If the conductivity of any one of the layers of a horizontally stratified earth varies exponentially with depth with or without a discontinuity at the interface the corresponding expressions for apparent resistivity for Wenner-Schlumberger sounding arrays can be formulated. The general case has been broadly divided into three categories for mathematical simplicity. One particular application of this present study is for the probing of roof thickness in tunnels in coal mines.

Apparent resistivity of a multilayered earth with a layer having exponentiality varying conductivity

An earth model with a transition layer (anisotropic inhomogeneous) is considered. The inhomogeneity in σv (vertical conductivity) of the transition layer is represented by a power law variation. Expressions for potential distribution in the upper layer, transition layer and bottom layer are obtained by solving appropriate differential equation for each layer. By utilizing the boundary conditions, expressions of apparent resistivity for Wenner and Schlumberger configurations are derived. Numerical analysis is performed for linear and quadratic variation of σv. The results are presented in the form of theoretical apparent resistivity curves for both configurations. Negative apparent resistivities are the interesting feature of this analysis.

Theoretical resistivity sounding results over a transition layer model

Parameter estimation by Differential Search Algorithm from horizontal loop electromagnetic (HLEM) data

For curves over a horizontally stratified earth where any of the layers has a conductivity variation proportional to (1 +β·z)N, where β and N are arbitrary constants and z is the depth to the layer, expressions for apparent resistivity for Wenner and Schlumberger sounding are derived. No assumption has been made about the continuity of conductivity at the interface. It is shown that most of the previous investigations in this connection can be regarded as particular cases of the present study.

Resistivity sounding on a multilayered earth containing transition layers

Master curves are presented for three-layer earth-sections, the electrical resistivity in the intermediate layer of which has a linear variation with depth. A new approach is proposed to interpret the sounding data with the help of RMS difference in apparent resistivity values.

Resistivity Sounding on a Layered Transitional EARTH

The expression for the potential due to a point source of current, placed on the surface of a horizontal three-layer earth, has been derived when conductivity in the second layer varies linearly with depth and changes abruptly at the boundaries. Master curves for Wenner and Schlumberger configurations have been presented for an insulating basement and for one value of conductivity gradient in the second layer.

Resistivity sounding on a three-layer transitional model*

As an extension of the eddy current pattern computed by Koefoed and Kegge (1968) for a thin vertical infinitely-conducting half-plate in presence of oscillating magnetic dipoles, this paper computes the contribution to the (electro-) magnetic anomaly at the receiver by each element of the vein separately. Twelve contour diagrams for such elemental contributions are presented as samples. Two points of general interest stand out: (1) The contributions from different portions of the vein are not all of one sign; the contribution from one part may cancel that from another; and (2) The portion of the vein nearest to the transmitter-receiver system does not necessarily make the largest contribution to the total measured signal.

Contribution to signal by elements of thin vertical conducting vein in dipolar em systems

Dividing a vertical conducting vein into horizontal strips, response of each of them is obtained for various transmitter receiver orientations.

Electromagnetic response pattern of a conducting vein

An analysis is made to ascertain the effect of conductivity variation with temperature on the temperatures within the crust. It shows that this effect is very small and can safely be neglected.

Sheel C. Jain

Papers

Resistivity sounding on a three-layer transitional model*

Resistivity Sounding on a Layered Transitional EARTH

Contribution to signal by elements of thin vertical conducting vein in dipolar em systems

Electromagnetic response pattern of a conducting vein

On temperatures in the crust: The effect of temperature dependence of conductivity