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MT data inversion suffers from the non-uniqueness problem of its solution. The problem rises due to the non-linear relations between transfer functions and EM fields, employed in MT exploration, and also the limited number of imprecise data points. In most common MT inversion algorithms, this problem is solved by introducing the smoothest model constraint (Фm) to the inversion objective function: E(m)= Φd+ τ Φm However, in situations where geological and previous geophysical data (ex. well-log and seismic data) confirm the presence of uniform subsurface structures detached by sharp boundaries, the implementation of the smoothest model constraint can lead to unrealistic geological results. In this study we investigate how the application of tear zone and sharp boundary inversions could improve the interpretation of MT data? For this purpose, four synthetic models were considered and their MT responses were calculated using a finite element forward modeling approach (Wannamaker et al 1986) and contaminated with noises. In the next step, they were employed as input data through smoothest model, tear zone and sharp boundary inversion procedures. The results indicate that the incorporation of other geophysical data in the inversion starting model as tear zones and sharp boundaries, allows accurately measuring the space of the model parameters and obtaining more precise results. We applied a multi-site- multi-frequency approach of Mc-Neice and Jones (2001) for dimensionality and strike analysis as well as to separate and remove galvanic distortions (twist and shear angles) and contaminated impedance responses of the regional geoelectric structure. The method employs a least square approach to fit the measured data with a seven-parameter model describing strike direction and telluric distortion parameters. The results show a clear minimum in RMS for a strike angle of zero degree (figure8). Shear angles lie predominantly within the range of [-45˚, 45˚] (left column in figure 9) and the observed twist angles fall mostly within the range of [-60˚, 40˚] (right column in figure 9). Then, we applied the smoothest model, tear zone, and sharp boundary inversions for data modeling and interpretation whose results are presented in the figures (10), (11) and (12), respectively. We can effectively derive three alternative classes of models from magnetotelluric (MT) data. The results are consistent with the conceptual model presumed for a high enthalpy geothermal region. Unaltered surface rocks and porous Basalt exhibit a high resistive overburden underlain by relatively more conductive Paleozoic sediments. In deeper parts, a common signature of hydrothermal systems appears and resistivity increases beneath a highly conductive clay cap (feature C3). An oblique conduit (feature C2) dipping to the northwest of the Moil valley connects the surficial clay cap with a deep conductor (feature C1). The conduit (feature C2) is parallel to the prevalent direction of faults and fractures of the area and shows that the linear structures constitute pathways where convective fluid flow can take place. The absence of this feature beneath the profile P03 shows that the lateral extension of the geothermal reservoir is limited to the west of profile P03.

We investigated an MT dataset composed of 284 broadband (10-4-3414 sec) MT stations along seven profiles to unravel the electrical properties of sub-surface structures in the Nasr-Abad region, west Central Iran. The region is composed of five Tertiary salt diapirs developed along the Abshirin-Shurab strike-slip fault zone. The MT profiles are extended perpendicular to the general trend of the Zagros orogenic belt (in an SW-NE direction) which is one of the main structural elements controlling regional deformation in the Iranian plateau.The analysis of impedance data shows that a more complex conductivity structure is expected beneath the SW of the profile. a shallow conductive layer appears throughout the study region which extends to the deeper part beneath the NE of the profile. Furthermore, The Abshirin-Shurab fault significantly influences the apparent resistivity at the SW end of most profiles.In the next step, we characterize the structural dimensionality of MT data by commonly used Bahr rotational invariants (κ, μ, η, ∑) and the phase tensor skew angle (β). The phase-sensitive skew (η), the regional 1-D indicator (μ), and β skew angle depend on the phase information inherent in the impedance tensor. Therefore, they are affected primarily by large-scale induction anomalies and are immune to low-frequency galvanic distortions. The thresholds assigned for μ, η, and β are 0.1, 0.3, and 3˚, respectively. The skew values calculated from the Nasr-Abad MT data set suggest that the regional conductivity structure is 2D rather than 3D or 1D as the calculated η remains below 0.3 and μ above 0.1. The appropriate category of data is therefore, responses from a regional 2D structure contaminated by galvanic distortion effects.   We applied the phase tensor analysis for regional strike determination. It does not require any assumption about regional conductivity structure, and its results are not susceptible to galvanic distortion. The method determines the electrical strike from the axis direction of phase tensor ellipses. The analysis reveals a scatter pattern of strikes at short periods (<1 sec) due to the small sampling area of EM fields at these periods. As the period increases an strike azimuth, preferentially aligned N30°W is obtained for the regional geoelectric structure.

