Solid Earth mass rearrangement and ocean water redistribution caused by great earthquakes are made visible by their time-dependent gravity signature, nowadays detectable by space gravity missions. In the perspective of exploiting space gravity data also for investigating earthquakes of moderate magnitude (MW 7-8), we model the co-seismic and post-seismic gravity anomalies for a wide range of earthquake scenarios at the different spatial resolutions of the past, on-going and next space gravity missions (GRACE, GRACE-FO, GOCE and NGGM) by means of spherically symmetric self-gravitating compressible Maxwell Earth models based on PREM. The fault dimensions and slip distribution vary with the seismic moment magnitude and are prescribed according to the circular fault model by Eshelby (1957), under the assumption of different stress drops. The effect of the ocean water redistribution is also accounted for in order to distinguish between the cases of earthquakes occurring inland and off-shore. We thus provide the expected amplitudes of the earthquake signatures evolving in time and how they depend on the spatial resolution of the space gravity mission. By analyzing the spherical harmonic degree variance up to spherical harmonic degree 3000, we also define the characteristic spatial scales of the earthquake gravity signatures and show how they evolves through time and how they depend on the earthquake mechanism, depth and rheological stratification. Particularly, we show how the co-seismic gravity signature is characterized by spatial scales slightly greater than the fault dimensions and that increase increasing the fault depth. The post-seismic gravity signature, instead, is characterized by two spatial scales which reflect the depth range of the low viscous asthenospheric layer and slightly change with time.

Area B - Board 180

We investigated seismic and volcanic processes in the Kuril-Kamchatka subduction zone using SAR interferometry, GNSS and GRACE data on time varying gravity field
We first studied the Olutor MW=7.6 (Kamchatka, Russia) April 20, 2006 earthquake and two its strong aftershocks, both of magnitude 6.6 that occurred on April 29 and May 22, 2006, using SAR interferometry. The intriguing feature of these earthquakes is that surface ruptures of 140 km long showed mostly right-lateral slip whereas CMT solution revealed predominantly thrust movement. Besides, the surface ruptures dip to SE whereas aftershocks mostly occurred in a 75 km wide area to the NW from the surface ruptures. An interferogram constructed using ERS and ENVISAT images covering the main seismic event of April 20, 2006 and April 29 aftershock showed that the main LOS displacements also occurred to the NW from the ruptures mapped at the Earth` surface.
We model the SAR displacement field with a complex fault plane model involving a main rupture plane on a blind thrust extending to the NW from the surface ruptures and a secondary strike slip fault reaching the Earth surface and mapped by field geology. Hence, SAR interferometry allowed constructing a detailed model of the rupture that satisfy both seismology and field geology data.
Then with GRACE gravity time series we investigated the coseismic and postseismic processes in the area of the Simushir Mw=8.3 earthquake of November 2006. The magnitude 8.3 coseismic jump in the gravity field appeared to be too small to be registered by the GRACE data However, a growth of positive gravity anomaly started a few months after the event synchronously with aftershocks activation on the downdip extension of the coseismically ruptured fault plane. Simultaneously changes in the direction and average velocity of the horizontal displacements were registered on the sites of the regional GPS network.
We used both GPS and GRACE data to construct a coseismic rupture model and performed numerical modelling of possible postseismic viscoelastic relaxation or postseismic creep. We found that a postseismic creep along the down-dip extension of the coseismic rupture below the 100 km depth better fit GPS and gravity data. We estimated that the total displacements since the beginning of the growth of the gravity anomaly up to July 2012, is about3.0 m in the upper part of the plate’s contact and 1.5 m in the lower part stretching to 100 km depth. The released total energy would be equivalent to an a Mw = 8.5 magnitude event. Therefore we suggest that the growth of the gravity anomaly is due to a large-scale aseismic creep over an area much larger than the coseismic rupture one. We note that such a process could only been revealed by adding satellite gravity information to seismology and geodetic ones.
This study was supported by grant of the Russian Ministry of Education and Science under contract №14.W03.31.0033 and by the IPGP-IPE cooperation program.

Area B - Board 181

In the last years, the unparalleled spatial homogeneity provided by satellite-only global gravity models has been successfully exploited to obtain estimates on mass distribution in the solid Earth. Among these, the depth of the crust-mantle boundary (Mohorovicic discontinuity), has been a successful target of regional and global studies. Even when simplified to a sharp density discontinuity surface, its knowledge enables a reliable infill between terrestrial data, chiefly from seismic methods, and can be applied to the evaluation and comparison of different crustal models, at similar spatial scales.

Owing to the high degrees of GOCE-based GGMs, the theoretical resolving power can be estimated on the order of 0.1 km depth-wise, at less than 1 arc-degree of horizontal resolution. Such estimate assumes a perfectly isolated signal, i.e. no unmodelled masses in the data reductions, in a correctly constrained inversion (no unknown a-priori parameters, e.g. crust-mantle density contrast).
The Moho depth can be estimated from gravity data by solving the inverse problem relating the relief of a density discontinuity to the observed gravity field. This problem requires two input parameters, a density contrast and a reference depth; it is also necessary to isolate the signal due to Moho relief from all other contributions to the gravity field.

Input parameters are usually constrained by seismic data. Data reductions, applied to isolate a "residual anomaly", commonly consists in the forward-modelled effect of topography, of masses both above (e.g. sediments, upper crustal boundaries), and below the crust-mantle boundary (e.g. lateral density variations in the mantle).
Any variance in the input densities and geometries used in the data reduction, if not accounted for, and any uncertainty in the adopted constraints, is mapped in the inversion results, and thus propagated in any subsequent modelling that makes use of crustal thickness (e.g. temperature, rheology, velocity corrections). An uncertainty estimate is now commonly distributed alongside Moho depth models.

Starting from the theoretical Moho depth-error estimate, obtained from formal errors in the global gravity model, we compute the uncertainty effect that each data reduction step adds to this estimate. The gravity uncertainty is then propagated to a depth estimate using a reference inversion operator. This provides a quantitative assessment of the suitability of satellite-only GGMs in detecting Moho features, at different wavelengths, in a realistic geophysical framework. It also highlights where improvement in critical parameters would be more rewarding in terms of uncertainty reduction.
Up to degree and order 280, the cumulative reduction uncertainty can exceed 200 mGal, in terms of gravity anomaly. This results in local Moho depth uncertainties in the order of 10 km. A 10 points percent simulated improvement in the sediment thickness error improves the Moho depth uncertainty range by up to 1 km. This indicates that even slight improvements, such as the harmonisation of existing near-surface data, can pay off in terms of quality of gravity inversion estimates.

