ALBERT

Description: Monthly means of the magnetic field measurements at ground observatories are a key data source for studying temporal changes of the core magnetic field. However, when they are calculated in the usual way, contributions of external (magnetospheric and ionospheric) origin may remain, which make them less favourable for studying the field generated by dynamo action in the core. We remove external field predictions, including a new way of characterizing the magnetospheric ring current, from the data and then calculate revised monthly means using robust methods. The geomagnetic secular variation (SV) is calculated as the first annual differences of these monthly means, which also removes the static crustal field. SV time-series based on revised monthly means are much less scattered than those calculated from ordinary monthly means, and their variances and correlations between components are smaller. On the annual to decadal timescale, the SV is generated primarily by advection in the fluid outer core. We demonstrate the utility of the revised monthly means by calculating models of the core surface advective flow between 1997 and 2013 directly from the SV data. One set of models assumes flow that is constant over three months; such models exhibit large and rapid temporal variations. For models of this type, less complex flows achieve the same fit to the SV derived from revised monthly means than those from ordinary monthly means. However, those obtained from ordinary monthly means are able to follow excursions in SV that are likely to be external field contamination rather than core signals. Having established that we can find models that fit the data adequately, we then assess how much temporal variability is required. Previous studies have suggested that the flow is consistent with torsional oscillations (TO), solid body-like oscillations of fluid on concentric cylinders with axes aligned along the Earth's rotation axis. TO have been proposed to explain decadal timescale changes in the length-of-day. We invert for flow models where the only temporal changes are consistent with TO, but such models have an unacceptably large data misfit. However, if we relax the TO constraint to allow a little more temporal variability, we can fit the data as well as with flows assumed constant over three months, demonstrating that rapid SV changes can be reproduced by rather small flow changes. Although the flow itself changes slowly, its time derivative can be locally (temporally and spatially) large, in particular when and where core surface secular acceleration peaks. Spherical harmonic expansion coefficients of the flows are not well resolved, and many of them are strongly correlated. Averaging functions, a measure of our ability to determine the flow at a given location from the data distribution available, are poor approximations to the ideal, even when centred on points of the core surface below areas of high observatory density. Both resolution and averaging functions are noticeably worse for the toroidal flow component, which dominates the flow, than the poloidal flow component, except around the magnetic equator where averaging functions for both components are poor.

Description: SUMMARY We present new dedicated core surface field models spanning the decade from 2000.0 to 2010.0. These models, called gufm-sat , are based on CHAMP, Ørsted and SAC-C satellite observations along with annual differences of processed observatory monthly means. A spatial parametrization of spherical harmonics up to degree and order 24 and a temporal parametrization of sixth-order B-splines with 0.25 yr knot spacing is employed. Models were constructed by minimizing an absolute deviation measure of misfit along with measures of spatial and temporal complexity at the core surface. We investigate traditional quadratic or maximum entropy regularization in space, and second or third time derivative regularization in time. Entropy regularization allows the construction of models with approximately constant spectral slope at the core surface, avoiding both the divergence characteristic of the crustal field and the unrealistic rapid decay typical of quadratic regularization at degrees above 12. We describe in detail aspects of the models that are relevant to core dynamics. Secular variation and secular acceleration are found to be of lower amplitude under the Pacific hemisphere where the core field is weaker. Rapid field evolution is observed under the eastern Indian Ocean associated with the growth and drift of an intense low latitude flux patch. We also find that the present axial dipole decay arises from a combination of subtle changes in the southern hemisphere field morphology.

Description: SUMMARY We present new dedicated core surface field models spanning the decade from 2000.0 to 2010.0. These models, called gufm-sat , are based on CHAMP, Ørsted and SAC-C satellite observations along with annual differences of processed observatory monthly means. A spatial parametrization of spherical harmonics up to degree and order 24 and a temporal parametrization of sixth-order B-splines with 0.25 yr knot spacing is employed. Models were constructed by minimizing an absolute deviation measure of misfit along with measures of spatial and temporal complexity at the core surface. We investigate traditional quadratic or maximum entropy regularization in space, and second or third time derivative regularization in time. Entropy regularization allows the construction of models with approximately constant spectral slope at the core surface, avoiding both the divergence characteristic of the crustal field and the unrealistic rapid decay typical of quadratic regularization at degrees above 12. We describe in detail aspects of the models that are relevant to core dynamics. Secular variation and secular acceleration are found to be of lower amplitude under the Pacific hemisphere where the core field is weaker. Rapid field evolution is observed under the eastern Indian Ocean associated with the growth and drift of an intense low latitude flux patch. We also find that the present axial dipole decay arises from a combination of subtle changes in the southern hemisphere field morphology.