The main purpose of this research is to analyze and model the audio-magnetotelluric (AMT) data to study the regional structure and deep groundwater of the Sena- the Shonbe aquifer system in central Zagros. We used challenging methods to determine the dimensionality of the regional structure, evaluate the degree of inherent distortion caused by small-scale, near-surface inhomogeneities, quantify these effects and remove them from MT measurements, and retrieve the main features of the regional geoelectric structure (e.g., its strike direction). Data were collected at 19 stations along the profile in the southeast of the folded belt (SFB) of the Zagros folded belt. First, the regional subsurface structure was classified using impedance and MT tensors rotational invariants (Bahr and WAL invariants). Then, the phase tensor method was used to estimate the strike direction of the regional geo-electric structure. The results of Bahr and WAL invariants confirm regional 1D and 2D structures with local galvanic distortion at most periods. Rotating the data into the strike direction of the regional structure, isotropic two-dimensional inversions of the different polarizations of the impedance data and tipper vectors were performed. The computer program used for this purpose uses the nonlinear conjugate gradient (NLCG) algorithm to minimize the cost function, which consists of data misfit and model roughness. Several numerical tests were performed to determine the optimal values of the parameters regulating this algorithm: τ, α, β, and H/V ratio. Finally, interpretations related to the resulting electrical resistivity cross-section are provided.

Magnetic survey data are generally used to map faults, geologic contacts and magnetic ore bodies. The spatial distribution of magnetic sources will be determined during the mapping process. Variation in depth, magnetization and geometrical parameters generate magnetic anomaly waveform. Direction of the remanent and induced magnetization vector will also affect the shape of these waveforms. A magnetic anomaly waveform includes amplitude, phase and wavelength. Putting these parameters altogether makes the interpretation of the magnetic data a difficult task. There are different useful methods for interpretation of a magnetic map. Generally, these methods are based on reduction data to a simpler form, so that the edges and center of the causative bodies will be determined easily.
In recent years many methods have been used to balance the difference between various anomaly amplitudes. Each method is designed to determine a specific parameter of the magnetic anomalies. Local phase filters are commonly used in potential field data interpretation. They are high-pass filters based on horizontal and vertical derivatives, such as total horizontal derivative, tilt angle, theta map, etc.
Edge detection of a magnetic structure is one of the most important issues in the interpretation of magnetic data. In the present study we have used two local phase filters for this Tilt angle (TDR) and Total Gradient of Tilt angle (TAHG). Although the tilt angle filter is used to determine the boundary of anomaly sources, but it is relatively less sensitive to the source depth, so it can resolve shallow and deep sources as well. As the tilt angle is a function of vertical derivatives normalized by horizontal derivatives of magnetic field intensity (THDR), it does not contain information on the strength of the geomagnetic field nor the susceptibility of the causative bodies. The tilt angle amplitudes depend strongly on magnetic field inclination. Their maximum occurs at the center of the magnetic sources and they disappear over the anomaly edges.
Another enhancing method employed in this study to determine the structure boundaries, is the tilt derivative of horizontal gradient. It is defined by taking the arctangent of the vertical derivative of the THDR, divided by the modulus of the horizontal gradient of THDR:TAHG=arctan⁡〖((∂THDR/∂z)/√(〖(∂THDR/∂x)〗^2〖(∂THDR/∂y)〗^2 ))〗
TAHG equalizes the signals obtained from shallow and deep sources. This method has two notable features: I- it produces maximum amplitudes over the edges of the sources, II- it gives suitable resolution and is less dependent on the structure depths. However, like the TDR, this method depends on the inclination of magnetic field.
We applied these methods for synthetic noise-free and noisy data. Magnetic responses of synthetic models as well as calculations of different edge detection methods have all been done in MATLAB. In comparison with common methods like horizontal gradient and analytic signal, it delineates the edges of sources more efficiently and accurately. Furthermore the TAHG method has better resolution in determining the boundaries of deeper sources than TDR method.
We applied the TAHG method for the aeromagnetic dataset from Zanjan region. The Zanjan depression is a narrow and continuous igneous basin, located in the north western Zanjan province. There are many young active and basement faults in the study area. Total magnetic anomaly map of the region, shows two major structural trends in NW-SE and NE-SW, respectively. Applying different edge detection algorithms we obtained the hidden boundaries of the basement which is not detectable in the geological maps because of the thick sedimentary covers. The results show that TAHG method is suitable for determining the basement faults and boundaries, as well as mapping the contacts of magnetic units.