Area B - Board 182

The Corinth Rift (Greece) is one of the narrowest and fastest extending continental regions worldwide, and has one of the highest seismicity rates in the Euro-Mediterranean region. At its western termination, several active faults are located beneath the city of Patras and the surrounding area, a region of major socio-economic importance for Greece.
The Corinth Rift (Greece) is one of the narrowest and fastest extending continental regions worldwide, It is bounded on both sides by active normal faults, on- and off-shore (Moretti et al., 2003; Palyvos et al., 2007) with cumulated offset ~3 km and a series of tilted blocks along the south coast (Doutsos and Poulimenos, 1992; Koukouvelas et al., 1999). It has one of the highest seismicity rates in the Euro-Mediterranean region with, on average, one Mw > 6 earthquake per decade. Recent large earthquakes include Alkyonides 1981 (M = 6.7), Galaxidi 1992 (Mw = 5.8), Aigion 1995 (Mw = 6.1) and Movri 2008 (Mw = 6.4). This last event is located outside of the rift, but is connected to it and is crucial for deciphering the deformation processes at the western termination of the rift and its junction with the Gulf of Patras, where, several active faults are located beneath the city of Patras and the surrounding area, a region of major socio-economic importance for Greece. Previous geodetic studies conducted, which were based on GPS observations observations, revealed North – South extension rates across the gulf of up to about 1.5 cm/yr [Clarke et al., 1997; Briole et al., 2000; Avallone et al., 2004] during the last 20 years.
The Corinth Rift Laboratory (CRL) institution (http://crlab.eu) is based on the joint efforts of various European institutions to study fault mechanics and related hazards in the study area. It is included in Geohazards Natural Laboratories of the GEO Supersites and will be one of the Near Fault Observatories (NFO) of European Plate Observing System (EPOS).
Displacement rates for the period 2002-2010 obtained from ascending and descending ASAR/ENVISAT multi-temporal interferometry are combined with Global Positioning System measurements from permanent and campaign stations to produce a map of vertical and east-west ground velocities. More specifically initial datasets derived from Persistent Scatterers and Small baselines Subsets techniques. These datasets has been doubled by performing a second running with different initial parameters. Combination of ascending and descending tracks has been used to calculate the east-west and vertical deformation components rates. The wealth of information provided by the availability of eight measurements per original pixel and the combination of several original pixels, allows tracking efficiently the unwrapping errors. Finally improved vertical and east-west velocities were calculated by using an averaging filter and a cutoff threshold based on r.m.s. scattering.
In the city of Patras and through the gulf of Patras, the northern continuation of the 2008 Movri earthquake fault (Serpetsid;aki et al., 2014) is connected to the oblique transform zone of Rio. The Rio-Patras fault is off-shore, in front of downtown Patras and penetrates inland between Patras and Rio. Then it rotates progressively and connects with the Psathopyrgos normal fault at the entrance to the Corinth rift. To model the GPS and InSAR velocities, we assume a fault system locked in part of the crust and slowly slipping elsewhere. The deformation shape of the Rio-Patras fault indicates a shallow locking depth and suggests slow slipping below that depth. The large gradient of strike-slip velocities between the south and the north coast at both ends of the Rio-Antirio bridge support a model of deformation accumulation in a very narrow locked layer in the crust, with the rest being unlocked, and therefore not associated with strong seismicity (at least in the last decades until present).

References:
Avallone, A., Briole, P., Agatza-Balodimou, A. M., Billiris, H., Charade, O., Mitsakaki, C. A., et al. (2004). Analysis of eleven years of deformation measured by GPS in the Corinth Rift Laboratory area. Comptes Rendus Geoscience. https://doi.org/10.1016/j.crte.2003.12.007

Briole, P., Rigo, A., Lyon-Caen, H., Ruegg, J.C., Papazissi, K., Mitsataki, C., et al. (2000). Active deformation of the Corinth rift, Greece: Results from repeated Global Positioning System surveys between 1990 and 1995. Journal of Geophysical Research, 105(B11), 25,605-25,625. https://doi.org/10.1029/2000JB900148

Clarke, P., Davies, R., England, P., Parsons, B., Billiris, H., Paradissis, D., et al. (1997). Geodetic estimate of seismic hazard in the Gulf of Korinthos. Geophysical Research Letters, 24(11). https://doi.org/10.1029/97GL01042

Doutsos T., & Poulimenos G. (1992). Geometry and kinematics of active faults and their seismotectonic significance in the western Corinth - Patras Rift (Greece). Journal of Structural Geology, 14(6), 689-699. https://doi.org/10.1016/0191-8141(92)90126-H

Koukouvelas, I., Asimakopoulos, M., & Doutsos T. (1999). Fractal characteristics of active normal faults: an example of the eastern Gulf of Corinth, Greece. Tectonophysics, 308(1-2), 263-274. https://doi.org/10.1016/S0040-1951(99)00087-6

Moretti, I., Sakellariou, D., Lykousis, V., & Micarelli L. (2003). The Gulf of Corinth: an active half graben? Journal of Geodynamics, 36(1-2), 323-340. https://doi.org/10.1016/S0264-3707(03)00053-X.

Palyvos, N., Pantosti, D., Stamatopoulos, L., & De Martini, P. M. (2007). Geomorphological reconnaissance of the Psathopyrgos and Rion-Patras fault zones (Achaia, NW Peloponnesus). Bulletin of the Geological Society of Greece, 40, 1586-1598.

Serpetsidaki, A., Elias, P., Ilieva, M., Bernard, P., Briole, P., Deschamps, A., et al. (2014). New Constraints from Seismology and Geodesy on the Mw=6.4 2008 Movri (Greece) Earthquake. Evidence for a Growing Strike Slip Fault System. Geophysical Journal International, 198(3), 1373-1386. https://doi.org/10.1093/gji/ggu212

Area B - Board 183

On 2017 and 2018 four strong/moderate earthquakes occurred at shallow focal depths in the East Mediterranean. They share a common characteristic, which is that a large part of the induced ground deformation is offshore, thus a part of the deformation footprint is missing. Assuming that the deformation source of an earthquake can be modelled by the slip on a rectangular fault buried in an elastic and homogenous halfspace and through inversion, exploiting GPS and multitrack InSAR (with different weight in each case), as well as seismological data, we demonstrate the efficiency and the contribution of the space geodesy to the seismology, even in such adverse conditions. The seismological and geodetic data, on a case by case basis, are used in synergy to extract the maximum likelihood solution. Moreover simultaneous geogetic and seismological approaches are used for better validation and triggers discussion of the differences between their findings. The four cases are:
1. Between 6 and 12 February 2017, a shallow seismic sequence of moderate events with magnitudes between 5.0≤Mw≤5.2 (NOA), struck the region of Gulpinar-Babakale, onshore northwestern Anatolia, Turkey. We use InSAR (Sentinel-1) to identify the seismic fault (striking N110°E) and seismological data so as to refine its geometry and kinematics using inversion techniques. Despite the moderate magnitudes of the earthquakes, the total surface deformation is 2.2 fringes and it is well visible with InSAR because of the shallow depth of the four main events (6–8 km) and the high coherence of the backscatter phase. Our geodetic inversion showed that the fault has normal-slip kinematics, dimensions of 6 by 6 km (length, width) and dips at 45°. The InSAR data are fitted by a uniform slip of 28 cm. The dip-direction of the fault is not retrievable from InSAR, but a south-dipping plane is clear from seismology and the aftershocks distribution. The spatial distribution of relocated events indicates the activation of one fault with a rupture zone length of about 10 km, a result of the occurrence of off-fault aftershocks along strike the main rupture.
2. On June 12, 2017, a strong Mw=6.3 shallow, normal-faulting sequence offshore Lesvos (Aegean Sea, Greece) occurred. We use jointly geodetic and seismological data to identify the ESE-WNW striking seismic fault and to refine its geometry and kinematics using inversion techniques. Again, the fault-dip direction is not retrievable from GPS/InSAR but a south-dip is inferred from the aftershocks distribution and sea-bottom geomorphology. The spatial distribution of relocated events shows the activation of one fault with a total length of about 20 km, at depths 5-15 km. Despite the large magnitude of the mainshock (M6.3), the surface deformation is not visible with InSAR because of the offshore occurrence of the earthquake, however, cm-size co-seismic horizontal offsets were recorded by the continuous GPS stations (of two private networks) operating at both Lesvos and Chios islands. This absence of visible signal is consistent with the slip-model predictions, based on the GPS models.
3. On July 20, 2017, a strong Mw = 6.6 earthquake occurred offshore Kos (Greece) and Bodrum (Turkey). We also derive a co-seismic fault model from joint inversion of geodetic data (GNSS and InSAR). The GNSS observations constrain well most of the model parameters but do not permit to discriminate between south- and north-dipping planes. The interferograms, produced from C-band ESA Sentinel 1 SAR data, give a clear preference to the north-dipping plane. The orientation of the GNSS vectors and the absence of InSAR fringes onshore Kos constrain the fault's length. We also mapped surface motion away from the satellite along the Turkish coast (from Bodrum towards east) which reached about 20 cm onshore islet Karaada. The best-fit model was obtained with a 37° north-dipping normal fault, in agreement with the published moment tensor solutions. The slip vector is dominantly normal in a ESE-WNW direction with a component of left-lateral motion (5°). The fault plane extends 14 km along strike by 12.5 km wide. Our geodetic model is in agreement with relocated seismicity distribution (about 1160 events) from regional networks, which indicates an aftershock occurrence towards both ends of the rupture. Subsidence mapped near Bodrum coast from InSAR is consistent with the flooding observed at coastal localities according to field survey. Post-earthquake field observations mention a first negative wave motion (receding wave) also visible on the Intergovernmental Oceanographic Commission (IOC) of UNESCO tide gauge. This observation also agrees with the fault model proposed herein, where the dip-direction of the normal fault is pointing towards Bodrum at the north, which is located upon the hanging-wall side of the fault.
4. On October 25, 2018, a strong Mw = 6.7 (NOA) earthquake occurred at shallow depth southwest of Zakynthos Island in Ionian Sea, Greece. This earthquake occurred on the west Hellenic Arc along the megathrust of the Aegean plate on top of the subducting African plate. A small tsunami was also observed at Ionian Sea tide gauges. The GPS data showed that the central-south part of the Island moved 5 cm southwest. We derive a co-seismic fault model from inversion of permanent GPS. The preliminary fault plane extends 22km along strike by 22km wide dipping at 24°. The slip vector (estimated at 2m) is dominantly right lateral with a small reverse component and a SSW-NNE direction. The hypocenter is located at 14 km depth. The synthetic interferograms produced by the model predicts less than one fringe of ground deformation (at C-band, with the incidence angle of the corresponding SENTINEL-1 tracks) throughout the island but it is not clearly visible in the single interferograms which are strongly suffering from tropospheric noise. The tropospheric noise can be minimized by estimating and removing it, using high-resolution NWP of 1km x 1km models, GNSS zenith tropospheric delays (both running operationally through the Corinth Rift Observatory – http://crlab.eu ) and/or averaging of the unwrapped interferograms. The discrimination between south- and north-dipping planes are currently an open issue but the implementation of more GPS and the availability of clear interferometric products are resolving this ambiguity.
We acknowledge support of this research by the project ‘‘HELPOS—Hellenic System for Lithosphere Monitoring’’ (MIS 5002697)

