Mailing Address
Dieter Werthmüller
Geothermal Energy & Geofluids
Institute of Geophysics
NO F 57
Sonneggstrasse 5
CH-8092 Zurich Switzerland
https://orcid.org/0000-0002-8575-2484Contact
| +41 44 633 2751 | |
| dieter.werthmuller@eaps.ethz.ch |
Administration
| Prisca Maurantonio | |
| +41 44 632 3465 | |
| prisca.maurantonio@eaps.ethz.ch | |
Research Interests
My research interest is the characterisation of the subsurface with geophysical methods for energy (geothermal, CO2 storage, H2 storage), resources (groundwater, mining), and environmental (landslides, salt water intrusions, permafrost degradation) reasons. My particular focus lies on electromagnetic (EM) methods, the accurate modelling of EM fields in the subsurface, and the inversion of EM data. I have a passion for open-source software, community-driven developments, and computational reproducibility. The near surface, the soil and rocks we are living on, hold many challenges that we must tackle collaboratively for a successful energy transition and a safe living in an ever more populated world.
Publications
[Go to Proceedings Refereed] [Go to Proceedings Non-Refereed] [Go to Theses]
Underlined names are links to current or past GEG members
REFEREED PUBLICATIONS IN JOURNALS
14.
Oudshoorn, C., D. Werthmüller, E. Slob, and D. Voskov, Numerical experiment on data assimilation for geothermal doublets using production data and electromagnetic observations, Geophysics, 89(6), pp. M227-M237, 2024. https://doi.org/10.1190/geo2023-0463.1 [Download] [View Abstract] 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.
13.
Naranjo, D., L. Parisi, S. Jónsson, P. Jousset, D. Werthmüller, and C. Weemstra, Ocean Bottom Seismometer Clock Correction using Ambient Seismic Noise, Seismica, 3, 2024. https://doi.org/10.26443/seismica.v3i1.367 [Download] [View Abstract]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.
12.
Carrizo Mascarell, M., D. Werthmüller, and E. Slob, Estimation of electrical conductivity models using multi-coil rigid-boom electromagnetic induction measurements, Computers & Geosciences , 193, pp. 105732, 2024. https://doi.org/10.1016/j.cageo.2024.105732 [Download] [View Abstract]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.
11.
Aigner, L., D. Werthmüller, and A. Flores Orozco, Sensitivity analysis of inverted model parameters from transient electromagnetic measurements affected by induced polarization effects, Journal of Applied Geophysics , 223, pp. 105334, 2024. https://doi.org/10.1016/j.jappgeo.2024.105334 [Download] [View Abstract]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.
10.
Li, L., E. Slob, D. Werthmüller, L. Wang, and H. Lu, An Introduction to the Application of Marine Controlled-Source Electromagnetic Methods for Natural Gas Hydrate Exploration, Journal of Marine Science and Engineering, 11(1), 2023. https://doi.org/10.3390/jmse11010034 [Download] [View Abstract]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.
9.
Eltayieb, M., D. Werthmüller, G. Drijkoningen, and E. Slob, Feasibility Study of Controlled-Source Electromagnetic Method for Monitoring Low-Enthalpy Geothermal Reservoirs, Applied Sciences, 13(16), 2023. https://doi.org/10.3390/app13169399 [Download] [View Abstract]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.
8.
Grayver, A.V., A. Kuvshinov, and D. Werthmüller, Time-Domain Modeling of Three-Dimensional Earth's and Planetary Electromagnetic Induction Effect in Ground and Satellite Observations, Journal of Geophysical Research: Space Physics, 126(3), pp. e2020JA028672, 2021. https://doi.org/10.1029/2020JA028672 [Download] [View Abstract]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.
7.
Werthmüller, D., W. Mulder, and E. Slob, Fast Fourier transform of electromagnetic data for computationally expensive kernels, Geophysical Journal International, 226(2), pp. 1336-1347, 2021. https://doi.org/10.1093/gji/ggab171 [Download] [View Abstract]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.
6.
Werthmüller, D., R. Rochlitz, O. Castillo-Reyes, and L. Heagy, Towards an open-source landscape for 3D CSEM modelling, Geophysical Journal International, 227(1), pp. 644-659, 2021. https://doi.org/10.1093/gji/ggab238 [Download] [View Abstract]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.
5.
Werthmüller, D., K. Key, and E. Slob, A tool for designing digital filters for the Hankel and Fourier transforms in potential, diffusive, and wavefield modeling, Geophysics, 84(2), pp. F47-F56, 2019. https://doi.org/10.1190/geo2018-0069.1 [Download] [View Abstract]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, controlled-source 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.
4.
Werthmüller, D., W. Mulder, and E. Slob, emg3d: A multigrid solver for 3D electromagnetic diffusion, The Journal of Open Source Software, 4(39), pp. 1463, 2019. https://doi.org/10.21105/joss.01463 [Download]
3.
