F. E. M. Lilley

On Kinematic Dynamos

The method developed by Bullard & Gellman, to test flows of electrically conducting fluid in a sphere for dynamo action, is applied further to the two-component T1S2c2 flow pattern they proposed. In agreement with Gibson & Roberts, it is found that the results of the test are negative, which substantiates the indication from Braginskii’s work that the T1S2c2 flow pattern has too great a symmetry for it to act as a dynamo. However, the addition of a third component, S2s2, to the flow pattern reduces the symmetry and produces results which indicate strongly that the three-component T1S2c2S2s2 flow does act as a dynamo. Harmonics of magnetic field up to degree six have been taken into account, and this level of truncation appears to be justified. The streamlines of the T1S2c2S2s2 flow form a distinctive whirling pattern in three dimensions, and this may be a physical characteristic necessary for dynamo action. The main magnetic fields of the T1S2c2S2s2 dynamo are all toroidal, and the possibility is established that the geomagnetic dynamo is similar, with the dominant components of field being completely contained within the core. Variation of the subsidiary poloidal components of the field may then produce secular variation and even dipole reversals, without major change in the series of interactions between the toroidal components that form the basic dynamo.

Magnetotelluric analysis using Mohr circles

The Mohr circle, most commonly met in the analysis of mechanical stress, is used to depict magnetotelluric impedance information, taking the real and quadrature parts of magnetotelluric tensors separately. The magnetotelluric concepts of two‐dimensionality, three‐dimensionality, skew and anisotropy are then all given quantitative expression on a diagram, as are various magnetotelluric invariants. In particular, a new invariant, the “central impedance,” becomes evident in a discussion of effective impedances. Some insight is gained into impedance rotations, and an anisotropy angle is defined, analogous to skew angle. Mohr circles are also tested to depict the effects of the shear and twist operations on a regionally two‐dimensional structure. Generally, the application of shear or twist results in an impedance tensor with a Mohr circle of typical three‐dimensional form.

Magnetotelluric tensor decomposition: Part I, Theory for a basic procedure

The problem of expressing a general 3-D magnetotelluric (MT) impedance tensor in the form of a 2-D tensor that has been distorted in some way is addressed first in terms of a general theorem. This theorem shows that when the real and quadrature parts of a tensor are analyzed separately as distinct matrices, all that is necessary to make a matrix with 2-D characteristics from one with 3-D characteristics is to allow the electric and magnetic observing axes to rotate independently. The process is then examined in terms of the operations of twist and pure shear (“split”) on such matrices. Both of two basic sequences of split after twist, and twist after split, produce a typical 3-D matrix from one initially 1-D, with the parameters of split contributing 2-D characteristics to the final matrix. Taken in reverse, these sequences offer two basic paths for the decomposition of a 3-D matrix, and are seen to be linked to the initial theorem. The various operations on matrices are expressed diagrammatically using t...

Electrical conductivity profiles and implications for the absence or presence of partial melting beneath central and southeast Australia

Abstract A previous paper presented measurements by Australian magnetometer arrays of Earth response to the magnetic daily-variation source field, and interpreted these data by simple representative models of one-dimensional structure found by “forward model-fitting”. This paper now supplements the earlier interpretation by seeking to clarify the ranges of acceptable models which fit the data; that is, to demonstrate the extent of the non-uniqueness of the interpretation. Searches for models which fit the data have been carried out on both a systematic and a random basis, with similar results. The major conclusion of the earlier paper is confirmed; that there is a substantial difference in conductivity structure between central and southeast Australia. Beneath central Australia, the structure is consistent with a traditional continental geotherm and published laboratory measurements on the temperature dependence of the electrical conductivity of recognized upper-mantle crystalline olivine materials. Beneath southeast Australia, a higher conductivity by an order of magnitude in the depth range 200–300 km is most directly interpreted in terms of a small degree (perhaps 5%) of basalt melt. Such a partial-melt zone under southeast Australia is consistent with previous natural electromagnetic measurements for the area; has earlier and independently been indicated by a variety of seismic studies; and correlates with proposed thermal models which involve crustal intrusion from some sub-lithospheric magma source.

Electrical conductivity from Australian magnetometer arrays using spatial gradient data

Quiet daily magnetic variations recorded by magnetometer arrays in Australia are analysed to obtain electromagnetic response parameters for two parts of the Australian continent remote from electrical conductivity anomalies. The parameters are based on measurements of vertical-field and horizontal-field spatial gradient, and three different methods are followed in their computation. The response parameters are checked for consistency with a compilation of globally-determined Earth apparent resistivities, and are then interpreted for one-dimensional conductivity structure in the two different parts of the continent. There is evidence that the rise in electrical conductivity from 10−1 S m−1 to 100 S m−1 which occurs at a depth of order 500 km beneath central Australia may occur at a substantially shallower depth of order 230 km beneath southeast Australia.