Area B - Board 184

Tectonic geomorphology is a well-known branch of the earth sciences dealing with the analysis of landforms generated by tectonic activity. This is rather an analysis of the ongoing competition between tectonics and erosion in sculpting landscapes in tectonically active areas (Mayer, 1986). Recent incorporation of geomatic analyses and detailed terrain surveys by LiDAR-based digital elevation models has allowed an unprecedented improvement in geomorphological research (Papanikolaou et al., 2015).
Nowadays, the most advance methods of studying the deep structure are the geophysical techniques (Earth Resistivity Tomography - ERT and Ground Penetrating Radar - GPR), terrestrial laser scanning (Leckebusch, 2003; Wetzel et al., 2006; Schrott and Sass, 2008; Bubeck et al., 2015), seismic detection method (Aarre Victor et al., 2012), and radar remote sensing of the Earth's surface (Mironov and Mironova, 2015).
In Russia, a small number of research works have been devoted to identification of tectonic structures on the surface by means of digital terrain modeling (Chernova et al., 2005; Gil’manova et al., 2011; Zaitsev, Zlatopolskiy and Panina, 2013; Ermolaev and Semenov, 2014; Zlatopolskiy, 2015).
The area of research is characterized by a substantial development of the vegetation cover (middle taiga subzone of the northern taiga), weak partition and "youth" of the relief, due to the wide spread of the Valdai glacierization, with a large thickness of overlapping Quaternary deposits (40-200 m). At the moment, it is widely believed that after the Valdai glacierization the relief did not reach the stage of "maturity" with apparent tectonic disturbances of its basement and sedimentary cover. Nevertheless, studies show that manifestations of modern geodynamic regime are reflected in the surface relief (Kutinov et al., 2011).
The purpose of this research is to assess the inheritance nature of the basement structures in the modern relief of the northern part of the Russian plate through digital elevation modeling and GIS technologies. Direct inheritance of deep-laid structures in the surface relief or its absence will give the possibility to assess possible activation of faults in the development of mineral deposits, migration of deep fluids as well as lateral and vertical penetration of contaminants.
We used two digital elevation models (DEMs) in order to determine the inheritance nature of deep-laid structures in the surface relief.
First, we created a surface relief DEM based on ASTER GDEM V.2 (Tachikawa et al., 2011), which in its original form contains a large number of artifacts, pits and other errors, and therefore requires considerable adjustments for further research. DEM preparation included the following steps: 1) data extraction and consolidation; 2) replacement of abnormal values referring to altitude marks and pits; 3) elimination of roughness, noise and errors occurring during overprint of images; 4) “filling” of depressions (Mineev et al., 2015a, 2015b).
Data referring to the basement depth were obtained from the "Relief map of the basement surface" (scale 1: 1000000) (Yudahin, 2001). Obtaining DEM of the basement surface implied three stages: 1) scanning of the source material; 2) digitization of structural contours of the basement depths; 3) creating a digital depth model in the ESRI ArcGIS 10.2.2 environment using the Topo to Raster module.
Next, we compared two models. In order to provide correct graphical analysis, we normalized values of surface heights R (x) and basement depths F (x) varying from 0 to 1 using the following formula:
y^'=(y-y_min)/(y_max-y_min )
Next, we analyzed reflection of the basement structures in the surface relief using values of the difference matrices (M^-=〖MF〗_n-〖MR〗_n) and the summation matrices (M^+=〖MF〗_n+〖MR〗_n). Differences and sums of the normalized values describe certain forms of the basement and surface relief. In this case, direct forms referred to sites where surface elevation was observed in parallel to elevation of the basement or its subsidence was observed in parallel to the surface subsidence. The values of the matrix M^+, close to 0 or 2 most precisely characterize direct forms. Inverse forms referred to sites, in which surface elevation was observed in parallel to subsidence of the basement or elevation of the basement was observed in parallel to the surface subsidence. The values of the matrix M^- close to 1 or -1 most precisely characterize inverse forms.
We subdivided direct forms into two classes according to their internal structure:
1) high – high - areas where surface elevation was observed in parallel to elevation of the basement. Values of summation matrices close to 2 are characteristic of these areas;
2) deep – deep - areas where subsidence of the basement was observed in parallel to the surface subsidence. For these areas, we determined values of summation matrices close to 0.
We subdivided the inverse forms into two classes as well.
1) deep – high – areas where surface elevation was observed in parallel to subsidence of the basement. For these areas, we determined values of difference matrices close to -1;
2) high – deep - areas in which elevation of the basement was observed in parallel to the surface subsidence. Values of difference matrices close to 1 correspond to these areas.
We performed zoning with regard to relevant forms of basement structures in the surface relief, combining values of the previously mentioned difference and summation matrices (fig. 2).
We compared the materials referring to the probability of detecting oil and gas deposits using neotectonic data (Ryabukhina ey al., 1997). In the analysis, we used surface DEM and zoning map by reflection forms of basement structures in surface relief.
Preliminary results of our calculations indicate that manifestations of kimberlite magmatism correspond to the direct reflection forms of basement structures in the modern relief. These manifestations are structurally characterized as “high-high”. We believe that the Zimneberezhny kimberlite field, within which two diamond deposits are currently being developed (M.V. Lomonosov and V.P. Grib mine), refers to a direct form; we also assume that the explored Nenoksk and Belozersk kimberlite fields also refer to direct forms.
With a certain probability, we can assume that the areas of probable localization of oil and gas deposits correspond to elevations of the surface relief as well as to direct forms of basement structures of the modern relief, such as the high-high form.

Area B - Board 185

Modelling of the gravitational potential of the topographic masses is a significant issue of physical geodesy since its outcome is used for many applications, for instance, in the determination of the geoid or a computation of Bouguer gravity anomalies.