Description: SUMMARY Simulations of earthquake rupture on the southern San Andreas Fault (SAF) reveal large amplifications in the San Gabriel and Los Angeles Basins (SGB and LAB) apparently associated with long-range path effects. Geometrically similar excitation patterns can be recognized repeatedly in different SAF simulations (e.g. Love wave-like energy with predominant period around 4 s, channelled southwestwardly from the SGB into LAB), yet the amplitudes with which these distinctive wavefield patterns are excited change, depending upon source details (slip distribution, direction and velocity of rupture). We describe a method for rapid calculation of the sensitivity of such predicted wavefield features to perturbations of the source kinematics, using a time-reversed (adjoint) wavefield simulation. The calculations are analogous to those done in adjoint tomography, and the same time-reversed calculation also yields path-sensitivity kernels that give further insight into the excitation mechanism. For rupture on the southernmost 300 km of SAF, LAB excitation is greatest for slip concentrated between the northern Coachella Valley and the transverse ranges, propagating to the NE and with rupture velocities between 3250 and 3500 m s –1 along that fault segment; that is, within or slightly above the velocity range (between Rayleigh and S velocities) that is energetically precluded in the limit of a sharp rupture front, highlighting the potential value of imposing physical constraints (such as from spontaneous rupture models) on source parametrizations. LAB excitation is weak for rupture to the SW and for ruptures in either direction located north of the transverse transverse ranges, whereas Ventura Basin (VTB) is preferentially excited by NE ruptures situated north of the transverse ranges. Path kernels show that LAB excitation is mediated by surface waves deflected by the velocity contrast along the southern margin of the transverse ranges, having most of their energy in basement rock until they impinge on the eastern edge of SGB, through which they are then funnelled into LAB. VTB amplification is enhanced by a similar waveguide effect.

Description: We present a new model of the radial (1-D) conductivity structure of Earth's mantle. This model is derived from more than 10 yr of magnetic measurements from the satellites Ørsted, CHAMP, SAC-C and the Swarm trio as well as the global network of geomagnetic observatories. After removal of core and crustal field as predicted by a recent field model, we fit the magnetic data with spherical harmonic coefficients describing ring current activity and associated induction effects and estimate global C -responses at periods between 1.5 and 150 d. The C -responses are corrected for 3-D effects due to induction in the oceans and inverted for a 1-D model of mantle conductivity using both probabilistic and deterministic methods. Very similar results are obtained, consisting of a highly resistive upper mantle, an increase in conductivity in and beneath the transition zone and a conductive lower mantle. Analysis of the Hessian of the cost function reveals that the data are most sensitive to structures at depths between 800 and 1200 km, in agreement with the results obtained from the probabilistic approach. Preliminary interpretation of the inverted conductivity structure based on laboratory-based conductivity profiles shows that the recovered structure in the lower mantle either requires higher temperatures or the presence of material of high conductivity related to ponding of carbonate melts below the transition zone.

Description: SUMMARY Numerical modelling of dynamic rupture is conducted along faults separating similar and dissimilar materials. Supershear transition is enhanced in the direction of slip of the stiffer material (the negative direction) due to the bimaterial effect whereby a decrease in normal stress in front of the crack tip supports yielding ahead of the rupture. In the direction of slip of the more compliant material (the positive direction), an increase in normal stress ahead of the rupture tip delays or prevents the supershear transition, whereas the impact of the bimaterial effect on subshear ruptures is to promote rupture in the positive direction due to the tensile stress perturbation behind the rupture tip in this direction. We demonstrate that the material contrast and the parameter S control whether the transition from sub- to supershear velocity (supershear transition) is smooth or follows the Burridge–Andrews mechanism. Supershear transition along interfaces separating dissimilar materials is possible for higher values of the parameter S than supershear transition along material interfaces separating similar materials. The difference between pulse-like and crack-like rupture is small with regard to the supershear transition type.

