Another look at the calculation of fallout tephra volumes

The calculation of volumes of fallout tephra layers is difficult because of the nonlinear dependence of thickness on area and because of the extrapolations required at the vent and in distal regions. Calculation using the trapezoidal rule, straight lines on log-log plots of area versus thickness, straight lines on plots of log thickness versus area^1/2, and the crystal-concentration method are reviewed and the problems with each method discussed. The method using straight lines on plots of log thickness versus area^1/2 is the most geologically reasonable because most deposits thin exponentially from source and therefore plot as straight lines using these coordinates. Errors and uncertainties in previous derivations for using this method are discussed and more general formulas presented. The method is also used to gain perspective on the missing distal volumes calculated by the crystal-concentration method compared to those calculated based only on isopach data.