In particular, our study concentrates on gravity forward modelling (GFM) in the spectral domain. It means that Newton’s integral is evaluated through a transformation into the spectral domain. Because of the nonlinear relation between the topography and its implied gravity, the topographic potential is expressed by a series expansion of integer powers of the topography, which is expressed as a surface spheroidal harmonic expansion up to some n_max degree. As known, a band-limited topographic mass distribution generates gravitational potential far beyond a resolution of the input topography. This difference in the resolution is caused by the contribution due to higher order integer powers of the topographic heights. Thus, the pth power of the topography has to be expanded up to degree p x n_max. This results in a difference in resolution of the input topography (up to n_max) and its implied gravity field (up to p_max x n_max after the truncation of the infinite series).

Nowadays, spectral GFM is usually performed in spherical approximation, even though this may not be sufficient for applications requiring high accuracy or resolution. Therefore, we rely on ellipsoidal approximation of the mass distribution and expand the topographic gravitational potential into a series of spheroidal harmonic functions. Moreover, spheroidal harmonics may ensure a better convergence behaviour on the topography as opposed to spherical harmonics in some cases.

Our approach scales Legendre’s functions into Laurent series and use real functions p_nm and q_nm, which are well elaborated in Wang, Yang (2013). The functions p_nm and q_nm help us to avoid difficulties in the computation of Legendre’s functions of the first and second kind with a complex argument. While Wang and Yang (2013) expand the topographic potential in the most rigorous way, we expand the topography into a binomial and Taylor series. This dramatically simplify the numerical computations as compared to hundreds or even thousands of consecutive spheroidal harmonic analyses of the rigorous approach.

As the main result of this study, we present an equation for the computation of the topographic potential in spheroidal harmonics. Our method will be verified with results from the spatial domain technique, since the latter implicitly takes into account the additional high-frequency spectral constituents beyond the bandwidth of the input topography. We will also investigate the convergence behaviour of the derived equation on the Earth‘s surface and ultrahigh-degree harmonic syntheses.

Area B - Board 186

Global lithosphere models are usually based on stable continental settings (e.g. isostasy). However, subduction zones have a total different tectonic setting, where this assumption results in incorrect estimates of the subsurface. Satellite-derived gravity and gravity gradient models can provide new insights with respect to traditional seismic and tomographic models, with regard to geometry and density distributions of subducting plates and surrounding regions. Satellite-derived gravity gradient models have been used in modelling of several different subduction zones, but not yet for the Sumatra subduction zone, because of its particular complex geometry. There, the gradients can shed light on the density distribution of the plate, and whether a highly-debated slab tear is present under northern Sumatra.

The WINTERC 3.2 model is used as an initial model for the density distributions of the region around Sumatra. A synthetic slab is created using a top-slab surface model combining information from seismic information and tomography models. The slab is modelled as a bilinear deforming slab with along-dip varying thickness and density and along-strike voxels. Furthermore, we include a slab conduction model to determine the 3D density structure of the slab and an isostatic compensation model for the density in the mantle. A spectral forward modelling method is used to identify signals related to the slab. Spectral analysis will determine the optimal spherical harmonic bandwidth that contains most of the slab signal. An iterative algorithm is used to find the slab density distribution that fits gravity observations. A sensitivity analysis is performed to quantify the error in the used models (e.g. Moho depths) and their implications on the final slab model. Our first order results show that the slab geometry north of Sumatra is more complicated than the southern slab structure.

This research is part of the ESA’s Support to Science Element: 3D Earth – a Dynamic Living Planet

Area B - Board 187

The solution to the inverse gravimetric problem, i.e. to the problem of reconstructing the mass density distribution generating an observed gravity quantity, is generally ill-conditioned and non-unique. Several solutions have been proposed in literature, usually facing the problem by strong constraints and numerical regularizations. For instance, a widespread solution is the one developed by Oldenburg in 1974, where the uniqueness is achieved by assuming a two-layer model (i.e. a simple model in which the only unknown is the discontinuity surface between two layers with different known and homogeneous densities), while the numerical stability is retrieved by regularizing the high frequencies either in the gravity signal or in the discontinuity. In other classical solutions, like the one proposed by Li and Oldenburg in 1998, a complete 3D model of the density distribution of the subsurface is retrieved. However, the strong regularization required to obtain an acceptable solution, may cause very smooth density distributions. In this case, the identification of the boundaries between different geological formations becomes a difficult task.

In the current work, we present a new gravity inversion algorithm, based on a Bayesian approach, aiming to overcome the limitations of classical methods. This is basically done by introducing an a-priori geological knowledge within the gravity inversion. In particular, the investigated volume is subdivided into volume units (voxels), each of them characterized by two random variables: the so called “label” defining the geological formation (discrete) and the mass density (continuous). The a-priori geological information is translated in terms of this model, providing the mean density with the corresponding variability for each class of materials and the a-priori most probable label for each voxel with a set of proximity rules. The solution of the inverse gravimetric problem, retrieved by invoking the Maximum A Posteriori principle, is determined by applying Markov Chain Monte Carlo optimization algorithms.

The proposed method has been tested on both simulated and real case studies. In particular the simulated tests allow to assess the good performances of the algorithm when simple models are considered. Results show that the developed Bayesian approach performs better than the classical algorithms presented above when dealing with these simple scenarios. The real-case test allows to show the behavior of the algorithm in a complex scenario obtaining a model that is consistent with the a-priori knowledge, with smooth variations in terms of density distribution and sharp discontinuities at the boundary between different layers, and that generates a gravity field in agreement with the observed one.

Area B - Board 188

The velocity distribution inside the deep Earth can be illuminated using a wide range of seismological techniques. This has revealed a number of surprising structures, such as the Large Low Shear wave Velocity Provinces (LLSVPs), that have been linked to fundamental behaviour of Earth’s large scale convection. Since these structures should possess anomalous density, they are expected to be represented in Earth’s long wavelength gravity field, which was measured in recent years with high accuracy by ESA’s GOCE satellite.
However, it is unclear how to determine the density anomaly associated with deep mantle structures from seismology. Commonly it is assumed that velocity and density are correlated, due to their common dependence on temperature. However, in the deep mantle, the scaling of velocity to density is highly uncertain, due to incomplete knowledge of mineralogy and rock properties at high pressures. In addition, compositional variations become more important in the deep Earth, because thermal expansivity is reduced at high pressure. If velocity anomalies are caused by compositional variations, there might be no or even a negative correlation of density and velocity. These theoretical problems are further compounded by methodological differences between different seismological methods, which lead to disagreements in terms of velocity anomaly magnitude and spatial structure.
As an alternative to converting velocity to density, we propose to use the recently developed idea of votemaps. Votemaps codense information from several seismic models, by counting at each position how many of the seismic models show a significant velocity anomaly (relative to the velocity scale of each model). In this way, probable locations of anomalous features are defined. We use a linear inversion to determine the density of each feature, by fitting the measured gravity field. Since it is unclear how much deep Earth signals are hidden by shallow density anomalies in the lithosphere, we will use both the isostatic gravity anomaly and a gravity anomaly determined by stripping the gravity effect of the seismological model Crust1.0.
This study is part of the STSE “3D Earth”.

Area B - Board 189

The North-Western USA are a tectonically diverse region that is being influenced by a variety of processes including subduction of oceanic lithosphere and subduction related volcanism in the west as well as hotspot volcanism in Yellowstone. Towards the eastern edge of the study area, more stable cratonic lithosphere can be found. Magnetotelluric (MT) data from the MT transportable array component of the USArray has successfully been used to create resistivity models of the subsurface of this region. We investigate how these models can be improved by combining MT and satellite gravity data from the XGM2016 model in a joint inversion.