The atmospheric electric currents that varying in daily, seasonal, and latitude patterns above the Earth's surface act as a source that induces currents to flow in the conducting layers of the Earth. The magnitude, direction, and depth of penetration of the induced currents are determined by the characteristics of the source currents as well as the distribution of electrically conducting materials in the Earth. The solar quiet (Sq) magnetic field variation is a manifestation of an ionospheric current system. Heating at the dayside and cooling at the nightside of the atmosphere generates tidal winds which drive ionospheric plasma against the geomagnetic field inducing electric fields and currents in the dynamo region between 80-200 km in height. The current system remains relatively fixed to the Earth-sun line and produces regular daily variations which are directly seen in the magnetograms of geomagnetic “quiet” days, therefore the name Sq. The Sq field variations are dominated by 24-, 12-, 8-, and 6-hr spectral components and can penetrate in the conductive earth to depth between 100 to 600 km. For the situation in which field measurements are available about a spherical surface that separates the source from the induced currents (and a current doesn’t flow across this surface), Gauss (1838) devised a special solution of the differential electromagnetic field equations that is separable in the spherical coordinates r, θ, and φ. In Gauss’s solution, the field terms that represent radial dependence appear as two series. One with increasing powers of the sphere radius, r, and one with increasing powers of 1/r. As the value of r becomes larger (outward from the sphere) the first series produces an increased field strength, as if approaching external current sources. As the value of r decreases (toward the sphere center) the second series of 1/r terms indicate increased field strength, as if approaching internal current sources. Gauss had devised the way to separately represent the currents that were external and internal to his analysis At the Earth's surface the observed mixture of fields from the source and induced currents can be separated by spherical harmonic analyses and the relationship between the internal and external amplitudes and phases can be used to infer the Earth's conductivity profile at great depths. A spherical harmonic analysis (SHA) was applied to obtain a separation into internal and external field coefficients. The magnetic scalar potential, V, in colatitude θ and longitude φ described at the Earth's surface by In which the cosine (A) and sine (B) coefficients of the expansion for the external (ex) and internal (in) parts are taken to be: After separating the geomagnetic field into internal and external part by SHA we can use Schmucker’s (1970) method for profiling the Earth's substructure. In the method outlined by Schmucker formulas are developed that provide the depth (d) and conductivity () of apparent layers that would produce surface-field relationships similar to the observed components. These profile values, need to be determined for each n, m set of SHA coefficients using the real z and imaginary p parts of a complex induction transfer function,, given as: We calculate the Electrical conductivity properties of the upper by employing the 6, 8, 12, 24 hour spectral components of the quiet-day geomagnetic field variation. The Gauss coefficients obtained from an spherical harmonic analysis of the two components of the quiet daily variation field for the solar-quiet year 2009 were applied to Schmucker's model (Schmucker, 1970). The findings coincide with the results of previous solar quite years and demonstrate that electrical conductivity varies exponentially with depth between 150 and 530 Km.

