Leonty A. Tabarovsky

On the influence of 3-D structures in the interpretation of transient electromagnetic sounding data

The limitations of a standard 1-D inversion applied to multidimensional (synthetic) data are investigated. Simple correction procedures for interpreting field data distorted by 3-D structures are suggested. Two different transmitter/receiver configurations of the transient electromagnetic (TEM) sounding method are examined: a central loop configuration for the near zone (sometimes called short offset) and a fixed transmitter/moving receiver configuration for the far zone (long offset). The 3-D models are structural depressions and highs in both resistive and conductive basements. The fixed transmitter (grounded dipole) in the long offset TEM configuration is located at a distance significantly greater than both the size and depth of the structure. In all cases, 1-D interpretation of the central loop soundings recovers geoelectric parameters of the section with good reliability, although fictitious layers may appear near vertical boundaries. The 1-D interpretation of long offset soundings does not, in most...

Real time 2d inversion of induction logging data

Real time 2D inversion for an induction logging instrument may be achieved using a fast forward modeling and special inversion strategy. The fast forward modeling employs a low-frequency approximation of an induction response known as Dolls geometric factor. Modeling geometric factors is much faster than modeling the electromagnetic field in the frequency domain. To transform real data into the Dolls limit, multi-frequency skin-effect correction is applied. The correction technique involves an asymptotic theory of the integral equation for a 2D boundary value problem. The inversion is based on separating the parameter space into subspaces of lower dimension. Initially, adaptive overlapping windows split logging data into manageable portions. Each window consists of three subwindows: the predictor, corrector and upgrader. Further separation of parameters is introduced by Dolls approximation: the low-frequency response is linear with respect to formation conductivity. This allows us to split inversion for conductivity and geometric parameters. The next level of splitting inversion is achieved by independently determining parameters of the near borehole zone and remote formation areas. This is done by utilizing different subsets of sensors. The inversion does not require initial guess: layers are introduced dynamically, if necessary. The resolution is improved in sequential iterations by adding finer details to the previously obtained models. The final selection of parameters satisfies a variety of a priori constraints formulated as target resistivity distributions. The technique for imposing constraints is based on the analysis of data mapping into the model space. Interpretation of synthetic and real data confirms the viability of the method.

2.5-D modeling in electromagnetic methods of geophysics

Abstract Understanding, using, or eliminating three-dimensional (3-D) effects in electromagnetic methods of geophysics are critical requirements. Numerous achievements in 3-D modeling sometimes give the impression that they are widely available today in geophysical practice. This is not necessarily true. Existing 3-D modeling packages prove that we know how to perform 3-D modeling. However, the computer resources and costs involved make the practical application of 3-D EM modeling in geophysical applications very limited. A practical compromise, or even alternative, is represented by 2.5-D modeling characterized by the use of a 3-D source in a 2-D medium. This combination allows one to mathematically describe the related boundary value problem as a sequence of independent two-dimensional problems. The typical technique leading to such a split formulation is Fourier analysis. That is why the individual terms of a split solution are often referred to as harmonics. Although each independent problem is two-dimensional, the algorithmic implementation of finite differences or integral equations for the higher harmonics has some specific features not present in the classical 2-D cases. In this paper, a hybrid scheme consisting of a combination of the finite difference technique with the integral equation approach for transient fields is described. Evaluation of algorithm accuracy is presented and a transient logging technique application is considered. The algorithm is fast and easily implemented on a personal computer