In a first step, we individually invert both MT and gravity data to obtain a resistivity and a density model, respectively. These models are not coupled or otherwise constrained and serve as a baseline for later comparisons. The resistivity model is in good agreement with previous studies using similar datasets and shows the signatures of different tectonic units in the North-Western USA (see figure). While the vertical structures resolved in the density model are geologically unrealistic due to the limitations of potential field data, lateral boundaries of geological bodies are nicely resolved.

In a second step, both datasets are inverted jointly using a cross-gradient approach. Thereby, the resulting resistivity and density models are coupled and show, where possible, the same structures. We compare these coupled models to the individual ones to demonstrate how complementary information is shared between the two sets of observations. Additionally, the modelled areas where the coupled models show different structures, i.e. the two datasets could not be fit by similar bodies are discussed. Generally, the resistivity model from the joint inversion shows sharper boundaries between resistive and conductive regions than the resistivity model based solely on MT data. Density anomalies in the combined model do not “stick” to the surface of the model to the same extent they to in the model created only from gravity data, but for a realistic density model more a-priori constraints would be needed.

Due to the global homogeneous coverage of the satellite data, this technique can be beneficial when applied to areas with sparse station coverage of ground-based datasets.

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Chemical composition of the upper mantle may have a large impact on density and material parameters controlling rheological behavior of mantle rocks. In particular, the magnitude of dynamic surface uplift, the degree and extent of partial melting associated with hot mantle plumes depend on the chemical composition of both the plume head and the ambient mantle. GOCE and GRACE satellite gravity data in combination with seismological observables, such as surface wave dispersion curves, provide important information on the physical properties and thermal state of the lithosphere and asthenosphere system, and, thus, can be used to test various hypotheses concerning the geodynamic evolution of hotspot volcanism.
We develop a simple analytic model linking the density and composition of a plume head with the spectral and spatial characteristics of the gravity anomalies at the satellite height. We proceed with synthetic numerical calculations using thermodynamic relations and petrophysical modeling aiming to infer the density of compositional mixtures comprising a hypothetical plume head within the upper mantle.
We apply the developed model for interpretation of geophysical data in the North Atlantic region with a particular focus on the Iceland hotspot. We also compare our synthetic model with a more computationally expensive direct inversion of global geophysical datasets for temperature and composition using the LitMod approach. Our preliminary results indicate a present-day composition of the asthenosphere underneath the central part of the North Atlantic region that corresponds to pyrolite mixed with a ~10-15% of basaltic material.

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Fluid shells are common in planets and moons of our solar system, whether in the form of subsurface oceans or liquid cores. Seismological and geodynamical studies suggest that there is topography at the Earth's core-mantle boundary and similar features are expected at the fluid interface in other planetary bodies as well. However, the effects of such a topography on the flow in the fluid layers are poorly understood.

This study offers an experimental analysis of the flow in a rotating cylinder forced by a libration in longitude, which is a periodic oscillation of a planet's or moon's rotation rate resulting from gravitational interactions with orbital partners. A removable sinusoidal topography can be attached to the bottom of the tank, which allows a comparison between the results with and without topography, the latter case serving as a reference. We characterise the flow regimes at various libration frequency and amplitude using 2D particle image velocimetry measurements in a plane perpendicular to the axis of rotation.

In the stable regime, we observe that a lower forcing is needed to attain a similar level of kinetic energy in the presence of the topography in comparison to the case of the flat cylinder. This indicates that the transfer of angular momentum to the fluid is more efficient with topography. Moreover, the onset of bulk instabilities occurs at a lower forcing as well.

The non-linear mechanisms underlying those instabilities are the so-called parametric resonances of inertial modes. We observe a frequency dependence of the fluid kinetic energy. The maxima correspond to the inertial mode resonance frequencies, which are dependent on the cavity shape, and thus on the presence of topography. We show that the modes are greatly influenced by the topographic wavelength.

Independently of the presence of topography, we observe a retrograde zonal flow in the stable regime and a prograde core flow in the unstable regime, even though the topography deforms the normally circular geostrophic contours. Finally, we show that the Taylor-Görtler vortices forming at the container walls do not influence the flow regimes in the interior of the fluid.

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Conventional methods of seismic tomography, topography and gravity data analysis constrain distributions of seismic velocity and density at depth, all depending on temperature and composition of the rocks within the Earth. However, modelling and interpretation of multiple data sets provide a multifaceted image of the true thermochemical structure of the Earth that needs to be appropriately and consistently integrated. A simple combination of gravity, petrological and seismic models alone is insufficient due to the non-uniqueness and different sensitivities of these models, and the internal consistency relationships that must connect all the intermediate parameters describing the Earth involved (density, seismic velocities etc.). In fact, global Earth models based on different observables often lead to rather different, even contradictory images of the Earth.

Here we present WINTERC, a new global thermochemical model of the lithosphere-upper mantle constrained by state-of-the-art global waveform tomography, satellite gravity (geoid and gravity anomalies and gradiometric measurements from ESA's GOCE mission), surface elevation and heat flow data. WINTERC is based upon an integrated geophysical-petrological approach where all relevant rock physical properties modelled (seismic velocities and density) are computed within a thermodynamically self-consistent framework allowing for a direct parameterization of the temperature and composition variables. The seismic tomography data used in WINTERC is based on seismic waveform fitting of an unprecedentedly large data set (≈1,250.000 events) using automated multimode inversion of surface- and shear-wave forms and a posteriori outlier analysis. Broadband Rayleigh and Love surface wave fundamental mode phase velocity dispersion curves are derived from global phase velocity maps computed in a broad period range using a large global dataset of phase velocity measurements via waveform inversion.

In a first step WINTERC uses a 1D non-linear gradient search inversion of surface wave, elevation and heat flow data combining steepest descent and local quadratic algorithms (Lavenberg-Marquardt), including adaptive damping to a reference model and regularization for smoothness, where the damping coefficients are inverted for as well. The parameter space includes crustal structure (three layers with constant density, seismic velocities, heat production and thickness), mantle structure (Lithosphere-Asthenosphere boundary depth and temperature, composition and temperature distribution within the sublithosphere) and seismic radial anisotropy. WINTERC is parallelized and several lithospheric columns can be inverted simultaneously in different processors of a cluster. In the second step WINTERC uses a fully parallelized spherical harmonic formalism to invert 3D satellite gravity field data (geoid and gravity anomalies, gravity gradients) along with surface elevation (isostasy, dynamic topography). In this second stage the thermal structure is kept fixed and the parameter space is defined in terms of bulk mantle composition. In order to close the loop the chemical structure constrained by satellite gravity measurements is used as prior information in a subsequent thermochemical inversion of surface wave, elevation and heat flow data.

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Satellite magnetic field missions and airborne and marine magnetic surveys have shown that many subductions zones exhibit a strong magnetic anomaly while others do not. The explanation of this phenomenon remains an open question.The presence of magnetic field anomalies over subduction zones has been explained by now in two ways. The first relies on mantle magnetization. While the mantle is expected on average, globally, to be non-magnetic, at subduction zones it could be magnetized due to serpentinization (Blakely et al., 2005). An alternative mechanism evokes the thermal state of the subduction zone. Arkani-Hamed&Strangway, 1987, based on Magsat satellite data, explained the differences in the magnetic signal over the subductions zones of Kuril-Kamchatka, Peru-Chile and Kermadec-Tonga in terms of differences in their age and thermal state.

Nowadays, thanks to the CHAMP and Swarm magnetic field satellite missions and the World Digital Magnetic Anomaly Map, we are able to model the lithospheric magnetic field with a much higher spatial resolution and accuracy than during the Magsat epoch. Moreover, more precise thermal models are currently available. In this study we investigate the relationship between the thermal state and geometry of a given subduction zone and its observed magnetic signature. For this, we estimate through forward modeling the expected magnetic signature of 13 subductions zones around the globe based on the thermal models derived by Syracuse et al., 2010 and the geometry of the subducting slab according to the Slab1.0 compilation (Hayes et al., 2012). We compare the results of our forward calculations with the LCS-1 lithospheric magnetic field model (Olsen et al., 2017), based on Swarm and CHAMP magnetic field measurements, and with the Spherical Harmonic model based on the second version of the World Digital Magnetic Anomaly Map (Lesur et al., 2016).

