THE TRANSMISSIVE TIMESCALE: A SYSTEM PARAMETER THAT CONTROLS THE PRESENCE (OR ABSENCE) OF EXCESS AR

An essential requirement for the ⁴⁰Ar/³⁹Ar dating technique in slowly cooled systems is that radiogenic ⁴⁰Ar is rapidly lost from large volumes of rock material while the ⁴⁰Ar-producing minerals are still diffusively “open”.  In order to prevent the buildup of excess ⁴⁰Ar in those minerals, ⁴⁰Ar must rapidly escape from the system via the intergranular transporting medium (ITM) to some sink for Ar located a distance L away.  The amount of excess ⁴⁰Ar in a system depends on a parameter called the transmissive timescale, t_T.  t_T is the characteristic time required for ⁴⁰Ar to escape from the local ⁴⁰Ar source to the sink.  Effective sinks for ⁴⁰Ar may exist at the macro-, meso-, or micro-scale and may include the atmosphere, any rock unit with a relatively small t_T, or any sufficiently capacitive local minerals, respectively. 

For Ar transport by bulk diffusion, t_T=t_D=L²/D*, where D* is the total effective bulk diffusivity of Ar in the ITM.  For Ar transport by fluid advection, t_T=t_A=L/V*, where V* is the total effective fluid velocity.  D*=D_f/(MK_d) where, D_f is the Ar diffusivity in the ITM (tortuosity corrected), M is the mass ratio of the ⁴⁰Ar-producing mineral to the ITM, and K_d is the ⁴⁰Ar-producing mineral/ITM partition coefficient for Ar.  V* is similarly defined.  Numerical modeling shows that the amount of excess Ar in the minerals of a system at steady state, is directly proportional to t_T, depending on the specific boundary conditions characterizing the system.  Furthermore, the time required for a system to evolve to the characteristic steady state excess Ar profile is proportional to t_T×(1+1/MK_d), accounting for the potential importance of the local ITM as a significantly capacitive medium for Ar.  Field data from Simplon Pass, Switzerland demonstrate these relations well.

The relationship between t_T and excess Ar content permits a predictive ability and understanding of Ar transport processes.  Where independent constraints on t_T are available, predictions can be made regarding the amount of excess Ar in the minerals of the system.  Conversely, given independent constraints on the amount of excess Ar, t_T may be inferred, and investigations of both L and the Ar transmissivity (i.e. D* or V*) characterizing the particular geologic system are possible.