Paul Dennis edited untitled.tex  over 8 years ago

Commit id: b284d771a66e896404516870fc5400473de87bcc

deletions | additions      

       

\[t = \frac{{\pi \cdot \left( {3.3 \times {{10}^{ - 4}} \cdot V - 0.5} \right)^2}}{{1 \times {{10}^{ - 6}}}}\]  Table 2 lists values of t for different values of V. The values of V were chosen corresponding to the volumes of fluid expelled from an overpressured 40km x 1000m thick sediment sequence at depthwithin the Edale basin  with incremental changes in porosity of 0.1, 1 and 10\% on dewatering. These approximate to the dimensions of the Carboniferous Edale basin to the north-east of the Derbyshire platform. The  porosity changes range from the smallest incremental changes calculated for individual dewatering pulses of overpressured sediments to the integrated maximum volume of fluid that might be expelled \citep{Cathles:1983tj}. The corresponding values of t are 16, 1723 and 173500 years respectively. These correspond to mean fluxes of 285, 26.5 and 0.26 litres.m^{-1}.hr^{-1}. Such flow rates are not geologically unrealistic. The highest rates associated with the smallest fluid pulses are on the order of the rates of effusion from springs that have been monitored for periods of several years following moderate earthquakes e.g (add refs by Nur and Tsuneishi et al., 1970). One can legitimately question the model details and parameter estimates but the point of this somewhat heuristic approach is not to be an accurate model. It is to give an indication of the flow rates that are needed to sustain the maximum observed thermal anomaly within the Dirtlow Rake and Castleton fault assuming a physical system that couples fluid overpressure and faulting. That the model may only be accurate to within a factor of 5 to 10 does not invalidate the central result that the fluid release must occur as pulses of short duration to sustain the thermal anomaly.