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SUMMARY By combining gravity and magnetic data in a joint inversion approach, 3-D information on the crustal structure of Wilkes Land, East Antarctica, is obtained and possible geological features become evident. Both data sets are combined through a coupling method which decreases the variation of information (VI) so data misfit and model dissimilarity are minimized simultaneously. In this manner, statistically compatible inversion results are obtained. The suitability of the method is demonstrated through a synthetic example using magnetic data and pseudo-gravity. Subsequently, we apply the method to gravity residuals and magnetic data and identify matching features of high magnitude density and susceptibility. Prominent structures in NW–SE direction along the edge of the Mawson craton and at the presumed Australo-Antarctic and Indo-Antarctic terrane boundaries are enhanced. Given the structural similarity between inverted susceptibility and density, and a strong indication of a parameter relationship, we suggest a clustering approach in order to differentiate distinct groups with similar parameter properties. The spatial distribution of these clusters reveals possible geological structures that agree with previous 2-D studies and rock measurements from the Indian and Australian continents. This shows that the VI joint inversion is a convenient approach for remote regions like East Antarctica with sparse geological samples.

When interpreting geophysical models, we need to establish a link between the models' physical parameters and geological units. To define these connections, it is crucial to consider and compare geophysical models with multiple, independent parameters. Particularly in complex geological scenarios, such as the rifted passive margin offshore Namibia, multi-parameter analysis and joint inversion are key techniques for comprehensive geological inferences. The models resulting from joint inversion enable the definition of specific parameter combinations, which can then be ascribed to geological units. Here we perform a user-unbiased clustering analysis of the two parameters electrical resistivity and density from two models derived in a joint inversion along the Namibian passive margin. We link the resulting parameter combinations to breakup-related lithology and infer the history of margin formation. This analysis enables us to clearly differentiate two types of sediment cover. The first type of sediment cover occurs near the shore and consists of thick, clastic sediments, while the second type of sediment cover occurs further offshore and consists of more biogenic, marine sediments. Furthermore, we clearly identify areas of interlayered massive, and weathered volcanic flows, which are usually only identified in reflection seismic studies as seaward-dipping reflectors. Lastly, we find a distinct difference in the signature of the transitional crust south of and along the supposed hotspot track Walvis Ridge. We ascribe this contrast to an increase in magmatic activity above the volcanic centre along Walvis Ridge and potentially a change in the melt sources or depth of melting. This change of the predominant volcanic signature characterizes a rift-related southern complex and a plume-driven Walvis Ridge regime. All of these observations demonstrate the importance of multi-parameter geophysical analysis for large-scale geological interpretations. Additionally, our results may improve future joint inversions using direct parameter coupling, by providing a guideline for the complex passive margin's parameter correlations.

The location, volume and physical states of magma reservoirs are primary controls on the eruptive behavior of volcanic systems. Fundamental to understanding and monitoring these systems is the ability to identify reservoir size and physical properties, in particular melt fraction which plays an important role in the rheology and stability of a magmatic system. Large silicic volcanic eruptions in the geological record suggest that extensive pockets of melt-rich silicic magma must exist in the subsurface but such melt pockets have not been detected by geophysics. This has led to the question of whether the reservoirs that feed large volcanic eruptions are only melt-rich for a short time and thus would only be detected by geophysics shortly prior to an eruption. Magnetotelluric data measure the electrical resistivity of the subsurface and are sensitive to subsurface fluids and partial melts making it a powerful tool for imaging subvolcanic magma reservoirs. This study examines the ability for magnetotelluric data to accurately estimate melt fraction using both stochastic Bayesian inversion and deterministic regularized inversion. Results from synthetic modelling indicate that magnetotelluric data are best able to predict the melt fraction for the thick melt-rich layer using both inversion methods, though both methods under-estimate the true amount of melt. In addition, magnetotelluric data can accurately detect changes in melt fraction from crystal- rich mush (0.1 melt fraction) to melt-rich magma (0.9 melt fraction) for thick layers. Thickness is a key parameter which provides a method to assess the total volume of melt present, but it is difficult to estimate using smooth regularized inversions. Fixed-dimension Bayesian inversions provide estimates of layer thickness and their un- certainties and it is shown that estimates of total volume of melt are more accurate for both thin (0.2 km) and thick (1 km) layers than individual estimates of melt fraction or thickness alone. The melt fraction of the thin melt-rich layer is under-estimated using both the deterministic inversion method and the most probable solution of the Bayesian inversion. The Bayesian distribution of solutions has long tails which includes the true solution and better represents the uncertainty of the modelled parameters. As we consider past large melt-rich caldera eruptions at Taupo (New Zealand), Toba (Indonesia), Yellowstone and Long Valley (USA), our analysis suggests that thin melt-rich, potentially eruptible zones involved in large (e.g. > 500 km3) eruptions could be systematically misinterpreted as thicker non-eruptible crystal-rich mush zones. Testing the sensitivity of MT to detect melt accumulation in active magmatic systems has important implications for volcanic hazard assessment and the use of Bayesian inversions allows for a better understanding of the range of possible interpretations., Journal of Volcanology and Geothermal Research, 423, ISSN:0377-0273

