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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 t

This chapter investigates the particular challenges for joint inversion in the context of hydrocarbon exploration. It reviews the current literature and introduces interesting approaches that have been developed in the context of hydrocarbon exploration and could potentially be used in other application areas as well. Joint inversion methods incorporating petro physical models of the reservoir can directly yield quantities of interest such as porosity and permeability, but have to be carefully tuned to the area under investigation. The chapter presents two detailed joint inversion case studies, one for subsalt imaging and one for sub basalt imaging. It also covers emulation of the forward calculation, a concept that can be applied generally in joint inversion, but has only been applied in hydrocarbon exploration. For a successful joint inversion, it is necessary to invert each dataset, construct different coupling approaches, and evaluate the impact on the final results.

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.

We present a three-dimensional resistivity model derived from a large-scale magnetotelluric experiment offshore Namibia. To obtain the model we use the inversion code "mtinv" based on an integral equation approach (see Avdeev&Avdeeva, 2009, Avdeeva et al., 2012 and Moorkamp et al., 2010). The code allows positioning of MT sites at the sea-floor and inclusion of bathymetry. However, the bathymetry is approximated with a rectilinear mesh, which is not optimal as a large portion of the computationally feasible grid is used up by bathymetry, at the same time reducing the resolution of the upper region. Nevertheless, we observe a good correlation of the boundaries of large-scale resistive anomalies with seismically identified lower crustal high-velocity structures. This gives us confidence in the large-scale features of the resistivity model. Together with information from 2-D seismic profiles and on-shore geology the resistivity model provides valuable insight into the spatial distribution of increased magmatic activity.

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.

We present both 2-D and 3-D joint inversions of seismic tomography, MT and gravity data from Faroe-Shetland Basin. The objective is to evaluate how far petrophysically-linked joint inversions can improve both the imaging and the interpretation of the basalt flows and the underlying structures. The investigation area is License006, where the presence of a borehole (BRUGDAN) and a 3-D reflection seismic survey allow a direct comparison and, hence, an evaluation of the quality of the joint inversion models. For the 2-D and 3-D investigations we use different joint-inversion codes that have other strengths and weaknesses. We observe that results from both 2-D and 3-D joint inversions are more consistent than the ones from the corresponding individual inversions and the shape of the basaltic sequence and structures underneath are better resolved. The 2-D joint inversion in particular gives precise basalt thicknesses, whereas the 3-D joint inversion determines a two-dimensional high-resistivity anomaly that is oriented in the same direction as general regional trends of basement.

One of the main problem of 3D time domain controlled source electromagnetic (CSEM) inversion is the high runtimes of forward modeling codes. We reduced the runtime of the 3D time domain finite difference CSEM code TEMDDD by the GPU-parallelization of expensive algorithms. The code solves the electromagnetic diffusion equation by discretization of spatial operators and subsequent calculation of eigenpairs. These eigenpairs are found by approximation of the eigenspace in a Kiylov subspace using the spectral Lanczos decomposition Method. This algorithm was in its original form not parallelizable due to implementation of the upper boundary condition at the air-water interface. We show for the marine case that replacing the original boundary condition at the air-water surface by a discretized air layer allows GPU parallelization of every time consuming algorithm of the code in the marine case. Speedups between 20 and 60 have been achieved compared to the original code for a larger 3-D model. In this model the bathymetry from a survey area offshore Egypt is used as an example demonstrating that the parallelized version of the code is applicable to real survey scenarios.

