Ocean-bottom seismometers (OBSs) are equipped with seismic sensors that record acoustic and seismic events at the seafloor, which makes them suitable for investigating tectonic structures capable of generating earthquakes offshore. One critical parameter to obtain accurate earthquake locations is the absolute time of the incoming seismic signals recorded by the OBSs. It is, however, not possible to synchronize the internal clocks of the OBSs with a known reference time, given that GNSS signals are unable to reach the instrument at the sea bottom. To address this issue, here we introduce a new method to synchronize the clocks of large-scale OBS deployments. Our approach relies on the theoretical time-symmetry of time-lapse (averaged) crosscorrelations of ambient seismic noise. Deviations from symmetry are attributed to clock errors. This implies that the recovered clock errors will be obscured by lapse crosscorrelations' deviations from symmetry that are not due to clock errors. Non-uniform surface wave illumination patterns are arguably the most notable source which breaks the time symmetry. Using field data, we demonstrate that the adverse effects of non-uniform illumination patterns on the recovered clock errors can be mitigated by means of a weighted least-squares inversion that is based on station-station distances. In addition, our methodology permits the recovery of timing errors at the time of deployment of the OBSs. This error can be attributed to either: i) a wrong initial time synchronization of the OBS or ii) a timing error induced by changing temperature and pressure conditions while the OBS is sunk to the ocean floor. The methodology is implemented in an open-source Python package named OCloC, and we applied it to the OBS recordings acquired in the context of the IMAGE project in and around Reykjanes, Iceland. As expected, most OBSs suffered from clock drift. Surprisingly, we found incurred timing errors at the time of deployment for most of the OBSs.@en

Electromagnetic induction measurements from multi-coil configuration instruments are used to obtain information about the electrical conductivity distribution in the subsurface. The resulting inverse problem might not have a unique and stable solution. In that case, a local inversion method can be trapped in a local minimum and lead to an incorrect solution. In this study, we evaluate the well-posedness of the inverse problem for two and three-layered electrical conductivity models. We show that for a two-layered model, uniqueness is ensured only when both in-phase and quadrature data are available from the measurements. Results from a Gauss–Newton inversion and a lookup table demonstrate that the solution space is convex. Furthermore, we demonstrate that for even a simple three-layered model, the data contained in such measurements are insufficient to reach a correct or stable solution. For models with more than 2 layers, independent prior information is necessary to solve the inverse problem. The insights from the numerical examples are applied in a field case.

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We investigate the application of the distance-based global sensitivity analysis (DGSA) to evaluate the sensitivity of electrical model parameters obtained from transient electromagnetic (TEM) data including induced polarization (IP) effects. We propose novel open-source forward modeling and inversion routines for single-loop TEM data including IP effects with the maximum phase angle model to model the frequency dependence of the complex resistivity. In a first step, we evaluate the accuracy of our forward modeling and inversion routines using numerical studies, where the actual variations of layer thicknesses and resistivities, as well as the frequency dependence of the complex resistivity is known. In a second step, we extend our investigation to field data and apply our approach to three distinct case studies in layered media: 1) a confined aquifer corresponding to conductive non-polarizable media, 2) a graphite deposit corresponding to highly conductive and polarizable anomalies in a resistive host rock and 3) an ice glacier corresponding to highly resistive polarizable media. Our DGSA results reveal that standard depth of investigation (DOI) approaches may overestimate the true sensitivity of the model obtained from the inversion. TEM data collected in conductive layered media without IP effects show reduced sensitivity above the predicted DOI. The case studies in polarizable media demonstrate that the maximum phase angle is more influential on the TEM model response than the relaxation time and dispersion coefficient. Our DGSA results for polarizable media reveal that TEM field data collected at the graphite deposit and at the ice glacier are sensitive to the geometry of the polarizable layer.

