Isopleth intersections in thermobarometry

Pseudosections, THERMOCALC updates

Following a recent conversation on the Discussion Board, I wanted to post about the use of pseudosections in thermobarometry.

It has become commonplace to quote a pressure–temperature estimate for a metamorphic rock using an intersecting isopleth calculation, i.e. to:

  1. Calculate a P–T pseudosection, and locate the assemblage field on it that matches the assemblage seen in the rock.
  2. Translate two measures of mineral composition from the rock into the composition variables used in the x-eos, and plot the associated mineral composition isopleths.
  3. Locate the intersection of the two chosen isopleths, preferably within the field identified in step 1.
  4. Quote the (P, T) of this isopleth intersection as the (P, T) recorded in the mineral assemblage.

An early and nuanced example is Štípská & Powell (2005; J Metamorphic Geol 23 627-647), but there are many recent examples that are described with much less caution.

As a developer of the x-eos (thermodynamic models/solution models) that underlie calculations in THERMOCALC, MAGEMin and similar programs, I am deeply sceptical about the isopleth-intersection approach. It demands enormous precision from the x-eos. They do not have this precision.

It is simple to show this in relation to a given rock sample. For a typical field on a pseudosection, there will be at least 5, and easily as many as 15, compositional variables for which isopleths could be calculated, representing major compositional variables in abundant minerals in the assemblage. In theory, they should all intersect at a single (P, T). I have never seen them even come close! If they do not intersect, it is misleading to select two of them and use those to define (P, T).

I mentioned isopleth intersections in the context of uncertainties in the x-eos in two talks in 2021, kindly made available to the public by ANU RSES Departmental Seminars and the Metamorphic Studies Group:

The talks refer to a method in THERMOCALC that combines isopleth loci in a statistical sense. This method is described in a manuscript (Green & Powell) that is currently under review.

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