A MODIFIED PSEUDOSECTION FOR RESISTIVITY AND IP

Geophysics ◽  
1977 ◽  
Vol 42 (5) ◽  
pp. 1020-1036 ◽  
Author(s):  
L. S. Edwards
Keyword(s):  
Relative Depth ◽  
Electrode Arrays ◽  
Anomalous Body ◽  
Vertical Scale ◽  
Depth Scale ◽  
Effective Depth ◽  
Definition Of ◽  
Empirical Coefficients ◽  
Theoretical Results ◽  
Depth Of Investigation

Dipole‐dipole induced‐polarization measurements are commonly presented as pseudosections, but results using different dipole lengths cannot be combined into a single pseudosection. By considering the theoretical results for simple earth models, a unique set of relative depth coefficients is empirically derived, such that measurements with different array parameters will “mesh” smoothly into a combined pseudosection. Application of these coefficients to a number of theoretical and field cases shows that they give reasonable results when applied to more complicated models. The empirical coefficients are compared with Roy’s theory of “depth of investigation characteristic,” and support that theory, if a modified definition of “effective depth” is accepted. This leads to an absolute depth scale for the modified pseudosection. It is shown that rough estimates of the depth to the top of an anomalous body can be made directly on the pseudosection, at true vertical scale. This definition of effective depth is applied to other electrode arrays. It is shown, by examples, that the resulting pseudosections give consistent estimates of depth to top, within the characteristic anomaly patterns of each array. The effective depths for various arrays are compared; the results agree with the traditional applications of each array.

Depth of investigation of collinear electrode arrays over homogeneous anisotropic half‐space in direct current methods

Geophysics ◽  
1981 ◽  
Vol 46 (5) ◽  
pp. 768-780 ◽  
Author(s):  
B. B. Bhattacharya ◽  
M. K. Sen
Keyword(s):  
Half Space ◽  
Direct Current ◽  
Inverse Relationship ◽  
Electrode Arrays ◽  
Definition Of ◽  
Depth Of Investigation

The definition of depth of investigation as suggested by Evjen (1938) [subsequently used by Roy and Apparao (1971) also for the study of depth of investigation of electrode arrays in direct current methods for homogeneous isotropic earth] has been used to study the depth of investigation of various collinear electrode arrays for a homogeneous anisotropic half‐space. It has been shown that some simple transformations are to be applied to the expressions of normalized depth of investigation characteristic (NDIC) of the same arrays over homogeneous isotropic earth to obtain normalized depth of investigation characteristic of various arrays placed over homogeneous anisotropic earth. The novelty of anisotropy is that the depth of investigation of collinear electrode arrays over homogeneous anisotropic half‐space bears an inverse relationship with the coefficient of anisotropy and also depends upon array length and dip of the plane of stratification. The effect of the coefficient of anisotropy is most pronounced for horizontally stratified anisotropic earth and is independent of it for vertically stratified anisotropic earth—entirely consistent with the concept of the “;paradox of anisotropy.” The depth of investigation of all the collinear arrays for inclined stratification lies somewhere between the values obtained for horizontal and vertical stratifications.

Depth of investigation of collinear symmetrical four‐electrode arrays

Geophysics ◽  
1989 ◽  
Vol 54 (8) ◽  
pp. 1031-1037 ◽  
Author(s):  
R. D. Barker
Keyword(s):  
Characteristic Curve ◽  
Electrode Array ◽  
Electrode Arrays ◽  
Definition Of ◽  
Depth Of Investigation

A study of collinear symmetrical four‐electrode arrays and their tripotential variations indicates the existence of an electrode array for which all the tripotential arrangements have the same depth of investigation. Examination of computer‐generated sounding curves confirms this result only when depth of investigation is defined as the median of the depth of investigation characteristic curve. The results lend support to this being the most practically useful definition of depth of investigation.

scholarly journals Pseudoinversion of degenerate metrics

2003 ◽  
Vol 2003 (55) ◽  
pp. 3479-3501 ◽  
Author(s):  
C. Atindogbe ◽  
J.-P. Ezin ◽  
Joël Tossa
Keyword(s):  
Differential Geometry ◽  
Large Class ◽  
Smooth Manifold ◽  
Differential Operators ◽  
Type Operator ◽  
Lorentzian Space ◽  
Lightlike Hypersurface ◽  
Definition Of ◽  
Lightlike Hypersurfaces ◽  
Theoretical Results

Let(M,g)be a smooth manifoldMendowed with a metricg. A large class of differential operators in differential geometry is intrinsically defined by means of the dual metricg∗on the dual bundleTM∗of 1-forms onM. If the metricgis (semi)-Riemannian, the metricg∗is just the inverse ofg. This paper studies the definition of the above-mentioned geometric differential operators in the case of manifolds endowed with degenerate metrics for whichg∗is not defined. We apply the theoretical results to Laplacian-type operator on a lightlike hypersurface to deduce a Takahashi-like theorem (Takahashi (1966)) for lightlike hypersurfaces in Lorentzian spaceℝ1n+2.

