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Interpretation of magnetotelluric (MT) data for three-dimensional (3-D) regional conductivity structures remains uncommon, and two-dimensional (2-D) models are often considered an adequate approach. In this paper we examine 2-D interpretation of 3-D data by considering the synthetic responses of a 3-D structure chosen specifically to highlight the advantages and limitations of 2-D interpretation. 2-D models were obtained from inversion of the synthetic 3-D data set with different conditions (noise and distortion) applied to the data. We demonstrate the importance of understanding galvanic distortion of the data and show how 2-D inversion is improved when the regional data are corrected prior to modelling. When the 3-D conductive structure is located below the profile, the models obtained suggest that the effects of finite strike are not significant if the structure has a strike extent greater than about one-half of a skin depth. In this case the use of only TM-mode data determined b...
Geophysical Journal International, 2002
Interpretation of magnetotelluric (MT) data for three-dimensional (3-D) regional conductivity structures remains uncommon, and two-dimensional (2-D) models are often considered an adequate approach. In this paper we examine 2-D interpretation of 3-D data by considering the synthetic responses of a 3-D structure chosen specifically to highlight the advantages and limitations of 2-D interpretation. 2-D models were obtained from inversion of the synthetic 3-D data set with different conditions (noise and distortion) applied to the data. We demonstrate the importance of understanding galvanic distortion of the data and show how 2-D inversion is improved when the regional data are corrected prior to modelling. When the 3-D conductive structure is located below the profile, the models obtained suggest that the effects of finite strike are not significant if the structure has a strike extent greater than about one-half of a skin depth. In this case the use of only TM-mode data determined better the horizontal extent of the 3-D anomaly. When the profiles are located away from the 3-D conductive structure the use of only TM-mode data can imagine phantom conductive structures below the profile, in this case the use of both polarizations produced a better determination of the subsurface structures. It is important to note that the main structures are identified in all the cases considered here, although in some cases the large data misfit would cause scepticism about features of the models.
Journal of Geophysical Research, 2011
Geophysical Journal International, 2005
Traditional methods for interpretation of magnetotelluric (MT) profile data are based on 2-D inversion, under the assumption that 3-D complications in the data can be treated as 'geological noise'. We show with synthetic models that fitting 3-D data with a 2-D inversion can result in spurious features, especially if transverse electric (TE) data are used. Inversion of a single profile of MT data with a 3-D algorithm results in significantly more realistic images of structure beneath the data profile, and also allows some resolution of nearby off-profile structure. We also consider the importance of including the on-diagonal impedance tensor terms, Z xx and Z yy , in the inversion. In synthetic test cases, fitting these diagonals improves the accuracy of images of off-profile structure, particularly near the edge of a conductive feature.
Geophysical Journal International, 1998
Although the galvanic distortion due to local, near-surface inhomogeneities is frequencyindependent, its effect on the magnetotelluric data becomes, in a 3-D structure, frequency-dependent. Therefore, both the apparent resistivity and the phase responses are disturbed, and a correction should be carried out prior to the 3-D interpretation in order to retrieve the 3-D regional impedance tensor. In many cases, the structure is 2-D for depths corresponding to a first range of periods and 3-D for longer periods (called 2-D/3-D). For these cases, a simple method which allows us to retrieve the 3-D regional impedance tensor (except the static shift) is presented. The method proposed uses the Groom & Bailey decomposition of the distortion matrix for the short periods. Three examples are presented: two using synthetic data and one employing real data. These examples show the effect of the galvanic distortion over a regional 2-D/3-D model and the retrieval of the regional transfer functions from the distorted ones.
On the assumption of causality, it is shown that for general (three-dimensional) conduc- tivity distributions integrable over any cuboid region of the Earth, the magnetotelluric field possesses very restrictive analytic properties: the singularities of the electric and magnetic field components are all simple zeros confined on the positive imaginary axis of the complex frequency plane. This means that transfer functions comprising simple ratios of orthogonal electric and magnetic field components should also have simple poles and zeros located on the positive imaginary axis. Three-dimensional impedance tensors can be reduced to diagonal or anti-diagonal forms with elements comprising simple ratios of orthogonal field components, using such methods, as the Canonical Decomposition or the SVD, which can be shown to constitute 3-D rotations. Then, it can be shown that the Schmucker Response function derived from the characteristic (singular) values of the impedance tensor can be cast in...
