Abstract
On a relationship between the rate of fire-outbreak ; y and the rate of building destruction ; x following an earthquake, Dr. Kawasumi found a following logarithm law from date of Kantoh-earthquake. ln(y)=a×ln(x)+b. This Kawasumi-formula was modified and applied on estimations of number of fire-outbreaks by an earthquake. Any theoretical base of this formula was not made clear. The aim of this paper is to discuss the reason why the Kawasumi-formula hold and the restriction for application. Through consideration from a view of stochastic process, the probabilities of fire-outbreak and building collapse can be expressed by Gumbel's extreme distributions (minimum type) which are functions of a variable expressing earthquake-force. By eliminating the variable, a following relation between probability of fire-outbreak ; y and one of building collapse ; x is obtained. ln(-ln(1-y))=a×ln(-ln(1-x))+b. By mathematical discussion, it is proved that the Kawasumi formula is an approximation of the above stochastic formula.
