Inversion of multi-transient EM data from anisotropic media

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 ccount 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.Applied GeophysicsGeotechnologyCivil Engineering and Geoscience

Time-Domain CSEM Modelling Using Frequency- and Laplace-Domain Computations

Modelling time-domain electromagnetic data with a frequency-domain code requires the computation of manyfrequencies 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.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Applied Geophysics and Petrophysic

emg3d: A multigrid solver for 3D electromagnetic diffusion

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 byEApplied Geophysics and Petrophysic

A tool for designing digital filters for the Hankel and Fourier transforms in potential, diffusive, and wavefield modeling

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.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Applied Geophysics and Petrophysic

Fast Fourier transform of electromagnetic data for computationally expensive kernels

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.Applied Geophysics and Petrophysic

Sensitivity analysis of inverted model parameters from transient electromagnetic measurements affected by induced polarization effects

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.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Applied Geophysics and Petrophysic

Feasibility Study of Monitoring Delft Geothermal Project Using Land Controlled- Source Electromagnetic Method

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.Applied Geophysics and PetrophysicsGeoscience and Engineerin

Determining clock errors of ocean-bottom seismometers: an ambient-noise based method designed for large-scale ocean bottom deployments

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.Applied Geophysics and PetrophysicsGeoscience and Engineerin

Towards an open-source landscape for 3-D CSEM modelling

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.Petroleum Engineerin

An Introduction to the Application of Marine Controlled-Source Electromagnetic Methods for Natural Gas Hydrate Exploration

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.Applied Geophysics and PetrophysicsGeoscience and Engineerin