Kathy Whaler

Deep structure of the Baringo Rift Basin (central Kenya) from three‐dimensional magnetotelluric imaging: Implications for rift evolution

Three-dimensional modeling of data from 31 vertical electrical and 24 magnetotelluric soundings collected in the Baringo-Bogoria Basin (central Kenya Rift Valley) shows a thick succession of well-defined tectonostratigraphic units beneath the Recent deposits of the Marigat-Loboi Plain. They include from top to bottom, a sedimentary basin, ∼1.5 km thick, controlled by N-S and N140° structural trends, and a thick homogeneous resistive layer related to the bottom of the basin, overlying a conductive structure, which cannot be clearly correlated with the Proterozoic basement. It is suggested that the resistive layer correlates with the mid-Miocene plateau-type flood phonolites which flowed over the early Kenya Rift during a major volcanic activity period. The conductive structure overlain by these lava flows could be a sedimentary basin developed during the initial phase of rifting, during the Oligocene-Miocene. The absence of a significant gravity low associated with this deep basin suggests a zone of dense intrusion deeper than 5–10 km, not discernible with the magnetotelluric data but required to explain the gravity anomalies. The recognition of a deeply buried sedimentary succession lying between 4 and 8 km beneath the lower Miocene volcanic series of the Baringo valley would provide new insights into the regional volcano-sedimentary stratigraphie succession and the rift development of the Kerio and Baringo Basins.

The electrical resistivity structure of the crust beneath the northern Main Ethiopian Rift

Abstract 18 audio-frequency magnetotelluric (MT) sites were occupied along a profile across the northern Main Ethiopian Rift. The profile covered the central portion of the Ethiopia Afar Geoscientific Lithospheric Experiment (EAGLE) line 1 along which also a number of broadband seismic receivers were deployed, a controlled-source seismic survey was shot, and gravity data were collected. Here, a two-dimensional model of the MT data is presented and interpreted, and compared with the results of other methods. Shallow structure correlates well with geologically mapped Quaternary to Jurassic age rocks. Within it, a small, shallow conducting lens, at less than 1 km depth, beneath the Boset volcano may represent a magma body. The 100 Θm resistivity contour delineates the seismically inferred upper crust beneath the northern plateau. The Boset magmatic segment is characterized by conductive material extending to at least lower crustal depths. It has high velocity and density in the upper to mid-crust and upper mantle. Thus, all three results suggest a mafic intrusion at depth, with the MT model indicating that it contains partial melt. There is a second, slightly deeper, more conductive body in the lower crust beneath the northern plateau, tentatively interpreted as another zone containing partial melt. The crust is much more resistive beneath the southern plateau, and has no resistivity contrast between the upper and lower crust. The inferred geoelectric strike direction on the plateaus is approximately parallel to the trend of the rift border faults, but rotates northwards slightly within the rift, matching the orientation of the en echelon magmatic segments within it. This follows the change in orientation of the shear wave splitting fast direction.

Minimal crustal magnetizations from satellite data

Abstract The minimum amplitude crustal magnetization needed to explain Magsat vector anomaly data is found using harmonic splines as basis functions (Shure et al., 1982, Phys. Earth Planet. Inter., 28: 215–229), and choosing a subset of the original basis (Parker and Shure, 1982, Geophys. Res. Lett., 9: 812–815) to represent magnetization. We suggest the optimum model of this type is obtained by associating representers only with north and vertically downwards data points, given the larger uncertainties associated with east-component Magsat data. Following Parker et al. (1987, Rev. Geophys., 25: 17–40) we find a model minimizing the r.m.s. volume integral of magnetization over the magnetized lithosphere. The numerical effort involved in producing a regional- or continental-scale model with given horizontal spatial detail with our method is less than that for an equivalent source dipole model (when the magnetization is not assumed induced), approximately equal to that for an induced magnetization equivalent dipole model, and considerably less than that for a spherical harmonic apparent susceptibility model. The method is demonstrated by producing a solution for two regions—the contiguous USA, for comparison with previously published models, and Africa and its continental margins. Magnetization models fit the data slightly worse than those of the downward-continued anomaly field at the Earths surface. Comparison of our component of magnetization for the USA in the direction of the core field with the induced magnetization equivalent dipole model of Mayhew (1984, Earth Planet. Sci. Lett., 71: 290–296) is very good. As expected for magnetization either induced by, or frozen remanently in, an approximately dipole field either parallel or antiparallel to the current rotation axis, the east component of magnetization is much smaller than the north and vertically downwards components. We make no assumptions about the relative contributions of remanent and induced magnetization, and the resulting models have a substantial remanent component. However, our models suffer from the severe non-uniqueness common to all magnetization models, whereby magnetization in a uniform (susceptibility and thickness) shell concentric with the Earths centre owing to any internal magnetic field that is then ‘switched off’ generates no external magnetic field.