According to our results, the thermal state and geometry of several subduction zones explains to a large degree the observed magnetic field anomaly. However, there are several subduction zones for which the observed magnetic field anomaly exhibits important differences in respect to the magnetic signature as predicted by the input thermal models and the Slab1.0 compilation. These differences pertain either to the location or the geometry of the magnetic field anomaly or both. Our results can be used in future interdisciplinary studies to further refine our knowledge about these subduction zones.

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Advancement in the Global Geodetic Observing Systems demands regionally constrained loading models. These are in general accomplished by local Green's functions calculated for a spherically symmetric earth model with regionally adapted parameterisation using Farrell's approach.
The wide range of spatio-temporal scales of surface mass transport in the ocean, atmosphere, continental hydrosphere and cryosphere motivates a global approach, where the lateral heterogeneities of the elastic earth structure are considered in a consistent set up. Based on seismic tomography and laboratory experiments on anelastic properties of mantle material, we assess lateral heterogeneities of elasticity in the Earth's crust and mantle, and its impact on surface loading.
We calculate surface loading in a laterally heterogeneous and self-gravitating spherical Earth model and compare the results to the usually applied transfer functions proposed by Farrell. We demonstrate the effects of laterally heterogeneous elastic moduli in terms of response to large-scale loads, and assess the deviations from regionally constrained 1D-earth approximations.

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We present a new model of Earth's magnetic field variation that covers the recent two decades and is entirely based on geomagnetic observatory data. Like in a previous field modelling attempt, the C3FM2, we use secular variation estimates as model input. However, this time we employ annual differences of observatory daily means, to explore characteristics of the short term secular variation. Interannual and annual variations of the internal magnetic field are masked by external field variations, while semi-annual external field variations can be treated in our modelling approach, the sufficient removal of a 2.5 years signal requires further analyses. Interestingly, the 2.5 years oscillation is also observed in recent geomagnetic field models that are based on geomagnetic satellite data, and are suspected to be related to the quasi-biennial oscillation (QBO) in the ionosphere. To what extend this oscillation induces a secondary field in Earth needs to be understood. However, once the QBO signal is removed from our internal magnetic field model, then advanced studies that compares magnetic and gravitational variations of core origin can be initiated.

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Magnetic data carry key information to understand the dynamic of the liquid outer core where is generated the Earth’s main magnetic field. This information is not easily retrieved because core field signals have first to be separated from other source signals that are contributing to magnetic field measurements at all spatial and temporal scales. It is therefore necessary to build magnetic field models of all main sources and provide prior information on their spatial and temporal behaviour.

We present a model of the core field with a high temporal resolution that has been build sequentially, month after month, using Kalman filters. The prior information is provided for the core contribution using output of numerical dynamo experiments. For other contributions, like those of the lithospheric and magnetospheric fields, the prior information is provided through correlation structures that were derived as in Holschneider et al. (2016). Preliminary results show that the obtained core field model has all the characteristics of a model derived through a classic spherical harmonic decomposition but with higher temporal resolution. Furthermore, the technique used allows for the separation of large-scale signals generated in the lithosphere from those generated in the core. This reduces significantly the level of noise in core field models and ultimately leads to more robust core flow model estimates.

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Virtual observatories (VOs) use satellite measurements to provide estimates of the mean magnetic field (MF) over a specified period (usually one or four months) at a fixed location in space, mimicking the mean values obtained at ground-based observatories (GOs). These permit secular variation (SV) estimates anywhere on the globe, thereby mitigating the effects of uneven GO coverage, whose concentration in the northern hemisphere leaves much of the Earth poorly constrained. VO estimates of the internally-generated MF suffer from two key contamination sources: local time sampling biases due to satellite orbital dynamics, and MFs generated in regions external to the Earth such as the magnetosphere and ionosphere. Current VOs employ various methods to alleviate this contamination but each has drawbacks: first, averaging over four months, rather than one month as is typical for GOs, removes the local time sampling bias at the cost of reduced temporal resolution; second, stringent data selection criteria such as night-time, quiet-time only data greatly reduce, but do not entirely remove, external MF contamination but result in a small subset (<5%) of the available data being used; third, removing model predictions for external MFs from the measurements also reduces noise, however such parameterisations cannot fully describe these physical systems and some of their signal remains in the data.
We propose an alternative approach to calculating VOs that retains the monthly resolution, uses all available vector satellite data and removes contamination from orbital effects and external MFs. It uses the eigensystem method implemented in the MagPySV Python software, previously applied to GOs, to rotate data into various “noisy” eigendirections, i.e. those that contribute most to geomagnetic residuals (the difference between the observed and modelled SV), under the assumption that the residuals provide information about sampling errors and external MFs that are present in the VO estimates but not in the internal field model. A key challenge in using this method is identifying the underlying physical mechanisms of the different eigendirections, so that the appropriate noisy directions are removed from the data whilst unmodelled signals that originate from the core are retained. To that end, we have produced synthetic VOs using modelled satellite track data for external (magnetosphere and ionosphere) MFs. We have done this for a CHAMP-like single satellite and a Swarm-like three satellite constellation. Subsequent eigenanalyses of these synthetics, and Fourier analyses of the rotated residuals, have shown how simplified representations of external MFs and their biased time sampling with the VO method manifest in the noisy eigendirections. Informed by the synthetic tests, we have produced denoised VOs for CHAMP and Swarm, which we compare to VOs calculated using standard methods.

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Magnetic data are widely used geophysical data for investigating the crustal structure. Joint inversion of aeromagnetic and/or satellite magnetic data can recover the susceptibility from surface to deep crust. Consequently, one can link resulting magnetic properties to underlying geological structure.
Magnetic inversions suffer from two limitations. Firstly, it is difficult to simultaneously determine magnetic properties and model geometry. Thus, information from other geophysical methods is required in addition to the magnetic data. Typically, it is assumed that the Moho boundary is the lower limit of magnetization. Secondly, magnetic susceptibility inversion problems are usually regularized using the classical Tikhonov approach. This forces the solutions to remain close to prior information. Due to the lack of detailed knowledge about underlying rock units and their properties, a priori information is usually unspecific and merely limits the solution to a wide range of plausible susceptibility values. As a result, the inverted susceptibility directly reflects the patterns of the original input data, but cannot reveal detailed structures. In principle, gravity data can provide additional constraints on geological units. However, gravity and magnetic data are often analyzed and inverted independently.
We propose a clustering inversion method that makes use of gravity and magnetic data to improve the recovery of susceptibility. An existing lithospheric density model is used to define different rock units by applying k-means clustering to the density distribution. The domains defined by these clusters are then used in a susceptibility inversion. Utilizing different priori information to these domains lead to plausible models of susceptibility which can be further analyzed.
We tested our approach on a high quality, large-scale magnetic compilation covering the entire Australia continent. The model geometry was constrained using an existing high-resolution lithospheric density model. We assumed that different clustering domains have different magnetic properties, namely different mean susceptibilities. To investigate the efficacy of our proposed method, we used the different combinations of a priori information for the clustering domains. We find that clustering inversion result can provide more detailed structures than magnetic data only inversion result.

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East Antarctica is the least understood piece of continental crust on Earth. With an extension comparable to the conterminous United States of America it contains key clues into the origin, evolution and demise of three supercontinents and it forms the cradle for the largest ice sheet remaining on our planet.

Here I review some previous and ongoing aeromagnetic anomaly interpretations that are being carried out within a new project of ESA ADMAP 2.0+ that is part of the 3D Earth initative. ADMAP 2.0+ is transforming our ability to study East Antarctica.

These interpretations of the aeromagnetic data place key new constraints into the extent of an Archean microcontinent, Paleoproterozoic banded iron formations, and an inferred Mesoproterozoic continental magmatic arc, as well as proposed oceanic arc belts further in the interior of East Antarctica.

