INTERPRETATION OF BURIED ELECTRODE RESISTIVITY DATA USING A LAYERED EARTH MODEL

Geophysics ◽  
1978 ◽  
Vol 43 (5) ◽  
pp. 988-1001 ◽  
Author(s):  
Jeffrey J. Daniels
Keyword(s):  
Direct Current ◽  
Field Data ◽  
Apparent Resistivity ◽  
Current Source ◽  
Well Logs ◽  
Earth Model ◽  
Layered Earth ◽  
Resistivity Data ◽  
True Resistivity ◽  
Resistivity Logging

The layered earth model is a fundamental interpretation aid for direct current resistivity data. This paper presents a solution for the layered earth problem for a buried current source and a buried receiver. The model is developed for source and receiver electrodes buried anywhere within a horizontally stratified layered earth containing an arbitrary number of resistivity layers. Model results for the normal well‐logging array indicate that large departures between true and apparent resistivity can be caused by thin beds or highly resistant layers. A true resistivity distribution from well logs can be established by modeling when the effects from borehole rugosity and fluid resistivity are negligible. The equations derived for resistivity well logs can be used to interpret hole‐to‐hole, hole‐to‐surface, and conventional surface array data. A field example demonstrates that deviations between hole‐to‐hole field data and model results, based on well logs in the receiver hole, can be accounted for by combining the resistivity logging models in the receiver holes with information from geologic logs. Differences between the field data and the layered‐model results are attributed to lateral changes between or near the source and receiver holes.

Reply by the author to Pierre Valla

Geophysics ◽  
1996 ◽  
Vol 61 (3) ◽  
pp. 919-919
Author(s):  
Umesh C. Das
Keyword(s):  
Asymptotic Behavior ◽  
Direct Current ◽  
Apparent Resistivity ◽  
Intermediate Step ◽  
Controlled Source ◽  
Layered Earth ◽  
Asymptotic Expressions ◽  
Higher Order Terms ◽  
Earth Structures ◽  
Subsurface Resistivity

I thank Pierre Valla for his interest in my paper (Das, 1995a). Transformation of controlled source electromagnetic (CSEM) measurements into apparent resistivities is carried out as an intermediate step in order to enhance interpretation. Duroux (1967; and hence Valla, 1984) derives, using asymptotic expressions (higher order terms are dropped out), apparent resistivities from CSEM measurements. Valla mentions, ‘those apparent resistivities do not have the nice asymptotic behavior’, and they can not be used as an intermediate step to estimate the layer resistivities and thicknesses in the subsurface. My aim in the paper has been not to work a ‘miracle’ but to derive a function to reflect the subsurface resistivity distributions of the layered earth structures directly. The calculations on a few models indicate that such a function can be derived which yields an unambiguous apparent resistivity. The apparent resistivity curves are similarly useful in interpretation as the direct current and magnetotelluric apparent resistivity curves. Inclusion of Duroux’s work would have given the readers a chance to appreciate my definition.

Hole‐to‐surface resistivity measurements

Geophysics ◽  
1983 ◽  
Vol 48 (1) ◽  
pp. 87-97 ◽  
Author(s):  
Jeffrey J. Daniels
Keyword(s):  
Electric Field ◽  
Current Source ◽  
Surface Resistivity ◽  
General Nature ◽  
Earth Model ◽  
Geoelectric Section ◽  
Layered Earth ◽  
Resistivity Measurements ◽  
Surface Electric Field ◽  
Drill Holes

Hole‐to‐surface resistivity measurements over a layered volcanic tuff sequence illustrate procedures for gathering, reducing, and interpreting hole‐to‐surface resistivity data. The magnitude and direction of the total surface electric field resulting from a buried current source is calculated from orthogonal potential difference measurements for a grid of closely spaced stations. A contour map of these data provides a detailed map of the distribution of the electric field away from the drill hole. Resistivity anomalies can be enhanced by calculating the difference between apparent resistivities calculated from the total surface electric field and apparent resistivities for a layered earth model. Lateral discontinutities in the geoelectric section are verified by repeating the surface field measurments for current sources in several drill holes. A qualitative interpretation of the anomalous bodies within a layered earth can be made by using a three‐dimensional (3-D) resistivity model in a homogeneous half‐space. The general nature of resistive and conductive bodies causing anomalies away from the source drill holes is determined with the aid of data from several source holes, layered models, and 3-D models.

Interpretation of multifrequency complex resistivity data for a layered Earth model

1988 ◽  
Vol 26 (4) ◽  
pp. 399-408 ◽  
Author(s):  
S.F. Mahmoud ◽  
S.G. Tantawi ◽  
J.R. Wait
Keyword(s):  
Earth Model ◽  
Complex Resistivity ◽  
Layered Earth ◽  
Resistivity Data

NUMERICAL RESISTIVITY INTERPRETATION: GENERAL INHOMOGENEITY

Geophysics ◽  
1960 ◽  
Vol 25 (6) ◽  
pp. 1184-1194 ◽  
Author(s):  
K. Vozoff
Keyword(s):  
Linear Approximation ◽  
Arbitrary Function ◽  
Apparent Resistivity ◽  
Current Source ◽  
Resistivity Data ◽  
Resistivity Method ◽  
The Earth ◽  
Local Current ◽  
The Individual

A linear approximation is developed for the equation of conduction in a medium where resistivity is an arbitrary function of x, y, and z. This is applied by assuming the earth to be subdivided into small, homogeneous blocks of arbitrary resistivity. Under this approximation, the apparent resistivity is just the sum of the effects of the individual blocks. The equations are linear, and surface apparent resistivity data can be inverted to yield block resistivities. The quality of the approximation has been checked by comparison with model measurements in two situations: remote current source (telluric method), and local current source (resistivity method). It was found that the results are satisfactory provided that the proper type of expression is used for the effect of the resistivity contrast of each block.