Estimating depth of investigation in dc resistivity and IP surveys

Geophysics ◽  
1999 ◽  
Vol 64 (2) ◽  
pp. 403-416 ◽  
Author(s):  
Douglas W. Oldenburg ◽  
Yaoguo Li
Keyword(s):  
Electrode Array ◽  
Physical Property ◽  
Model Space ◽  
Visual Assessment ◽  
Order Estimate ◽  
Dc Resistivity ◽  
Electrode Arrays ◽  
The Earth ◽  
Surface Data ◽  
Depth Of Investigation

In this paper, the term “depth of investigation” refers generically to the depth below which surface data are insensitive to the value of the physical property of the earth. Estimates of this depth for dc resistivity and induced polarization (IP) surveys are essential when interpreting models obtained from any inversion because structure beneath that depth should not be interpreted geologically. We advocate carrying out a limited exploration of model space to generate a few models that have minimum structure and that differ substantially from the final model used for interpretation. Visual assessment of these models often provides answers about existence of deeper structures. Differences between the models can be quantified into a depth of investigation (DOI) index that can be displayed with the model used for interpretation. An explicit algorithm for evaluating the DOI is presented. The DOI curves are somewhat dependent upon the parameters used to generate the different models, but the results are robust enough to provide the user with a first‐order estimate of a depth region below which the earth structure is no longer constrained by the data. This prevents overinterpretation of the inversion results. The DOI analysis reaffirms the generally accepted conclusions that different electrode array geometries have different depths of penetration. However, the differences between the inverted models for different electrode arrays are far less than differences in the pseudosection images. Field data from the Century deposit are inverted and presented with their DOI index.

Scaled quantum mechanical force fields for trifluoromethyl selenium derivatives. I. The CF3SeCN and CF3SeCH3 molecules

2006 ◽  
Vol 84 (12) ◽  
pp. 1626-1631 ◽  
Author(s):  
L E Fernández ◽  
E L Varetti
Keyword(s):  
Density Functional ◽  
Force Fields ◽  
Chemical Species ◽  
Mechanical Force ◽  
Force Constants ◽  
Quantum Mechanical ◽  
Functional Theory ◽  
Definition Of ◽  
Theoretical Results ◽  
Mechanical Force Fields

Force fields and vibrational properties were calculated for the trifluoromethyl selenium derivatives, CF3SeCN and CF3SeCH3, by means of density functional theory (DFT) techniques. The existing experimental data and assignments for these molecules were confirmed by the theoretical results. These data were subsequently used in the definition of scaled quantum mechanical force fields for such chemical species. The obtained force constants are compared with results previously published for similar compounds.Key words: trifluoromethyl selenium, force constants, structure, DFT calculation.

A COMPARISON OF IP ELECTRODE ARRAYS

Geophysics ◽  
1973 ◽  
Vol 38 (4) ◽  
pp. 737-761 ◽  
Author(s):  
J. H. Coggon
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Method Comparison ◽  
Horizontal Resolution ◽  
The Finite Element Method ◽  
Electrode Arrays ◽  
Depth Discrimination ◽  
Effective Depth ◽  
The Asymmetry ◽  
Element Method

The responses of dipole‐dipole, pole‐dipole, and gradient arrays to a set of ten structures have been computed using the finite element method. Comparison of the responses indicates that: (1) The dipole‐dipole array usually gives the largest anomalies, but the anomalies rarely give information on dip of a structure and are strongly influenced by overburden irregularities. This array gives best overall resolution. (2) Pole‐dipole anomalies are almost as large as dipole‐dipole ones and have the same general form but show less resolution. The lower resolution and the asymmetry of this array make results more difficult to interpret. (3) The gradient array provides dip information and good horizontal resolution. Responses to thin vertical structures are weak, anomalies are strongly affected by overburden irregularities, and there is no effective depth discrimination.

scholarly journals Review of top notch electrode arrays for geoelectrical resistivity surveys

2020 ◽  
pp. 147-155
Author(s):  
Henry Ekene Ohaegbuchu ◽  
F. C. Anyadiegwu ◽  
P. O. Odoh ◽  
F. C. Orji
Keyword(s):  
Signal To Noise Ratio ◽  
Electrode Arrays ◽  
Signal To Noise ◽  
Noise Ratio ◽  
Geoelectrical Resistivity ◽  
Depth Of Investigation ◽  
Horizontal Layers

The different arrangements of electrodes used in geoelectrical resistivity surveys and measurements are referred to as electrode arrays. In this review, we have revisited most of the widely used electrode arrays as well as the uncommon ones, which are nonetheless, useful in certain situations. This review has provided detailed information about eleven (11) of the top notch electrode arrays employable in our regular resistivity surveys, making it clear that in practice, the arrays that are most commonly used for 2-D imaging surveys are the Wenner, Dipole-Dipole, Wenner-Schlumberger, Pole-Pole and the Pole-Dipole arrays. They have their strengths and weaknesses. They are typically described by their signal-to-noise ratio. Their depth of investigation, ability for lateral location of the target and their mapping abilities of horizontal layers or steeply dipping structures among other factors determine which array to adopt.

