Constraints on the frequency–magnitude relation and maximum magnitudes in the UK from observed seismicity and glacio-isostatic recovery rates

Earthquake populations have recently been shown to have many similarities with critical-point phenomena, with fractal scaling of source sizes (energy or seismic moment) corresponding to the observed Gutenberg–Richter (G–R) frequency–magnitude law holding at low magnitudes. At high magnitudes, the form of the distribution depends on the seismic moment release rate M˙ and the maximum magnitude m _max . The G–R law requires a sharp truncation at an absolute maximum magnitude for finite M˙ . In contrast, the gamma distribution has an exponential tail which allows a soft or 'credible' maximum to be determined by negligible contribution to the total seismic moment release. Here we apply both distributions to seismic hazard in the mainland UK and its immediate continental shelf, constrained by a mixture of instrumental, historical and neotectonic data. Tectonic moment release rates for the seismogenic part of the lithosphere are calculated from a flexural-plate model for glacio-isostatic recovery, constrained by vertical deformation rates from tide-gauge and geomorphological data. Earthquake focal mechanisms in the UK show near-vertical strike-slip faulting, with implied directions of maximum compressive stress approximately in the NNW–SSE direction, consistent with the tectonic model. Maximum magnitudes are found to be in the range 6.3–7.5 for the G–R law, or 7.0–8.2 m _L for the gamma distribution, which compare with a maximum observed in the time period of interest of 6.1 m _L . The upper bounds are conservative estimates, based on 100 per cent seismic release of the observed vertical neotectonic deformation. Glacio-isostatic recovery is predominantly an elastic rather than a seismic process, so the true value of m _max is likely to be nearer the lower end of the quoted range.