Description: Following the creation described in Part I of a deformable edge finite-element simulator for 3-D magnetotelluric (MT) responses using direct solvers, in Part II we develop an algorithm named HexMT for 3-D regularized inversion of MT data including topography. Direct solvers parallelized on large-RAM, symmetric multiprocessor (SMP) workstations are used also for the Gauss–Newton model update. By exploiting the data-space approach, the computational cost of the model update becomes much less in both time and computer memory than the cost of the forward simulation. In order to regularize using the second norm of the gradient, we factor the matrix related to the regularization term and apply its inverse to the Jacobian, which is done using the MKL PARDISO library. For dense matrix multiplication and factorization related to the model update, we use the PLASMA library which shows very good scalability across processor cores. A synthetic test inversion using a simple hill model shows that including topography can be important; in this case depression of the electric field by the hill can cause false conductors at depth or mask the presence of resistive structure. With a simple model of two buried bricks, a uniform spatial weighting for the norm of model smoothing recovered more accurate locations for the tomographic images compared to weightings which were a function of parameter Jacobians. We implement joint inversion for static distortion matrices tested using the Dublin secret model 2, for which we are able to reduce nRMS to ~1.1 while avoiding oscillatory convergence. Finally we test the code on field data by inverting full impedance and tipper MT responses collected around Mount St Helens in the Cascade volcanic chain. Among several prominent structures, the north–south trending, eruption-controlling shear zone is clearly imaged in the inversion.

Description: We have developed an algorithm, which we call HexMT, for 3-D simulation and inversion of magnetotelluric (MT) responses using deformable hexahedral finite elements that permit incorporation of topography. Direct solvers parallelized on symmetric multiprocessor (SMP), single-chassis workstations with large RAM are used throughout, including the forward solution, parameter Jacobians and model parameter update. In Part I, the forward simulator and Jacobian calculations are presented. We use first-order edge elements to represent the secondary electric field ( E ), yielding accuracy O ( h ) for E and its curl (magnetic field). For very low frequencies or small material admittivities, the E -field requires divergence correction. With the help of Hodge decomposition, the correction may be applied in one step after the forward solution is calculated. This allows accurate E -field solutions in dielectric air. The system matrix factorization and source vector solutions are computed using the MKL PARDISO library, which shows good scalability through 24 processor cores. The factorized matrix is used to calculate the forward response as well as the Jacobians of electromagnetic (EM) field and MT responses using the reciprocity theorem. Comparison with other codes demonstrates accuracy of our forward calculations. We consider a popular conductive/resistive double brick structure, several synthetic topographic models and the natural topography of Mount Erebus in Antarctica. In particular, the ability of finite elements to represent smooth topographic slopes permits accurate simulation of refraction of EM waves normal to the slopes at high frequencies. Run-time tests of the parallelized algorithm indicate that for meshes as large as 176 x 176 x 70 elements, MT forward responses and Jacobians can be calculated in ~1.5 hr per frequency. Together with an efficient inversion parameter step described in Part II, MT inversion problems of 200–300 stations are computable with total run times of several days on such workstations.

Description: Palaeointensity variation is investigated for an inferred time period spanning from 2.34 to 1.96 Ma. Twenty-nine consecutive lava flows are sampled along cliffs 350 m high generated by normal faulting on the Dobi section of Afar depression, Ethiopia. Magnetostratigraphy and K–Ar measurements indicate a lava sequence of R–N–R–N geomagnetic field polarities in ascending order; the lower normal polarity is identified as the Réunion Subchron. Reliability of palaeomagnetic data is ascertained through careful thermal demagnetization and by the reversal test. The Tsunakawa–Shaw method yielded 70 successful palaeointensity results from 24 lava flows and gave 11 acceptable mean palaeointensities. Reliability in palaeointensity data is ascertained by the similar values obtained by the IZZI–Thellier method and thus 11 reliable mean values are obtained from our combined results. After the older reverse polarity with the field intensity of 19.6 ± 7.8 μT, an extremely low palaeointensity period with an average of 6.4 μT is shown to occur prior to the Réunion Subchron. During the Réunion Subchron, the dipole field strength is shown to have returned to an average of 19.5 μT, followed by second extreme low of 3.6 μT and rejuvenation with 17.1 ± 5.3 μT in the younger reverse polarity. This ‘W-shape’ palaeointensity variation is characterized by occurrences of two extremely weak fields lower than 8 μT prior to and during the Réunion Subchron and a relatively weak time-averaged field of approximately 15 μT. This feature is also found in sedimentary cores from the Ontong Java Plateau and the north Atlantic, indicative of a possibly global geomagnetic field phenomenon rather than a local effect on Ethiopia. Furthermore, we estimate a weak virtual axial dipole moment of 3.66 (±1.85) x 10 22 Am 2 during early stage of the Matuyama Chron (inferred time period of 2.34–1.96 Ma).

