ALBERT

Description: We present the first inversion of geomagnetic Sq data in a framework of 3-D conductivity models. This problem has been considered as immensely difficult due to the complex spatial structure of the Sq source which, in addition, varies with season and solar activity. Recently, we developed a 3-D electromagnetic (EM) inversion solution that allows one to work in a consistent manner with data that originates from sources, irrespective of their spatial complexity. In this paper, we apply our 3-D EM inversion scheme to Sq data collected during the Australian Wide Array of Geomagnetic Stations project. Within this project, three components of the geomagnetic field were recorded between 1989 November and 1990 December with the use of 53 portable vector magnetometers. The instruments were distributed over the Australian mainland with an average spacing of 275 km between sites. Inverting this unique—in a sense of its spatial regularity, density and long operational time—data set, we recovered the 3-D conductivity distribution beneath Australia at upper mantle depths (100–520 km). This depth range was justified in the paper from resolution studies using checkerboard tests. In addition, we performed extensive modelling to estimate quantitatively the influence of various factors on Sq signals, namely from hypothetical anomalies, inaccuracy in the source, ocean, and model discretization. As expected, the ocean (coastal) effect appeared to be the largest so that it has to be accounted for during 3-D inversion as accurately as possible. Our 3-D inversions—of data from either single or multiple days—revealed a strong offshore conductor near the south-east coast of Australia, which persists at all considered depths. Varying in details, this anomaly is remarkably robust irrespective of the considered day(s). We compared our results to those obtained from a different inversion scheme and an independent induction data set, and observed encouraging similarity. Combination of the two results suggests, that this conductor continues to the base of the mantle transition zone at 660 km. The nature of this anomaly is not fully understood but one possible explanation is that it is attributed to a reservoir responsible for three hotspots in the region.

Description: A 3-D magnetotelluric (MT) inversion code using unstructured tetrahedral elements has been developed in order to correct the topographic effect by directly incorporating it into computational grids. The electromagnetic field and response functions get distorted at the observation sites of MT surveys because of the undulating surface topography, and without correcting this distortion, the subsurface structure can be misinterpreted. Of the two methods proposed to correct the topographic effect, the method incorporating topography explicitly in the inversion is applicable to a wider range of surveys. For forward problems, it has been shown that the finite element method using unstructured tetrahedral elements is useful for the incorporation of topography. Therefore, this paper shows the applicability of unstructured tetrahedral elements in MT inversion using the newly developed code. The inversion code is capable of using the impedance tensor, the vertical magnetic transfer function (VMTF), and the phase tensor as observational data, and it estimates the subsurface resistivity values and the distortion tensor of each observation site. The forward part of the code was verified using two test models, one incorporating topographic effect and one without, and the verifications showed that the results were almost the same as those of previous works. The developed inversion code was then applied to synthetic data from a MT survey, and was verified as being able to recover the resistivity structure as well as other inversion codes. Finally, to confirm its applicability to the data affected by topography, inversion was performed using the synthetic data of the model that included two overlapping mountains. In each of the cases using the impedance tensor, the VMTF and the phase tensor, by including the topography in the mesh, the subsurface resistivity was determined more proficiently than in the case using the flat-surface mesh. Although the locations of the anomalies were not accurately estimated by the inversion using distorted impedance tensors due to the slightly undervalued gain, these locations were correctly estimated by using undistorted impedance tensors or adding VMTFs in the data. Therefore, it can be concluded that the inversion using the unstructured tetrahedral element effectively prevents the misinterpretation of subsurface resistivity and recovers subsurface resistivity proficiently by representing the topography in the computational mesh.

Description: With advancing computational resources, 3-D inversion techniques have become feasible in recent years and are now a more widely used tool for magnetotelluric (MT) data interpretation. Galvanic distortion caused by small-scale near-surface inhomogeneities remains an obstacle for 3-D MT inversion which so far has experienced little attention. If not considered properly, the effect on 3-D inversion can be immense and result in erroneous subsurface models and interpretations. To tackle the problem we implemented inversion of the distortion-free phase tensor into the ModEM inversion package. The dimensionless phase tensor components describe only variations of the conductivity structure. When inverting these data, particular care has to be taken of the conductivity structure in the a priori model, which provides the reference frame when transferring the information from phase tensors into absolute conductivity values. Our results obtained with synthetic data show that phase tensor inversion can recover the regional conductivity structure in presence of galvanic distortion if the a priori model provides a reasonable assumption for the regional resistivity average. Joint inversion of phase tensor data and vertical magnetic transfer functions improves recovery of the absolute resistivity structure and is less dependent on the prior model. We also used phase tensor inversion for a data set of more than 250 MT sites from the central San Andreas fault, California, where a number of sites showed significant galvanic distortion. We find the regional structure of the phase tensor inversion results compatible with previously obtained models from impedance inversion. In the vicinity of distorted sites, phase tensor inversion models exhibit more homogeneous/smoother conductivity structures.