Deep crustal constraint is often carried out using deterministic inverse methods, sometimes using seismic refraction, gravity and electromagnetic datasets in a complementary or "joint" scheme. With increasingly powerful parallel computer systems it is now possible to apply joint inversion schemes to derive an optimum model from diverse input data. These methods are highly effective where the uncertainty in the system is small. However, given the complex nature of these schemes it is often difficult to discern the uniqueness of the output model given the noise in the data, and the application of necessary regularization and weighting in the inversion process means that the extent of user prejudice pertaining to the final result may be unclear. We can rigorously address the subject of uncertainty using standard statistical tools but these methods also become less feasible if the prior model space is large or the forward simulations are computationally expensive. We present a simple Monte Carlo scheme to screen model space in a fully joint fashion, in which we replace the forward simulation with a fast and uncertainty-calibrated mathematical function, or emulator. This emulator is used as a proxy to run the very large number of models necessary to fully explore the plausible model space. We develop the method using a simple synthetic dataset then demonstrate its use on a joint data set comprising first-arrival seismic refraction. MT and scalar gravity data over a diapiric salt body. This study demonstrates both the value of a forward Monte Carlo approach (as distinct from a search-based or conventional inverse approach) in incorporating all kinds of uncertainty in the modelling process, exploring the entire model space, and shows the potential value of applying emulator technology throughout geophysics. Though the target here is relatively shallow, the methodology can be readily extended to address the whole crust.

Imaging of sub-basalt sediments with reflection seismic techniques is limited due to absorption, scattering and transmission effects and the presence of peg-leg multiples. Although many of the difficulties facing conventional seismic profiles can be overcome by recording long offset data resolution of sub-basalt sediments in seismic sections is typically still largely restricted. Therefore multi-parametric approaches in general and joint inversion strategies in particular (e.g. Colombo et al., 2008, Jordan et al., 2012) are considered as alternative to gain additional information from sub-basalt structures. Here, we combine in a 3-D joint inversion first-arrival time tomography, FTG gravity and MT data to identify the base basalt and resolve potential sediments underneath. For sub-basalt exploration the three methods complement each other such that the null space is reduced and significantly better resolved models can be obtained than would be possible by the individual methods: The seismic data gives a robust model for the supra-basalt sediments whilst the gravity field is dominated by the high density basalt and basement features. The MT on the other hand is sensitive to the conductivity in both the supra- and sub-basalt sediments. We will present preliminary individual and joint inversion result for a FTG, seismic and MT data set located in the Faroe-Shetland basin. Because the investigated area is rather large (~75 x 40 km) and the individual data sets are relatively huge, we use a joint inversion framework (see Moorkamp et al., 2011) which is designed to handle large amount of data/model parameters. This program has moreover the options to link the individual parameter models either petrophysically using fixed parameter relationships or structurally using the cross-gradient approach. The seismic data set consists of a pattern of 8 intersecting wide-angle seismic profiles with maximum offsets of up to ~24 km. The 3-D gravity data set (size :~ 30 x 30 km) is coll

Geophysical datasets sensitive to different physical parameters can be used to improve resolution of Earth's internal structure. Herein, we jointly invert long-period magnetotelluric (MT) data and surface-wave dispersion curves. Our approach is based on a joint inversion using a genetic algorithm for a one-dimensional (1-D) isotropic structure, which we extend to 1-D anisotropic media. We apply our new anisotropic joint inversion to datasets from Central Germany demonstrating the capacity of our joint inversion algorithm to establish a 1-D anisotropic model that fits MT and seismic datasets simultaneously and providing new information regarding the deep structure in Central Germany. The lithosphere/asthenosphere boundary is found at approx. 84 km depth and two main anisotropic layers with coincident most conductive/seismic fast-axis direction are resolved at lower crustal and asthenospheric depths. We also quantify the amount of seismic and electrical anisotropy in the asthenosphere showing an emerging agreement between the two anisotropic coefficients.

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.

