deletions | additions       diff --git a/discussion_bulk isotopes.tex b/discussion_bulk isotopes.tex  index 9afad2c..b5e4f33 100644  --- a/discussion_bulk isotopes.tex  +++ b/discussion_bulk isotopes.tex 
...
\section{Discussion}  There are four, possibly five, distinct diagenetic carbonate phases in the Visean carbonates of the Peak District \citep{Walkden_1991, Hollis_2002}. The vein carbonates at Dirtlow Rake are equivalent to the zone 4 diagenetic carbonates of this scheme. Such carbonates are associated with Pb-Zn mineralization and occur as fracture and vein fill. They are ascribed to burial diagenesis as a result of the migration of tectonically derived formation waters sourced from the sedimentary basins surrounding the Derbyshire Platform. The range of $\delta$^{13}C and $\delta$^{18}O values for zone 4 calcites reported by Hollis and Walkden (2002) for the northern margin of the platform is coincident with those we report here. The positive $\delta$^{13}C values ($\approx$+3 to +4‰_{VPDB}) and moderately depleted $\delta$^{18}O values ($\approx$-7 to -10‰_{VSMOW}) suggest precipitation from warm formation fluids that have evolved under closed system conditions with low water to rock ratios. We develop these ideas in the discussion using data for the clumped isotope temperature to constrain the likely source of the mineralizing fluids and outline a simple two component mixing process between formation waters from the Edale Basin and groundwaters local to the site of mineralization. We identify a temperature anomaly associated with upwelling hot waters along the Dirtlow rake Rake  fault and use a simple thermal model to estimate the necessary rates of fluid migration required to sustain the temperature anomaly. Finally, we attempt a synthesis of the data in terms of a simple basin evolution model, the development of overpressure as a result of gas generation, the initiation of seismic activity and subsequent fluid flow along high permeability rupture zones i.e. a seismic valve.\subsection{Temperature}  The data for the temperature at which calcite precipitated at Dirtlow Rake are the first measurements made for the southern Pennines using the clumped isotope technique. It's pertinent to ask if these temperatures are robust and representative of the hydrothermal fluid temperatures. We see a temperature range of 40$^{\circ}$C to 100$^{\circ}$C. The most direct comparison we can make is with fluid inclusion homogenization temperatures. Several fluid inclusion studies have been completed, largely using fluorite but also with a limited number of data points for calcite. Overall there is wide variation in the reported homogenization temperatures ranging from 60$^{\circ}$C to greater than 240$^{\circ}$C. Our temperature estimates fall towards the lower end of this range and are consistent with the homogenization temperatures reported for type 2 (62$^{\circ}$-82$^{\circ}$C), type 3 (64.9$^{\circ}$-98.9$^{\circ}$C), type 4 (63.4$^{\circ}$-106$^{\circ}$C) and type 5 (66.3$^{\circ}$-68.3$^{\circ}$C) inclusions in fluorite reported by Atkinson (1983). The type 1 inclusions reported on by Atkinson (1983) have higher homogenization temperatures of 119.5$^{\circ}$ - 157$^{\circ}$C. These are higher than the maximum temperatures we have observed for this part of the orefield. A difficulty in making a comparison is that the different types of inclusions are thought to relate to different stages in the mineral paragenesis and may not directly relate to the calcite veins at Dirtlow Rake.  The vein calcite at Dirtlow Rake is from zone 4 of the paragenetic sequence outlined by Walkden and xxxx. Hollis and Walkden have published limited fluid inclusion data for calcites from this zone.   \subsection{Thermal constraints on fluid flux}  To a first approximation we can use the estimated temperatures of the fluid end members to constrain the flux of fluid needed to develop a thermal anomaly similar to that observed at Dirtlow Rake. The question is how much fluid and how fast does it have to flow along the fault to (i) heat the rock in the fault zone and (ii) prevent significant heat loss via conduction through the walls of the fault? The problem is illustrated in Figure 8. Hydrothermal fluid at an initial temperature $\Theta$_{i} enters the fault at depth \textit{x}_{1} and flows up along the fault to a depth of \textit{x}_{2} where it has cooled to a temperature $\Theta$_{1}. We assume that the heat lost from the fluid (i) heats the immediate fault zone to the temperature of the fluid ($\Theta$_1) and; (ii) is lost through thermal diffusion perpendicular to the fault walls. For a parallel plate slab we can express this energy balance per metre length of fault as:  \[V \cdot \left( {{\Theta _i} - {\Theta _1}} \right) \cdot C_p^w \cdot {\rho _w} = \left[ {({x_1} - {x_2}) \cdot h \cdot \left( {\frac{{{\Theta _1} - {\Theta _2}}}{2}} \right) + \left( {{\Theta _1} - {\Theta _2}} \right) \cdot \left( {{x_1} - {x_2}} \right) \cdot {{\left( {\frac{{kt}}{\pi }} \right)}^{0.5}}} \right] \cdot C_p^r \cdot {\rho _r}\]  where V is the volume of fluid expelled along the fault, h is the effective width of the fault, C_{p}^{w} and C_{p}^{r} are the specific heat capacities of water and rock respectively, $\rho$_{w} and $\rho$_{r} the densities of water and rock, and \textit{k} the thermal diffusivity of rock. Noting that $C_{p}^{w}$ $\cdot$ $\rho_{w}$ $\approx$ 2 $\cdot$ $C_{p}^{r}$ $\cdot$ $\rho_{r}$ and selecting values of 120$^{\circ}$, 100$^{\circ}$ and 40$^{\circ}$C respectively for $\Theta$_{i}, $\Theta$_{1} and $\Theta$_{2}, 3000m for \textit{x}_{1}, 1000m for \textit{x}_{2} and an effective fault width of 1m we find that the maximum duration (s) for an individual fluid pulse is:  \[t = \frac{{\pi \cdot \left( {3.3 \times {{10}^{ - 4}} \cdot V - 0.5} \right)^2}}{{1 \times {{10}^{ - 6}}}}\]  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 depth 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.  A corollary of the pulsed nature of fluid release is that mineralization is episodic with separate events spanning limited periods up to several thousand to several ten thousand years separated by periods of stasis. This observation is convergent with recent data on the Zn content of mineralizing fluids determined from fluid inclusions in several MVT provinces that suggests mineralization events could be of durations as short as 10,000 years \citep{Bodnar:2009hc, Wilkinson06022009}.