Novel multi-response 3-D MT inverse solution: concept and development

The exploration of natural resources requires a non-invasive investigation of the physical properties of the subsurface. Magnetotellurics (MT) is a geophysical method enabling to image the subsurface’s electrical conductivity and is often used for the exploration of hydrocarbons, ore deposits or geothermal resources. The main advantage of the MT method is that no active source is required; instead the natural occurring time-varying electromagnetic (EM) fields are recorded and analyzed. Further advantages are the wide depth range of investigation, ranging from hundreds of meters till hundreds of kilometers, and the relative ease to cover large areas during a MT survey. The EM field recordings are usually interpreted through the impedance tensor, which relates the electric and magnetic fields in the frequency domain. Interpretation of the impedance tensor can be challenging in the presence of local small-scale heterogeneities in the shallow subsurface. These heterogeneities, which are not the target of the MT survey, galvanically distort the electric field and thereby the impedance tensor. One of the remedies to overcome the problem of a galvanically distorted impedance tensor, is to derive the MT phase tensor from the impedance tensor. The MT phase tensor is free from galvanic distortion. Other response functions used to interpret MT data are the vertical magnetic transfer function and the inter-site quasi-electric, electric and magnetic tensors. The latter two relate the electric or magnetic field, respectively, the base and a field site, and the quasi-electric tensor links the magnetic field at the base site with the electric field at a field site. A three-dimensional (3-D) image of the electrical conductivity of the subsurface can be obtained by an inversion of a two-dimensional array of any of the aforementioned responses. Several 3-D MT inverse solvers have been developed during the past two decades. With the aim of these inverse solvers being the same – i.e. reconstructing the 3-D electrical conductivity distribution of the subsurface – there are major differences between the individual inverse solvers. Differences lie in the way the forward problem is solved, which type of optimization is used to find the solution to the inverse problem, how the inverse problem is regularized, whether the code is parallelized and to which extent, the way the sensitivities are calculated and which response functions are used during inversion. It is important to note that the non-unique character of the solution of the MT inverse problem often complicates the interpretation of the obtained inverse results. In this thesis, I first address the problem of galvanically distorted MT responses by introducing two new phase tensors that are (almost) resistant to galvanic distortion. I propose to derive phase tensors from the electric and quasi-electric tensor in a similar way as the MT phase tensor is derived from the impedance tensor. The electric phase tensor is only affected by galvanic distortion, if present, at the base site. The quasielectric phase tensor is free from galvanic distortion. Using a synthetic data-set, I show that the sensitivity of the MT phase tensor, the quasi-electric phase tensor and the electric phase tensor is comparable for our model under consideration. Furthermore, I demonstrate that stable (quasi-) electric phase tensors can be recovered from a real dataset with the use of existing processing software. In addition I provide a formalism to propagate the uncertainties from the estimated (quasi-) electric and impedance tensors to their respective phase tensors. The uncertainties of the (quasi-) electric phase tensors appeared to be of the same order of magnitude as the uncertainties of the MT phase tensor. Bearing in mind that electric field measurements are less cost intensive to perform than magnetic field measurements, I conclude that the (quasi-) electric phase tensors are an attractive complement to the standard MT response functions. Second, I present a novel 3-D MT inverse solver EMJoy. The forward problem within EMJoy is tackled using a contracting integral equation technique and the inverse problem is solved with a limited memory quasi-Newton optimization method. The gradient of the data-misfit with respect to the model parameters is calculated by means of the adjoint approach. EMJoy has a modular structure, allowing for an easy inclusion of additional features. Further, EMJoy is parallelized both over frequency and source polarization. During inversion, the traditional MT responses can be utilized plus the newly introduced (quasi-) electric phase tensors. EMJoy was successfully tested using a number of synthetic data-sets.