Early Analogue Modeling Experiments and Related Studies to Today s Problems of Geo-electromagnetic Exploration

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1 Journal of Earth Science, Vol. 20, No. 3, p , June 2009 ISSN X Printed in China DOI: /s y Early Analogue Modeling Experiments and Related Studies to Today s Problems of Geo-electromagnetic Exploration László Szarka* Geodetic and Geophysical Research Institute of the Hungarian Academy of Sciences, University of West-Hungary, H-9401 Sopron POB 5, Hungary ABSTRACT: As I learned it from extensive geo-electromagnetic analogue modeling experiments, some specific nonconventional interpretation parameters, in certain conditions, give more detailed information about the geometry of subsurface resistivity inhomogeneities than the routinely used parameters. In this article, I show several examples, and I present how these early results influenced our later research. An enhanced geometric sensitivity may be due to special array geometry (as we call it null array ), or it may be due to a narrow and very special frequency range (i.e., the so-called keyhole range). Nonconventional but physically based interpretation parameters (like the Poynting vector) or higher order invariants of resistivity or impedance tensors may also give useful additional information about the shape of subsurface bodies. One should be very careful in their application because a large part of these nontraditional approaches are strongly constrained by measuring errors and geological noise. KEY WORDS: electromagnetic method, analogue modeling, null component, rotational invariant. INTRODUCTION In geophysics, geometric and physical features of the subsurface are interpreted in terms of various model parameters, where the model itself is already a rough simplification of the reality. The models, constructed by geophysicists, have been well adapted to the existing measuring and interpretation techniques. In electromagnetic geophysics, numerical (mathematical) and analogue (physical) modeling are two alternative ways in determining the response due to subsurface inhomogeneities. This study was supported by the Hungarian Scientific Research Fund (Nos , 68475). *Corresponding author: szarka@ggki.hu Manuscript received December 1, Manuscript accepted February 9, In numerical (computational) geophysics, at first, sequences of horizontal layers (the one-dimensional model or 1D) and then various two-dimensional (2D) models were used. Nowadays, it is possible to calculate the effects of three-dimensional (3D) subsurface models. In the induction domain, the analogue (or scale) modeling is based on the possibility of reducing the characteristic field dimension R f (e.g., the transmitterreceiver distance) into laboratory dimension R m, if the electromagnetic induction length (reciprocal k f, where k f is the electromagnetic wave number ) is reduced by the same factor into 1/k m. The electromagnetic similitude law is k f R f =k m R m (Frischknecht, 1988). In geometrical sense, the analogue modeling is inherently 3D. Therefore, in analogue modeling, a lot of 3D experiences had already been accumulated, when it was not yet possible to study the same phenomena by

2 Early Analogue Modeling Experiments and Related Studies to Today s Problems of Geo-electromagnetic Exploration 619 using numerical modeling calculation. Analogue modeling experiments, carried out in the Sopron electromagnetic modeling laboratory (Märcz et al., 1986; Ádám et al., 1981), turned my attention to the fact that, in several nonconventional circumstances (e.g., in case of nonconventional geometry or in nonconventional frequency range), more details about the shape of subsurface resistivity structures could be observed than in conventional situations. NULL ARRAYS As an analogue modelist, I found very useful to measure those electromagnetic field components, which are zero on the surface of the homogeneous half-space. We call these components null components, and the array, where null components are measured, is called as null array. Early Null-Array Observations It is known from theory that, in case of a homogeneous half-space, a vertical electric dipole (VED), with one current electrode on the surface and one electrode in the borehole at depth, at the surface has strong radial electric field (E r ), and it has no vertical magnetic component H z (Szarka and Nagy, 1992). A controlled VED source, surface-measuring technique, has been reported recently, for example, by He (2008). I constructed a physical model (a high-resistivity circular disk, representing an oil reservoir model) and carried out CSAMT experiments in the modeling tank filled up with salt water. The disk model was penetrated by eccentrically positioned borehole models (as it is shown in Fig. 1), along profiles spreading radially from the borehole. I observed that the E r map shows local maxima over the model edges only far from the borehole, whereas in the H z map, the disk is surrounded by a well-measurable sharp minimum zone, as they are shown in Fig. 2. Figure 1. Cross view: all VED positions in the analogue model experiment. Plan view: 16 measuring profiles around a borehole crossing a high-resistivity disk model. Results in Fig. 2 were obtained using electrodes A2 and B22, along profiles 1 8 (Szarka and Nagy, 1992).

