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Earthquake‐triggered landslides are a severe hazard and contribute to landscape evolution. To understand their process and controlling factors, we model the onset of seismically‐triggered slip on pre‐existing slip surfaces governed by laboratory‐based rate‐and‐state friction, including wave propagation effects. Through numerical simulations and theoretical analysis, we identify how friction properties, landslide thickness and incident wave attributes (frequency, duration, amplitude) control slope stability. We find that the frictional state variable tracks the cyclic fatigue of the slip surface, its progressive weakening with each wave cycle. Wave propagation effects introduce two regimes depending on frequency relative to the two‐way travel time across the landslide thickness: the stability criterion is well approximated by a threshold on incident peak acceleration at low frequencies, and on peak velocity at high frequencies. We derive analytical approximations, validated by simulations, suitable to apply the model to evaluate landslide stability under arbitrary input motions. Plain Language Summary: Landslides induced by earthquake shaking cause human and economic losses. Understanding their triggering mechanism is a key to reduce their impact. Here we propose a new model for the onset of seismically‐triggered landslide slip using a friction law based on laboratory experiments. Studying the model mathematically and through computer simulations, we identify the specific attributes of the landslide and incident seismic waves that control slope stability. We find that the decrease of the frictional state variable is a good proxy for the approach to instability. The landslide triggering criterion is well described by a peak acceleration threshold if the landslide is shallow or the earthquake shaking is dominated by low frequencies, and by a peak velocity threshold for deep landslides or high‐frequency shaking. Finally, we develop equations that can be used to assess landslide stability to shaking without the need for computer simulations. Key Points: Numerical and analytical modeling of earthquake‐induced landslides on slip surfaces governed by rate‐and‐state frictionThe frictional state variable tracks the landslide fatigue manifested by progressive weakening of the slip surfaceLandslide triggering by low‐ and high‐frequency shaking is controlled by peak acceleration and velocity, respectively [ABSTRACT FROM AUTHOR]

Quito, the capital of Ecuador, with more than 2.5 M inhabitants, is exposed to a high seismic hazard due to its proximity to the Pacific subduction zone and active crustal faults, both capable of generating significant earthquakes. Furthermore, the city is located in an intermontane piggy-back basin prone to seismic wave amplification. To understand the basin's seismic response and characterize its geological structure, 20 broad and medium frequency band seismic stations were deployed in Quito's urban area between May 2016 and July 2018 that continuously recorded ambient seismic noise. We first compute horizontal-to-vertical spectral ratios to determine the resonant frequency distribution in the entire basin. Secondly, we cross-correlate seismic stations operating simultaneously to retrieve interstations surface-wave Green's functions in the frequency range of 0.1–2 Hz. We find that Love waves travelling in the basin's longitudinal direction (NNE–SSW) show much clearer correlograms than those from Rayleigh waves. We then compute Love wave phase-velocity dispersion curves and invert them in conjunction with the HVSR curves to obtain shear-wave velocity profiles throughout the city. The inversions highlight a clear difference in the basin's structure between its northern and southern parts. In the centre and northern areas, the estimated basin depth and mean shear-wave velocity are about 200 m and 1800 ms−1, respectively, showing resonance frequency values between 0.6 and 0.7 Hz. On the contrary, the basement's depth and shear-wave velocity in the southern part are about 900 m and 2500 ms−1, having a low resonance frequency value of around 0.3 Hz. This difference in structure between the centre-north and the south of the basin explains the spatial distribution of low-frequency seismic amplifications observed during the M w 7.8 Pedernales earthquake in April 2016 in Quito. [ABSTRACT FROM AUTHOR]