We present an analytical, seismologically consistent expression for the surface area of the region within which most landslides triggered by an earthquake are located (landslide distribution area). This expression is based on scaling laws relating seismic moment, source depth, and focal mechanism with ground shaking and fault rupture length and assumes a globally constant threshold of acceleration for onset of systematic mass wasting. The seismological assumptions are identical to those recently used to propose a seismologically consistent expression for the total volume and area of landslides triggered by an earthquake. To test the accuracy of the model we gathered geophysical information and estimates of the landslide distribution area for 83 earthquakes. To reduce uncertainties and inconsistencies in the estimation of the landslide distribution area, we propose an objective definition based on the shortest distance from the seismic wave emission line containing 95 % of the total landslide area. Without any empirical calibration the model explains 56 % of the variance in our dataset, and predicts 35 to 49 out of 83 cases within a factor of 2, depending on how we account for uncertainties on the seismic source depth. For most cases with comprehensive landslide inventories we show that our prediction compares well with the smallest region around the fault containing 95 % of the total landslide area. Aspects ignored by the model that could explain the residuals include local variations of the threshold of acceleration and processes modulating the surface ground shaking, such as the distribution of seismic energy release on the fault plane, the dynamic stress drop, and rupture directivity. Nevertheless, its simplicity and first-order accuracy suggest that the model can yield plausible and useful estimates of the landslide distribution area in near-real time, with earthquake parameters issued by standard detection routines.

Triggered landslides are a significant secondary hazard of earthquakes, and
may be the dominant cause of damage to infrastructure and lifelines,
especially roads

Several global or regional compilations of earthquake-induced landslide data
have reported

Here we show that this same treatment may be used to predict the shape and size of the landslide distribution area. First, we present the basis for an expression of the landslide distribution area and the landslide maps and compilations of estimated landslide distribution areas against which model predictions can be compared. Then we assess the validity and accuracy of our theoretical approach and discuss its limitations, and finally we suggest directions for future improvements.

Earthquakes trigger landsliding due to transient accelerations during ground
shaking, which can shift the force balance in a slope and cause damage in the
substrate, reducing its cohesion and resistance to failure

Following

To construct a simplified ground shaking model that is consistent with first-order seismological observations and landslide triggering we use the scaling
of the near-source acceleration,

With these considerations, both the fault rupture length and near-source wave
amplitude can be estimated from the seismic moment and fault type. Thus
Eq. (

In the model, the critical seismic moment above which

Total area affected by landsliding against seismic moment and moment
magnitude for 83 earthquakes. Vertical error bars represent different
estimate of

Data summary. Earthquake location and country where US, NZ,
CN, and IT are for United States, New Zealand, China, and Italy. Fault gives
the focal mechanism (reverse, strike-slip, or normal). Depth is the hypocentre
depth. The best estimate of

Continued.

Our model predicts the landslide distribution area

To assess if our theoretical framework captures the observed scaling between

For 10 earthquakes, detailed landslide inventories with comprehensive maps
of the landslide as polygons are available, allowing an objective
characterization of

It is important to secure consistency between estimates of

We propose a robust, alternative approach to define

Predicted landslide distribution area plotted against estimated
landslide distribution areas for 83 earthquakes. For visibility, cases where
the predicted area is 0 are set to 1 km

Our treatment differs from previous definitions of the maximum distance for
landsliding

Most of our landslide distribution area data fall within the range of
theoretical predictions from Eq. (

Distribution of landsliding (yellow polygons) and predicted
landslide distribution area (green circles) for the Northridge

For comparison, an empirical fit of

To quantify the error of the model we evaluate the proportion of the total
area affected by landsliding located within the

Summary of the emission length

Same as Fig.

For the 10 earthquakes for which we have comprehensive landslide
inventories, the model distribution area always contains between 88 and
100 % of the cumulative surface area of all mapped landslides (Table 2).
These numbers indicate that the model always captures the region of most
intense landsliding, but that it sometimes overpredicts the affected area,
with its limit well beyond the outermost mapped landslide in most directions,
as for the Niigata and Iwate cases (Fig.

Relative and absolute errors in the prediction of the distance from
the wave emission line containing 95 % of the total landslide area
plotted against the seismic moment. Horizontal black lines delimit cases
where the relative error is within

We stress that the 5 % of the total landsliding outside of

We have shown that a first-order a priori seismic shake map coupled with a universal shaking threshold for landsliding can reproduce reasonably well the landslide distribution areas in a compilation of 83 cases, and that it matches the surface area encompassing 95 % of the total landslide area for most of the cases for which we have comprehensive landslide inventories. In this section, we identify and try to quantify the different sources of uncertainties and potential ways to improve the model.

For the Niigata, Iwate, and Nagano earthquakes, the difference between the
observed and predicted area of landsliding would be greatly reduced if we
treated the earthquake as a single point source centred on the largest
slip patch (Fig.

This has no significance for large earthquakes and long faults where

Equation (

Inverted value of the threshold of acceleration for damage,

Nevertheless, it is interesting to focus on those earthquakes that have the
lowest inverted values of

The near-source wave amplitude,

We have shown that our model can predict the general distance from the
emission line to a contour containing 95 % of all the landslides as
measured by their cumulative surface area, with a reasonable reliability.
However, this 1-D parameter does not describe potential 2-D complexities in
the shape of the landslide distribution area. For example, across-strike
asymmetry often exists for thrust faults where the hanging wall may
experience larger shaking

To further explore these effects, we attempt to quantify asymmetry of the
landslide distribution and in the rupture mechanism with very simple
parameters available for most cases. We define a landslide asymmetry indicator

Hypocentre asymmetry (0

For Epi

We have presented an analytical expression for the distribution area of
earthquake-induced landslides. It shares its derivation with the model of

The data used in this study is available through the data table or through the literature.

OM collected and analysed all data. OM conceived the study and wrote the paper with assistance and inputs from NH and PM.

The authors declare that they have no conflict of interest.

The authors thank Chong Xu and Tolga Gorum for providing their landslide inventories and two anonymous referees for comments that have helped improve the clarity of the manuscript. The authors have gratefully used Aster GDEM V2, a product of METI and NASA. The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association.Edited by: Thomas Glade Reviewed by: two anonymous referees