Many rocks and layered/fractured sequences have a clearly expressed electrical anisotropy although it is rare in practice to incorporate anisotropy into resistivity inversion. In this contribution, we present a series of 2.5-D synthetic inversion experiments for various electrode configurations and 2-D anisotropic models. We examine and compare the image reconstructions obtained using the correct anisotropic inversion code with those obtained using the false but widely used isotropic assumption. Superior reconstruction in terms of reduced data misfit, true anomaly shape and position, and anisotropic background parameters were obtained when the correct anisotropic assumption was employed for medium to high coefficients of anisotropy. However, for low coefficient values the isotropic assumption produced better-quality results. When an erroneous isotropic inversion is performed on medium to high level anisotropic data, the images are dominated by patterns of banded artefacts and high data misfits. Various pole–pole, pole–dipole and dipole–dipole data sets were investigated and evaluated for the accuracy of the inversion result. The eigenvalue spectra of the pseudo-Hessian matrix and the formal resolution matrix were also computed to determine the information content and goodness of the results. We also present a data selection strategy based on high sensitivity measurements which drastically reduces the number of data to be inverted but still produces comparable results to that of the comprehensive data set. Inversion was carried out using transversely isotropic model parameters described in two different co-ordinate frames for the conductivity tensor, namely Cartesian versus natural or eigenframe. The Cartesian frame provided a more stable inversion product. This can be simply explained from inspection of the eigenspectra of the pseudo-Hessian matrix for the two model descriptions.
Abstract We present a set of 2.5D synthetic inversion experiments for a model comprising an isotropic block embedded within an anisotropic background. We examine and compare the image reconstructions obtained using the correct anisotropic code and those obtained using code based on the inappropriate but widely adopted isotropic assumption. Superior reconstruction in terms of reduced data misfit, true anomaly shape and position, and anisotropic background parameters were obtained when the correct anisotropic code was employed for media characterized by moderate to high coefficients of anisotropy. However, for low coefficient values, the isotropic inversion produced slightly better results because there are fewer parameters to determine. When an erroneous isotropic inversion is performed on medium to high level anisotropic data, the images are dominated by patterns of banded artefacts and high data misfits.
In this paper we develop analytic solutions for the electric potential, current density and Fréchet derivatives at any interior point within a 3-D transversely isotropic medium having a tilted axis of symmetry. The current electrode is assumed to be on the surface of the Earth and the plane of stratification given arbitrary strike and dip. Profiles can be computed for any azimuth. The equipotentials exhibit an elliptical pattern and are not orthogonal to the current density vectors, which are strongly angle dependent. Current density reaches its maximum value in a direction parallel to the longitudinal conductivity direction. Illustrative examples of the Fréchet derivatives are given for the 2.5-D problem, in which the profile is taken perpendicular to strike. All three derivatives of the Green’s function with respect to longitudinal conductivity, transverse resistivity and dip angle of the symmetry axis (dG/dσ l , dG/dσ t , dG/dθ0) show a strongly asymmetric pattern compared to the isotropic case. The patterns are aligned in the direction of the tilt angle. Such sensitivity patterns are useful in real-time experimental design as well as in the fast inversion of resistivity data collected over an anisotropic earth.
Many rocks possess electrical properties with a clearly expressed anisotropy. The anisotropic character of the rocks is often overlooked in forming the Fréchet derivatives or sensitivity functions for parameter updating during the inversion of DC resistivity data. In this study we have compared the sensitivity patterns for an isotropic, homogeneous model with that for a transversely isotropic (i.e. anisotropic) model having a tilted axis of symmetry using a pole–pole array. The sensitivity functions are expressed in terms of the derivatives of the electric potential U with respect to the average conductivity σm (geometric mean of the longitudinal and transverse conductivities) and the coefficient of anisotropy λ. Results are plotted in both cross-section form and plan view for various dip and strike angles of the axis of symmetry. The derivative dU/dλ decreases more rapidly than the isotropic value dU/dσ, and shows pronounced asymmetry and weakening of magnitude with increasing dip of the plane of symmetry. The derivative dU/dσm also exhibits the asymmetric pattern (except for vertical and horizontal dip cases). The positive region between the electrodes only extends to a small depth compared to the isotropic derivative, even in the case of a vertical axis of symmetry (VTI medium). The ratio of this anisotropic derivative to the isotropic derivative, when plotted as a function of position and depth shows prominent differences in both the sign and the magnitude of the sensitivities, especially for steep dips and for strongly anisotropic rocks. The plot highlights the dangers of an isotropic assumption. Even for mildly anisotropic rocks (λ<1.2) the possibility for error in interpretation is considerable. Combined borehole and surface measurements are needed to diagnose anisotropy. Further work is needed to design optimal electrode configurations in anisotropic situations.
