On: “Depth of investigation of collinear electrode arrays over homogeneous anisotropic half‐space in direct current methods,” by B. B. Bhattacharya and M. K. Sen (May 1981 GEOPHYSICS, 46, p. 768–780).

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1936-1941
Author(s):  
A. Apparao ◽  
G. S. Srinivas
Keyword(s):  
Half Space ◽  
Basic Equation ◽  
Homogeneous Medium ◽  
Current Strength ◽  
Senior Author ◽  
Electrode Arrays ◽  
The Subject ◽  
Geoelectrical Methods ◽  
Electrode Systems ◽  
Depth Of Investigation

Bhattacharya and Sen (1981) are the first to study the depths of investigation of various collinear electrode arrays for a homogeneous anisotropic half‐space. In their study they substituted the aniosotropic medium by an appropriate homogeneous medium of resistivity [Formula: see text]. However, they committed a serious error at assuming their basic equation‐13 as the “expression of potential at a point (X, y, Z) due to a point source of current strength I placed over a semi‐infinite homogeneous isotropic medium of resistivity [Formula: see text]”. The error is that X and Z in equation (13) are not independent coordinates. As a consequence, all their expressions for NDICs for different electrode arrays become incorrect. Consequently, their results and conclusions also become invalid. The mistake was detected only recently by the senior author of this paper (A. Apparao) in the course of his writing a book on ‘Developments in geoelectrical methods’. Since the subject of anisotropy is very interesting, there arises an urgent need to derive the correct expressions of the depth investigation characteristics for different electrode arrays. We present in this paper the expressions for normalized depth investigation characteristics (NDIC) for homogeneous and anisotropic half spaces for different electrode systems, including dipolar systems.

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.

Neurology

PEDIATRICS ◽  
1949 ◽  
Vol 4 (6) ◽  
pp. 855-855
Keyword(s):  
Young People ◽  
Senior Author ◽  
Psychiatric Research ◽  
Special Treatment ◽  
University Of Illinois ◽  
Junior Author ◽  
Standard Text ◽  
The Subject ◽  
Neurological Surgery ◽  
And Training

The senior author is Director of the Institute for Psychosomatic and Psychiatric Research and Training and Chairman of the Department of Neuropsychiatry of the Michael Reese Hospital, Chicago, Ill. The new junior author is Professor of Neurological Surgery, University of Illinois, Chicago, III. Changes in this extensively revised new edition include the omission of the first few chapters of previous editions. Much of that material has been incorporated in the remaining text. No special treatment of the subject of neurology in young people and children is presented in the text. The subject as presented is reliable and complete with this exception. The book should be a standard text.

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.

A Copper Trade Object from the Headwaters Lakes Aspect in Manitoba

1949 ◽  
Vol 15 (2) ◽  
pp. 157-160
Author(s):  
Chris Vickers ◽  
Ralph D. Bird
Keyword(s):  
Senior Author ◽  
Black Duck ◽  
Junior Author ◽  
Close Relationship ◽  
The Subject ◽  
The City ◽  
Factual Data

The spread of the Headwaters Lakes Aspect in a northwesterly direction through Manitoba, has been the subject of previous comment by the senior author. The manifestations of the aspect in this area, have a marked resemblance to the Black Duck Focus, and have been defined as the Manitoba Focus.The factual data upon which this conclusion is based are derived from three controlled excavations in Manitoba. Hecker and Hlady excavated the Lockport site, north of the city of Winnipeg, in August, 1947. Hecker reports the presence of sherds that show a “close relationship” to the Black Duck Focus. During 1947 and 1948 the junior author conducted excavations on the Scott site near Brandon, Manitoba. This site is located on the S.W. Sec. 35, T. 10, R. 20, W. 1, and has yielded a good collection of Manitoba Focus sherds, with an associated artifact complex that closely corresponds to that outlined by Wilford for the Headwaters Lakes Aspect.

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.