Description: SUMMARY Data from recent satellite missions have vastly increased the resolution of models of the geomagnetic field, and its first and second time derivatives – secular variation (SV) and secular acceleration (SA). The spectra of both SV and SA are ‘blue’ at the core–mantle boundary, both well-fit by functions proportional to l ( l + 1) where l is the spherical harmonic degree. The ratio of the two spectra defines a timescale for geomagnetic variations of approximately 10 yrs for all resolvable harmonic degrees. The blue spectra should prevent meaningful maps of the SV being generated; nevertheless, the coherence of the maps up to harmonic degree 13 suggests that it is possible to obtain useful insight from their examination. Low SV is confirmed under the Pacific, but also revealed under the North Atlantic and Antarctica. These features are more readily explained in terms of dynamo control through thermal core–mantle coupling than by electromagnetic screening. Comparison with maps from measurements prior to the recent satellites, using the ‘Comprehensive Model’, suggests that models back to at least 1970 are sufficiently good to enable direct comparison of the SV.

Description: SUMMARY Simulations of earthquake rupture on the southern San Andreas Fault (SAF) reveal large amplifications in the San Gabriel and Los Angeles Basins (SGB and LAB) apparently associated with long-range path effects. Geometrically similar excitation patterns can be recognized repeatedly in different SAF simulations (e.g. Love wave-like energy with predominant period around 4 s, channelled southwestwardly from the SGB into LAB), yet the amplitudes with which these distinctive wavefield patterns are excited change, depending upon source details (slip distribution, direction and velocity of rupture). We describe a method for rapid calculation of the sensitivity of such predicted wavefield features to perturbations of the source kinematics, using a time-reversed (adjoint) wavefield simulation. The calculations are analogous to those done in adjoint tomography, and the same time-reversed calculation also yields path-sensitivity kernels that give further insight into the excitation mechanism. For rupture on the southernmost 300 km of SAF, LAB excitation is greatest for slip concentrated between the northern Coachella Valley and the transverse ranges, propagating to the NE and with rupture velocities between 3250 and 3500 m s –1 along that fault segment; that is, within or slightly above the velocity range (between Rayleigh and S velocities) that is energetically precluded in the limit of a sharp rupture front, highlighting the potential value of imposing physical constraints (such as from spontaneous rupture models) on source parametrizations. LAB excitation is weak for rupture to the SW and for ruptures in either direction located north of the transverse transverse ranges, whereas Ventura Basin (VTB) is preferentially excited by NE ruptures situated north of the transverse ranges. Path kernels show that LAB excitation is mediated by surface waves deflected by the velocity contrast along the southern margin of the transverse ranges, having most of their energy in basement rock until they impinge on the eastern edge of SGB, through which they are then funnelled into LAB. VTB amplification is enhanced by a similar waveguide effect.

Description: We present CHAOS-4, a new version in the CHAOS model series, which aims to describe the Earth's magnetic field with high spatial and temporal resolution. Terms up to spherical degree of at least n  = 85 for the lithospheric field, and up to n  = 16 for the time-varying core field are robustly determined. More than 14 yr of data from the satellites Ørsted, CHAMP and SAC-C, augmented with magnetic observatory monthly mean values have been used for this model. Maximum spherical harmonic degree of the static (lithospheric) field is n  = 100. The core field is expressed by spherical harmonic expansion coefficients up to n  = 20; its time-evolution is described by order six splines, with 6-month knot spacing, spanning the time interval 1997.0–2013.5. The third time derivative of the squared radial magnetic field component is regularized at the core–mantle boundary. No spatial regularization is applied to the core field, but the high-degree lithospheric field is regularized for n  〉 85. CHAOS-4 model is derived by merging two submodels: its low-degree part has been derived using similar model parametrization and data sets as used for previous CHAOS models (but of course including more recent data), while its high-degree lithospheric field part is solely determined from low-altitude CHAMP satellite observations taken during the last 2 yr (2008 September–2010 September) of the mission. We obtain a good agreement with other recent lithospheric field models like MF7 for degrees up to n  = 85, confirming that lithospheric field structures down to a horizontal wavelength of 500 km are currently robustly determined.