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In agriculture, there is a demand for new methods to monitor the dynamics of fresh rainwater lenses overlaying on saline seeping groundwater. For this purpose, integrating different geoelectrical measurements is a non-invasive and low-cost approach to obtaining subsurface information. Geoelectric methods such as electromagnetic induction (EMI) and electrical resistivity tomography (ERT) have proven effective in characterizing subsoil electrical properties, which can be correlated to petrophysical properties such as fluid salinity. These methods have different sensitivities and can provide complementary information about the electrical conductivity and geometry of the subsurface. This study explores the effectiveness of a methodology that combines EMI measurements with laterally constrained inversion as prior information for ERT inversion. We investigate the usefulness of the method using synthetic data and data from a coastal Dutch polder system. The findings are promising, demonstrating improved delineation of changes in electrical conductivity, potentially linked with salinity fluctuations in the subsoil. This methodology proves effective in mapping in-depth variations in electrical conductivity. It could facilitate the impact assessment of level-controlled drainage systems on augmenting shallow rainwater lenses and mitigating salinization in Dutch polders.@en

The data assimilation process for geothermal reservoirs often relies on well data, which primarily offer insights into the immediate vicinity of the borehole. However, integrating geophysical methods can provide valuable information beyond well proximity, possibly enhancing reservoir predictions. Current methods of monitoring geothermal reservoirs struggle to maintain a good signal-to-noise ratio for deep reservoirs. Diffusive electromagnetic (EM) methods can be sensitive to the decreasing conductivity from heat extraction in geothermal reservoirs and offer promising additional value. To test their potential effectiveness, numerical examples are simulated. A scheme to incorporate diffusive EM observations into a data assimilation process for geothermal reservoirs is presented and implemented in this study. First, an ensemble of prior models representing the reservoir uncertainty is used to determine the moments of the resulting temperature field using a forward geothermal simulation. Subsequently, a conductivity model is calculated from the temperature field using an empirical relationship. The expected electric field response can then be simulated using an EM forward model. EM sources are placed on the surface around the expected cold plume location. The receiver is placed at reservoir depth. To assimilate the data, the ensemble smoother with multiple data assimilation method is used. The findings demonstrate that the incorporation of EM data provides valuable information regarding the temperature field. This improves the accuracy of the temperature forecast of the entire reservoir when combined with the localized data from the production well and, therefore, helps to resolve the complex migration of the cold front. These results highlight the monitoring potential of EM observations for geothermal reservoirs.@en

Rigid boom electromagnetic surveys that use coil-coil configurations are often used to obtain information about the subsurface conductivity. Semi-analytic solutions help to simulate electromagnetic induction measurements for a large number of horizontally layered models, which can then be stored and used as a lookup table. This procedure is performed once and then used to find the corresponding model that produces the best data fit, eliminating the need for running numerous simulations in every minimization step of an inversion scheme for large field datasets. We apply this methodology to a numerical example and field data acquired in The Netherlands. Our results from both cases using the global search demonstrate its ability to estimate electrical conductivity distributions in two-layered models in a fast and accurate manner. Furthermore, we apply the workflow using a lookup table based on low induction number approximation-derived measurements. The outcome of implementing this methodology using the low induction number lookup table shows poor accuracy in the electrical conductivity estimations for both the numerical example and the field data in comparison to the semi-analytical approach.@en

To optimize geological structures a multi-physics inversion of electromagnetic and gravity data is carried out. With the TERRASYS’ Joint Inversion Framework JIF and its modules for 3D EM (here CSEM) and for 3D GRAV (gravity and gradients) the geometry of a salt body located in the Nordkapp Basin is optimized. The physical effects of a complex structural model, derived from seismic interpretations, are fitted to the field data by optimizing salt shape and rock parameter distributions simultaneously. Exemplary model features of the optimized models illustrate the improved solution space of the joint inversion compared to the respective per-datatype inversions. By means of this case study, benefits, preconditions and limits of joint inversion were discussed, as well as general quality criteria to evaluate achieved multi-data and multi-physics model optimizations.@en