A magnetometer array study in northwest India

Abstract A magnetometer array study has been carried out in northwest India, from Rajasthan across the Indo-Gangetic Plain into the Himalayan foothills. Over the three months of operation, a wide variety of natural geomagnetic events has been recorded. The analysis of a simple substorm, polarized just west of north, shows a strong anomaly in the form of a reversal of the vertical component of the fluctuation, both in the Himalayan foothills and on the Ganga Plain. The magnetic fluctuations pattern observed is most directly interpreted in terms of a path of concentrated current flow in the Earth, striking across the Himalaya. It is evidently aligned with the Aravalli belt which outcrops further south, and may indicate that some geological structure in the sub-basement is of abnormally high electrical conductivity. The path of such a current concentration across the foothills raises the question whether some transverse structure in the Himalaya is not acting as a bridge to Peninsular India for current induced in the Tibetan plateau to the northeast.

An application of thin-sheet electromagnetic modelling to the Tasman Sea

Abstract The method of thin-sheet approximation is invoked for the ocean layer to model and interpret magnetotelluric (MT) data observed on the floor of the Tasman Sea, between Australia and New Zealand. A technique to remove 3D distortion from the observed seafloor MT data is developed from the thin-sheet model MT responses; the ‘de-distorted’ data then appear isotropic, and are reinverted using 1D procedures. This approach thus assists interpretation through a combination of 3D forward-modelling procedures and 1D inversion. A seafloor sediment layer is shown to have a strong effect on observed seafloor MT data. Also, an exercise is carried out to compare the results given by the vertical gradient sounding (VGS) method with seafloor MT data. The electrical conductivity structure beneath the Tasman Sea is analysed in terms of an upper-mantle lithosphere and asthenosphere, and a highly conducting lower mantle. The observed anisotropy in seafloor MT data is diagnostic of a lithospheric conductivity of less than 10−4 S m−1. Conductivity rises by two orders of magnitude below 80 km, to greater than 10−2 S m−1, and is probably related to an asthenospheric layer in the upper mantle. Seismic interpretations similarly place a low-velocity zone below a depth of 70 km. At a depth of approximately 400 km, the conductivity is approximately 1 S m−1, consistent with global estimates for the lower mantle. There is little evidence for major change with age in the structure across the Tasman Sea.

Abyssal currents during the formation and passage of a warm-core ring in the East Australian Current

Abstract Measurements of currents and temperatures at abyssal depths in the Tasman Sea are compared with near-surface observations of the East Australian Current (EAC) System to ascertain the extent to which the deep and near-surface flows are related. The deep measurements come from three instruments which were moored at different locations on the Tasman Abyssal Plain from early December 1983 to late March 1984. They included an Anderaa current meter, recording velocity and temperature, a second temperature sensor, and an instrument which recorded fluctuations in temperature and the vertical component of the ambient electric field (from which zonal velocity is inferred). During this period a meander of the East Australian Current moved southwards and pinched off to form a warm-core ring. Both the current meter and the vertical electric field instrument recorded current surges to the east when the surface front first arrived at their positions. The maximum speed recorded by the current meter was 35 cm s−1 (when the flow was southward). Strong abyssal currents (over 10 cm s−1) were usually in the same approximate direction as the surface current at the EAC front and associated with the movement of the front before the ring pinched off. The abyssal temperature fluctuations increased in magnitude with the increase in water velocity as the front moved past, but the temperature records do not indicate that any thermal effect of the eddy extended to the sea floor.

Diagrams for magnetotelluric data

Observed magnetotelluric data are often transformed to the frequency domain and expressed as the relationship E1E2=z11z12z21z22H1H2,where E1, E2 and H1, H2 represent electric and magnetic components measured along two orthogonal axes (in this paper, for simplicity, to be north and east, respectively). The elements zij comprise the magnetotelluric impedance tensor, and they are generally complex due to phase differences between the electric and magnetic fields. All quantities in equation (1) are frequency dependent. For the special case of “two‐dimensional” geology (where structure can be described as having a certain strike direction along which it does not vary), z11=-z22 with z12≠-z21. For the special case of “one‐dimensional” geology (where structure varies with depth only, as if horizontally layered), z11=z22=0 and z12=-z21.

Linear relationships in geomagnetic variation studies

Abstract The linear properties of Maxwells equations enable the primary and secondary fields of geomagnetic variations to be related together by an induction tensor. Variations of total field which are confined on or near a plane, as described first by Parkinson, can occur formally only under certain conditions on either the induction tensor (that it have a simple degeneracy), or on the primary variation field components (that they consistently obey the same linear relationship over all time). The second condition is implausible for typical transient variations observed on earth, and examination of the first condition demonstrates that for variations with no consistent correlation of the horizontal components, the existence of a well-determined Parkinson vector means that observed vertical variations are secondary fields, induced by observed horizontal variations. This conclusion has important implications for the theoretical explanation of the geomagnetic “coast effect”. That primary fields be spatially uniform is a tacit condition of much theoretical work on geomagnetic variations, though the condition can in fact be relaxed to require spatial uniformity of the primary fields just within some “induction region”. If however the primary fields are not uniform over the induction region a poor Parkinson-vector determination may result. This may be most noticeable at sites which have their induction regions greatly extended by a process such as current channelling.