Description: Adopting a model with two half-spaces that consist of solid and porous materials, we numerically investigate the seismoelectric conversion at the solid–porous interface. First, the wave fields in a low-porosity two-layer model are compared with those in a homogeneous full-space model. The consistency of seismic waves is a validation of our program. We are interested in the quasi-coseismic electromagnetic (EM) signals recorded in the solid area near the interface because they seemingly accompany seismic waves. Then, further numerical simulations on an ordinary two-layer model are conducted. On the basis of time slice snapshots and theoretical analysis, we determine that quasi-coseismic EM signals are essentially non-coseismic EM fields, which include radiation and evanescent EM waves. Evanescent EM waves are induced by the seismic waves that arrive at the interface with the incident angle greater than the critical angle. These waves decay faster than radiation EM waves when moving away from the interface. In the porous layer, evanescent EM waves can hardly be recognized unless they are separated from coseismic EM signals. This finding can be the reason why evanescent EM waves have not been identified in previous seismoelectric studies. Awareness of the fact that seismoelectric conversion at an interface can generate evanescent and EM waves is likely to result in a comprehensive understanding and improved interpretation of the seismoelectric coupling phenomenon.

Description: We present a new grand mean palaeomagnetic pole (Plong: 222.1°, Plat: –64.0°, A 95 : 2.6°, N = 49) for the ca. 1110 Ma Umkondo large igneous province (LIP) of the Kalahari Craton. New palaeomagnetic data from 24 sills in Botswana and compiled reprocessed existing data are used to develop a palaeomagnetic pole as the Fisher mean of cooling unit virtual geomagnetic poles (VGPs). The mean and its associated uncertainty provide the best-constrained pole yet developed for the province. Comparing data from individual cooling units allows for evaluation of palaeosecular variation at this time in the Mesoproterozoic. The elongation of the population of VGPs is consistent with that predicted by the TK03.GAD model lending support to the dipolar nature of the field in the late Mesoproterozoic. In our new compilation, 4 of 59 (~7 per cent) of the igneous units have northerly declinations while the rest are south-directed indicating that a geomagnetic reversal occurred during magmatic activity. Interpreting which of these polarities corresponds with a normal or reversed geomagnetic field relative to other continents can constrain the relative orientations between cratons with time-equivalent data. This interpretation is particularly important in comparison to Laurentia as it bears on Kalahari's involvement and position in the supercontinent Rodinia. The dominance of south-directed declinations within the Umkondo Province was previously used to suggest that these directions are the same polarity as reversed directions from the early magmatic stage of the Keweenawan Midcontinent Rift of Laurentia. Two Umkondo sills with northerly declinations have U-Pb baddeleyite ages of ca. 1109 Ma that are temporally close to dated Midcontinent Rift units having reversed directions. Based on this comparison, and palaeomagnetic data from younger units in the Kalahari Craton, we favour the option in which the sites with northerly declinations from the Umkondo Province correspond to the reversed polarity directions from the early magmatic stage in the Midcontinent Rift. This interpretation allows for the Namaqua-Natal metamorphic belt of Kalahari to be a conjugate to the Grenville margin of North America and for Kalahari to have become conjoined with Laurentia within the supercontinent Rodinia subsequent to Umkondo LIP magmatic activity.