Tracking temperature changes by measuring the resulting resistivity changes inside low-enthalpy reservoirs is crucial to avoid early thermal breakthroughs and maintain sustainable energy production. The controlled-source electromagnetic method (CSEM) allows for the estimation of sub-surface resistivity. However, it has not yet been proven that the CSEM can monitor the subtle resistivity changes typical of low-enthalpy reservoirs. In this paper, we present a feasibility study considering the CSEM monitoring of 4–8 Ω·m resistivity changes in a deep low-enthalpy reservoir model, as part of the Delft University of Technology (TU Delft) campus geothermal project. We consider the use of a surface-to-borehole CSEM for the detection of resistivity changes in a simplified model of the TU Delft campus reservoir. We investigate the sensitivity of CSEM data to disk-shaped resistivity changes with a radius of 300, 600, 900, or 1200 m at return temperatures equal to 25, 30, …, 50 °C. We test the robustness of CSEM monitoring against various undesired effects, such as random noise, survey repeatability errors, and steel-cased wells. The modelled differences in the electric field suggest that they are sufficient for the successful CSEM detection of resistivity changes in the low-enthalpy reservoir. The difference in monitoring data increases when increasing the resistivity change radius from 300 to 1200 m or from 4 to 8 Ω·m. Furthermore, all considered changes lead to differences that would be detectable in CSEM data impacted by undesired effects. The obtained results indicate that the CSEM could be a promising geophysical tool for the monitoring of small resistivity changes in low-enthalpy reservoirs, which would be beneficial for geothermal energy production.@en

Natural gas hydrates have been an unconventional source of energy since the beginning of this century. Gas-hydrate-filled reservoirs show higher resistivity values compared with water-filled sediments. Their presence can be detected using marine controlled-source electromagnetic methods. We classify acquisition configurations into stationary and moving receiver configurations, which are described in terms of the design group, the operational details, and where they have been used successfully in the field for natural gas hydrate exploration. All configurations showed good numerical results for the detection of a 700 m long gas hydrate reservoir buried 200 m below the seafloor, but only the stationary configurations provided data that can be used to estimate the horizontal boundaries of the resistive part of the reservoir when the burial depth is known from seismic data. We discuss the operational steps of the configurations and provide the steps on how to choose a suitable configuration. Different CSEM configurations were used together with seismic data to estimate the edge of the gas hydrate reservoir and the total volume of the gas hydrates, to optimize the drilling location, to increase production safety, and to improve geological interpretations. It seems that CSEM has become a reliable method to aid in the decision-making process for gas hydrate reservoir appraisal and development.@en

The timing of the recordings of ocean-bottom seismometers (OBSs) is critical for accurate earthquake location and Earth model studies. GNSS signals, however, cannot reach OBSs deployed at the ocean bottom. This prevents their clocks from being synchronized with a known reference time. To overcome this, we developed OCloC, a Python package that uses time-lapse cross-correlations of ambient seismic noise to synchronize the recordings of large-scale OBS deployments. By simultaneously quantifying deviations from symmetry of a set of lapse cross-correlations, OCloC recovers the incurred clock errors by means of a least-squares inversion. In fact, because non-uniform noise illumination patterns also break the symmetry of (lapse) cross-correlations, we introduce a distance-based weighted least-squares inversion. This mitigates the adverse effect of the noise illumination on the recovered clock errors. Using noise recordings from the IMAGE project in Reykjanes, Iceland, we demonstrate that OCloC significantly reduces the time and effort needed to detect and correct timing errors in large-scale OBS deployments. In addition, our methodology allows one to evaluate potential timing errors at the time of OBS deployment. These might be caused by incorrect initial synchronization, or by rapidly changing temperature conditions while the OBS is sunk to the sea bottom. Our work advances the use of OBSs for earthquake studies and other applications.@en

