The structure of a magnitude-frequency relation for debris flows conditioned by earthquake shock

Debris flow is a major secondary geological process associated with the 2008 M7.9 Wenchuan Earthquake area, causing the loss of around 200 lives as well as extensive property damage. Based on data developed over the past 21 years (1998-2018) of continuous monitoring of debris flow events in Sichuan, the temporal and spatial aspects of debris flows have been analyzed, including magnitude and frequency. The 21-year study period is divided into three time-intervals: 1998-2007 (pre-earthquake), 2008-2013 (short-term post-earthquake), and 2014-2018 (long-term post-earthquake). Distribution maps are plotted to compare debris flow distribution density in the three periods and to visualize debris flow development throughout Sichuan Province from 1998 to 2018. Many large-scale debris flows occur in groups immediately following the earthquake (2008-2013). After 2014, the magnitude and frequency of debris flows begin to decrease and gradually returned near to the pre-earthquake level as the damaged landscape recovered. The effect of rainfall is investigated by analyzing a 21-year record of precipitation; Following the earthquake the threshold rainfall values for debris flow triggering decrease only to recover to pre-earthquake levels as the landscape heals. Magnitude-frequency (M-F) relations for debris flows of the three periods were developed, and the distribution can be well fitted by a power-law function. Finally, the work done by debris flow was defined by multiplying the magnitude by frequency. At the regional scale, the work peaks in the three time periods have been determined and it is found that the peaks corresponded with the larger debris flow sizes. The concept of offset is introduced to describe the shift of the work peak in relation to the probability peak and is termed the Wolman-Miller offset. It is concluded that with a greater offset in the short-term post-earthquake period, more work has been done by larger events and that the greater proportion of the volume being mobilized by larger events occurring more frequently is a key process in the landscape returning to a pre-earthquake (equilibrium) state. The recovery of an earthquake-damaged landscape represents a transient period of high hazard that should be considered in any hazard assessment of earthquake-triggered landslides (in addition to co-seismic landslides).