Will Wilkinson has by far the best survey and treatment of this question. Here is one excerpt:
By far the boldest claim, advanced in this 2002 paper by Mark Skidmore of the University of Wisconsin-Whitewater and Hideki Toya of Nagoya City University in Japan, is that some disasters can boost GDP by forcing upgrades in technology and infrastructure, and offering the opportunity for critical reappraisal of ingrained modes of economic activity, leading to a higher level of productivity and, eventually, to net gains in growth. They find that this holds for some weather-related disasters, but not for geological disasters. They find persistent, long-run negative effects for geological catastrophe, suggesting any upside from Japan’s earthquake and tsunami is unlikely. The argument of this paper, which is as strong as the disaster-bonus case gets, is a touchstone for a good deal of later research.