Revised tephra volumes for Cascade Range volcanoes

Isopach maps from tephra eruptions from Mount St. Helens were reported in Carey et al. (1995) and for tephra eruptions from Glacier Peak in Gardner et al. (1998). For exponential thinning, the isopach data only define a single slope on a log thickness versus square root of area plot. Carey et al. (1995) proposed a model that was used to estimate a second slope, and volumes were presented in both studies using this model. A study by Sulpizio (2005) for estimating the second slope and square root of area where the lines intersect involves a systematic analysis of many eruptions to provide correlation equations. The purpose of this paper is to recalculate the volumes of Cascades eruptions and compare results from the two methods. In order to gain some perspective on the methods for estimating the second slope, we use data for thickness versus distance beyond the last isopach that are available for some of the larger eruptions in the Cascades. The thickness versus square root of area method is extended to thickness versus distance by developing an approximate relation between the two assuming elliptical isopachs with the source at one of the foci. Based on the comparisons made between the Carey et al. (1995) and Sulpizio (2005) methods, it is felt that the later method provides a better estimate of the second slope. For Mount St. Helens, the estimates of total volume using the Sulpizio (2005) method are generally smaller than those using the Carey et al. (1995) method. For the volume estimates of Carey et al. (1995), the volume of the May 18, 1980, eruption of Mount St. Helens is smaller than six of the eight previous eruptions. With the new volumes using the Sulpizio (2005) method, the 1980 eruption is smaller in volume than the upper end of the range for only three of the layers (Wn, Ye, and Yn) and is the same size as layer We. Thus the 1980 eruption becomes representative of the mid-range of volumes rather than being in the lower range.