Werthmüller, D., An open-source full 3D electromagnetic modeler for 1D VTI media in Python: empymod, Geophysics, 82(6), pp. WB9-WB19, 2017. https://doi.org/10.1190/geo2016-0626.1 [Download] [View Abstract]The Python-code empymod computes the 3D electromagnetic field in a layered earth with vertical transverse isotropy by combining and extending two earlier presented algorithms in this journal. The bottleneck in frequency- and time-domain calculations of electromagnetic responses derived in the wavenumber-frequency domain is the transformations from the wavenumber to the space domain and from the frequency to the time domain, the so-called Hankel and Fourier transforms. Three different Hankel transform methods (quadrature, quadrature-with-extrapolation [QWE], and filters) and four different Fourier transform methods (fast Fourier transform [FFT], FFTLog, QWE, and filters) are included in empymod, which allows us to compare these different methods in terms of speed and precision. The best transform in terms of speed and precision depends on the modeled frequencies. Published digital filters for the Hankel transform are very fast and precise for frequencies in the range of controlled-source electromagnetic data, but they fail in the frequency range of ground-penetrating radar. Conventional quadrature, on the other hand, is in comparison very slow but can model any frequency. Examples comparing empymod with analytical solutions and with existing electromagnetic modelers illustrate the capabilities of empymod.
2.
Werthmüller, D., A. Ziolkowski, and D. Wright, Predicting CSEM responses from seismic velocities, Interpretation, 2(3), pp. SH115-SH131, 2014. https://doi.org/10.1190/INT-2013-0153.1 [Download] [View Abstract]We created a workflow to predict controlled-source electromagnetic (CSEM) responses from seismic velocities and compared the predicted responses with CSEM data. The first step was to calculate a resistivity model from seismic velocities in a Bayesian framework to account for the uncertainties. The second step was to estimate the electric anisotropy and improve the resistivity model for the depths at which there was no well control. The last step was to use this updated resistivity model to forward-model CSEM responses and compare the result with CSEM data. The comparison with real data revealed that the measured CSEM responses were generally within plus and minus one standard deviation of the predicted responses. This workflow was able to predict CSEM responses, which can prove very useful for feasibility studies before acquisition and interpretation after acquisition of CSEM data.
1.
Werthmüller, D., A. Ziolkowski, and D. Wright, Background resistivity model from seismic velocities, Geophysics, 78(4), pp. E213-E223, 2013. https://doi.org/10.1190/geo2012-0445.1 [Download] [View Abstract]We developed a methodology to estimate resistivities from seismic velocities. We applied known methods, including rock physics, depth trends, structural information, and uncertainty analysis. The result is the range of background resistivity models that is consistent with the known seismic velocities. We successfully tested the methodology with real data from the North Sea. These 2D or 3D background resistivity models yield a detailed insight into the background resistivity, and they are a powerful tool for feasibility studies. They could also serve as starting models or constraints in (iterative) forward modeling of electromagnetic data for the determination of subsurface resistivities.
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THESES
2.
Werthmüller, D., Bayesian estimation of resistivities from seismic velocities, Dissertation, Edinburgh University, pp., 2014. [Download PDF] [View Abstract]I address the problem of finding a background model for the estimation of resistivities in the earth from controlled-source electromagnetic (CSEM) data by using seismic data and well logs as constraints. Estimation of resistivities is normally done by trial-and-error, in a process called “inversion”, by finding a model of the earth whose responses match the data to within an acceptable error; what comes out of the inversion is what is put into the model by the geophysicist: it does not come out of the data directly. The premise underlying this thesis is that an earth model can be found that satisfies not only the CSEM data but also the seismic data and any well logs. I present a methodology to determine background resistivities from seismic velocities using rock physics, structural constraints, and depth trends. The physical parameters of the seismic wave equation are different from those in the electromagnetic diffusion equation, so there is no direct link between the governing equations. I therefore use a Bayesian framework to incorporate not only the errors in the data and our limited knowledge of the rock parameters, but also the uncertainty of our chosen and calibrated velocity-to-resistivity transform. To test the methodology I use a well log from the North Sea Harding South oil and gas field to calibrate the transform, and apply it to seismic velocities of the nearby Harding Central oil and gas field. I also use short-offset CSEM inversions to estimate the electric anisotropy and to improve the shallow part of the resistivity model, where there is no well control. Three-dimensional modelling of this resistivity model predicts the acquired CSEM data within the estimated uncertainty. This methodology makes it possible to estimate background resistivities from seismic velocities, well logs, and other available geophysical and geological data. Subsequent CSEM surveys can then focus on finding resistive anomalies relative to this background model; these are, potentially, hydrocarbon-bearing formations.
1.
Werthmüller, D., Inversion of multi-transient EM data from anisotropic media, MSc Thesis, Delft University of Technology, pp., 2009. [Download PDF] [View Abstract]Forward modelling demonstrates that resistivity anisotropy has a huge effect on Multi-Transient ElectroMagnetic step and impulse responses. The earth is never isotropic – even a stack of isotropic layers behaves anisotropically – and there is a great need to account for resistivity anisotropy in order to delineate the true target depth and target transverse resistance in ElectroMagnetic surveying. I account for resistivity anisotropy by (a) deriving apparent anisotropy formulae and using them together with apparent resistivities for a fast iterative inversion scheme, and (b) by including anisotropy into a 1D full waveform inversion scheme. Full anisotropic inversions result in much smoother models than isotropic inversions. Sharp resistivity boundaries result in anisotropy anomalies, as horizontal and vertical resistivities are not affected in the same way. Anisotropic inversion results yield a good indication of the present background anisotropy. Carrying out inversions with fixed anisotropies, e.g. determined in a free anisotropic inversion, can improve the result significantly compared with an isotropic inversion.