Intracortical Somatosensory Stimulation to Elicit Fingertip Sensations in an Individual With Spinal Cord Injury

Neurology ◽  
2021 ◽  
pp. 10.1212/WNL.0000000000013173
Author(s):  
Matthew Stephen Fifer ◽  
David P McMullen ◽  
Luke E Osborn ◽  
Tessy M Thomas ◽  
Breanne P Christie ◽  
...  
Keyword(s):  
Spinal Cord ◽  
Spinal Cord Injury ◽  
Pulse Amplitude ◽  
Electrode Arrays ◽  
Somatosensory Stimulation ◽  
Cord Injury ◽  
Human Participant ◽  
The Subject ◽  
Tactile Sensations ◽  
Clinical Trial Information

Background and Objectives:The restoration of touch to fingers and fingertips is critical to achieving dexterous neuroprosthetic control for individuals with sensorimotor dysfunction. However, localized fingertip sensations have not been evoked via intracortical microstimulation (ICMS).Methods:Using a novel intraoperative mapping approach, we implanted electrode arrays in the finger areas of left and right somatosensory cortex and delivered ICMS over a 2-year period in a human participant with spinal cord injury.Results:Stimulation evoked tactile sensations in 8 fingers, including fingertips, spanning both hands. Evoked percepts followed expected somatotopic arrangements. The subject was able to reliably identify up to 7 finger-specific sites spanning both hands in a finger discrimination task. The size of the evoked percepts was on average 33% larger than a fingerpad, as assessed via manual markings of a hand image. The size of the evoked percepts increased modestly with increased stimulation intensity, growing 21% as pulse amplitude increased from 20µA to 80µA. Detection thresholds were estimated on a subset of electrodes, with estimates of 9.2-35µA observed, roughly consistent with prior studies.Discussion:These results suggest that ICMS can enable the delivery of consistent and localized fingertip sensations during object manipulation by neuroprostheses for individuals with somatosensory deficits.Clinical Trial Information:This study is registered on ClinicalTrials.gov with identifier NCT03161067.

Applying Slim Dipole Sonic Tool to Evaluate Hydraulic Fracture Geometry and Orientation Using the Differential Sonic Method

2022 ◽  
Author(s):  
Azzan Al-Yaarubi ◽  
Sumaiya Al Bimani ◽  
Sataa Al Rahbi ◽  
Richard Leech ◽  
Dmitrii Smirnov ◽  
...  
Keyword(s):  
Hydraulic Fracturing ◽  
Oil Recovery ◽  
Critical Role ◽  
Differential Method ◽  
Optimum Number ◽  
Well Test ◽  
Fracture Geometry ◽  
The Subject ◽  
Fracture Height ◽  
Depth Of Investigation

Abstract Successful hydraulic fracturing is critical for hydrocarbon recovery from tight reservoirs. Fracture geometry is one essential quality indicator of the created fracture. The geometry provides information about the size of the created fracture and containment and verifies the pre-job modeling. Different techniques are applied to determine fracture geometry, and each has its own advantages and limitations. Due to its simplicity, the radioactive tracer log is commonly used to determine fracture placement and fracture height. Its main drawbacks include shallow depth of investigation, time dependency, and the requirement for multiple interventions for multistage fracturing operations. The crosswell microseismic technique probes a larger volume and it is potentially capable of providing fracture height, length, and orientation. Operational complexity and long processing turnaround time are the main challenges of this technique. Time-lapse shear slowness anisotropy analysis is an effective method to determine hydraulic facture height and orientation. In this technique, the shear slowness anisotropy is recorded before and after the fracture is created. The observed shear anisotropy difference indicates the intervals where the fractures were created, allowing these intervals lengths to be measured. Combining this analysis with gyroscopic data allows determining the fracture orientations. Compared to a tracer log, the differential casedhole sonic anisotropy (DCHSA) has a deeper depth of investigation, and it is time independent. Thus, the repeated log can be acquired at the end of the multistage fracturing operations. Compared to the microseismic technique, this new technique provides more precise fracture height and orientation. The new generation slim dipole sonic technology of 2.125-in. diameter extends the applicability of the DCHSA technique to smaller casing sizes. The shear differential method was applied to a vertical well that targeted the Athel formation in the south of the Sultanate of Oman. This formation is made of silicilyte and is characterized by very low permeability of about 0.01 md on average. Thus, hydraulic fracturing plays a critical role for the economic oil recovery in this reservoir. Aiming to achieve a better zonal contribution, the stimulation design was changed from a limited number of large fractures to an extensive multistage fracturing design in the subject well. Sixteen hydraulic fracturing stages were planned. The DCHSA was applied to provide accurate and efficient fracture geometry evaluation. The DCHSA accurately identified fracture intervals and their corresponding heights and orientations. This enabled effectively determining the created fracture quality and helped explain the responses of the production logs that were recorded during the well test. This study provided a foundation for the placement and completion design of the future wells in the subject reservoir. It particularly revealed adequate fracturing intervals and the optimum number of stages required to achieve optimum reservoir coverage and avoid vertical overlapping.

