Conductivity Models and Banks' Data

Abstract

Summary The magnetic response data of Banks has been used to determine an ensemble of conductivity models. Each model consists of a uniformly conducting thick shell surrounding a perfectly conducting inner sphere. The conductivity and thickness of the shell are found for each observed response measurement in the frequency range. The results show that the data leads to inconsistencies, and confirms the conclusions by Parker concerning this data. It is also found here that the low frequency response measurements, in particular, are unreliable. It is concluded that, neglecting the low frequency measurements, Banks’ data requires the conductivity to be low for the first 550km, or so, from the surface, followed by a gradual rise. The thickness of the transition region is uncertain, but could be as great as 300 km. Geomagnetic response measurements are used to determine the global distribution of electrical conductivity within the mantle. Measurements are available at a number of discrete frequencies corresponding to; the quiet day daily variation (Sq), the 27-day variation and its principal harmonics, the semi-annual, and annual variations. In addition, estimates of the response at close intervals in the range 0.01 to 0-225cpd, have been derived (Banks 1969), and published in tabular form (Banks 1972). References to earlier work are contained in a review of the subject by Price (1 970). Parker (1970) has used the continuum response estimates to determine a conductivity profile for the mantle. The general method of Backus & Gilbert (1967, 1968, 1970) was used to invert the data, and it was found that whatever conductivity model was used as an initial approximation, the iterative scheme failed to converge. Assuming that the initial starting model was accurate enough, Parker concluded that no conductivity model exists that satisfies Banks’ data. A further application of Backus-Gilbert inversion theory to Banks’ data was made recently by Parker (1972). The self-consistency of data pairs were examined with the use of two simple models. One consists of an infinitesimally thin surface shell of conductor surrounding a non-conducting inner core, the other consists of a non-conducting thick layer surrounding a perfectly conducting inner core. Parker found that, ignoring the effects of experimental error in the data, the consistency conditions are not satisfied by several pairs of data values. Because of the importance to the problem of conductivity modelling in the mantle, of accurate response measurements in the same frequency range as Banks’ data, these data are further examined here, by using a model which is physically more realistic