These elements can now be linked much more tightly with similar features in the Gawler Craton and in the more cryptic Coompana block and Madura oceanic domains in Australia and begin to paint a new picture of the processes of crustal growth in East Antarctica and its linkages with subduction of oceanic lithosphere surrounding the Nuna supercontinent. New views of linkages between the processes occurring in East Antarctica and Laurentia are also emerging.

The improved understanding of East Antarctica in Paleoproterozoic to Mesoproterozoic times that is emerging is important not only for our understanding of Nuna- arguably the first true supercontinent on Earth- but also sheds new light into the extent of the Antarctic continent prior to the development of Rodinia- which is likely to further help reduce the ambiguties and uncertainties in Rodinia reconstructions too.

Several of the key accretionary processes that are beginning to be recognised on the Australian side of East Antarctica seem to also be imaged on the Indian side, where a long-lived but relatively younger Mesoproterozoic to Neoproterozoic accretionary orogen is also aeromagnetically imaged. There is still much debate as per whether this accretionary domain collided with the rest of East Antartica at ca 1 Ga or if collided and then rifted off again as part of Rodinia break-up to eventually re-collide with East Antarctica during Pan-African age orogenic events that led to the assembly of Gondwana. Even larger uncertainty surrounds the proposed accretionary and collisional stages in interior East Antarctica, in particular in the so called Gamburtsev Domain where remarkably thick crust and lithosphere is preserved.

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Nowadays, the main Earth’s magnetic field is accurately monitored from satellites placed in a low orbit. Together with records of the Earth’s rate of rotation, the magnetic field observations give precious information about magnetohydrodynamic (MHD) waves in the Earth’s fluid core. The propagation of these waves is sensitive to the properties of the core-mantle boundary: height of the interface with respect to a mean sphere; electrical conductivity of the solid mantle adjacent to the fluid core. The aim of the study is to develop a 2-D reduced model of the fluid dynamics that would account for the non-spherical core-mantle boundary. The simplification of such a quasi-geostrophic model rests on the invariance of the fluid velocity parallel to the rotation axis. This type of model has already been applied to investigate thermal convection without a magnetic field or to investigate the propagation of magnetic waves in a perfectly spherical cavity. Here, we combine these approaches and give a model description for arbitrary containers and introduce newly developed curvilinear coordinates for ellipsoids, which give an interesting case for the study of topography. These tools let us investigate and quantify the torque on the mantle through topographic coupling of MHD waves.

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The Earth's magnetic field is generated by the motion of conductive fluid in its outer core. There are various ways to study the details of this mechanism. While direct numerical simulations can reproduce a number planetary magnetic fields’ features, these simulations cannot currently access the parameter regime relevant to planetary dynamos, and often produce flows which are too complicated to be physically interpreted. In an attempt to better characterise what kind of flow structures produce particular magnetic field features, we consider a simplified approach to the problem, the “kinematic dynamo approximation”. Here, a time-invariant fluid flow is prescribed and the resulting magnetic field is considered, neglecting the back-reaction of the magnetic field on the fluid flow. Dynamo action is achieved if the fluid flow is capable of sustaining a growing magnetic field against dissipation. The parameter which controls the strength of inductive to diffusive effects is the magnetic Reynolds number, Rm. The onset of dynamo action occurs at the critical magnetic Reynolds number, Rm_c. The aim of our study is to find the simplest and most efficient axisymmetric flows which act as kinematic dynamos in a sphere. These flows may be able to shed light on the essential physical processes which are necessary to generate dynamo action.
We present optimised versions of three axisymmetric kinematic dynamos first proposed by Dudley and James (Proc. R. Soc. Lond. A, 425:407-429, 1989). These flows, which contain only one toroidal and one poloidal mode, are some of the simplest known functioning dynamos. Using a Lagrangian optimisation technique for steady flows in a sphere developed by Chen et al. (J. Fluid Mech, 839: 1-32, 2018), we found the smallest critical magnetic Reynolds number for each flow type when Rm is measured using an enstrophy-based norm. A Galerkin method was used, in which the spectral coefficients of the fluid flow and magnetic field expansions were updated in order to maximise the final magnetic energy after two diffusion times. The optimised flows display Rm_c that are up to four times smaller than the original Dudley-James flows. All Rm_c are quite similar, suggesting that there is only a weak preference for a flow dominated by particular modes. Two of the three flows display good alignment of the velocity and vorticity in the inner region of the sphere, resulting in significant helicity, known to enhance dynamo action.
When seeking kinematic dynamos with the simplest possible flow structure, it is natural to consider single mode flows. However, no such dynamos are currently known to work. Using the Lagrangian optimisation algorithm, we also present a strategy to seek purely poloidal single mode kinematic dynamos, in an attempt to find the simplest possible kinematic dynamo.

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We study the lithospheric structure of the British Isles using a methodology that allows for forward modelling of the Curie temperature depth based on seismic, elevation and gravity observations within an integrated geophysical-petrological approach (LitMod3D). We compute 3D thermal models and self-consistently determine the density in the mantle based on temperature, pressure and bulk composition. Finally, we derive Curie temperature depth maps and forward calculate magnetic anomalies at the airborne level using a spherical magnetic modelling software (magnetic tesseroids) to estimate the geothermal magnetic signal. Our results show lateral lithospheric variations across the model domain, with Great Britain being characterized in general by thicker and colder lithosphere, especially in the south-east, and the thinnest and warmest lithosphere being located beneath west Scotland, Northern Ireland and in the north-west oceanic area. Our estimated Curie temperature depth map resembles the values obtained using other techniques (spectral method and surface heat flow inversion) in some areas, but discrepancies are notable in general. We determine that the effect of typical lateral temperature variations (i.e., Curie isotherm depth) accounts for 5-15%, on average, and up to 70% locally of the crustal magnetic signal at the airborne level (5 km altitude). Our lithospheric models are in general agreement with published tomography models as well as other geophysical studies.
This project is funded by the Science Foundation Ireland grant iTHERC to J. Fullea (16/ERCD/4303).

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Curie depths are an important parameter for the interpretation of petrological properties in the lithosphere. It is defined as the 580°C isotherm which can be used to estimate heat flow and temperature distribution within the Earth, estimating thermal regimes etc.. In recent studies global estimations were made with global magnetic data like EMAG2 or WDMAM. Most approaches analyse the radially averaged power spectrum. Slopes of a specific frequency band are estimated and used for the depth estimation. The choice of the window size of the analysed area and the frequency band vary the results significantly. In addition, filters applied to the magnetic data have also large impact to the final results. We show that these techniques are highly dependent on the input data and global results should be carefully interpreted as they seem to be not as reliable as expected. We compare these power spectrum estimates of the Curie depth with results derived from MCMC inversion algorithms which provide also different results even when used with the same input data.

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The important means to probe physical properties of the mantle is geomagnetic deep sounding (GDS), which can potentially recover the 3-D electrical conductivity distribution in the Earth’s mantle. Quite recently a few groups – by interpreting ground-based geomagnetic field variations due to magnetospheric ring current – reported the first global 3-D conductivity models at mid-mantle (MM) depths (400 – 1500 km). However there is a great interest in mapping conductivity at upper-mantle (UM) depths. Probing conductivity at UM depths requires field variations in a period range between a few hours and one day. This is a challenging period range for GDS since the ionospheric (Sq) source, which dominates these periods, has a much more complex spatial structure than the magnetospheric source. This, in particular, means that conventional, local, GDS responses used to constrain the MM conductivities cannot be exploited. An innovative concept which allows to handle the complex Sq source structure relies on an array of global-to-local transfer functions (TFs) that relate (in frequency domain) local radial field with expansion coefficients describing Sq source. This, in particular, means that the concept requires an adequate parameterization of the Sq source. So far, such a parameterization was based on a spherical harmonic (SH) expansion. In this presentation we propose an alternative parameterization of the Sq source, which is based on spatial modes coming from principal component analysis of a physics-based model of the Sq source. Using this parameterization we estimate new TFs and compare them with SH-based TFs.