Description: The northeastern Caribbean island arc, which materializes the boundary between the North American and Caribbean plates, is particularly exposed to large earthquakes and tsunamis. The low level of preparedness of a large part of its population and the lack of risk reduction provisions in public policies in many countries of the region put their population and economy at high risk in case of large telluric events. Here, we investigate the impact of three possible earthquake scenarios, consistent with the regional seismotectonic setting, on northern Haiti through inundation by tsunami waves. These scenarios simulate the effect of a M 8.0 earthquake on the Septentrional strike-slip fault (possibly similar to the 1842 earthquake), a M 8.1 earthquake on the offshore thrust fault system north of Haiti, and an earthquake rupturing a large portion of the offshore thrust fault system north of Haiti and the Dominican Republic. We calculate run-up heights along the northern coast of Haiti, in particular in the densely populated Cap Haitien. We find that the rupture of the offshore North Hispaniola thrust fault could result in wave heights up to 10 m with inundation up to 4 km inland, with only 10–15 min between ground shaking and the first wave arrivals. The city of Cap Haitien is particularly exposed, with potential flooding of most of the city and its suburbs, including the international airport. We also find that the historical reports available for the 1842 earthquake, when compared to our simulations, favor a rupture of the North Hispaniola thrust fault, although much uncertainty remains. If the 1842 earthquake did not rupture the Septentional fault offshore Haiti, then it is currently capable of at least a M w 7.7 earthquake, significantly larger than previously thought. The simulations presented here provide a basis for developing conservative maps of run-up heights that can be transferred, with added factors of safety, into practical implementation for tsunami preparedness and protection.

Description: There exists a fundamental as well as practical interest in being able to accurately forecast the future evolution of Earth's magnetic field at decadal to secular ranges. This work enables such forecasts by combining geomagnetic data with an Earth-like numerical model of a convection-driven fluid dynamo. The underlying data assimilation framework builds on recent progress in inverse geodynamo modelling, a method which estimates an internal dynamic structure for Earth's core from a snapshot of the magnetic field and its instantaneous rate of change at the surface, and takes advantage of linear relationships and long-range correlations between observed and hidden state variables. Here the method is further evolved into a single-epoch ensemble Kalman filter, in order to initialise at a given epoch an ensemble of states compatible with the observations and representative of the uncertainties in the estimation of hidden quantities. The ensemble dynamics, obtained by subsequent numerical integration of the prognostic model equations, are found to be governed by a thermal wind balance or equilibrium between buoyancy forces, the Coriolis force and the pressure gradient. The resulting core fluid flow pattern is a quasi-steady eccentric gyre organised in a column parallel to Earth's rotation axis, in equilibrium with a longitudinal hemispheric convective density anomaly pattern. The flow provides induction for the magnetic field, which also undergoes a realistic amount of diffusion. Predictions of the present magnetic field from data taken within the past century show that the ensemble has an average retaining good consistency with the true geomagnetic evolution and an acceptable spread well representative of prediction errors, up to at least a secular range. The predictability of the geodynamo thus appears to significantly exceed previous theoretical expectations based on the chaotic divergence of ensemble members. The assimilation generally outperforms the linear mathematical extrapolations from a 30-yr prediction range onwards, with a 40 per cent improvement in Earth-surface error at a secular range. The geomagnetic axial dipole decay observed over the past two centuries is predicted to continue at a similar pace in the next century, with a further loss of $1.1\pm 0.3 \hspace{2.84526pt}\mathrm{\mu T}$ by year 2115. The focal (or minimum intensity) point of the South Atlantic geomagnetic anomaly is predicted to enter the South Pacific region in the next century, with the anomaly itself further deepening and widening. By year 2065, the minimum intensity is predicted to decrease by $1.46\pm 0.4 \hspace{2.84526pt}\mathrm{\mu T}$ at the Earth surface and the focal point to move 12.8 ± 1.4 deg westwards with a slight northward component. This corresponds to a drift rate of 0.26 deg yr –1 , similar to the typical geomagnetic westward drift observed over the past four centuries. The same drift rate is also predicted until 2115 with a further (but more uncertain) intensity decrease.