SUMMARY Galvanic distortion of magnetotelluric (MT) data is a common effect that can impede the reliable imaging of subsurface structures. Recently, we presented an inversion approach that includes a mathematical description of the effect of galvanic distortion as inversion parameters and demonstrated its efficiency with real data. We now systematically investigate the stability of this inversion approach with respect to different inversion strategies, starting models and model parametrizations. We utilize a data set of 310 MT sites that were acquired for geothermal exploration. In addition to impedance tensor estimates over a broad frequency range, the data set also comprises transient electromagnetic measurements to determine near surface conductivity and estimates of distortion at each site. We therefore can compare our inversion approach to these distortion estimates and the resulting inversion models. Our experiments show that inversion with distortion correction produces stable results for various inversion strategies and for different starting models. Compared to inversions without distortion correction, we can reproduce the observed data better and reduce subsurface artefacts. In contrast, shifting the impedance curves at high frequencies to match the transient electromagnetic measurements reduces the misfit of the starting model, but does not have a strong impact on the final results. Thus our results suggest that including a description of distortion in the inversion is more efficient and should become a standard approach for MT inversion.

SUMMARY We present a new approach that allows for the inversion of quantities derived from the observed data using non-diagonal data covariance matrices. For example, we can invert approximations of apparent resistivity and phase instead of magnetotelluric impedance using this methodology. Compared to the direct inversion of these derived quantities, the proposed methodology has two advantages: (i) If an inversion algorithm allows for the specification of a full data covariance matrix, users can invert for arbitrary derived quantities by specifying the appropriate covariance matrix instead of having to rely on the inversion code to have implemented this feature. (ii) It is fully compatible with the assumptions of least-squares optimization and thus avoids potential issues with bias when inverting quantities that are nonlinear functions of the original data, We discuss the theory of this approach and show an example using magnetotelluric data. However, the same method can be applied to other types of geophysical data, for example gravity gradient measurements.

Refereed/Peer-reviewed The tectonic history of southern Africa includes Archean craton formation, multiple episodes of subduction and rifting and some of the world's most significant magmatic events. These processes left behind a compositional trail that can be observed in xenoliths and measured by geophysical methods. The abundance of kimberlites in southern Africa makes it an ideal place to test and calibrate mantle geophysical interpretations that can then be applied to less well-constrained regions. Magnetotellurics (MT) is a particularly useful tool for understanding tectonic history because electrical conductivity is sensitive to temperature, bulk composition, accessory minerals, and rock fabric. We produced three-dimensional MT models of the southern African mantle taken from the SAMTEX MT data set, mapped the properties of ∼36,000 garnet xenocrysts from Group I kimberlites, and compared the results. We found that depleted regions of the mantle are uniformly associated with high electrical resistivities. The conductivity of fertile regions is more complex and depends on the specific tectonic and metasomatic history of the region, including the compositions of metasomatic fluids or melts and the emplacement of metasomatic minerals. The mantle beneath the ∼2.05 Ga Bushveld Complex is highly conductive, probably caused by magmas flowing along a lithospheric weakness zone and precipitating interconnected, conductive accessory minerals such as graphite and sulfides. Kimberlites tend to be emplaced near the edges of the cratons where the mantle below 100 km depth is not highly resistive. Kimberlites avoid strong mantle conductors, suggesting a systematic relationship between their emplacement and mantle composition. Plain Language Summary: The present-day composition of Earth's tectonic plates results from past geological processes. We can learn about Earth's composition from deep rock samples that are carried to the surface during volcanic eruptions and by probing its physical properties, like electrical conductivity, with geophysics. In southern Africa, there are extensive deep rock samples, which have been brought to the surface by kimberlite volcanoes that also host diamonds, and also extensive geophysical data. In this article, we compare the rock compositions with electrical conductivity to learn more about Earth's composition. Our results show that the oldest parts of the plates, which retain compositions similar to their initial composition, appear resistive. On the other hand, regions that have been intruded by deep fluids or molten rock can be resistive or conductive, depending on the types of minerals that were formed during the intrusion. The kimberlite volcanoes mostly erupted through the edges of the most resistive parts of the plates and did not erupt through the conductors. These results will help us to make more accurate interpretations about the composition of parts of the Earth where we do not have deep rock samples.

