Three empirical methods for the calculation of distal volume of tephra-fall deposits

Three empirical methods for the calculation of distal tephra-fall volumes are presented and tested. The three methods allow calculation of approximate distal tephra-fall volumes under different conditions and abundances of field data. All methods use proximal data to extrapolate the distal situation. They are based on: i) shape and dispersal axis of proximal isopachs (method of ellipses), ii) break-in-slope distance on Log T vs. √A diagram where one distal isopach is available (method of √Aip with one distal isopach), and iii) distal thinning rate and break-in-slope distance on Log T vs. √A diagram (method of k1 vs. √Aip). The application of the three methods to published data of 23-32 eruptions in which it is possible to define at least two segments on the Log T vs. √A diagram yields different results. The method of ellipses yields good results if the thickness of reconstructed distal isopachs is greater than about 1 cm, whereas the method of √Aip with one distal isopach is more accurate if the distal isopach has a thickness below the half thickness at the break-in-slope distance (T < 0.5Tip). The method of distal thinning rate (k1) vs. break-in-slope distance (√Aip) allows calculation of distal thinning rate and break-in-slope distance from only proximal data. In this case, calculated distal volumes approximate the actual one only if the deposits have a proximal volume/total volume ratio greater than 0.7, otherwise they must be considered as minimum values to be added to the proximal volumes. An empirical correlation between proximal thinning rate (k) and column height (Ht = 7.6k−0.47; R = 0.90) is also presented. Column heights calculated in this way are within ±20% of the observed/published values in 94% of the examined cases.