Description: Mantle control on the geodynamo is often simulated using numerical dynamos with imposed outer boundary heat flux inferred from lower mantle tomography, assuming that seismic and thermal anomalies in the lowermost mantle are highly correlated. However, non-thermal effects might perturb this idealized linear seismic–thermal mapping. Here we use a probabilistic tomography model to isolate the thermal part of the seismic anomaly in order to impose a more realistic core–mantle boundary heat flux pattern on the outer boundary of numerical dynamo simulations. We demonstrate that on time average these dynamo models have more low-latitude convective and magnetic activity than corresponding models with conventional tomographic heat flux. In addition, the low-latitude magnetic flux and kinetic energy contributions are more time-dependent in the dynamo models with a probabilistic tomography heat flux, and thus may recover the observed latitudinal distribution of geomagnetic flux on the core–mantle boundary, which we propose as a morphological criterion for Earth-like dynamo models.

Description: Was the Yukon-Tanana Terrane (YTT), a California-sized part of south-central Yukon, an autochthonous or para-autochthonous part of northern British Columbia in the Early Cretaceous or was it part of a proposed allochthonous ‘Baja B.C.’ continent offshore of southern California? To answer this fundamental question, a paleomagnetic study has been completed on 347 specimens from 24 sites in the 114.7 ± 1.1 Ma Quiet Lake batholith. This 1300 km 2 pluton is composed mostly of massive medium-to-coarse grained biotite quartz monzonite that exhibits no evidence of either deformation or metamorphism, and that intrudes metamorphosed pre-Cretaceous basement rocks of the YTT in southern Yukon. The paleomagnetic analysis utilized thermal and alternating field step demagnetization, and saturation isothermal remanence methods. A well-defined characteristic remanent magnetization (ChRM) direction was isolated throughout the 500–585 °C temperature range at Decl. = 340.6°, Incl. = 77.4° ( N = 14 sites, k = 51.2, A 95 = 5.6°). The ChRM resides in magnetite with a low titanium content and is interpreted to be a primary thermoremanent magnetization. After correction for 490 km of geologically demonstrable dextral displacement on the inboard Tintina fault zone, the Quiet Lake batholith's paleopole is not significantly different at 95 per cent confidence from the co-eval 115 Ma reference paleopole for North America, giving non-significant translation and rotation estimates of 1.4° ± 5.1° (1) northwestwards and 10° ± 13° (1) clockwise, respectively. Thus, this is the first Early Cretaceous paleopole to show clearly that the YTT in Yukon is a para-autochthon that was part of North America's continental margin at that time. Further, after correction for Tintina fault displacement, the eight available Mesozoic YTT paleopoles agree closely with the North American apparent polar wander path (APWP). In contrast, the 22 paleopoles from the Intermontane Belt show the expected behaviour of an allochthonous thin-skin of terranes (i.e. ‘Baja B.C.’ behaviour) and record ~8° of northward translation and ~50° of clockwise rotation relative to both the YTT and North American APWPs during the Mesozoic and Paleogene.

Description: Feldspars are the most abundant rock-forming minerals in the Earth's crust, but their magnetic properties have not been rigorously studied. This work focuses on the intrinsic magnetic anisotropy of 31 feldspar samples with various chemical compositions. Because feldspar is often twinned or shows exsolution textures, measurements were performed on twinned and exsolved samples as well as single crystals. The anisotropy is controlled by the diamagnetic susceptibility and displays a consistent orientation of principal susceptibility axes; the most negative or minimum susceptibility is parallel to [010], and the maximum (least negative) is close to the crystallographic [001] axis. However, the magnetic anisotropy is weak when compared to other rock-forming minerals, 1.53 x 10 –9 m 3 kg –1 at maximum. Therefore, lower abundance minerals, such as augite, hornblende or biotite, often dominate the bulk paramagnetic anisotropy of a rock. Ferromagnetic anisotropy is not significant in most samples. In the few samples that do show ferromagnetic anisotropy, the principal susceptibility directions of the ferromagnetic subfabric do not display a systematic orientation with respect to the feldspar lattice. These results suggest that palaeointensity estimates of the geomagnetic field made on single crystals of feldspar will not be affected by a systematic orientation of the ferromagnetic inclusions within the feldspar lattice.