Deciphering the State of the Lower Crust and Upper Mantle With Multi-Physics Inversion

The composition of the lower crust is a key factor in understanding tectonic activity and deformation within the Earth. In particular, the presence or absence of melt or fluids has strong control on tectonic evolution. Multi-physics inversion results from the western United States indicate that tectonic inheritance plays a much stronger role in determining the location of melt in the lower crust than previously thought. Even in a currently active area such as the Yellowstone Hotspot, the results suggest that fluid dominated structures and fluid free regions are located directly next to each other. This is incompatible with the commonly used model of recent tectonic activity as a main controlling factor for the presence of fluids or melt. These results have global implications for how geophysical models are interpreted and how they can be related to geodynamic simulations

Parallel computation of optimized arrays for 2-D electrical imaging surveys

Modern automatic multi-electrode survey instruments have made it possible to use non-traditional arrays to maximize the subsurface resolution from electrical imaging surveys. Previous studies have shown that one of the best methods for generating optimized arrays is to select the set of array configurations that maximizes the model resolution for a homogeneous earth model. The Sherman–Morrison Rank-1 update is used to calculate the change in the model resolution when a new array is added to a selected set of array configurations. This method had the disadvantage that it required several hours of computer time even for short 2-D survey lines. The algorithm was modified to calculate the change in the model resolution rather than the entire resolution matrix. This reduces the computer time and memory required as well as the computational round-off errors. The matrix–vector multiplications for a single add-on array were replaced with matrix–matrix multiplications for 28 add-on arrays to further reduce the computer time. The temporary variables were stored in the double-precision Single Instruction Multiple Data (SIMD) registers within the CPU to minimize computer memory access. A further reduction in the computer time is achieved by using the computer graphics card Graphics Processor Unit (GPU) as a highly parallel mathematical coprocessor. This makes it possible to carry out the calculations for 512 add-on arrays in parallel using the GPU. The changes reduce the computer time by more than two orders of magnitude. The algorithm used to generate an optimized data set adds a specified number of new array configurations after each iteration to the existing set. The resolution of the optimized data set can be increased by adding a smaller number of new array configurations after each iteration. Although this increases the computer time required to generate an optimized data set with the same number of data points, the new fast numerical routines has made this practical on commonly available microcomputers

Integrated Geophysical Analysis of Passive Continental Margins: Insights into the Crustal Structure of the Namibian Margin from Magnetotelluric, Gravity, and Seismic Data

Passive continental margin research amalgamates the investigation of many broad topics, such as the emergence of oceanic crust, lithospheric stress patterns and plume-lithosphere interaction, reservoir potential, methane cycle, and general global geodynamics. Central tasks in this field of research are geophysical investigations of the structure, composition, and dynamic of the passive margin crust and upper mantle. A key practice to improve geophysical models and their interpretation, is the integrated analysis of multiple data, or the integration of complementary models and data. In this thesis, I compare four different inversion results based on data from the Namibian passive continental margin. These are a) a single method MT inversion; b) constrained inversion of MT data, cross-gradient coupled with a fixed structural density model; c) cross-gradient coupled joint inversion of MT and satellite gravity data; d) constrained inversion of MT data, cross-gradient coupled with a fixed gradient velocity model. To bridge the formal analysis of geophysical models with geological interpretations, I define a link between the physical parameter models and geological units. Therefore, the results from the joint MT and gravity inversion (c) are correlated through a user-unbiased clustering analysis. This clustering analysis results in a distinct difference in the signature of the transitional crust south of- and along the supposed hot-spot track Walvis Ridge. I ascribe this contrast to an increase in magmatic activity above the volcanic center along Walvis Ridge. Furthermore, the analysis helps to clearly identify areas of interlayered massive, and weathered volcanic flows, which are usually only identified in reflection seismic studies as seaward dipping reflectors. Lastly, the clustering helps to differentiate two types of sediment cover. Namely, one of near-shore, thick, clastic sediments, and one of further offshore located, more biogenic, marine sediments

Comparison of Different Coupling Methods for Joint Inversion of Geophysical data: A case study for the Namibian Continental Margin

Integration of multiple geophysical data is a key practice to reduce model uncertainties and enhance geological interpretations. Electrical resistivity models resulting from inversion of marine magnetotelluric (MT) data, often lack depth resolution of lithological boundaries and distinct information for shallow model parts. This is due to the diffusive nature of electromagnetic fields, enhanced by deficient data sampling and model regularization during inversion. Thus, integrating data or models to constrain layer thicknesses or structural boundaries is an effective approach to derive better constrained and more detailed resistivity models. We investigate the different impacts of three cross-gradient coupled constraints on 3D MT inversion of data from the Namibian passive continental margin. The three constraints are a) coupling with a fixed structural density model; b) coupling with satellite gravity data; c) coupling with a fixed gradient velocity model. Here we show that coupling with a fixed model (a and c) improves the resistivity model the most. Shallow conductors imaging sediment cover are confined to a thinner layer in the resulting resistivity models compared to the MT-only model. Additionally, these constraints help to suppress vertical smearing of a conductive anomaly attributed to a fracture zone, and clearly show that the seismically imaged Moho is not accompanied by a change in electrical resistivity. All of these observations help to derive an Earth model, which will form the basis for future interpretation of the processes that lead to continental break-up during the early Cretaceous