Physical constraints for the analysis of the geomagnetic secular variation

Abstract Slow changes in the magnetic field are believed to originate in the core of the Earth. Interpretation of these changes requires knowledge both of the vertical component of the field and of its rate of change at the core-mantle boundary (CMB). While various spherical harmonic models show some agreement for the field at the CMB, those for secular variation (SV) do not. SV models depend heavily on annual means at relatively few and poorly distributed magnetic observatories. In this paper, the SV at the CMB is modelled by fitting 15-year differences in the annual means of the X, Y and Z components (from 1959 to 1974). The model is made unique by imposing the constraint that ⨍ CMB B r 2 d S be a minimum, using the method of Shure et al. (1982). If SV is attributed to motions of core fluid, then this model will yield, in some sense, the slowest core motions. The null space is determined by the distribution of observations, and therefore, to be consistent, only those observatories have been retained which recorded almost continuously throughout the interval 1959–1974. The method allows misfit between the model and the observations. The best value for the misfit can be derived from estimates of errors in the data, or alternatively, because larger misfit leads to smoother models (i.e., smaller ⨍ B r 2 d S ), the best value can be estimated subjectively from the final appearance of the model. Both procedures have their counterparts in the conventional spherical harmonic expansion approach, when smoothing is achieved by lowering the truncation level. The new proposal made in this paper is to use objective criteria for determining the misfit, based on the assumption that diffusion is negligible, in which event all integrals ∫ B r 2 d S will vanish when Si is a region on the CMB bounded by a contour of zero vertical component of field. For the 1965 definitive model which is adopted here, and for most other contemporary models, there are six such areas, giving five independent integrals (the integrals over the six regions must sum to zero if ▿ · B = 0). Tabulating these integrals for various choices of the misfit gives minimum values near 2 nT y−1. It is impossible to achieve this good a fit to the data using a reasonable model derived by truncating the spherical harmonic expansion. The value 2 nT y−1 corresponds to errors of ∼ 20 nT in individual annual means, which is rather larger than expected from the scatter in the data.

THE 1969 GEOMAGNETIC IMPULSE AND SPIN-UP OF THE EARTH'S LIQUID CORE

We relax the steady motions assumption in inversions for the velocity field at the core surface, allowing the flow to change instantaneously at the jerk epoch, then allowing one, and, finally, two spherical harmonic flow coefficients to change continuously with time. The period 1965–1975 covering the 1969 magnetic jerk epoch has been investigated using spherical harmonic models of the geomagnetic field and secular variation. An instantaneous change in the flow cannot account for the jerk signal. An otherwise steady flow with one coefficient changing with time can produce a jerk signal in the SV at the surface of the Earth, but the statistics show that the fit to the input models is only modestly improved. We find evidence of spin-up of the core, in the increase of the axisymmetric flow component after the jerk, from a series of flows each assumed steady over 5 yrs. An inversion with two coefficients dependent on time further demonstrates the acceleration of the flow and also shows a lag of the solid body flow component behind an equatorial acceleration, suggesting that the spherical geometry of the core-mantle boundary has a strong influence on the core dynamics. An estimate of the spin-up time of 5 yrs gives an approximate eddy viscosity for the core of 7 m2 s−1. Neglecting magnetic fields and buoyancy, the results suggest that hydrodynamics of spin-up in a spherical container with a turbulent Ekman boundary layer occurs in the same manner as with a laminar boundary layer. Toroidal fields at the core surface of the order of 1 mT and weak stratification 10−9 K/km attenuate the action of boundary layers. However, poloidal magnetic field of strength 1 mT and stratification of the order 10−2 K/km can produce two-dimensional flow in an electrically insulating cylindrical container. If the container is conducting, the interaction of the Hartmann currents in the fluid and container produces two-dimensional flow on a spin-up time scale of 5 yrs involving a weakly conducting whole mantle, with mean conductivity of 0.1 S m−1.

Geomagnetism, Earth rotation and the electrical conductivity of the lower mantle

Abstract A new approximation is derived for the electromagnetic torque acting on an electrically conducting mantle as a result of fluid flow in the core. The torque considered is that associated with the toroidal field induced in the mantle by advection of poloidal field (which is assumed to be frozen into an infinitely conducting liquid core) by the flow of liquid at the top of the core. The expression relies on the assumption that the mantle is an insulator apart from a ‘thin’ (with respect to the core radius) layer of finite conductance adjacent to the core-mantle boundary. This allows the toroidal field scalar in the mantle to be expressed as a first-order Taylor approximation. The time-dependent torque calculated at a sequence of epochs this century is compared with the torque which has previously been inferred from astronomical observations of the length of day. Although the initial results appear unpromising, a significant correlation exists when poorly determined components of the velocity field, which contribute substantially to variations in the calculated torque, are ignored. By regression analysis the conductance of the assumed thin layer is determined as 6.7 × 108 S and the lag of the electromagnetic torque behind the astronomical torque as 6 years, which is interpreted as the delay time for electromagnetic signals through the mantle. Finally, the implications of these results for the conductivity of the lower mantle are discussed. They imply that the bottom few hundred kilometres of the mantle probably have a conductivity of a few hundred to a few thousand siemens per metre; previously published lower-mantle conductivity models are examined in light of this conclusion. The close correlation of the variations in the calculated electromagnetic torque, which depend primarily on fluctuations in the core velocity field, with the length of day torque provides independent evidence that core flow is not steady on the decade time-scale.

