and implications for the maximum depth of LEFM applicability (at least in the study area)
For most fracture types a linear relation exists between length L and maximum displacement Dmax. Field evidence usually shows that
where a = 1 and g ranges between 0.1 and 0.001. This rule works surprisingly
well for a given fracture population that is not restricted by mechanical
discontinuities; the observed data scattering is explained by the difference
in linkage stage among the studied fracture population . The value
taken by g depends on rock type, water content, and planetary size (gravity).
Figure 1 : Location of the study area in Ethiopia
The exponent of this population is 0.48 (Figure 2). The behaviour of silicic and basaltic dykes is not significantly different; counting them in the same population improves the correlation coefficient (0.69) .
Figure 2: Length vs. maximum displacement for 39 studied Ethiopia dykes and other dykes and veins which dimensions were found in previous papers. These populations are better fit by a square-root law (dashed lines) than a linear law (dotted lines) .
where KIC is fracture toughness in mode I (opening), n is Poisson's ratio, and E the Young's modulus of the basaltic rock mass, shows this square-root dependence.
However, this equation considers that dyke is infinitely tall. It is clear though that all the silicic dykes and many basaltic dykes should have erupted , and it can be shown that a more realistic fracture toughness is ~1/3 the value given by this equation , which gives 77 < KIC < 273 MPa.m1/2. Similar KIC values have been obtained in publications on other dyke populations.
Figure 3: Interpreted magmatic and magnetic fabric of dykes from the studied populations showing mixed-mode emplacement. The diagram for mode I is to illustrate the theoretical patterns expected in case of dyke propagation in pure opening .
... which may help identify eruptive dykes!
In construction... See the paper by Mège and Korme in the publications list (JVGR n°131) for more information.
 R.A. Schultz, R. Soliva, C. Okubo and D. Mège, 2009, Fault populations. In R.A. Schultz and T.R. Watters (Eds), Planetary Tectonics. Cambridge Univ. Press, 456-509.
 R.A. Schultz, D. Mège and H. Diot, 2008, Emplacement conditions of igneous dikes in Ethiopian Traps. J. Volc. Geotherm. Res., doi:10.1016/j.jvolgeores. 2008.08.012.
 D. Mège, and T. Korme 2004, Fissure eruption of flood basalts from statistical analysis of dyke fracture length. J. Volc. Geotherm. Res., 131, 77-92, doi:10.1016/S0377-0273(03)00317-2.
 D. Mège and T. Korme, 2004, Dyke swarms in the Ethiopian Large
Igneous Province: not only a matter of stress. J. Volc. Geotherm. Res.,
132/4, 283-310, doi:10.1016/S0377-0273(03)00318-4.