Where several different kinds of geophysical datasets have been acquired from a particular region, each of these can contain valuable information about the Earth, which may not be present in the other datasets. Jointly determining a common model, therefore, often gives a more thorough and more constrained description of the Earth structure than considering each dataset individually. For example, a seismic velocity inversion is only weakly constrained by first arrival seismic refraction data, but considering it alongside Magneto-Telluric (MT) and gravity data can greatly assist in the constraint (Jegen-Kulcsar et al., 2009). Strategies for joint inversion are therefore an active area of research. To date, most schemes for accomplishing this have been deterministic in nature. Using a deterministic technique often means that it is conceptually difficult to include prior beliefs about the system under determination, uncertainties both in measurement and the relationship between the different physical quantities (velocity, resistivity, density), and the discrepancy between the model and the real Earth. Statistical strategies such as MCMC (Markov Chain Monte Carlo) model searches exist for assessing this kind of problem, but the number of potentially computationally expensive forward model runs required to effectively sample the whole model space and thus achieve a meaningful result is normally prohibitively high (> 105), even for simple 1D models, so such schemes are not generally implemented. However, a technique known as emulation is used in various scientific fields eg. cosmology (Vernon and Goldstein, 2009), whereby computationally expensive forward modelling code (a simulator) is approximated by an uncertainty-calibrated computationally cheap function. Here we apply emulation to the problem of stochastic joint model determination. We show that emulation can be used to quickly exclude large areas of implausible model space, allowing fast updating of beliefs about an

Joint inversion strategies for geophysical data have become increasingly popular since they allow to combine complementary information from different data sets in an efficient way. Here, we present a non-linear joint inversion scheme, in which data from different methods are inverted separately and are joined through constrains accounting for parameter relationships. To avoid that the convergence behavior of the inversions is not profoundly disturbed by this coupling, the strengths of the constraints are re-adjusted at each iteration. In contrast to a joint inversion with a fixed parameter relationship, where data is inverted to one common model, this scheme requires no relative weighting of the data sets from different methods. Moreover, we observe that the adaption of the coupling strengths makes the convergence of the inversions much more robust. When we test our scheme with and without adaption on a synthetic 2-D model with seismic tomography, gravity and MT data, the final results with adaption were significantly closer to the true model. Finally, we observe that the adaptive scheme can to some extent handle models with structures for which the assumed parameter relationships are invalid.

We present an approach to calculate scalar and tensor gravity utilizing the massively parallel architecture of consumer graphics cards. Our parametrization is based on rectilinear blocks with constant density within each blocks. This type of parametrization is well suited for inversion of gravity data or joint inversion with other datasets, but requires the calculation of a large number of model blocks for complex geometries. For models exceeding 10,000 cells we achieve an acceleration of a factor of 40 for scalar data and 30 for tensor data compared to a single thread on the CPU. This significant acceleration allows fast computation of large models exceeding 106 model parameters and thousands of measurement sites.

We present joint inversion of magnetotelluric, receiver function, and Raleigh wave dispersion data for a one‐dimensional Earth using a multiobjective genetic algorithm (GA). The chosen GA produces not only a family of models that fit the data sets but also the trade‐off between fitting the different data sets. The analysis of this trade‐off gives insight into the compatibility between the seismic data sets and the magnetotelluric data and also the appropriate noise level to assume for the seismic data. This additional information helps to assess the validity of the joint model, and we demonstrate the use of our approach with synthetic data under realistic conditions. We apply our method to one site from the Slave Craton and one site from the Kaapvaal Craton. For the Slave Craton we obtain similar results to our previously published models from joint inversion of receiver functions and magnetotelluric data but with improved resolution and control on absolute velocities. We find a conductive layer at the bottom of the crust, just above the Moho; a low‐velocity, low‐resistivity zone in the lithospheric mantle, previously termed the Central Slave Mantle Conductor; and indications of the lithosphere‐asthenosphere boundary in terms of a decrease in seismic velocity and resistivity. For the Kaapvaal Craton both the seismic and the MT data are of lesser quality, which prevents as detailed and robust an interpretation; nevertheless, we find an indication of a low‐velocity low‐resistivity zone in the mantle lithosphere. These two examples demonstrate the potential of joint inversion, particularly in combination with nonlinear optimization methods.