scholarly journals EXPRESS MONITORING OF THE MAIN PARAMETERS OF CLOUDS FROM THE EARTH’S SURFACE

2019 ◽  
Vol 46 (3) ◽  
pp. 116-128
Author(s):  
A. G. Yakunin
Keyword(s):  
Cloud Cover ◽  
Minimum Cost ◽  
Fixed Time ◽  
Time Interval ◽  
Weather Forecasts ◽  
Key Points ◽  
Web Camera ◽  
Definition Of ◽  
Empirical Coefficients ◽  
Official Sources

Objectives The paper proposes a technique that allows the main types of clouds and cloud cover parameters (ceiling, direction and speed of cloud movement) to be determined at minimum cost via observations from the Earth’s surface. The aim is to avoid using meteorological information derived from official sources, which may not always be available for a specific place and time of observation.Method The method is based on the well-known Ippolitov formula that connects air humidity on the Earth’s surface with the cloud ceiling, whose empirical coefficients depend on the type of the cloud cover. In order to determine this type, a method based on elliptic cloud contour approximation is proposed.Results Additional classification features were the number of approximating ellipses in the image frame, the proximity of their mutual location, the total area that they occupy in the frame and the area occupied by the largest ellipse. The speed and direction of the clouds are determined through shifting the common key points in image frames obtained over a small fixed time interval. Each point is described by a descriptor calculated using the SURF method from the open image processing library OpenCV.Conclusion Despite the simplicity of the required software and hardware (web camera, humidity sensor, and OEM – Arduino module), this method provides a definition of these parameters with an error within 20%. Monitoring systems based on this method may be used in private automatic weather stations, such as the Wunderground, for obtaining more information that could improve the accuracy of weather forecasts, as well as for research in meteorology and climatology. 

scholarly journals Relation between Planck’s Constant and Speed of Light, Predicting Proton Radius More Accurately

2019 ◽  
Vol 11 (5) ◽  
pp. 1
Author(s):  
Anna C. M. Backerra
Keyword(s):  
Gravitational Waves ◽  
Conversion Factor ◽  
Elementary Particles ◽  
Accurate Prediction ◽  
Quantum Mechanical ◽  
Speed Of Light ◽  
Proton Radius ◽  
Definition Of ◽  
Physical Phenomena ◽  
Theoretical Results

In twin physics, descriptions of phenomena on a quantum-mechanical as well as astronomical scale are reconciled by considering them in a complementary way. This is in agreement with the view of Heisenberg and carried out by using the definition of complementarity as given by Max Jammer. The obtained theoretical results can be identified with basic physical phenomena like the forces of nature, a series of elementary particles and gravitational waves. If the proton as described by twin physics is combined with the early ideas of Einstein about the energetic equivalence of mass and radiation, a relation between the Planck’s constant and the speed of light is found, in which the mass and radius of the proton occur, together with a factor four. This factor acts as a conversion factor from mass to radiation. Besides of that, this relation leads to a more accurate prediction of the radius of the proton.

What is the depth of investigation of a resistivity measurement?

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. W1-W10 ◽  
Author(s):  
Enrique Gómez-Treviño ◽  
Francisco J. Esparza
Keyword(s):  
Apparent Resistivity ◽  
Resistivity Measurement ◽  
Weighted Average ◽  
Sensitivity Function ◽  
Resistivity Sounding ◽  
Practical Applications ◽  
Resistivity Profile ◽  
Definition Of ◽  
Homogeneous Media ◽  
Depth Of Investigation

Ever since the first computation of resistivity sounding curves, there has been the impression that somehow they are averages of the vertical resistivity profile. This prompted the idea to represent apparent resistivity as an integral over depth and to define depth of investigation using the integrands of the integrals as elementary contributions. However, elementary contributions for a boundary value problem cannot be uniquely defined and are not physically meaningful. Many practical applications that have been derived from this approach might be at stake regarding their theoretical basis. On the other hand, a sensitivity function has a definite physical meaning and it is uniquely defined, but it offers a different picture for a layered earth. The concept of elementary contributions must then be abandoned as not real, as some respected scholars have suggested, or it must be put on solid ground if we are going to continue using it. Our claim is that any definition of elementary contributions must comply with the concept of sensitivity; otherwise, it must be discarded not because it might be proved wrong, but because we cannot have multiple functions pretending to represent the depth of investigation of a resistivity measurement. We determined that both concepts can be unified and reconciled into a single formulation. That is, one and the same function of depth can be interpreted as an elementary contribution or as the local sensitivity. To further support the effectiveness of the concept, we applied it beyond its traditional application to homogeneous media. We developed an approximate formula for computing apparent resistivity as a weighted average of the vertical resistivity profile. The formula works in the way of a toy model; it is an approximation, but it provides immediate insights into how a vertical resistivity profile relates to its sounding curve.

Sign in / Sign up

Export Citation Format

Share Document