A Fast Method for Determining the Layer Distribution From the Raised Kernel Function in Geoelegtrical Sounding*

Koefoed, O.

doi:10.1111/j.1365-2478.1970.tb02129.x

Cited by 74 publications

(47 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…layer thickness, layer true resistivity) can be expressed by an integral equation considering an earth model consisting of homogeneous and isotropic layers. Following (Koefoed, 1970) we write the equation as follows…”

Section: Forward Modelingmentioning

confidence: 99%

See 1 more Smart Citation

Inversion of Schlumberger resistivity sounding data from the critically dynamic Koyna region using the Hybrid Monte Carlo-based neural network approach

Maiti¹,

Gupta²,

Erram³

et al. 2011

Nonlin. Processes Geophys.

View full text Add to dashboard Cite

Abstract. Koyna region is well-known for its triggered seismic activities since the hazardous earthquake of M = 6.3 occurred around the Koyna reservoir on 10 December 1967. Understanding the shallow distribution of resistivity pattern in such a seismically critical area is vital for mapping faults, fractures and lineaments. However, deducing true resistivity distribution from the apparent resistivity data lacks precise information due to intrinsic non-linearity in the data structures. Here we present a new technique based on the Bayesian neural network (BNN) theory using the concept of Hybrid Monte Carlo (HMC)/Markov Chain Monte Carlo (MCMC) simulation scheme. The new method is applied to invert one and two-dimensional Direct Current (DC) vertical electrical sounding (VES) data acquired around the Koyna region in India. Prior to apply the method on actual resistivity data, the new method was tested for simulating synthetic signal. In this approach the objective/cost function is optimized following the Hybrid Monte Carlo (HMC)/Markov Chain Monte Carlo (MCMC) sampling based algorithm and each trajectory was updated by approximating the Hamiltonian differential equations through a leapfrog discretization scheme. The stability of the new inversion technique was tested in presence of correlated red noise and uncertainty of the result was estimated using the BNN code. The estimated true resistivity distribution was compared with the results of singular value decomposition (SVD)-based conventional resistivity inversion results. Comparative results based on the HMC-based Bayesian Neural Network are in good agreement with the existing model results, however in some cases, it also provides more detail and precise results, which appears to be justified with local geological and structural deCorrespondence to: S. Maiti (saumen maiti2002@yahoo.co.in) tails. The new BNN approach based on HMC is faster and proved to be a promising inversion scheme to interpret complex and non-linear resistivity problems. The HMC-based BNN results are quite useful for the interpretation of fractures and lineaments in seismically active region.

show abstract

Section: Forward Modelingmentioning

confidence: 99%

“…Following Koefoed (1970) we write recurrence relationship of the resistivity transform function, T (λ) as,…”

Section: Forward Modelingmentioning

confidence: 99%

Inversion of Schlumberger resistivity sounding data from the critically dynamic Koyna region using the Hybrid Monte Carlo-based neural network approach

Maiti¹,

Gupta²,

Erram³

et al. 2011

Nonlin. Processes Geophys.

View full text Add to dashboard Cite

show abstract

“…Here, J 1 (λs) is the first order Bessel function of first kind, T (ρ i , d i ; λ) is the electrical impedance at the surface -defined as the resistivity transform function (Koefoed, 1970) of layer resistivities and thicknesses and λ is the integration variable. On the basis of the above discussion we can write the corresponding expression of apparent chargeability-resistivity for Schlumberger configuration as…”

Section: Theoretical Considerationsmentioning

confidence: 99%

Combined straightforward inversion of resistivity and induced polarization (time-domain) sounding data

Niwas

Gupta

2011

Journal of Applied Geophysics

View full text Add to dashboard Cite

“…Furthermore, a distortion over a small segment of the VES curve will cause a distortion over a correspondingly larger segment on the transformed TKF curve. Koefoed (1965Koefoed ( , 1966Koefoed ( , 1968) used the raised kernel function H(\) instead of the Stefanesco kernel function 9(A) and subsequently (Koefoed, 1970) introduced graphs to accelerate the evaluation of the layer thicknesses and resistivities from the raised kernel function H(X). Other students of the direct interpretation of resistivity data in the kernel domain include Crous (1971), Meinardus (1967Meinardus ( , 1970, Onodera (1960), Pekeris (1940), andVozoff (1958).…”

Section: '0mentioning

confidence: 99%

Automatic interpretation of Schlumberger sounding curves, using modified Dar Zarrouk functions

Zohdy¹

1975

View full text Add to dashboard Cite

Formulas defining two types of modified Dar ^arrouk curves are used to invert Schlumberger sounding curves, using an iterative procedure. The number of layers, which is equal to the number of points on the inverted curve, is reduced by AUTOMATIC INTERPRETATION OF SCHLUMBERGER SOUNDING CURVES, USING MODIFIED DAR ZARROUK FUNCTIONSBy ADEL A. R. ZOHDY ABSTRACT For horizontally stratified media, Schlumberger VES (vertical electrical sounding) curves with slopes of greater than -1 not only resemble but commonly almost coincide with their corresponding DZ (Dar Zarrouk) curves. By considering an n-point Schlumberger VES curve to be an n-layer DZ curve, and by solving for the layering from the DZ curve, we obtain a first approximation to the actual layering in the form of an nlayer section. However, the minimum slope for DZ curves is 1, whereas on some VES curves negative slopes may be as low as 3; therefore, these VES curves cannot be considered to be a first approximation to their corresponding DZ curves. Formulas are obtained for calculating two types of MDZ (modified DZ) curves whose positive and negative slopes are not limited to +1 and 1, respectively. Therefore, for any VES curve, there exists a corresponding MDZ curve that lies close to it. The automatic interpretation is made by an iterative procedure in which, for the first approximation, the observed VES curve is assumed to be the sought MDZ curve. This MDZ curve is solved for layer thicknesses and resistivities; then, by means of a convolution technique, a VES curve is calculated for the obtained layering, and the calculated VES curve is compared with the observed one. A second approximation to the sought MDZ curve is obtained by utilizing the differences between the observed and calculated VES curves. The iteration is continued until a match, within a prescribed fitting tolerance, is obtained between observed and calculated VES curves. The number of layers in the resulting model (detailed solution) is always equal to the number of points used to define the observed VES curve. Equivalent solutions composed of a fewer number of layers are determined by automatically smoothing the DZ curve of the detailed solution and inverting it. Special equivalent solutions that are subject to certain geologic or geoelectric constraints can be found by manual adjustments of the detailed n-layer DZ curve. Excellent automatic matches were obtained when the method was tested with several theoretical VES curves and with several hundreds of field VES curves of different forms. The average processing time per VES curve (extending over more than three logarithmic cycles) on the IBM 360/65 computer is about 8 seconds. For distorted and incomplete field curves, the average processing time is approximately doubled. El E2 TECHNIQUES IN DIRECT-CURRENT RESISTIVITY EXPLORATION

show abstract

A Fast Method for Determining the Layer Distribution From the Raised Kernel Function in Geoelegtrical Sounding*

Cited by 74 publications

References 1 publication

Inversion of Schlumberger resistivity sounding data from the critically dynamic Koyna region using the Hybrid Monte Carlo-based neural network approach

Inversion of Schlumberger resistivity sounding data from the critically dynamic Koyna region using the Hybrid Monte Carlo-based neural network approach

Combined straightforward inversion of resistivity and induced polarization (time-domain) sounding data

Automatic interpretation of Schlumberger sounding curves, using modified Dar Zarrouk functions

Contact Info

Product

Resources

About