to decrease for weeks after the co-seismic drop, attributed to enhanced water infiltration along earthquake-induced fractures and landslide-generated cracks, transiently increasing water content and reducing rigidity in lacustrine deposits.
• Critical threshold and kinematics: The landslide consistently entered motion when dv/v fell below an empirical threshold of about −1.2%; when dv/v recovered above this threshold, motion slowed or ceased, indicating a critical-state control by bulk rigidity.
• Role of small earthquakes: In June–August 2018, 30 low-PGV events (PGV < 1 cm/s; mainly ML < 4.5) occurred versus 13 during the same period in 2017. Recovery of dv/v after the wet season began mid-July 2017 but was delayed until late August 2018, despite similar seasonal timing and lower precipitation after May 2018. The higher rate of small events in 2018 likely inhibited healing while water remained in the mass, maintaining the critical regime. Two late-August 2018 events with PGV ~1 cm/s did not suppress recovery once soils had dried, suggesting water content modulates small-event effectiveness.
• Self-sustaining feedbacks: Landslide motion promotes crack formation, creating preferential infiltration pathways that can further reduce rigidity and sustain activity during wet periods.
• Implications: Medium-intensity earthquakes (ML < 5.5) can significantly accelerate slow-moving landslides when coincident with or closely timed to precipitation, and clusters of small events (ML 3.2–3.6) can prolong critical-state conditions when water content is high.

The study quantitatively shows that landslide kinematics in Maca depend on the interplay between seismic shaking and hydrological state. Earthquake-induced damage reduces bulk rigidity (captured by dv/v drops), and when water is available, infiltration along newly formed or reopened fractures maintains low rigidity, pushing the landslide into and prolonging a critical regime characterized by accelerated displacement. The empirical dv/v threshold (~−1.2%) delineates transitions between stable and critical regimes, linking internal mechanical state to surface kinematics. During dry periods, the material heals logarithmically toward higher rigidity, ending motion unless another forcing intervenes. Small, frequent earthquakes can impede healing when soils remain wet, demonstrating that the timing and density of seismic events relative to rainfall critically control landslide persistence in the critical state. These findings substantiate the hypothesized damage–infiltration mechanism behind post-earthquake increases in landslide activity and provide a framework for forecasting landslide response based on dv/v monitoring, rainfall, and seismicity patterns. The results have implications for hazard prediction and for assessing the seismic mass balance, emphasizing the need to account for slow-moving landslides and moderate-to-small earthquakes, especially under varying hydrological conditions.

This work combines continuous GPS and ambient noise interferometry to quantify how rainfall and earthquakes jointly govern the mechanics and motion of a slow-moving landslide. Key contributions are: (1) demonstrating that combined rainfall and seismic shaking produce greater displacement than either alone; (2) identifying shaking-induced damage (not undrained loading or minor water table fluctuations) as the primary cause of co-seismic dv/v drops in the landslide body; (3) establishing an empirical dv/v threshold (~−1.2%) that marks entry into a critical regime of motion; and (4) revealing that clusters of small earthquakes can delay mechanical healing during wet periods, prolonging instability. Future research could generalize critical dv/v thresholds across landslides with different geology and thickness, improve physics-based models coupling damage, hydrology, and kinematics, integrate dv/v with pore pressure and moisture sensing for forecasting, and assess regional mass balances by incorporating slow-moving landslides and small-to-moderate earthquakes under evolving climate-driven precipitation patterns.

• Site specificity: Conclusions are based on a single, well-instrumented landslide (Maca). While mechanisms are likely general, quantitative thresholds and responses may vary with geology, thickness, and saturation.
• Data gaps and saturation: Seismic records include gaps and frequent sensor saturation during larger events, requiring GMPE-based PGV estimates with substantial relative error (~56%). dv/v uncertainties increase by ~30% during high seismicity due to decorrelation.
• Hydrological ambiguity: During wet seasons, dv/v recovery is difficult to separate from drainage processes; water content was inferred rather than directly measured (no in situ pore-pressure or moisture sensors reported).
• Modeling assumptions: Rock physics parameters (porosity, compaction coefficient) and mineral moduli were assumed or calibrated; undrained loading and water table models simplify complex stratigraphy and flow paths.
• Meteorological representativeness: Temperature data from a nearby station (Madrigal) were used as a proxy; small spatial variability could affect ET estimates.
• Empirical threshold: The dv/v critical threshold (−1.2%) is empirically defined for this site and frequency band; transferability to other settings requires validation.