Delft geothermal project (DAPwell) is a planned geothermal well doublet, where relatively cold water is going to be injected through one well into a low enthalpy geothermal reservoir to produce hot water from the other well. The volume of the cold water around the injection well will increase over time and, in the end, result in a thermal breakthrough. Thus, it is essential to trace the time-lapse change in the volume of the cold water to monitor the DAPwell efficiently. The invaded reservoir volume by the cold water is associated with a decrease in the pore fluid temperature and salinity. This increases the electrical resistivity of the geothermal reservoir, where the cold front is located. Hence, estimating the time-lapse change in the electrical resistivity of the geothermal reservoir can be used to identify the distribution of the cold water. From a theoretical point of view, the controlled-source electromagnetic (CSEM) method can be used to get information about the change in the electrical resistivity within the geothermal reservoir. In this study, we investigate the feasibility of monitoring a geoelectric model of the DAPwell using land CSEM forward modelling. The optimal survey design is investigated as well as the influence of cold water volumetric changes on the time-lapse electric field response. The impact of measurements undesired effects on time-lapse CSEM response is analysed and then synthesized. A subsurface model of the DAPwell is illuminated by a horizontal electric dipole source, which emits a sinusoidal field with several frequencies. Based on the numerical experiments, surface measurements do not pick up sufficient time-lapse signal to use them for field applications. On the other hand, the difference in the z-component of the electric field, determined along a depth section, allows for a successful detection of the electrical resistivity changes within the geothermal reservoir. The correlation between the spatial distribution of the cold water and the difference in time-lapse electric field responses is clarified. Finally, it is noticed that the difference in time-lapse signal is measurable in the presence of the different sources of noise. @en

Electric currents induced in conductive planetary interiors by time-varying magnetospheric and ionospheric current systems have a significant effect on electromagnetic (EM) field observations. Complete characterization of EM induction effects is difficult owing to nonlinear interactions between the three-dimensional electrical structure of a planet and spatial complexity of inducing current systems. We present, a general framework for time-domain modeling of three-dimensional EM induction effects in heterogeneous conducting planets. Our approach does not assume that the magnetic field is potential, allows for an arbitrary distribution of electrical conductivity within a planet, and can deal with spatially complex time-varying current systems. The method is applicable to both data measured at stationary observation sites and satellite platforms, and enables the calculation of three-dimensional EM induction effects in near real-time settings.

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3-D controlled-source electromagnetic data are often computed directly in the domain of interest, either in the frequency domain or in the time domain. Computing it in one domain and transforming it via a Fourier transform to the other domain is a viable alternative. It requires the evaluation of many responses in the computational domain if standard Fourier transforms are used. This can make it prohibitively expensive if the kernel is time-consuming as is the case in 3-D electromagnetic modelling. The speed of modelling obtained through such a transform is defined by three key points: solver, method and implementation of the Fourier transform, and gridding. The faster the solver, the faster modelling will be. It is important that the solver is robust over a wide range of values (frequencies or times). The method should require as few kernel evaluations as possible while remaining robust. As the frequency and time ranges span many orders of magnitude, the required values are ideally equally spaced on a logarithmic scale. The proposed fast method uses either the digital linear filter method or the logarithmic fast Fourier transform together with a careful selection of evaluation points and interpolation. In frequency-to-time domain tests this methodology requires typically 15-20 frequencies to cover a wide range of offsets. The gridding should be frequency-or time-dependent, which is accomplished by making it a function of skin depth. Optimizing for the least number of required cells should be combined with optimizing for computational speed. Looking carefully at these points resulted in much smaller computation times with speedup factors of ten or more over previous methods. A computation in one domain followed by transformation can therefore be an alternative to computation in the other domain domain if the required evaluation points and the corresponding grids are carefully chosen.

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Large-scale modelling of 3-D controlled-source electromagnetic (CSEM) surveys used to be feasible only for large companies and research consortia. This has changed over the last few years, and today there exists a selection of different open-source codes available to everyone. Using four different codes in the Python ecosystem, we perform simulations for increasingly complex models in a shallow marine setting. We first verify the computed fields with semi-analytical solutions for a simple layered model. Then we validate the responses of a more complex block model by comparing results obtained from each code. Finally, we compare the responses of a real-world model with results from the industry. On the one hand, these validations show that the open-source codes are able to compute comparable CSEM responses for challenging, large-scale models. On the other hand, they show many general and method-dependent problems that need to be faced for obtaining accurate results. Our comparison includes finite-element and finite-volume codes using structured rectilinear and octree meshes as well as unstructured tetrahedral meshes. Accurate responses can be obtained independently of the chosen method and the chosen mesh type. The runtime and memory requirements vary greatly based on the choice of iterative or direct solvers. However, we have found that much more time was spent on designing the mesh and setting up the simulations than running the actual computation. The challenging task is, irrespective of the chosen code, to appropriately discretize the model. We provide three models, each with their corresponding discretization and responses of four codes, which can be used for validation of new and existing codes. The collaboration of four code maintainers trying to achieve the same task brought in the end all four codes a significant step further. This includes improved meshing and interpolation capabilities, resulting in shorter runtimes for the same accuracy. We hope that these results may be useful for the CSEM community at large and that we can build over time a suite of benchmarks that will help to increase the confidence in existing and new 3-D CSEM codes.@en

