Scaling multiblast craters: General approach and application to volcanic craters

Most volcanic explosions leave a crater in the surface around the center of the explosions. Such craters differ from products of single events like meteorite impacts or those produced by military testing because they typically result from multiple, rather than single, explosions. Here we analyze the evolution of experimental craters that were created by several detonations of chemical explosives in layered aggregates. An empirical relationship for the scaled crater radius as a function of scaled explosion depth for single blasts in flat test beds is derived from experimental data, which differs from existing relations and has better applicability for deep blasts. A method to calculate an effective explosion depth for nonflat topography (e.g., for explosions below existing craters) is derived, showing how multiblast crater sizes differ from the single-blast case: Sizes of natural caters (radii and volumes) are not characteristic of the number of explosions, nor therefore of the total acting energy, that formed a crater. Also, the crater size is not simply related to the largest explosion in a sequence but depends upon that explosion and the energy of that single blast and on the cumulative energy of all blasts that formed a crater. The two energies can be combined to form an effective number of explosions that is characteristic for the crater evolution. The multiblast crater size evolution has implications on the estimates of volcanic eruption energies, indicating that it is not correct to estimate explosion energy from crater size using previously published relationships that were derived for single-blast cases.