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.

Apparent resistivity curves in controlled‐source electromagnetic sounding directly reflecting true resistivities in a layered earth

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 53-60 ◽  
Author(s):  
Umesh C. Das
Keyword(s):  
Direct Current ◽  
Apparent Resistivity ◽  
Dipole Source ◽  
Current Dipole ◽  
Text Data ◽  
Electromagnetic Sounding ◽  
Controlled Source ◽  
Electric And Magnetic Fields ◽  
Em Field ◽  
Subsurface Resistivity

Conversion of the measured voltages in direct current resistivity sounding methods into apparent resistivity [Formula: see text] is a useful step since [Formula: see text] data provide information about the subsurface resistivity variations with depth. This resistivity information then helps select a model for inverting the sounding data. In the controlled‐source electromagnetic method (CSEM), conversion of the measured electric and magnetic fields into apparent resistivity values has not been popular. This attitude may be attributed to the difficulties in the inversion of the resistivity of a half‐space from the electromagnetic (EM) field components as well as to the nonunique nature of the inversion giving two resistivity values for a single measurement. Two measured components—the vertical magnetic field [Formula: see text] and the tangential electric field [Formula: see text] as a result of a vertical magnetic dipole source—are combined to derive an exact apparent resistivity in a way similar to that used in direct current resistivity methods. Conversion of the measured [Formula: see text] and [Formula: see text] field components into apparent resistivity is found to be simple and can be carried out on a programmable pocket calculator. Theoretical apparent resistivity curves for frequency‐domain electromagnetic sounding show features similar to magnetotelluric (MT) and direct current dipole‐dipole apparent resistivity curves.

On: “Apparent resistivity curves in controlled‐source electromagnetic sounding directly reflecting true resistivities in a layered earth”, by U. C. Das (January‐February 1995 GEOPHYSICS, 60, 53–60).

Geophysics ◽  
1996 ◽  
Vol 61 (3) ◽  
pp. 918-918 ◽  
Author(s):  
Pierre Valla
Keyword(s):  
Magnetic Dipole ◽  
Apparent Resistivity ◽  
Electromagnetic Sounding ◽  
Controlled Source ◽  
Layered Earth ◽  
Vertical Magnetic Dipole ◽  
Em Field ◽  
Depth Sounding

Using a clever mix of two components of the EM field caused by a vertical magnetic dipole, U. C. Das derives what he claims to be an exact apparent resistivity for use in EM depth sounding.

On: “Apparent resistivity curves in controlled‐source electromagnetic sounding directly reflecting true resistivities in a layered earth”, by U. C. Das (January‐February 1995 GEOPHYSICS, 60, 53–60).

Geophysics ◽  
1996 ◽  
Vol 61 (3) ◽  
pp. 917-917
Author(s):  
Brian R. Spies ◽  
James R. Wait
Keyword(s):  
Apparent Resistivity ◽  
Previous Literature ◽  
Electromagnetic Sounding ◽  
Controlled Source ◽  
Layered Earth

Das has made a number of fundamental errors in his paper on apparent resistivity in controlled‐source EM sounding, and has ignored the previous literature.

A RESISTIVITY COMPUTATION METHOD FOR LAYERED EARTH MODELS

Geophysics ◽  
1966 ◽  
Vol 31 (1) ◽  
pp. 192-203 ◽  
Author(s):  
Harold M. Mooney ◽  
Ernesto Orellana ◽  
Harry Pickett ◽  
Leonard Tornheim
Keyword(s):  
Apparent Resistivity ◽  
Complete Separation ◽  
Computation Method ◽  
Layered Earth ◽  
Electrode Arrangement ◽  
Number Of Layers ◽  
Earth Structures ◽  
Recursion Formulas ◽  
Single Set ◽  
Numerical Integration Procedure

A procedure is given to compute apparent resistivity and induced‐polarization results for layered earth structures. The method is designed for use with large computers. Results may be obtained for any number of layers, and for any of the commonly used electrode configurations. Specific expressions are given for Schlumberger, Wenner, azimuthal‐dipole, axial‐dipole, and for the potential function. The method consists in expanding a portion of the integrand as a series in [Formula: see text] and integrating analytically term by term. Convergence of the resulting series is established. The required coefficients for each term in the series can be obtained by recursion formulas from preceding coefficients. Accuracy of the results can be estimated and can be preselected. For the Schlumberger electrode arrangement with spacing L, for example, the error produced by truncating the series after M terms will be no greater than [Formula: see text]. A more rigid bound on the error is also given. Accuracy of the method was further checked against published apparent resistivity data and against a numerical integration procedure devised for this purpose. The following characteristics make the method well suited for use with digital computers: (1) The formulation is relatively simple and easily programmed. (2) A single program will handle any number of layers. (3) The computer can be made to generate the required coefficients internally. (4) The computer can be programmed to terminate the computation as soon as any preselected accuracy has been achieved. (5) Complete separation is attained between earth structure and electrode arrangement; thus, a single set of stored coefficients can be used repeatedly for different electrode spacings and different electrode arrangements.

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.

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