Difficulties in detecting and characterising shallow objects close the surface with seismic shear waves are often problematic because of dominant surface waves. By sequencing a specific combination of two data driven processing steps followed by diffraction tomography can overcome these problems. Small scattering objects become visible in the final image that can have importance of the understanding of subsurface locations, such as areas of archaeological interest. On the other hand, deep changes in the electric resistivity on land are often problematic to detect and especially to monitor time-lapse change over long periods of time. The usual electrodes slowly erode and vanish. Geothermal heat production environments often lead to changes in the resistivity between in-situ water-filled formations and cooler injected water-filled formations of less than one order of magnitude. A dedicated set of capacitively coupled electrode could overcome to erosion problem. When placed in a well with composite casing, these could be used in measurements of much enhanced detectability. In that case it is necessary to have electrodes in a zone from below to above the target layer. By changing the source offset at the surface, optimal measurements can be done to detect the small and deep changes in resistivity.@en

Modelling time-domain electromagnetic data with a frequency-domain code requires the computation of many frequencies for the Fourier transform. This can make it computationally very expensive when compared with timedomain codes. However, it has been shown that frequency-domain codes can be competitive if frequencydependent modelling grids and clever frequency selection are used. We improve existing schemes by focusing on (a) minimizing the dimension of the required grid and (b) minimizing the required frequencies with logarithmicallyspaced Fourier transforms and interpolation. These two changes result in a significant speed-up over previous results. We also tried to further speed-up the computation by using the real-valued Laplace domain instead of the complex-valued frequency domain. Computation in the Laplace domain results in a speed-up of roughly 30% over computation in the frequency domain. Although there is no analytical transformation from the Laplace to the time domain we were able to derive a digital linear filter for it. While this filter works fine for exact analytical responses it turned out that it is very susceptible to the smallest error. This makes it unfortunately unsuitable for iterative 3D solvers which approximate the solution to a certain tolerance.@en

The open-source code fdesign makes it possible to design digital linear filters for the Hankel and Fourier transforms used in potential, diffusive, and wavefield modeling. Digital filters can be derived for any electromagnetic (EM) method, such as methods in the diffusive limits (direct current, controlledsource EM [CSEM]) as well as methods using higher frequency content (ground-penetrating radar [GPR], acoustic and elastic wavefields). The direct matrix inversion method is used for the derivation of the filter values, and a brute-force minimization search is carried out over the defined spacing and shifting values of the filter basis. Included or user-provided theoretical transform pairs are used for the inversion. Alternatively, one can provide layered subsurface models that will be computed with a precise quadrature method using the EM modeler empymod to generate numerical transform pairs. The comparison of the presented 201 pt filter with previously presented filters indicates that it performs better for some standard CSEM cases. The derivation of a longer 2001 pt filter for a GPR example with a 250 MHz center frequency proves that the filter method works not only for diffusive EM fields but also for wave phenomena. The presented algorithm provides a tool to create problem specific digital filters. Such purpose-built filters can be made shorter and can speed up consecutive potential, diffusive, and wavefield inversions.@en

Controlled-source electromagnetic (CSEM) surveys are a common geophysical investigationtool in the search for, amongst other, groundwater, hydrocarbons, and minerals. The nu-merical modelling of CSEM data requires the solution of the Maxwell equations. These canbe simplified in the particular case of CSEM, as the frequencies used in surveys are usuallysufficiently low to ignore any displacement currents. A diffusive problem remains, which hasthe resulting system of equations given in the frequency domain byE@en