3 620 László Szarka Figure 2. E r (left column) and H z (right column) anomalies over a circular high-resistivity disk at a characteristic intermediate zone (model frequency=1 MHz). Top: measured values along profiles 1 8 (in relative units). Center: values along profiles 1 8, normalized by the mean curve of those shown in the top. Bottom: map of the normalized values. The E r map shows local maxima over the model edges only far from the borehole; in the H z map the disk is surrounded by a sharp minimum zone (Szarka and Nagy 1992). Similar observations were also obtained in a DC analogue modeling study (Szalai, 2001). The component, which is nearly zero in homogeneous half-space, proved to be much more sensitive to a given conductivity change in the subsurface than the components, which are present in the primary field. Systematic Null-Array Studies On a basis of analogue modeling results, we elaborated a noncolinear null array (Szalai et al., 2002) and then various colinear null arrays (Szalai et al., 2004) (the latter one is easier to be realized in field conditions). All null arrays proved to be able to detect subsurface fracture zones in field conditions, which could not be observed by using traditional arrays. We found altogether about 25 independent null arrays, already published in the literature (Szalai and Szarka, 2008a), and we started to investigate systematically the specific characteristics of all null arrays. Szalai et al. (2009) recently made a comparative study about

4 Early Analogue Modeling Experiments and Related Studies to Today s Problems of Geo-electromagnetic Exploration 621 the depth of investigation of all possible DC arrays. It has been shown that vertical resolution and depth of investigation are inversely related to each other. Consequently, it is possible to increase depth of investigation at the expense of decreasing vertical resolution until signal levels drop below the noise level. We also produced parameter sensitivity maps for all DC electrode arrays (Szalai and Szarka, 2008b, c). Null array studies led among others to a successful detection of multidimensional fissures in a karstic basement (Szalai et al., 2005). Tensor Invariants The magnetotelluric response can be formulated in the form of complex impedance tensors. As known, rotational invariants of these tensors depend neither on the direction of the primary field nor on the measuring orientation (e.g., Szarka and Menvielle, 1997; Szarka, 1997b). Because the number of independent rotational invariants in the magnetotelluric impedance tensor (containing 2 2 complex elements, that is 8 realvalued elements) is 7, and the eighth parameter is the measuring orientation itself, it is possible to construct various sets of seven independent rotational invariants. Having a lot of magnetotelluric soundings over an area, each rotational invariant provides a specific period-dependent image about the subsurface. Among the seven independent invariants, two invariants reflect exclusively the behavior of the main components, and five invariants are functions of various null components. At the same time, in DC apparent resistivity tensors, which contain four real-valued parameters, the number of independent rotational invariants is 3. They are as follows: a resistivity estimation, a 2D indicator, and a 3D indicator. In the latter two, the so-called null components dominate. In a recent near-surface (archeological) application (Varga et al., 2008), the resistivity estimation (the basic invariant) gave very reliable results with measured data (not shown here), but the 2D and the 3D indicators (those are the two null component-related ones) failed. They proved to be too sensitive to the actual measuring and geological noise. Consequently, 2D and especially 3D invariants can only be applied very carefully, both in DC and magnetotellurics. KEYHOLE IMAGING At some specific ( keyhole ) frequencies, the image about the subsurface bodies can be more closely connected to their pattern than at lower or higher frequencies. Early Keyhole Observations In a CSAMT sounding analogue modeling experiment (carried out by Szarka (1991), in frames of an enhanced oil recovery project), we observed that the anomalies over thin sheet-like 3D models, with complicated geometry (see Fig. 3), may be, in certain conditions, especially closely connected to the model pattern. This enhanced imaging sensitivity was detected in a very narrow period window (see Fig. 4), always somewhere at the end of the so-called overshooting period range of the corresponding sounding curve. The phenomenon was observed both in the amplitude and phase of various components and related interpretation parameters. The keyhole frequencies for various apparent resistivity and phase parameters were analytically calculated for the plane wave case Figure 3. Left panel: the measuring area and the transmitter-receiver layout (CSAMT frequency sounding by using equatorial dipole-dipole configuration). Right panel: models, with mass center in the center of the measuring area (Szarka and Menvielle, 1999).