Magnetotelluric (MT) and wide-angle seismic reflection/refraction surveys play a fundamental role in understanding the crustal rheology and lithospheric structure of the Earth. In recent years, the...

Large earthquakes away from plate boundaries pose a significant threat to human lives and infrastructure, but such events typically occur on previously unknown faults. Most cases of intra-plate seismicity result from compression related to far-field plate boundary stresses. The April 2017 MW 6.5 earthquake in central Botswana, and subsequent events, occurred in a region with no previously known large earthquakes, occurred away from major present day tectonic activity, and accommodate extension rather than compression. Here, we present results from an integrated geophysical study that suggests the recent earthquakes may be a sign of future activity, controlled by the collocation of a weak upper mantle and weak crustal structure, between otherwise strong Precambrian blocks. Magnetotelluric data highlights Proterozoic continent accretion structure within the region, and shows that recent extension and seismicity occurred along ancient thrust faults within the crust. Our seismic velocity and resistivity models suggest a weak zone in the uppermost mantle, that does not persist to greater depths, and is therefore unlikely to represent mantle upwelling. The Botswana events may therefore be indicative of top-down extension as a response to large scale extensional forces.

In active volcanic arcs such as the Andean volcanic mountain belt, magmatically‐sourced fluids are channelled through the brittle crust by faults and fracture networks. In the Andes, volcanoes, geothermal springs and major mineral deposits have a spatial and genetic relationship with NNE‐trending, margin‐parallel faults and margin‐oblique, NW‐trending Andean Transverse Faults (ATF). The Tinguiririca and Planchón‐Peteroa volcanoes in the Andean Southern Volcanic Zone (SVZ) demonstrate this relationship, as their spatially associated thermal springs show strike alignment to the NNE‐oriented El Fierro Thrust Fault System. We constrain the fault system architecture and its interaction with volcanically sourced hydrothermal fluids using a combined magnetotelluric (MT) and seismic survey that was deployed for 20 months. High conductivity zones are located along the axis of the active volcanic chain, delineating fluids and/or melt. A distinct WNW‐trending cluster of seismicity correlates with resistivity contrasts, considered to be a reactivated ATF. Seismicity occurs below 4 km, suggesting activity is limited to basement rocks, and the cessation of seismicity at 9 km delineates the local brittle‐ductile transition. As seismicity is not seen west of the El Fierro fault, we hypothesize that this structure plays a key role in compartmentalizing magmatically‐derived hydrothermal fluids to the east, where the fault zone acts as a barrier to cross‐fault fluid migration and channels fault‐parallel fluid flow to the surface from depth. Increases in fluid pressure above hydrostatic may facilitate reactivation. This site‐specific case study provides the first three‐dimensional seismic and magnetotelluric observations of the mechanics behind the reactivation of an ATF.

Supplementary data are available at GJ I online. https://academic.oup.com/gji/article-lookup/doi/10.1093/gji/ggy140#supplementary-data Figure S1. (a) Teleseismic events (Mw > 5.8) recorded by SCANLIPS2 between July 2007 and September 2009 for P-receiver function study. (b) Teleseismic events (Mw > 5.8) recorded by SCANLIPS3D between July 2013 and September 2014 for P-receiver function study. In both cases the blue star corresponds to the centre of the seismic array. Figure S2. (a) Synthetic P-receiver functions for a Moho depth of 43 km and Vp/Vs of 1.73 from three crustal models. In red, a model with two layers (upper and lower crust) for the crust and step discontinues. In green, a model with three layers (upper, lower crust and transitional Moho with highVp) and step discontinuities. In blue, a gradual model between upper crust and Moho. (b) Sensibility of amplitude of direct P arrival and Ps conversion for different slowness and for two crustal model (on the left a step Moho model and on the right a gradual Moho model). Table S1. Informations about seismic stations and number of events used in this study for each instruments (70XX: SCANLIPS2 -13XX: SCANLIPS3D). Table S2. Compilation of P-RFs analysis and previous works (Ottemoller & Midzi ¨ 2003; Olsson et al. 2008; Silvennoinen et al. 2014).

