Scaling laws of the size distribution Scaling laws of the size distribution of monogenetic volcanoes within of monogenetic volcanoes within

the Michoacan-Guanajuato the Michoacan-Guanajuato Volcanic Field (Mexico)Volcanic Field (Mexico)

Michoacan-Guanajuato Volcanic Michoacan-Guanajuato Volcanic FieldField

• 1040 monogenetic volcanoes– Mainly basaltic cinder cones

• Used size of m-volcano defined by basal diameter

– 1 or very few magma pulses

• Rivera and Cocos plate subduction– Transmexican Volcanic Belt (TMVB)

– Largest intra continental volcanic arc

• Estimated morphometric parameters (height, diameter [base and crater], and volume)– Gathered information from topo maps and measurements in the field

• Similar power-law to Gutenberg-Richter– Respect to size-distribution

• Log10[N(size>Wco)] = a – b log10[Wco]– b: rate of occurrence between small/large volcanoes– N: # volcanoes with diameter greater than Wco (1.33km)

• a = 2.98, b = 5.02, Wco > 1.33 km

• Self-organized criticality phenomenon– Monogenetic fields distributed as fractal in size

• Formula can be applied to future volcanoes– Assess hazard– B-paramater directly related to monogenetic volcanic activity– Size distribution does not occur randomly

ConclusionsConclusions

Gutenberg-Richter LawGutenberg-Richter Law

• The number of earthquakes of magnitude M is proportional to 10-bM

• Look at the graph (all the earthquakes in 1995)– red line gives the Gutenberg-Richter prediction with b = 1. The

value of b seems to vary from area to area, but worldwide it seems to be around b=1.