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: 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: The Rogaland Igneous Complex (RIC) in southern Norway intruded into post-Sveconorwegian granulite facies crust ~930 Ma. It includes three massif anorthosites, several small leuconorite bodies and the ~7 km thick norite-quartz mangerite layered Bjerkreim-Sokndal (BKS) intrusion. The intrusion consists of five rhythmic megaunits created by repeated magma influxes topped by a transition zone and more evolved mangerites and quartz mangerites. Over 70 palaeomagnetic sites have been collected in the BKS, sampling all the megacyclic subunits and overlying mangerites. Remanence within the BKS is held in hemo-ilmenite-only rocks (lower parts of the megacyclic units), mixed hemo-ilmenite and magnetite rocks (upper parts of the lower megacyclic units) and magnetite only rocks in the upper highest megacyclic unit and overlying mangerites. Due to the different oxides present magnetic susceptibility varies over four orders of magnitude with a bimodal distribution (mean susceptibility of 6.4 x 10 –3 SI for hemo-ilmenite rocks, and 8.7 x 10 –2 SI for magnetite rocks). NRM values do not show a strong bimodal distribution as many of the rocks lacking magnetite have hemo-ilmenite with strong lamellar magnetism; average NRM for the entire suite is 8.83 A m –1 . All sites within the cyclic part of the intrusion have stable remanence and produce well-clustered site means. Samples from the upper mangerite rocks, dominated by MD magnetite, are commonly unstable and not all sites provide acceptable data. Mean directions for 66 sites spanning the entire intrusion are I = –73.5°, D = 303.4°, with α 95 = 3.7° and k = 24. The resulting pole position is at 35.9°S and 217.9°E, with a palaeolatitude for this part of Baltica of –59.4°. Examination of the magnetic mineralogy combined with geochronology for RIC rocks and cooling rates for the region yields an age of magnetization of 916 Ma. Metamorphic country rocks yield similar directions at least 10 km from the contact, confirming the presence of a contact aureole around the intrusion. Comparison to other early Neoproterozoic palaeomagnetic poles from southern Scandinavia confirms the high southern latitude position of Baltica at this time, and combined with the few other ~900 Ma poles from Baltica affirm the presence of the Rodinia supercontinent at this time.

Description: An exploratory 3-D model of the electrical conductivity structure of the Australian continent is presented. The model is derived from the inversion of vertical magnetic-field transfer functions from the Australia-wide Array of Geomagnetic Stations. Crustal conductivity anomalies evident in the model are consistent with those previously mapped by independent magnetometer array studies and new electrical structures are suggested in the upper mantle. The model represents a seamless continent-scale basis for further models likely to be derived from subsequent studies. The model reveals three upper-mantle enhanced-conductivity anomalies beneath Archaean cratonic regions and two upper-mantle anomalies beneath Phanerozoic terranes in eastern Australia. Two of these anomalies have been investigated by recent magnetotelluric (MT) surveys, one in the Yilgarn Craton–Officer Basin–Musgrave Block the other in the Gawler Craton region, and are consistent with the MT results. Across much of central Australia enhanced conductivity at depths of 50–100 km is observed in the model. This region corresponds well with a recognized seismic velocity gradient at 75–100 km. Conductivity differences are also observed beneath Archaean cratons in Western Australia. The Pilbara Craton is represented as an enhanced conductivity anomaly at about 100 km, corresponding well with the lower-velocity anomaly evident in surface wave tomography models. The Yilgarn Craton is imaged as a low-conductivity body, with conductivity two orders of magnitude lower than the Pilbara Craton, continuing to greater depths.

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: A new methodology to estimate magnetotelluric (MT) tensor relationships, called Estimation of Local transfer-functIons by Combining Interstation Transfer-functions (ELICIT), is proposed whereby the MT tensor relationships of the local site are derived using only interstation transfer functions. The MT impedance tensor and the geomagnetic transfer function at the local site are characterised by combining interstation tensor relationships between electric and magnetic fields at the local site with the horizontal magnetic fields acquired at a neighbouring site. The main property of the proposed method is that the employed interstation transfer functions are independently constrained, without the need to acquire the electric and the magnetic fields at the local site simultaneously to recover the local MT tensor relationships. Due to this property, the ELICIT method offers new possibilities for MT data acquisition and processing, providing significant improvements when the magnetic time-series at the local site are affected by local noise or are truncated. Error analysis shows that, even when magnetic fields are truncated, the quality of the results obtained following the ELICIT method are similar to those we would obtain if the magnetic fields had not been truncated. Another important property is that different neighbouring sites can be used to recover the tensor relationships at the local site. Averaging of results obtained using different neighbouring sites can be performed to improve the statistics. For our example data, when the ELICIT method is used to improve the statistics, errors of the estimates for periods between 1000 and 20 000 s periodicities are clearly reduced. All interstation transfer functions are calculated doing remote reference and the bootstrap method is used to compute the errors, when necessary. Long period magnetotelluric data acquired in the Pyrenees and in the Atlas Mountains in Morocco, and magnetic data provided by Fürstenfeldbruck magnetic observatory have been used to test the proposed ELICIT method, with positive results. Due to the lack of requirement that the electric and the magnetic fields of the local site be acquired simultaneously, the proposed method also offers new possibilities for MT data acquisition, optimizing the available instrumentation.

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.