In this review, I discuss the basic principles of joint inversion and constrained inversion approaches and show a few instructive examples of applications of these approaches in the literature. Starting with some basic definitions of the terms joint inversion and constrained inversion, I use a simple three-layered model as a tutorial example that demonstrates the general properties of joint inversion with different coupling methods. In particular, I investigate to which extent combining different geophysical methods can restrict the set of acceptable models and under which circumstances the results can be biased. Some ideas on how to identify such biased results and how negative results can be interpreted conclude the tutorial part. The case studies in the second part have been selected to highlight specific issues such as choosing an appropriate parameter relationship to couple seismic and electromagnetic data and demonstrate the most commonly used approaches, e.g., the cross-gradient constraint and direct parameter coupling. Throughout the discussion, I try to identify topics for future work. Overall, it appears that integrating electromagnetic data with other observations has reached a level of maturity and is starting to move away from fundamental proof-of-concept studies to answering questions about the structure of the subsurface. With a wide selection of coupling methods suited to different geological scenarios, integrated approaches can be applied on all scales and have the potential to deliver new answers to important geological questions.

Recent advances in our understanding of arc magmatic systems indicate that melt is stored for long periods in low‐melt fraction crystal mushes, and that eruptible magma reservoirs are short‐lived and are assembled rapidly by buoyancy‐induced instabilities and draining of the crystal mush. Many aspects of their architecture remain unclear, particularly in relation to their geometry and shallow melt distribution. We investigate the storage of melt below the active Soufrière Hills Volcano (SHV), Montserrat, using joint geophysical inversion combined with a quantitative interpretation approach based on rock physics. We jointly inverted active‐source P‐wave traveltimes and gravity anomalies to derive coincident 3D models of P‐wave velocity and density to a depth of 8 km. Comparative analysis of the active SHV and extinct Centre Hills volcano and effective elastic medium computations allow us to constrain temperature, melt fraction and melt geometry. A continuous column of partial melt is inferred beneath SHV, at 4‐8 km depth. Melt fraction is ~6% (ranging from 3% to 13% depending on melt geometry) and is maximum at 5‐6 km depth. When under‐recovery of the low‐vP volume is taken into account, the melt fraction is revised to ~17% (ranging from 11 to 28%). Analysis of vP/density cross plots indicates that the melt distribution is best represented by low‐aspect ratio geometries. These likely span a multi‐scale spectrum ranging from grain‐scale inclusions and fractures to 100‐meter‐scale dykes and sills. Our results confirm the concept of vertically extensive crystal mush including one or multiple more melt‐rich layers. Plain Language Summary We use data from the Soufrière Hills Volcano on Montserrat to study the storage of magma in the plumbing system of an active volcano. By measuring the time it takes for seismic waves to travel from artificial sound sources to recording instruments located on the island and on the seabed around it, we can determine the speed of sound in the rocks. By measuring small variations in the gravitational attraction, we can determine the density distribution. We then jointly analyze the speed of sound and density and calculate that the degree of melting of the rocks is between 6% and 17% and the total volume of molten rocks is 1.5 km3 to 4.5 km3. The partially molten region extends from 4 to at least 8 km depth. Some more thoroughly molten layers are likely present but are too small to be imaged with our method. Our findings support a model of the magma storage system comprised mostly of solid crystals with a relatively small amount of molten rocks. Key Points Seismic and gravity data are jointly inverted to produce models of vP and density beneath an active volcano including the magma reservoir Temperature and melt distribution are estimated jointly from vP and are consistent with a mush zone with 6‐17% melt fraction Analysis of vP/density cross‐plot indicates low melt fraction and low‐aspect ratio melt inclusion geometry