5 622 László Szarka (Szarka, 1997a). The keyhole phenomenon for thin subsurface bodies was confirmed later using magnetotelluric numerical studies (Szarka and Menvielle, 1999), as shown in Fig. 5 by the high peak of the correlation coefficient between the resistivity and phase responses and the model geometry. For the analogue modeling results, see Szarka (1991). Because the effect is small in the magnitude of lateral resistivity and phase variation (only 1% 2%), this keyhole imaging has never been tested in the field. In some favorable situations, the keyhole images might be applied as an additional tool in practical problems where the main question is the detailed geometry of subsurface targets. This technique seems promising in marine electromagnetic explorations, where the noise level is very low. Figure 4. CSAMT frequency sounding curves (upper panel: amplitude of the horizontal electric component; lower panel: phase shift) measured in the center of the measuring area over the three different models, as a function of the relative wavelength, λ 1 /h (h is the model depth). The keyhole zone is encircled (Szarka and Menvielle, 1999). Phase Map and Basement Morphology Later, on a basis of keyhole-imaging experiences, we studied how it would be possible to get direct information about deep structures, even in presence of near-surface inhomogeneities (Szarka et al., 2004; Zhang et al., 2004). We calculated correlation coefficients between the geometry of the near-surface/deep models and various model responses. By means of so-called correlation sounding curves (that is, by putting together correlation coefficients at a sequence of frequencies), we studied the conditions for seeing through the near-surface thin sheet-like model and getting direct information about the deep structures. A systematic correlation sounding study is given by Szarka et al. (2004) and Zhang et al. (2004). It was also observed that phase maps at periods of small (either increasing or decreasing) phase anomalies are model geometry sensitive, whereas the phase map obtained at the period of the maximum phase anomaly shows zero correlation with the original model geometry (Zhang et al., 2004). Figure 5. Correlation (expressed in map units) between the anomaly map and the shape of model U. Phase peak: λ 1 /h=3.96; amplitude peak: λ 1 /h=5.10 (Szarka and Menvielle, 1999). ALTERNATIVE PARAMETERS From time to time, some new interpretation parameters are offered, which provide alternative image about the subsurface. Poynting Vector Maps In the 1980s, the Hungarian bauxite exploration

6 Early Analogue Modeling Experiments and Related Studies to Today s Problems of Geo-electromagnetic Exploration 623 needed DC electric potential gradient mappings (i.e., mapping of potential difference values in the central part of an area, between two distant current electrodes). We carried out extensive analogue modeling measurements using this technique. Inspired by the so-called magnetometric resistivity method (Edwards, 1974), I completed the potential gradient mapping with the measurement of the related DC magnetic field (Szarka, 1987). From the electric and DC magnetic field distributions, two interpretation parameters were derived: the ratio (impedance) and product (a Poynting vector component) of the corresponding electric and magnetic fields. The impedance maps proved to be more robust than the electric or DC magnetic anomaly maps, and the Poynting vector component map reflected especially well the shape of the high-resistivity horsts and sinks. As I found (see Fig. 6), the Poynting vector-related anomalies usually give information on much shallower depths than the impedance. It is again a noise-sensitive technique, which has not met any successful field application yet. Alternative Apparent Resistivity Definitions As it was suspected from our unpublished analogue modeling experiments and demonstrated with systematic 3D numerical modeling studies (Szarka et Figure 6. Anomaly maps calculated from DC electric and magnetic fields over two slightly different rectangular horsts (left and right columns) in the high-resistivity basement using two orthogonal current electrode layouts (the geometric mean values were calculated). Upper part: impedance maps; central part: Poynting maps; bottom part: model cross sections. The Poynting vector-related anomalies provide indispensable additional information about the shape of the horsts. The model widths (expressed in measuring distance) are 2 and 4 (Szarka, 1987).

