Magnitude-Frequency Distribution of Hummocks on Rockslide-Debris Avalanche Deposits and Its Geomorphological Significance

Abstract

A magnitude-frequency analysis of rockslide-debris avalanche deposits was performed. Hummocks are conical mounds formed in debris avalanche deposits from the catastrophic sector collapse of a mountain (often volcanic) that represent relatively cohesive fragments of the mountain edifice. Examination of 17 debris avalanche deposits in Japan and the Philippines showed that, in general, the larger the magnitude of the hummocks, the smaller their frequency. Hummocks followed an exponential distribution: log10N(x) = a – bx, where N(x) is the cumulative number of hummocks with magnitude ≥ x and a and b are constants; x is equal to log10A, where A is the area of a hummock. The constants a and b were positively correlated. The value of b, which differs among avalanches and in this analysis ranged between 1 and 3, may be controlled by the mobility of the debris avalanche. Avalanches with higher mobility (relatively longer runout) have higher b and potentially produce more numerous fragments forming hummocks (i.e., higher a). From the above correlation, the magnitude-frequency relationship can be used to roughly estimate the original height of the collapsed volcanic body, if the runout distance of the rockslide–debris avalanche can be estimated with sufficient accuracy.

Keywords

• magnitude-frequency relationship
• rockslide-debris avalanche
• hummock
• exponential distribution
• equivalent coefficient of friction
• Japan