In an electrically anisotropic media، current density is not aligned with the electric field and varies with the E-field direction. This can be considered as the spatial aliasing effects aroused by the subsurface structures whose individual dimensions are smaller than the inductive length scale of diffusively propagating EM fields. The role of these structures is particularly significant in tectonically active regions، where tectonic processes induced penetrating fabrics. Accordingly، identification، characterization and interpretation of electrical anisotropy have large implications to understand evolutionary aspects of geological structures، evaluate the economic resources and interpret hydrological flows (Wannamaker، 2005). Marti (2014) provides a comprehensive review of the works conducted to recognize electrical anisotropy imprints during MT data analysis and also different strategies used to model this property in case studies. Dimensionality analysis is a preliminary stage in MT data interpretation procedure to recover the strike direction of the regional geo-electric structure، characterize the distortion effects of superficial conductive bodies and also to adopt an appropriate modeling approach (1D، 2D or 3D)، coincident with the intrinsic dimension of the measured data. The application of the preliminary dimensionality tools، Swift’s and Bahr’s skews for synthetic and real MT data affected by anisotropy shows that they are disable to identify the anisotropy footprints and distinguish between structural and anisotropy strike directions (Heise and Pous، 2001). Weaver et al.، (2000) suggested a family of rotationally invariant parameters characterizing the dimensionality properties of the underlying geo-electric structures. Marti et al. (2009، 2010) published the WALDIM code based on these invariants and extended them to provide proper conditions from which isotropic and anisotropic structures could be differentiated. The main criteria proposed by the WALDIM code to differentiate anisotropic media from isotropic ones are as follows: The WAL rotational invariant values indicate a 2D regional structure، while the strike directions estimated from the first and second columns of impedance tensor are inconsistent. This situation is mentioned as “3D/2D anisotropy” in subsequent table and figures. We report here on the application of this scheme to analyze the dimensionality of MT responses from some principal anisotropic models representing complex geological settings at continental margins and also for MT data from an active continental margin in South-Central Chile، where the presence of electrical anisotropy has been previously recognized (mainly from geomagnetic transfer functions). In electrical anisotropy modeling resistivity is represented as a symmetric، positive definite tensor which can be diagonalized employing Euler’s elementary rotations to obtain its principal directions and their corresponding resistivities (principal resistivities: ρxx، ρyy، ρzz). These directions are known as the strike (αs)، dip (αD) and slant (αL) anisotropy angles. The non-zero values of these angles and the specified relationships between principal resistivities would determine the type and geometry of the electrical anisotropy. We restricted our study to uniaxial، azimuthal anisotropy، where αs≠0، αD= αL= 0 and also ρxx= ρzz≠ ρyy. Model responses were calculated employing the algorithm of Pek and Verner، 1997. The proposed models of geological settings are selected so that their complexity is gradually increasing. Dimensionality analysis results for the synthetic model responses and real data are depicted in figures (2، 3 and 4) and (6 and 7)، respectively. The results indicate that the proposed criteria is slightly firm in the sense that they could not identify electrical anisotropy in the presence of galvanic distortions caused by superficial conductive structures and complexities of regional structures.

Investigations made in current study illustrate that an application of 2-D isotropic inversion algorithm for magnetotelluric data affected by anisotropy could recover macro-anisotropy reasonably well. First anisotropy effects on common MT interpretation steps, dimensionality analysis and 2-D inversion modeling, are investigated. Two kinds of azimuthally anisotropic features (anisotropic block and anisotropic layer) which generally form a part of 2-D models are considered. The influence of different anisotropy strikes and resistivity contrasts on dimensionality analysis and on the behavior of induction arrows is studied. These investigations evince that, a strike direction close to the anisotropy strike can be chosen by the dimensionality analysis of the data. Then if the data are rotated to this angle, 2-D inversion would recover the anisotropy sensibly by means of macro-anisotropy. This procedure is tested successfully on a field data set where anisotropy had been previously recognized. The results show that the proposed approach reproduces the anisotropy acceptably via macro-anisotropy in the final inversion model.

Electrical anisotropy in the earth, the effect of current density dependency on the electric field orientation in a medium, has been considered significantly in recent Magnetotelluric (MT) observations. Several suggestions for electrical anisotropy are based upon MT observations of "phase splits", analogous to shear wave splits in seismology. The MT phase data is accentuated more than its amplitude responses since shallow small scale conductivity heterogeneities cause a significant distortion in MT amplitude responses (known as Galvanic Distortion), while MT phase responses remain immune. To investigate the MT phase response we will use the tensor representation of the MT phase introduced by Caldwell et al. (2004). This representation has the advantage of considerably simplifying the analysis of the Galvanic distortion effect. Moreover no assumption about the dimensionality of the underlying regional conductivity structure is essential. The properties of a generally asymmetric "phase tensor" are best understood in terms of the tensor's graphical representation as an ellipse (figure1). The tensor principal axes and principal values correspond to the major and minor axes and the lengths of the corresponding ellipse radii, respectively

The deep internal structure of the crust can be determined using appropriate seismic and electromagnetic methods. The natural source magnetotelluric (MT) method is the most suitable electromagnetic technique for probing into the deep crust. A long period magnetotelluric data set obtained in the Southern Chilean Andes is investigated in this paper. Dimensionality analysis shows that the data may be regarded as with a strike 2D direction aligned to the N-S direction. Results of a joint inversion of different MT data types indicate relatively high conductive structures in the middle to deep crust beneath the volcanic arc.