We have developed explicit expressions for the Fréchet derivatives or sensitivity functions in resistivity imaging of a heterogeneous and fully anisotropic earth. The formulation involves the Green’s functions and their gradients, and it is developed from a formal perturbation analysis and by means of a numerical (finite-element) method. A critical factor in the equations is the derivative of the electrical conductivity tensor with respect to the principal conductivity values and the angles defining the axes of symmetry. The Fréchet derivative expressions were derived for the 2.5D and 3D problems using constant-point and constant-block model parameterizations. Special cases such as an isotropic earth and tilted transversely isotropic (TTI) media emerge from the general solutions. Numerical examples were investigated for various sensitivities as functions of dip angle and strike of the plane of stratification in uniform TTI media.
ABSTRACTIn this paper we present and analyse DC resistivity sensitivity patterns for uniform anisotropic media and for various surface electrode arrays. The sensitivity functions (or Fréchet derivatives) give the responsive change in measured electric potential for a perturbation in a model parameter at a particular point in the subsurface for a specific electrode configuration. The anisotropic model investigated is the common tilted transversely isotropic medium, which is defined by four model parameters. We examine the changes in the Fréchet derivatives of the Green’s functions with respect to both the longitudinal and transverse conductivity and the dip and azimuth angle of the symmetry axis for varying model parameters. Anisotropic sensitivities are vastly different in strength and shape compared to the isotropic sensitivity pattern. The various arrays (pole‐pole, dipole‐dipole, Wenner and square array) produce distinctive patterns that are important in assessing resolution. Valuable insights were gained: the anisotropic Fréchet derivatives can vary greatly from the isotropic pattern in both strength and shape depending on the nature of the anisotropy. Also it was found that the relationship between components of current density (parallel and perpendicular to the symmetry axis) and the sensitivity patterns is somewhat akin to the dot product of the true source and adjoint source current density vectors in isotropic media. Understanding of the anisotropic sensitivity pattern variations will enable, through further analysis, computation of model resolution matrices and improvement of experimental design. Appreciation of the significant differences between isotropic and anisotropic sensitivities should help avoid errors in using inappropriate isotropic inversion schemes to interpret measurements made over anisotropic ground.
Introduction In this paper we present and analyse DC resistivity sensitivity patterns for uniform anisotropic media. The sensitivity functions (or Fréchet derivatives) give the responsive change in measured electric potential for a perturbation in a model parameter at a particular point in the subsurface for a specific electrode configuration. The anisotropic model investigated is the common tilted transversely isotropic medium (TTI) which is defined by four model parameters. We examine the changes in the Fréchet derivatives of the Green’s functions with respect to both the longitudinal and transverse conductivity and the dip and azimuth angle of the symmetry axis (dG/dσ1, dG/dσt, dG/dθ0, dG/dϕ0) for varying model parameters. Secondly, we wish to illustrate the differences that exist between the sensitivities calculated using an isotropic assumption and those computed with the correct anisotropic formulation. It is shown that in certain cases gross errors in inversion may occur if isotropic Fréchet derivatives are mistakenly used. Here we work with two special forms of the derivatives -one taken with respect to the mean conductivity and the other with respect to the magnitude of the anisotropy- and investigate a range of possible cases.