QUADRIPOLE‐QUADRIPOLE ARRAYS FOR DIRECT CURRENT RESISTIVITY MEASUREMENTS—MODEL STUDIES

Geophysics ◽  
1976 ◽  
Vol 41 (1) ◽  
pp. 79-95 ◽  
Author(s):  
Dariu Doicin
Keyword(s):  
Half Space ◽  
Electric Fields ◽  
Direct Current ◽  
Apparent Resistivity ◽  
Cross Product ◽  
Resistivity Measurements ◽  
Model Studies ◽  
True Resistivity ◽  
Vertical Contact ◽  
Source Dipole

For a quadripole‐quadripole array, in which current is sequentially injected into the ground by two perpendicular dipoles, an apparent resistivity can be defined in terms of the vectorial cross product of the two electric fields measured at the receiver site. Transform equations are derived (for horizontally layered media) which relate this apparent resistivity to the apparent resistivities obtained with conventional dipole‐dipole and Schlumberger arrangements. To evaluate the method, two mathematical models are used. The first model is a half‐space with an “alpha conductivity center,” and the second model is a half‐space with a vertical contact. For an idealized quadripole‐quadripole array, simple expressions are found for the apparent resistivity, which is shown to be independent of the orientation of the current quadripole. Theoretical anomalies calculated for the quadripole‐quadripole array are compared with those obtained for a dipole‐quadripole array. It is shown that whereas the apparent resistivity map for the dipole‐quadripole array varies greatly with the azimuth of the source dipole, the results obtained with the quadripole‐quadripole array consistently display a remarkable resemblance to the assumed distribution of true resistivity. This is especially true when the current quadripole is placed at a large distance from the surveyed area.

Implementation of Vendor-Independent Stochastic Inversion for Improving Quality and Efficiency of Well Placement on the Field of Novatek Company

2021 ◽  
Author(s):  
Danil Andreevich Nemushchenko ◽  
Pavel Vladimirovich Shpakov ◽  
Petr Valerievich Bybin ◽  
Kirill Viktorovich Ronzhin ◽  
Mikhail Vladimirovich Sviridov
Keyword(s):  
Real Time ◽  
Well Placement ◽  
Stochastic Inversion ◽  
Mathematical Algorithm ◽  
Service Companies ◽  
Resistivity Data ◽  
Resistivity Logging ◽  
Azimuthal Resistivity ◽  
Logging Tool ◽  
Single Approach

Abstract The article describes the application of a new stochastic inversion of the deep-azimuthal resistivity data, independent from the tool vendor. The new model was performed on the data from several wells of the PAO «Novatek», that were drilled using deep-azimuthal resistivity tools of two service companies represented in the global oilfield services market. This technology allows to respond in a timely manner when the well approaches the boundaries with contrasting resistivity properties and to avoid exit to unproductive zones. Nowadays, the azimuthal resistivity data is the method with the highest penetration depth for the geosteering in real time. Stochastic inversion is a special mathematical algorithm based on the statistical Monte Carlo method to process the readings of resistivity while drilling in real time and provide a geoelectrical model for making informed decisions when placing horizontal and deviated wells. Until recently, there was no unified approach to calculate stochastic inversion, which allows to perform calculations for various tools. Deep-azimuthal resistivity logging tool vendors have developed their own approaches. This article presents a method for calculating stochastic inversion. This approach was never applied for this kind of azimuthal resistivity data. Additionally, it does not depend on the tool vendor, therefore, allows to compare the data from various tools using a single approach.

Inversion of helicopter electromagnetic data to a magnetic conductive layered earth

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1211-1223 ◽  
Author(s):  
Haoping Huang ◽  
Douglas C. Fraser
Keyword(s):  
Magnetic Permeability ◽  
Field Data ◽  
Model Parameters ◽  
Relative Importance ◽  
Magnetic Polarization ◽  
Inversion Algorithm ◽  
Layered Earth ◽  
Electromagnetic Data ◽  
Airborne Electromagnetic ◽  
True Values

Inversion of airborne electromagnetic (EM) data for a layered earth has been commonly performed under the assumption that the magnetic permeability of the layers is the same as that of free space. The resistivity inverted from helicopter EM data in this way is not reliable in highly magnetic areas because magnetic polarization currents occur in addition to conduction currents, causing the inverted resistivity to be erroneously high. A new algorithm for inverting for the resistivity, magnetic permeability, and thickness of a layered model has been developed for a magnetic conductive layered earth. It is based on traditional inversion methodologies for solving nonlinear inverse problems and minimizes an objective function subject to fitting the data in a least‐squares sense. Studies using synthetic helicopter EM data indicate that the inversion technique is reasonably dependable and provides fast convergence. When six synthetic in‐phase and quadrature data from three frequencies are used, the model parameters for two‐ and three‐layer models are estimated to within a few percent of their true values after several iterations. The analysis of partial derivatives with respect to the model parameters contributes to a better understanding of the relative importance of the model parameters and the reliability of their determination. The inversion algorithm is tested on field data obtained with a Dighem helicopter EM system at Mt. Milligan, British Columbia, Canada. The output magnetic susceptibility‐depth section compares favorably with that of Zhang and Oldenburg who inverted for the susceptibility on the assumption that the resistivity distribution was known.

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