Die Anwendung von Krylov Unterraum Methoden zur Berechnung von Forwärts Lösungen und Model Sensitivitäten von 3D mariner, aktiver elektromagnetischer Probleme im Zeitbereich

To reduce the run-times of 3D modeling and inversion software for the interpretation of marine controlled source electromagnetics (CSEM) in time domain, the implementation of efficient algorithms on massive parallel hardware is presented. Two forward modeling implementations as well as an implementation for sensitivity calculation are illustrated. The first forward code is an implementation of the spectral Lanczos decomposition method on a graphics processing unit (GPU). The applicability of the code for a CSEM system, how it is used at GEOMAR, is demonstrated. In the second forward code, the SLDM is replaced by the more efficient Rational Krylov Subspace Method (RKSM). This reduces the dimension and run-time of the problem drastically. The accuracy of the code is investigated for different models and conductivity contrasts. The run-times of SLDM and RKSM are compared on different architectures. The sensitivities are computed with the MOR-method (Model Order Reduction). It is shown that the method works and the applicability to a real data set is shown.Zur Reduzierung der Laufzeiten von 3D Modellierungs- und Inversions-Software für die Interpretation von mariner, aktiver Elektromagnetik (engl. CSEM, controlled source electro magnetics) im Zeitbereich, werden effiziente Algorithmen und Implementierungen auf massiv-paralleler Hardware vorgestellt. Zwei Implementierungen zur Berechnung der Vorwärts Modellierung, sowie eine Implementierung zur Berechnung der Sensitivitäten werden dargestellt. Bei dem ersten Vorwärts Code handelt es sich um eine Implementierung der Spektralen Lanczos Zerlegung (engl. SLDM, Spectral Lanczos Decomposition Method) auf dem Prozessor von Graphik Karten (engl. GPU, Graphics Processing Unit). Die Anwendbarkeit des Codes wird für ein CSEM System demonstriert, wie es am GEOMAR im Einsatz ist. Bei dem Zweiten Vorwärts Code wird die SLDM durch das effektivere Rationale Krylov Unterraum Verfahren (engl. RKSM, Rational Krylov Subspace Method) ersetzt. Die Genauigkeit des Codes wird für verschiedene Modelle und Kontraste des elektrischen Leitwertes untersucht. Ein Laufzeitvergleich von SLDM und RKSM wird gegeben.Die Sensitivitäten werden mit dem MOR-Verfahren (engl. Model Order Reduction) berechnet. Es wird gezeigt, dass die Methode funktioniert und seine Anwendbarkeit auf einen echten Datensatz demonstriert

The application of Krylov subspace methods for the calculation of forward solutions and model sensitivities of 3D time domain marine controlled source electromagnetic problems

To reduce the run-times of 3D modeling and inversion software for the interpretation of marine controlled source electromagnetics (CSEM) in time domain, the implementation of efficient algorithms on massive parallel hardware is presented. Two forward modeling implementations as well as an implementation for sensitivity calculation are illustrated. The first forward code is an implementation of the spectral Lanczos decomposition method on a graphics processing unit (GPU). The applicability of the code for a CSEM system, how it is used at GEOMAR, is demonstrated. In the second forward code, the SLDM is replaced by the more efficient Rational Krylov Subspace Method (RKSM). This reduces the dimension and run-time of the problem drastically. The accuracy of the code is investigated for different models and conductivity contrasts. The run-times of SLDM and RKSM are compared on different architectures. The sensitivities are computed with the MOR-method (Model Order Reduction). It is shown that the method works and the applicability to a real data set is shown

Numerical study of underground CO2 storage and the utilization in depleted gas reservoirs

