Velocity–conductivity relationships for mantle mineral assemblages in Archean cratonic lithosphere based on a review of laboratory data and Hashin–Shtrikman extremal bounds

Abstract

Can mineral physics and mixing theories explain field observations of seismic velocity and electrical conductivity, and is there an advantage to combining seismological and electromagnetic techniques? These two questions are at the heart of this paper. Using phenomologically-derived state equations for individual minerals coupled with multi-phase, Hashin-Shtrikman extremal-bound theory we derive the likely shear and compressional velocities and electrical conductivity at three depths, 100 km, 150 km and 200 km, beneath the central part of the Slave craton and beneath the Kimberley region of the Kaapvaal craton based on known petrologically-observed mineral abundances and magnesium numbers, combined with estimates of temperatures and pressures. We demonstrate that there are measurable differences between the physical properties of the two lithospheres for the upper depths, primarily due to the different ambient temperature, but that differences in velocity are negligibly small at 200 km. We also show that there is an advantage to combining seismic and electromagnetic data, given that conductivity is exponentially dependent on temperature whereas the shear and bulk moduli have only a linear dependence in cratonic lithospheric rocks. Focussing on a known discontinuity between harzburgite-dominated and lherzolitic mantle in the Slave craton at a depth of about 160 km, we demonstrate that the amplitude of compressional (P) wave to shear (S) wave conversions would be very weak, and so explanations for the seismological (receiver function) observations must either appeal to effects we have not considered (perhaps anisotropy), or imply that the laboratory data require further refinement.