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We consider a general case of a magnetotelluric (MT) study to reveal three-dimensional (3D) distribution of the electrical conductivity within the Earth based on measurements of electromagnetic (EM) fields by a two-dimensional (2D) array. Such an MT array observation can be regarded as a spatially discrete sampling of the MT responses (impedances), and each observation site can be regarded as a sampling point. This means that MT array measurements must follow the Nyquist–Shannon sampling theorem. This paper discusses how the sampling theorem is applied to MT array studies and what kind of consideration is required in the application on the basis of synthetic model calculations, with special attention to spatial resolutions. With an aid of the EM scattering theory and the sampling theorem, we can show that an observation array resolves some features of the MT impedance but does not others. We call the resolvable and unresolvable features the MT signal and noise, respectively. This study introduces the spatial Fourier transform of array MT data (impedances) which helps us investigating sampling effects of lateral heterogeneity from a different angle (in the wavenumber domain). Shallow heterogeneities cause a sharp spatial change of impedance elements near structural boundaries. High wavenumber Fourier components are required to describe such a feature, which means the site spacing must be sufficiently short to be able to resolve such features. Otherwise, a set of array MT data will suffer from aliasing, which is one of the typical causes of MT distortion (MT geologic noise). Conversely, a signal due to a deep-seated conductivity anomaly will have more reduced amplitude at higher wavenumbers, which means focused imaging of such an anomaly is generally difficult. Finally, it is suggested to properly consider the sampling theorem in an observation array design, so as to have best performance in resolving MT signals. [ABSTRACT FROM AUTHOR]

Using the 3-D axial anisotropy, the dipping anisotropy, and the azimuthal anisotropy as case studies, we investigated the influence of each anisotropic resistivity element on the magnetotelluric surface responses. To justify the strong and weak influence and edge effect, we have introduced the influence indices for the impedance components, and the edge effect indices for the tipper components. Interestingly, for decoupled modes, we found that ρ xx has a strong influence on Zxy, Zyy, and Ty, while ρ yy strongly affects Zyx, Zxx, and Tx. The three elements ρ zz , ρ xz , and ρ yz have only a very weak influence on all types of responses. For the coupled mode, ρ xx , ρ yy , and ρ xy display a strong influence on all responses. Based on our studies on the influence of the anisotropic resistivity elements, we design and propose two practical processes to replace the conventional axial, dipping, azimuthal, and general anisotropic inversions. First, the axial or dipping inversion can be approximately decoupled into ρ x -mode and ρ y -mode inversions. The decoupled mode inversions can be performed either independently and in parallel, or as a joint inversion. Second, since the three resistivity elements always show a weak influence, the general anisotropic inversion can be simplified to just the reduced coupled azimuthal anisotropic inversion with only three resistivity elements as outputs. Both proposed techniques can save a lot of the computational resources. Criteria to choose either the decoupled or coupled modes depend greatly on the magnitudes and distributions of the Zxx and/or Zyy, and Tx and/or Ty responses. [ABSTRACT FROM AUTHOR]

Phreatic and phreatomagmatic eruptions represent some of the greatest hazards occurring on volcanoes. They result from complex interactions at a depth between rock, water, and magmatic fluids. Understanding and assessing such processes remain a challenging task, notably because a large‐scale characterization of volcanic edifices is often lacking. Here we focused on Miyakejima Island, an inhabited 8‐km‐wide stratovolcano with regular phreatomagmatic activity. We imaged its plumbing system through a combination of four geophysical techniques: magnetotellurics, seismicity, self‐potential, and thermal image. We thus propose the first comprehensive interpretation of the volcanic island in terms of rock properties, temperature, fluid content, and fluid flow. We identify a shallow aquifer lying above a clay cap (<1 km depth) and reveal its relation with magmatic‐tectonic features and past eruptive activity. At greater depths (2–4.5 km), we infer a seismogenic resistive region interpreted as a magmatic gas‐rich reservoir (≥370°C). From this reservoir, gases rise through a fractured conduit before being released in the fumarolic area at ∼180°C. During their ascent, these hot fluids cross a ∼1.2‐km‐long liquid‐dominated zone causing local steam explosions. Such magmatic‐hydrothermal interaction elucidates (i) the origin of the long‐period seismic events and (ii) the mixing mechanism between magmatic and hydrothermal fluids, which was previously observed in the geochemical signature of fumaroles. Our results demonstrate that combining multidisciplinary large‐scale methods is a relevant approach to better understand volcanic systems, with implications for monitoring strategies. Key Points: An elongated aquifer (<1 km depth) lies between a resistive unsaturated layer and a conductive clay capA gas‐rich reservoir (2–4.5 km depth) feeds the main fumarolic areaMagmatic gases interact during their ascent with a 1.2‐km‐long water‐rich region creating local steam explosions [ABSTRACT FROM AUTHOR]

We use 2-D magnetotelluric (MT) problems as a feasibility study to demonstrate that 3-D MT problems can be solved with a direct solver, even on a standard single processor PC. The scheme used is a hierarchical domain decomposition (HDD) method in which a global computational domain is uniformly split into many smaller non-overlapping subdomains. To make it more efficient, two modifications are made to the standard HDD method. Instead of three levels as in the standard HDD method, we classify the unknowns into four classes: the interiors, the horizontal interfaces, the vertical interfaces and the intersections. Four sets of smaller systems of equations are successively solved with a direct method (an LU factorization). The separation significantly reduces the large memory requirements of a direct solver. It also reduces the CPU time to almost half that of the standard HDD method although it is still slower than the conventional finite difference (FD) method. To further enhance the speed of the code, a red-black ordering is applied to solve the horizontal and vertical interface reduced systems. Numerical experiments on a 2-D MT problem of a given size running on a single processor machine shows that CPU time and memory used are almost constant for any resistivity models, frequencies and modes. This is a clear advantage of our algorithm and is of particular importance if the method is applied to 3-D problems. We show that our new method results in reductions in both memory usage and CPU time for large enough domains when compared to the standard FD and HDD schemes. In addition, we also introduce a 'memory minimization map', a graphical tool we can use instead of trial-and-error to pre-select the optimal size of subdomains, which yield the best performance in both CPU time and memory even running on a serial machine. [ABSTRACT FROM AUTHOR]