The emission of atmospheric CO2 is the main contributor to global warming and climate change. Carbon capture and storage (CCS) is considered as the most promising technology for slowing down the atmospheric CO2 emissions. Meanwhile, CCS is beneficial for the circulation carbon economy. However, CCS has not been implemented on large scale because of the related risks and the lack of economic incentives. This thesis attempts to focus on these two problems and provide some strategies to address them. Regarding the risks associated with CCS, a parametric uncertainty analysis for CO2 storage was conducted and the general role of different geomechanical and hydrogeological parameters in response to CO2 injection was determined. Regarding the financial incentives of CCS operation, this thesis attempts to increase the cost-effectiveness of CCS through co-injecting CO2 with impurities associated with enhanced gas recovery (CSEGR) and using CO2 as cushion gas in the underground gas storage reservoir (UGSR). In order to understand the thermal-hydrological-mechanical (THM) process of CO2 storage, the THM coupled simulator TOUGH2MP (TMVOC)-FLAC3D was developed. By using the developed TOUGH2MP (TMVOC)-FLAC3D simulator, numerical simulation for hundreds of sampled data was performed for results generated by the Quasi-Monte Carlo method. Based on the simulation results, the general role of different geomechanical and hydrogeological parameters was determined in response to CO2 injection using distance correlation. In addition, a risk factor was defined to characterize the risks of the caprock due to CO2 injection. The results showed that the reservoir permeability and the injection rate are the two most important factors in determining the pressure change. Moreover, the reservoir Young’s modulus plays the most vital role in formation deformation including vertical displacement. The pressure change exhibits a much closer correlation with the risk factor in comparison to the formation deformation, indicating the importance of pressure change in the integrity assessment of the caprock. By using the machine learning approach in support vector regression (SVR), the SVR surrogate model was well-trained based on the data regarding simulated results, and its reliability was verified using the test data. Thereafter, the formation response including the pressure change as well as formation deformation, can be predicted using the trained SVR surrogate model within a very short time. The methods and working scheme applied in this work can be used to guide time and effort spent mitigating the uncertainty in these parameters to acquire trustworthy model forecasts and risk assessments in CCS projects. Attempting to decrease the cost of CCS operation, CO2 injection with impurity gas, i.e., N2 and O2, into a depleted gas reservoir was investigated. The impacts of the key parameters on the performance of CO2 storage and CSEGR were analyzed in detail. The results showed that the effect of impurities on CO2 storage capacity is dependent on the reservoir pressure and temperature conditions, and the concentration of impurities. The depleted gas reservoir with a relatively low temperature and low irreducible water saturation is favorable to the CO2 storage capacity. A low primary gas recovery for the depleted gas reservoir is in favor of CSEGR, while it is suitable for dedicated CO2 storage when the primary gas recovery is high. In addition, it is suggested to produce the CH4 as possible before the operation of CO2 storage and CSEGR. The chromatographic partitioning phenomenon may occur when N2 and O2 were co-injected with CO2 into depleted gas reservoirs, which could be used as a monitoring strategy for the CO2 front and potential CO2 leakage. In addition to the solubility and concentration of the impurity gas would affect this phenomenon, there is a critical water saturation for the occurrence of significant chromatographic partitioning phenomenon associated with determined type and concentration of impurity gas. To increase the cost-effectiveness of CCS, the suitability of utilizing CO2 as the cushion gas in the UGSR was analyzed based on the geological parameters of Donghae depleted gas reservoir in Korea. The cyclic CH4 production and injection were conducted over a period of 15 years to acquire the mixing behavior of CO2 and CH4 in a relatively long-term period. The results showed that the maximum CO2 concentration that can be used for cushion gas is 9% under the condition of production and injection for 120 and 180 days in a production cycle at a rate of 4.05 and 2.7 kg/s, respectively. The typical curve of the mixing zone thickness can be divided into four stages, i.e., the increasing stage, smooth stage, suddenly increasing stage, and periodic change stage. The CO2 fraction in the UGSR, reservoir permeability, and production rate have a significant effect on the breakthrough of CO2 in the production well, while the effect of water saturation and temperature is neglectable. For the purpose of utilizing more CO2 as cushion gas in the UGSR, CO2 is supposed to be injected for supplementation during the operation of UGSR. Generally, the parametric uncertainty analysis conducted in this thesis is beneficial for the risk assessments in CCS projects. Co-injecting CO2 with impurities associated with CSEGR and utilizing CO2 as cushion gas in UGSR are favorable for improving the economic incentives of CCS operation. Therefore, this thesis is beneficial for promoting the application of CCS and mitigating the atmospheric CO2 emissions

Multilevel Delayed Acceptance MCMC with Applications to Hydrogeological Inverse Problems

Quantifying the uncertainty of model predictions is a critical task for engineering decision support systems. This is a particularly challenging effort in the context of statistical inverse problems, where the model parameters are unknown or poorly constrained, and where the data is often scarce. Many such problems emerge in the fields of hydrology and hydro--environmental engineering in general, and in hydrogeology in particular. While methods for rigorously quantifying the uncertainty of such problems exist, they are often prohibitively computationally expensive, particularly when the forward model is high--dimensional and expensive to evaluate. In this thesis, I present a Metropolis--Hastings algorithm, namely the Multilevel Delayed Acceptance (MLDA) algorithm, which exploits a hierarchy of forward models of increasing computational cost to significantly reduce the total cost of quantifying the uncertainty of high--dimensional, expensive forward models. The algorithm is shown to be in detailed balance with the posterior distribution of parameters, and the computational gains of the algorithm is demonstrated on multiple examples. Additionally, I present an approach for exploiting a deep neural network as an ultra--fast model approximation in an MLDA model hierarchy. This method is demonstrated in the context of both 2D and 3D groundwater flow modelling. Finally, I present a novel approach to adaptive optimal design of groundwater surveying, in which MLDA is employed to construct the posterior Monte Carlo estimates. This method utilises the posterior uncertainty of the primary problem in conjunction with the expected solution to an adjoint problem to sequentially determine the optimal location of the next datapoint.Engineering and Physical Sciences Research Council (EPSRC)Alan Turing InstituteEngineering and Physical Sciences Research Council (EPSRC