S U M M A R YIn this paper, we start with the implementation of a data space conjugate gradient (DCG) method for 3-D magnetotelluric (MT) data. This code will be referred to as WSDCG3DMT. It is an extension of the 2-D method previously developed. Several experiments on both synthetic and real data sets show that WSDCG3DMT usually needs more computational time than the data space Occam's inversion (OCCAM) for which the corresponding code is referred to as WSINV3DMT. However, the memory requirement of WSDCG3DMT is only a fraction of that of WSINV3DMT. Based on the knowledge gained from several studies of both codes, we have created a new hybrid scheme called the DCG Occam's inversion (DCGOCC) and the corresponding code, WSDCGOCC3DMT, from combining aspects of the OCCAM and DCG methods. As with OCCAM, the DCGOCC method divides the inversion into two phases. In Phase I the misfit is brought down to a desired level. In Phase II unnecessary structures are smoothed out. Because its mathematical basis is of a similar form to that of DCG, its memory requirement is similarly low but more stable. However, DCGOCC is significantly faster than both methods. We demonstrate the computational performances with comparisons of all three methods with both synthetic and EXTECH field data sets.

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In this research, a new numerical method, called the hybrid finite difference-finite element (hybrid FD-FE) method, is developed to solve 2-D magnetotelluric modeling by taking advantage of both the finite difference (FD) and finite element (FE) methods. With the hybrid FD-FE method, the model is first discretized as rectangular blocks and separated into two zones: the FD and FE zones. The FD zone is set for the subregions where topography or bathymetry does not appear. The FD approximation, which is fast, accurate and requires less memory resources, is then applied. For the FE zones where topography or bathymetry exists, the rectangular blocks are transformed into quadrilateral elements to handle the topography or bathymetry appropriately. Then, the FE approximation with quadrilateral elements, which is more accurate for topography or bathymetry zones, is applied. The system of equations for the hybrid FD-FE method is then formed according to the FD and FE schemes. The obtained system is a combination of the FD and FE equations. Three numerical methods are applied to test models with and without topography and bathymetry. The accuracy and efficiency in terms of errors, computational time and memory storage are presented, compared and discussed. The numerical experiments indicate that the FD scheme has a shorter computational time than the other schemes when modeling without topography and retains accuracy equivalent to that of the FE method, whereas FE is more practical when modeling with topography and bathymetry. However, our proposed hybrid FD-FE method is efficient in both situations. Without topography or bathymetry, its efficiency and accuracy approach those of the FD scheme. With topography and bathymetry, the hybrid FD-FE method is as accurate as FE, but its speed is slightly slower than that of FD. In terms of memory storage, the hybrid FD-FE method consumes slightly more storage than the FD method. This hybrid FD-FE method can be further extended and implemented for 3-D magnetotelluric modeling for more efficient computation.

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A modified sol-gel method was used to successfully produce Na1/2Y1/2Cu3Ti4O12 ceramics with high dielectric permittivity. The dielectric permittivity of Na1/2Y1/2Cu3Ti4O12 ceramics reaches values larger than 104 at room temperature and 1 kHz. Moreover, these ceramics exhibit two distinct thermally induced dielectric relaxations over a broad temperature range. The loss tangent is indeed small, ~0.032–0.035. At low temperatures, dielectric relaxation was attributed to the oxygen vacancy effect, while at high temperatures, it was attributed to grain boundary and sample-electrode contact effects. Our calculations revealed that Y and Na ions are likely to occupy Ca and Cu sites, respectively. As a result, other Cu related phases, especially CuO, were observed at the grain boundaries. Based on our analysis, there is a charge compensation between Na and Y ions in Na1/2Y1/2Cu3Ti4O12. Additionally, the Cu+ and Ti3+ states observed in our XPS study originate from the presence of an oxygen vacancy in the lattice. Last, the primary cause of the enormous dielectric permittivity of Na1/2Y1/2Cu3Ti4O12 ceramics primarily comes from the internal barrier layer capacitor effect.