7 624 al., 2004, 2000), resistivity definitions based on f(rez) (that is, on function f of the real elements of the complex magnetotelluric impedance response) are much more effective in terms of shape resolution than resistivities computed from the imaginary elements, f(imz). They are also more effective than the resistivity computed traditionally from the absolute value Abs f(z) of the complex impedance response f(z). Various f functions were tested (e.g., determinant and sum of square of elements), and the conclusion was the same every time. For numerical illustrations, see Szarka et al. (2000). Later, we confirmed the results using field data (Szarka et al., 2005). Namely, the correlation coefficient between the series of basement depth values at 39 magnetotelluric sites and the apparent-resistivity values was found to be stronger (and high correlation appeared also at a shorter period) when it was computed with apparent resistivities based on the real tensor rather than with apparent resistivities based on the imaginary tensor. In the light of our studies, the f(rez)-based apparent resistivity and the impedance phase seem to be more informative than any other combination of magnetotelluric interpretation parameters. CONCLUSIONS I have presented examples showing how analogue modeling offered ideas to determine the geometry of subsurface bodies by using various surface geoelectromagnetic methods. There is no universal way to get such information, but in some special circumstances, it is possible to obtain much more information about the geometry than applying routine methods. I have shown examples for shape determination, inspired by analogue modeling experiments (1) by using special EM field components ( null components), (2) by using special frequency (e.g., the keyhole modeling), and (3) by alternative parameters. Measurements of null components (or use of null arrays) are still missing from routine application of multielectrode systems, but I think, in some cases (e.g., in archeological surveys, where the objective is to get a spatial rather than depth section images of the subsurface, or in monitoring applications), multielectrode arrays in the future will also apply such nonconventional ( null ) configurations. László Szarka The application of the keyhole-frequency range would be interesting, but it can be used only in case of extremely homogeneous host medium: for example, in marine environment, where the noise level is extremely low. The tensorial approach also has perspectives: nowadays, because of the instrumental and computational developments, it is possible to carry out much more dense 3D measurements. Therefore, it is possible to apply tensorial approach, and it is also possible to exploit the whole information content in the geo-electromagnetic visualization. The analogue (physical) modeling has been a creative tool in discovering newer possibilities. Analogue modeling should not be forgotten because it is a tool to test numerical computation results. ACKNOWLEDGMENTS This study was supported by the Projects and of the Hungarian Scientific Research Fund; I also thank Prof. J Wang for the invitation to the Wuhan ICEEG meeting. REFERENCES CITED Ádám, A., Pongrácz, J., Szarka, L., et al., Analogue Model for Studying Geoelectric Methods in the Geodetic and Geophysical Research Institute of the Hungarian Academy of Sciences. Acta Geod. Geoph. Mont. Hung., 16(2 4): Edwards, R. N., The Magnetometric Resistivity Method and Its Application to the Mapping of a Fault. Can. J. Earth Sci., 11: Frischknecht, F. C., Electromagnetic Physical Scale Modelling. In: Nabighian, M. N., ed., Electromagnetic Methods in Applied Geophysics Theory. Society of Exploration Geophysicists, Tulsa, Oklahoma, 1: He, Z. X., New Progress of Petroleum EM Prospecting and Case Studies in China. Review Paper S4_E07 Presented at the 19th International Workshop on Electromagnetic Induction in the Earth. Abstracts Märcz, G., Pongrácz, J., Szarka, L., Electromagnetic Scale Modeling Instrument for Geophysical Prospecting. Naucnaya Apparatura (Wroclaw), 1: Szalai, S., DC Null Arrays: [Dissertation]. University of West-Hungary, Sopron (in Hungarian) Szalai, S., Novák, A., Szarka, L., Depth of Investigation

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