Derivation and use of core surface flows for forecasting secular variation

Improving forecasts of the temporal and spatial changes of the Earths main magnetic field over periods of less than 5 years has important scientific and economic benefits. Various methods for forecasting the rate of change, or secular variation, have been tried over the past few decades, ranging from the extrapolation of trends in ground observatory measurements to computational geodynamo modeling with data assimilation from historical magnetic field models. We examine the utility of an intermediate approach, using temporally varying core surface flow models derived from relatively short periods of magnetic field data to produce, by advection, secular variation estimates valid for the Earths surface. We describe a new method to compute a core flow changing linearly with time from magnetic secular variation and acceleration data. We invert a combination of data from the CHAMP satellite mission and ground observatories over the period 2001.0 to 2010.0 for a series of such models. We assess their ability to forecast magnetic field changes by comparing them to CHAOS-4, a state-of-the-art model using data from 1997 to 2014.5. We show that the magnetic field predictions tend to have a lower root-mean-square difference from CHAOS-4 than the International Geomagnetic Reference Field or World Magnetic Map series of secular variation models.

Maps of the magnetic anomaly field at Earth's surface from scalar satellite data

Satellite measurements of the magnetic anomaly field intensity have been used to estimate components of the vector field at the Earths surface, using a linear approximation to relate satellite scalar measurements to downward-continued vector components. The relation between data and model was inverted using a depleted harmonic spline basis to find an almost minimum norm solution, enabling the detail present in satellite data to be preserved over continental-sized areas. In their development of the depleted basis method, Parker and Shure (1982) advocated using a subset of the original data as points in the depleted basis. Here, it is shown that a depleted basis formed from vertical component data kernels is much more satisfactory than a subset of measured intensity data kernels; however, we do form the depleted basis at the physical locations of actual data. The downward-continued map over Africa agrees well with its counterpart produced from Magsat orthogonal component data.

Consistency between the flow at the top of the core and the frozen-flux approximation

The flow just below the core-mantle boundary is constrained by the radial component of the induction equation. In the Alfvén frozen-flux limit, thought to be applicable to the outer core on the decade timescale of interest in geomagnetism, this gives a single equation involving the known radial magnetic field and its secular variation in two unknown flow components, leading to a severe problem of non-uniqueness. Despite this, we have two specific pieces of flow information which can be deduced directly from the frozen-flux induction equation: the component of flow perpendicular to null-flux curves, contours on which the radial magnetic field vanishes, and the amount of horizontal convergence and divergence at local extrema (maxima, minima and saddle points) of the radial magnetic field. To produce global velocity maps, we make additional assumptions about the nature of the flow and invert the radial induction equation for flow coefficients. However, it is not clear a priori that the flows thus generated are consistent with what we know about them along null-flux curves and at local extrema. This paper examines that issue. We look at typical differences between the null-flux curve perpendicular flow component, and convergence and divergence values at extrema, deduced directly from the induction equation and those from the inversions, investigate the effect of forcing the inversions to produce the correct null-flux curve and extremal values, and characterise the uncertainties on the various quantities contributing. Although the differences between the flow values from the induction equation directly and obtained by inversion seem large, and imposing the direct flow information as side constraints during inversion alters the flows significantly, we also show that these differences are within the likely uncertainties. Thus, we conclude that flows obtained through inversion do not contravene the specific flow information obtained directly from the radial induction equation in the frozen-flux limit. This result should reassure the community that frozen-flux flow inversion is a consistent process, even if including the extremal-value and null-flux conditions as additional information on flow inversion is unlikely to be useful. Solving for a time-dependent core-mantle boundary field model and flow simultaneously may be a good way to produce a temporally-varying field model consistent with the frozen-flux constraint; the ability to fit the data with such a model could be used to establish the timescale over which the frozen-flux assumption is valid.

Properties of steady flows at the core-mantle boundary in the frozen-flux approximation

Abstract Steady flows covering the epochs 1960–1980 produced by the method of Whaler and Clarke are examined in terms of the partitioning of energy between toroidal and poloidal, geostrophic and ageostrophic parts, the spatial and temporal fit to the data and the extent to which the flows are symmetric about the equator. It is found that, if they are not constrained to be so, the flows are neither nearly toroidal nor nearly tangentially geostrophic. This is in contrast to previous results in which the toroidal and geostrophic parts of the flow have been found to be considerably stronger than the poloidal and ageostrophic parts, respectively. The temporal fit reflects the choice of secular variation spherical harmonic models used in the inversion, while the spatial distribution of residuals shows no localised areas of high misfit, in contrast to those for toroidal or tangentially geostrophic models, which show large misfits over Africa or near the poles respectively. The equatorially symmetric component of the flow is more energetic and has less small-scale energy, as is the case for purely toroidal and tangentially geostrophic flows, supporting the assertion that it is the more important and better determined part of the flow.