The Interaction of a Cylindrical Elastic Inclusion with Semicircular Disconnected Curve and Linear Cracks in an Homogeneous Medium by SH-Waves

2007 ◽  
Vol 348-349 ◽  
pp. 357-360
Author(s):  
Qi Hui ◽  
Jia Xi Zhao
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Function Method ◽  
Dynamic Stress ◽  
Elastic Inclusion ◽  
Complex Function ◽  
Dynamic Stress Intensity Factor ◽  
Homogeneous Medium ◽  
Sh Waves

The scattering of SH waves by a cylindrical elastic inclusion with a semicircular disconnected curve and linear cracks in an homogeneous medium is investigated and the solution of dynamic stress intensity factor is given by Green’s function, complex function method. Firstly, we can divide the space into up-and-down parts along the X axis. In the lower half space, a new suitable Green’s function for the present problem is constructed.In the upper half space, the Green’s function has been given by reference [5]. Thereby the semicircular disconnected curve can be constructed when the two parts are bonded along the interface and the linear cracks can be constructed using the method of crack-division and the integral equations can be obtained by the use of continuity conditions at the X axis. Finally, some examples and results of dynamic stress intensify factor are given and the influence of the parameters is discussed.

scholarly journals Fourier Expansion to Elastic Vector Wave Functions and Applications of Wave Bases to Scattering in Half-Space

2012 ◽  
Vol 28 (1) ◽  
pp. 19-39 ◽  
Author(s):  
P.-J. Shih ◽  
T.-J. Teng ◽  
C.-S. Yeh
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Fourier Expansion ◽  
Homogeneous Medium ◽  
Wave Functions ◽  
Basis Set ◽  
Plane Boundary ◽  
Surface Boundary ◽  
Infinite Plane ◽  
Vector Wave

ABSTRACTThis paper proposes a complete basis set for analyzing elastic wave scattering in half-space. The half-space is an isotropic, linear, and homogeneous medium except for a finite inhomogeneity. The wave bases are obtained by combining buried source functions and their reflected counter-waves generated from the infinite-plane boundary. The source functions are the vector wave functions of infinite-space. Based on the source functions expressed in the Fourier expansion form, the reflected counter-waves are easily obtained by solving the infinite-plane boundary conditions. Few representations adopt Wely's integration, but the Fourier expansion is developed from it and applied to decouple the angular-differential terms of the vector wave functions. In addition to the scattering of the finite inhomogeneity, the transition matrix method is extended to express the surface boundary conditions. For the numerical application in this paper, the P- and the SV- waves are assumed as the incoming fields. As an example, this paper computes stress concentrations around a cavity. The steepest-descent path method yielding the optimum integral paths is used to ensure the numerical convergence of the wave bases in the Fourier expansion. The resultant patterns from these approaches are compared with those obtained from numerical simulations.

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