The suitability of MOSFETs (Metal Oxide Semiconductor Field Effect Transistors) for use in in-vivo dosimetry for IMRT prostate treatment and patient setup errors has been investigated in this work. MOSFETs were placed on entrance and exit surfaces of a number of different phantoms (with varying complexities from homogeneous to anthropomorphic). Dose measurements were then used to calculate a midpoint dose, which was compared with an IC placed at the isocentre. The agreements found between the calculated (MOSFETs) and the measured midpoint dose (IC) was: 0.7 % for a prostate treatment verification and 3.5 % for an IMRT treatment. MOSFETs placed on entry and exit surfaces can detect patient setup offsets of 2 cm, but do not have the sensitivity to confidently detect offsets of 1 cm or smaller.
We report on observations of the COROT IR01 field with the Berlin Exoplanet Search Telescope ( BEST). BEST is a small- aperture telescope with a wide field of view ( FOV). It is dedicated to searching for variable stars within the target fields of the COROT space mission to aid in minimizing false- alarm rates, and identifying potential targets for additional science. COROT's observational program started in 2007 February, with the "initial run'' field ( IR01) observed for about 2 months. BEST observed this field for 12 nights spread over 3 months in winter 2006. From the total of 30,426 stars observed in the IR01 field, 3769 were marked as suspected variable stars, and 54 of these showed clear periodicity. From these, 19 periodic stars are within the part of the COROT FOV covered in our data set.
The COROT space mission will monitor several target fields for up to 150 days to perform asteroseismology and to search for extrasolar planets by photometric transits. Variable stars in the target fields are important objects for additional scientific studies but can also disturb the search for planetary transits. A variability characterization of the target fields prior to COROT observations is therefore important for two reasons: to find interesting variable stars to monitor further and to make an analysis of the impact of the variable stars on detecting extrasolar planet transits with COROT The Berlin Exoplanet Search Telescope (BEST) is a small wide-angle telescope dedicated to high-precision photometry. It has observed a 9 deg(2) field of view centered at (alpha, delta) = (19(h)00(m) 00.0(s), +00 degrees 01'55.2") (J2000.0) over 98 nights to search for variable stars in the surroundings of the first long-run target field (LRc 1) of the COROT space mission. In this data set we identified 92 periodic variable stars 86 of which are new discoveries and 6 of which are known from the General Catalogue of Variable Stars (GCVS). For five of the GCVS stars, variability could not be confirmed. Forty-three of the 92 detected periodic variable stars are identified as eclipsing binaries. We have evaluated the completeness of our survey for eclipsing binaries by comparing it to the expected fraction of eclipsing binaries based on Hipparcos observations. From this evaluation we show that the BEST data set presented here has a completeness of 20%-30% for periods longer than 1 day and is complete relative to Hipparcos for short-period binaries.
According to a Sanef study (Stewart, 2005), the number of news media in South Africa has increased dramatically since the dawn of democracy. For example, between 1995 and 2004, the number of community newspapers has increased from 241 to 330, consumer magazines from 310 to 550 and radio stations from 71 to 117. Given this, it is only logical that there will be an increased demand for journalists and consequently for media trainers. From that (South African) perspective alone, this book should be welcomed.
The author sets out to provide a "new position" from which journalists can better understand their place in a society that has more news and news media than ever before, while journalists and the media are also, for various reasons, under severe criticism. He is not so much concerned with traditional criticisms like sensationalism, the invasion of privacy and the jeopardising of national security as with the consequences for journalism where news media are primarily driven and managed as business operations.
In die konteks van die Totale Aanslag, die bosoorlog en Suid-Afrika se destabilisering van buurstate het dit 'n minder onskuldige, selfs siniese, aanskyn gekry. Persoonlik was ek teleurgesteld. Maar dit illustreer waarskynlik bloot dat Das, soos ons almal, vol ambivalensies was: Joernalis, maar ook patriot - al stem ons dan nie saam oor wat n landsbelang was nie. 'n Mens kan weet dat hy ook dAt met totale toewyding en oorgawe gedoen het.