Art Raiche

The joint use of coincident loop transient electromagnetic and Schlumberger sounding to resolve layered structures

One‐dimensional earth models consisting of uniform horizontal layers are useful both as actual representations of earth structures and as host models for more complex structures. However, there are often inherent difficulties in establishing layer thicknesses and resistivities from one type of measurement alone. For example, the dc resistivity method is sensitive to both conductive and resistive layers, but as these layers become thin, nonuniqueness becomes a severe problem. Electromagnetic (EM) methods are good for establishing the parameters of conductive layers, but they are quite insensitive to resistive layers. The use of both coincident loop transient EM (TEM) and Schlumberger methods, together with a joint inverse computer program, can vastly improve interpretation of layered‐earth parameters. The final model is less dependent upon starting guesses, error bounds are much improved, and nonuniqueness is much less of a problem. These advantages are illustrated by interpretation of real field data as w...

Transient electromagnetic calculations using the Gaver-Stehfest inverse Laplace transform method

Calculations for the transient electromagnetic (TEM) method are commonly performed by using a discrete Fourier transform method to invert the appropriate transform of the solution. We derive the Laplace transform of the solution for TEM soundings over an N‐layer earth and show how to use the Gaver‐Stehfest algorithm to invert it numerically. This is considerably more stable and computationally efficient than inversion using the discrete Fourier transform.

Apparent resistivity and diffusion velocity

Formulas are derived to calculate transient electromagnetic (TEM) vertical diffusion velocity as a function of resistivity, time, and transmitter loop size. For large loops on very conductive earths, this velocity depends strongly on loop size. Diffusion velocity is used to calculate apparent resistivity pseudodepth sections (ARPDS) from apparent resistivity time sections. However, ARPDS do not seem to bear an easily discernible relationship to the geoelectric structure. Furthermore, it is shown that the apparent resistivity is not directly related to the volume through which TEM diffusion has occurred.

Comparison of apparent resistivity functions for transient electromagnetic methods

The use of transient electromagnetic (TEM) methods is increasing throughout the world because of their success in finding conductive anomalies in regions previously thought inappropriate for EM techniques. Most TEM systems now in use (SIROTEM UTEM, Crone Pulse EM, etc.) employ voltage measurements, i.e., measurements of the time derivative of the magnetic field. However, the success of SQUID based receiving systems in many fields has led research organizations (such as the Bureau of Mineral Resources, Australia) to investigate the use of SQUIDs in TEM systems to obtain direct measurements of the magnetic field.

Negative transient voltage and magnetic field responses for a half-space with a Cole-Cole impedance

In a recent paper, Lee (1981) developed an asymptotic formula for the coincident loop transient electromagnetic (TEM) response of a polarizable half‐space having a Cole‐Cole impedance. By using parameters corresponding to three different mineral deposits, Lee showed that negative transients would be obtained for delay times of 0.4 to 1.1 msec. The method developed by Knight and Raiche (1982) to calculate the transient response of layered earths was used to check these results for three reasons.

Calculation of apparent conductivity for the transient electromagnetic (coincident loop) method using an HP-67 calculator

The interpretation of coincident‐loop transient electromagnetic (TEM) surveys is often aided by the transformation of TEM data to apparent conductivity values. Present methods of calculating apparent conductivity have a limited usefulness or require access to a computer. This paper presents an algorithm for calculating apparent conductivity to an accuracy of better than 1 percent for values of the parameter x = σμA/4πt up to 10, where σ = conductivity, μ = magnetic permeability, A = loop area, and t = sample time. This range of x is sufficient for most situations encountered in field work. The algorithm has been programmed for an HP-67 pocket calculator, and the program steps and user instructions are given in standard format. Execution time ranges from 6 to 15 sec. The program should assist the interpretation of TEM surveys in the field.

Modelling and inversion -progress, problems, and challenges

Researchers in the field of electromagnetic modelling and inversion have taken advantage of the impressive improvements of new computer hardware to explore exciting new initiatives and solid extensions of older ideas. Finite-difference time-stepping methods have been successfully applied to full-domain 3D models. Another new method combines time-stepping with spatial frequency solutions. The 2D model 3D source (2.5D) problem is also receiving fresh attention both for continental and sea floor applications.The 3D inversion problem is being attacked by several researchers using distorted Born approximation methods. Q-domain inversions using transformation to pseudo-wave field and travel time tomography have also been successfully tested for low contrast problems. Subspace methods have been successful in dramatically reducing the computational burden of the under-determined style of inversion. Static magnetic field interpretation methods are proving useful for delineating the position of closely-spaced multiple targets.Novel (“appeals to nature”) methods are also being investigated. Neural net algorithms have been tested for determining the depth and offset of buried pipes from EM ellipticity data. Genetic algorithms and simulated annealing have been tested for extremal model construction.The failure of researchers to take adequate account of the properties of the mathematical transformation from algorithms to the number domain represented by the computing process remains a major stumbling block. Structured programming, functional languages, and other software tools and methods are presented as an essential part of the serial process leading from EM theory to geological interpretation.

The use of summary representation for electromagnetic modeling

The method of summary representation developed by G. N. Polozhii is a quasi-analytical method for solving self-adjoint, finite-difference boundary value problems expressed on regular meshes. In principle, the method should allow considerable savings in computing time as well as improved accuracy when compared to commonly used finite-difference schemes. We have used summary representation as the basis for a new hybrid scheme to solve the two-dimensional Helmholtz equation for electromagnetic modeling. The theory behind this hybrid scheme is presented. Preliminary results for the two-dimensional problem show that substantial computing time and storage savings can be made.

On: “Comparison of apparent resistivity functions for transient electromagnetic methods” by A. P. Raiche (GEOPHYSICS, v. 48, p. 787–789); discussion and reply

We have read with great interest this short note essentially showing some advantages of measuring the step response rather than the impulse response for depth sounding purposes. We have reached very similar conclusions in the interpretation of UTEM® transient data in depth sounding applications compared to pulse EM data: generally the step response itself or derived apparent resistivities show the effect of either deep or very conductive layers at earlier sampling times than does the pulse response, and the apparent resistivities are most often simpler in shape and single valued. For measurements outside the transmitter loop, both step and pulse responses are more complex, but in general the step response is relatively simpler and has its characteristic points at earlier times. To give two quantitative examples: for a vertical dipole source, the zero crossing for a thin horizontal conductive layer response occurs √3 times earlier for the step response; for a half‐space response, the ratio is quite close t...

Are 3D Electromagnetic Modeling And Inversion Useful

Where should we look and for what orebody style? Could EM methods find it? What would the EM response look like in different types of terranes? What system would best maximise and delineate target response? Does the data indicate a target worth drilling? Where is it, how deep and how big? Where is the best place to sink a drill hole? These are some basic questions of mineral exploration. EM modelling and inversion would appear to be critical tools in answering all but the first of these. In fact, they are critical only of they can give reliable answers and can be used easily within the context of the time and cost pressure environment of the explorationist.