Galvanic distortion of magnetotelluric (MT) data due to small-scale surficial bodies or due to topography is one of the major factors that prevents accurate imaging of the subsurface. We present a 3-D algorithm for joint inversion of MT impedance tensor data and a frequency-independent full distortion matrix that circumvents this problem. We perform several tests of our algorithm on synthetic data affected by different amounts of distortion. These tests show that joint inversion leads to a better conductivity model compared to the inversion of the MT impedance tensor without any correction for distortion effects. For highly distorted data, inversion without any distortion correction results in strong artefacts and we cannot fit the data to the specified noise level. When the distortion is reduced, we can fit the data to an RMS of one, but still observe artefacts in the shallow part of the model. In contrast, in both cases our joint inversion can fit the data within the assumed noise level and the resulting models are comparable to the inversion of undistorted data. In addition, we show that the elements of the full distortion matrix can be well resolved by our algorithm. Finally, when inverting undistorted data, including the distortion matrix in the inversion only results in a minor loss of resolution. We therefore consider our new approach a promising tool for the general analysis of field MT data.

Understanding the uncertainty associated with large joint geophysical surveys, such as 3D seismic, gravity, and magnetotelluric (MT) studies, is a challenge, conceptually and practically. By demonstrating the use of emulators, we have adopted a Monte Carlo forward screening scheme to globally test a prior model space for plausibility. This methodology means that the incorporation of all types of uncertainty is made conceptually straightforward, by designing an appropriate prior model space, upon which the results are dependent, from which to draw candidate models. We have tested the approach on a salt dome target, over which three data sets had been obtained; wide-angle seismic refraction, MT and gravity data. We have considered the data sets together using an empirically measured uncertain physical relationship connecting the three different model parameters: seismic velocity, density, and resistivity, and we have indicated the value of a joint approach, rather than considering individual parameter models. The results were probability density functions over the model parameters, together with a halite probability map. The emulators give a considerable speed advantage over running the full simulator codes, and we consider their use to have great potential in the development of geophysical statistical constraint methods.

Magnetotellurics (MT) uses a frequency-dependent impedance tensor estimated from the spectra of associated time-varying horizontal electric and magnetic fields measured at the Earth's surface to image the sub-surface of the Earth. Most current methods use Fourier transform based procedures to estimate power spectral densities and, therefore, assume that the signals are stationary over the record length. Stationarity in geomagnetic data, however, is not always ensured given the variety of source mechanism causing the geomagnetic variations at different time and spatial scales. Additional complication and bias may arise from the presence of noise in the recorded electric and magnetic file data. Sophisticated MT data processing account for a potential bias through windowing of the time series as well as robust estimates of the impedance. We explore a new heuristic method for dealing with the non-stationarity of MT time series based on empirical mode decomposition. It is a dynamic time series analysis method, in which complicated data sets can be decomposed into a finite and small number of simple intrinsic mode functions. In this paper, we use the empirical mode decomposition method to decompose MT data into intrinsic mode functions and calculate the instantaneous frequencies and spectra to determine the impedance tensor. We investigate the reliability of the impedance estimates on synthetic data by comparing the results to those obtained by analytical methods. Finally, we apply our processing scheme to data measured from the Costa Rica subduction zone, and compare the results from our new method to the frequently-used BIRRP processing method.

We present a 3-D joint inversion framework for seismic, magnetotelluric (MT) and scalar and tensorial gravity data. Using large-scale optimization methods, parallel forward solvers and a flexible implementation in terms of model parametrization allows us to investigate different coupling approaches for the various physical parameters involved in the joint inversion. Here we compare two different coupling approaches, direct parameter coupling where we calculate conductivities and densities from seismic slownesses and cross-gradient coupling, where each model cell has an independent value for each physical property and a structural similarity is enforced through a term in the objective function. For both types of approaches we see an improvement of the inversion results over single inversions when the inverted data sets are generated from compatible models. As expected the direct coupling approach results in a stronger interaction between the data sets and in this case better results compared to the cross-gradient coupling. In contrast, when the inverted MT data is generated from a model that violates the parameter relationship in some regions but conforms with the cross-gradient assumptions, we obtain good results with the cross-gradient approach, while the direct coupling approach results in spurious features. This makes the cross-gradient approach the first choice for regions were a direct relationship between the physical parameters is unclear.

SUMMARY We demonstrate a minor inconsistency in the appendix of ‘The magnetotelluric phase tensor’ by Caldwell et al. that can lead to incorrect results, and provide a simple solution for this problem.