In a prequel to this paper, it was shown that Schmucker response function derived from the characteristic values of the impedance tensor can be cast into a simple Cauer form (expansion). This representation epitomizes the properties of the magnetotelluric responses, which are a direct consequence of its sensu stricto causality. It may also form the basis for a practical means to test a measured magnetotelluric response function for realizability, i.e. physical validity and origin in a real and recoverable Earth structure. Moreover, owing to its analyticity, the Cauer representation may also be used to interpolate (reconstruct) distorted portions of the observed response functions. A procedure and algorithm to realize these objectives is presented herein and its effectiveness is demonstrated with a number of applications to synthetic and measured MT data.
Geophysical Journal International, 2000
In magnetotelluric (MT) studies, the observed response function (the MT impedance) usually su¡ers from galvanic distortions due to near-surface inhomogeneities. Removal of these e¡ects is essential to obtain an accurate model of the subsurface electrical conductivity structure. Galvanic distortion is usually expressed by a simple real tensor multiplying the undistorted regional impedance. The problem still remains of how to solve the ensuing linear equations in order to determine the distortion tensor and then to obtain the undistorted impedance. The methods presented and widely applied in previous works assume two-dimensionality for the undistorted impedance. This paper proposes a method that employs a relationship between the spatial derivatives of the horizontal electric ¢eld and the vertical geomagnetic component, which can be directly derived from Faraday's law. The identity derived from the relationship is written using the vertical magnetic transfer function, the impedance, and the spatial derivatives of the impedance and horizontal magnetic transfer functions. The present method determines the real distortion tensor so that the identity is satis¢ed. Therefore, the method has two major advantages: (1) galvanic distortion that is to be removed from the impedance tensor is clearly de¢ned, and (2) the method is applicable even when the regional structure is 3-D.
Geophysical Journal International, 2002
We develop an algorithm to model the magnetometric resistivity (MMR) response over an arbitrary 3-D conductivity structure and a method for inverting surface MMR data to recover a 3-D distribution of conductivity contrast. In the forward modelling algorithm, the second-order partial differential equations for the scalar and vector potentials are discretized on a staggeredgrid using the finite-volume technique. The resulting matrix equations are consequently solved using the bi-conjugate gradient stabilizing (BiCGSTAB), combined with symmetric successive over relaxation (SSOR) pre-conditioning. In the inversion method, we discretize the 3-D model into a large number of rectangular cells of constant conductivity, and the final solution is obtained by minimizing a global objective function composed of the model objective function and data misfit. Since 1-D conductivity variations are an annihilator for surface MMR data, the model objective function is formulated in terms of relative conductivity with respect to a reference model. A depth weighting that counteracts the natural decay of the kernels is shown to be essential in typical problems. All minimizations are carried out with the Gauss-Newton algorithm and model perturbations at each iteration are obtained by a conjugate gradient leastsquares method (CGLS), in which only the sensitivity matrix and its transpose multiplying a vector are required. For surface MMR data, there are two forms of fundamental ambiguities for recovery of the conductivity. First, magnetic field data can determine electrical conductivity only to within a multiplicative constant. Thus for a body buried in a uniform host medium, we can find only the relative conductivity contrast, not the absolute values. The choice of a constant reference model has no effect on the reconstruction of the relative conductivity. The second ambiguity arises from the fact that surface MMR cannot distinguish between a homogeneous half-space and a 1-D conductive medium. For a 3-D body in a 1-D layered medium, it is still difficult to obtain information concerning the general background 1-D medium, if sources and receivers are at the surface. Overall, the surface MMR technique is useful so long as significant current flows through the body. This happens when the overburden is thin and moderately conductive (less than 10 times the conductivity of the underlying basement) and if the current sources are placed so there is good coupling with the body. Our inversion method is applied to synthetic examples and to a field data set. The low-resolution image obtained from using traditional MMR data, involving one source and one magnetic component, illustrates the need for acquiring data from multiple sources if 3-D structure of complex geometries are sought.
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In this paper, I explore the concept of reality as an illusion, shaped by conscious agents, much like a simulation. Drawing on Donald Hoffman's theory that the physical world is merely an interface, I argue that there is no external, material world. Instead, reality is created by interacting minds, forming a shared virtual experience, similar to a Matrix-like system. We also delve into the idea of cyclical resets that occur every 6,000 years, with the fall of Atlantis as a possible event from a previous cycle. As we approach the end of the current cycle, the rise of AI may serve as the gateway to a new Golden Age, rather than a descent into chaos. Could AI be the tool that shifts us toward a higher state of consciousness, leading us to a profound new beginning?
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