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The majority of observed magnetic fields are the result of a dynamo, whereby turbulent fluid motions in the electrically conducting interiors sustain the magnetic field over long timescales. These settings are characterized by convective turbulence, rapid rotation and strong magnetic forces resulting in a wide range of spatial and temporal scales. Several key questions regarding the detailed physics of this process remain unanswered, including the degree to which the magnetic field influences the convective dynamics and the flow structures. The vast majority of current efforts to understand planetary dynamos use conventional numerical models that are hindered by computational limitations. However, model reductions that embrace the extreme parameter values and self-impose the dominant force balances they imply provide a pathway around these difficulties and enable simulation studies in regimes more relevant to planetary interiors.

We simulate numerically a convection-driven dynamo model that is valid in the asymptotic limits of rapid rotation and large magnetic diffusivity; a parameter combination that is directly relevant to the majority of planetary interiors. This model provides insight into the small scale turbulence in Earth’s outer core and is compared with traditional models to investigate the influence of altering the magnetic Prandtl number. This parameter measures the ratio of viscous to ohmic dissipation and influences both the turbulence in the system and the strength of the magnetic field.

We find that the presence of a large-scale, self-sustained magnetic field fundamentally alters the convection by increasing the heat transfer and saturating the depth-averaged flow at a length-scale that is comparable to that of the convection. This result is contrasted against the hydrodynamic large-scale vortex that has been observed previously. For strongly-driven flows with a more supercritical magnetic Prandtl number, jets form in a direction that minimizes ohmic dissipation; the jets then become shear unstable and lead to large-amplitude dynamo cycles.

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The lithospheric magnetic field, one of the main objectives of ESA's mission Swarm, is dictated by the magnetized rocks in the upper Earth. Although a full spectrum of this tiny field is not known due to a masking effect of the dominant core field, the lithospheric signal can be transformed into the susceptibility distribution to support geologic interpretation. The objective of this study is to present magnetic susceptibility maps obtained with Swarm-based data (geomagnetic models) like the vector or tensor components. These maps are based on our tile-wise inversion that allows to consider global domain with reasonably high spatial resolution (for satellite data) and with relatively low computational burden. In this work, the effect of remanent magnetization is subtracted with help from a prior model. We discuss is also the depth parameter that basically leads to three inversion options – a vertically-integrated, constant-depth or depth-defined (prior-knowledge) susceptibility map. Since there are multiple geomagnetic models available, individual susceptibility solutions are shown for these models. Finally, CHAOS-6 model is used to estimate the lithospheric signal at the satellite altitude over a period of 20 years. The lithospheric time variation is known to be a subtle signal but this effect deserves to be questioned as there are long time series of high-accuracy satellite magnetic data already accumulated (e.g., from CHAMP to Swarm).

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The Earth's core field, a primary driver of the geomagnetic field, is shaped by multiple internal and external sources. Nowadays, information on this complex system is provided by ESA's three-satellite mission Swarm. Traditionally, “smart” data selection and sophisticated procedures are used to get rid of the effects that are not questioned by a particular modeller (e.g., ionosphere if the target is the core field). Spherical harmonics then provide a usual means to characterize the potential fields. In this study, we show our experiments with the Poisson integral equation that is a spatial equivalent to spherical harmonics and it allows to handle potential field quantities essentially with the same quality. Our goal is to investigate whether it is possible to filter out (in the spatial domain) a high-frequency signal that is not related to the core field and that becomes negligible at the satellite altitude. Such filter is a global function running over all wavelengths but it is primarily controlled by the distance from the core-mantle boundary. Removing the smallest wavelengths from Swarm data can shorten time series needed to capture the core field of a certain spherical harmonic degree. The spatial filter can also benefit (compared to spherical harmonics) from uneven distribution of Swarm data, which is substantially denser in the north-south than in the east-west direction over a certain period of time.

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This presentation quantifies the sensitivity of Swarm data to lateral electrical conductivity inhomogeneities of the Earth's mantle when the conducting Earth is excited by a magnetic storm of low-degree P_j structure. The effectiveness of lateral conductivity variations in the mantle to generate a complex internal magnetic field (MF) is demonstrated for a model with an axially asymmetric, eccentrically nested sphere embedded in the Earth's mantle: the nested sphere has ten times larger electrical conductivity than the background sphere. The spectral coherence between the inducing (external) and induced (internal) MFs shows that the higher the degree j of the external forcing, the greater the difference of the spectral coherences from one. In addition, longer periods of the external forcing produce more pronounced effects of the 3D electrical conductivity structure. For instance, external MF forcing of degrees j=1 and j=5, and a period of 10 days, results in spectral coherence of 0.998 and 0.918, respectively. Hence, about 0.2% and 8% of the internal MF of degrees j=1 and j=5 are caused by a large-scale 3D electrical conductivity inhomogeneity in the mantle.

In the second step, the 3D electrical conductivity structure of the uppermost mantle (down to 330 km) has been derived from a surface waves seismic tomographic model (SL2013sv). The resulting 3D conductivity model consists of seven layers, which correspond to the depths of seismic tomographic layers. The conductivity model shows a clear difference between continents and oceans. We compute two 1D electrical conductivity models by spatially averaging the 3D conductivities over the oceanic and continental regions. These 1D models are excited by the external MF of degree j=3 with a period of 2.6 days. The differences between the internal MFs induced by the same forcing over oceanic and continental areas reach amplitudes of about 1% of the complete MF.

All the presented examples imply that large-scale lateral electrical conductivity inhomogeneities of the Earth's mantle generate a rather weak induced MF when the conducting Earth is excited by a magnetic storm of low-degree P_j structure. The induced internal MF due to 3D conductivity variations reaches amplitudes of a few per cent of the inducing external MF. This implies an important consequence for the analysis of Swarm data; all magnetic sources contributing to Swarm track data must be modelled carefully with an accuracy better than 1 nT. These disturbing signals should be removed from the track data prior to determining the external and internal magnetospheric MFs. This is not currently the case. Modelling of the MFs of field-aligned currents and polar electrojets and removing their effects on the Swarm track data remains to be done.

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The Swarm SCARF (Satellite Constellation Application and Research Facility), a consortium of several research institutions, has been established with the goal of deriving Level-2 products by combination of data from the three Swarm satellites. Here we present the latest results of the Swarm SCARF team at DTU Space and NASA Goddard who conducts the Comprehensive Inversion (CI) magnetic
field model processing chain; we present the results from using five years of Swarm data. The CI chain takes full advantage of the Swarm constellation by doing a comprehensive co-estimation of the magnetic fields from Earth’s core, lithosphere, ionosphere, and magnetosphere together with induced fields from Earth’s mantle and oceans using single and dual satellite gradient information. Recent developments have focused on the induced signal from the oceanic tides. These signals provide a unique insight into the water motion deeper in the oceans, motion which is not otherwise measured.
Another important result from the Comprehensive Inversion chain is the model of the magnetospheric signal and its induced counterpart which are the essential inputs to the mantle induction chain which is also part of the Swarm SCARF consortium by the teams at ETH in Zürich and CUP in Prague. So far, only the dipole terms of these magnetic field contributions have been of good quality and hence enabled consistent estimations of the 1-D mantle conductivity. Higher order terms have been inconclusive with respect to estimations of 3-D mantle conductivity. Recent progress to improve this situation will be presented.
Future improvements of the Comprehensive Inversion chain include a more sophisticated modeling of the ionospheric field contribution as well as a consistent modeling of the induced counterparts of both the magnetospheric and ionospheric magnetic fields.
Level-2 products containing the corresponding model parameter estimations will be generated regularly and distributed via ESA at ftp://swarm-diss.eo.esa.int/Level2longterm/ (see https://earth.esa.int/swarm on how to gain access).

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