In this paper we present, at first time in a geophysical journal, parameter sensitivity

maps of nonlinear and focussed electrode arrays. We present them as anomalies

due to electric dipoles forming on opposing surfaces of an elementary cube within the

subsurface at three different depths, and not only the total effect of the dipole, but

also of its components are shown. Parameter sensitivity maps of non-linear arrays,

compared to those of linear arrays, have in general 1. more equal sensitivity values

in x and y directions, 2. more chances for antisymmetry axes, 3. smoother lateral

distribution of sensitivity values. We recommend a systematic use of parameter sensitivity

maps in geoelectric prospecting, both in planning and interpretation of field

measurements

Szalai, Sándor

Szarka, László

English

This paper presents the general features of parameter sensitivity maps and illustrates their practical use. We deﬁne parameter sensitivity maps as geoelectric responses in the measuring plane (at the surface) due to an elementary cube within the subsurface at three diﬀerent depths. Responses of the three component as well as the total response of electrical dipoles formed on opposite cube surfaces are shown. In this paper we present such maps for 14 various linear electrode arrays. This paper is followed by an accompanying one about nonlinear and focusse

d arrays. Parameter sensitivity maps in these two papers provide a compact characterization of all known geoelectric arrays. We give several examples how to use them in planning and interpretation of ﬁeld measurements

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Amsterdam-New York-Tokyo Acta Geod.

Apparao A

Bobachev A A, Modin I N, Pervago E V 1999: Interpretation of resistivity sounding data – distorted by geological noise.

Kanli A I

Possibilities of three-dimensional geological structures by using electromagnetic geophysical methods. Thesis for the degree of Doctor of Science.

Szalai S 1997: 3D parameter-sensitivity of d.c. dipole arrays.

Szarka L 2008a: Acta Geod.

PARAMETER SENSITIVITY MAPS OF SURFACE GEOELECTRIC ARRAYS 

I. LINEAR ARRAYS

This paper presents the general features of parameter sensitivity maps and illustrates their practical use. We define parameter sensitivity maps as geoelectric responses in the measuring plane (at the surface) due to an elementary cube within the subsurface at three different depths. Responses of the three component as well as the total response of electrical dipoles formed on opposite cube surfaces are shown. In this paper we present such maps for 14 various linear electrode arrays. This paper is followed by an accompanying one about nonlinear and focussed arrays. Parameter sensitivity maps in these two papers provide a compact characterization of all known geoelectric arrays. We give several examples how to use them in planning and interpretation of field measurements

Szalai, S.

Szarka, L.

Parameter sensitivity maps of surface geoelectric arrays I. Linear arrays

In this paper we present, at first time in a geophysical journal, parameter sensitivity maps of nonlinear and focussed electrode arrays. We present them as anomalies due to electric dipoles forming on opposing surfaces of an elementary cube within the subsurface at three different depths, and not only the total effect of the dipole, but also of its components are shown. Parameter sensitivity maps of non-linear arrays, compared to those of linear arrays, have in general 1. more equal sensitivity values in x and y directions, 2. more chances for antisymmetry axes, 3. smoother lateral distribution of sensitivity values. We recommend a systematic use of parameter sensitivity maps in geoelectric prospecting, both in planning and interpretation of field measurements

Parameter sensitivity maps of surface geoelectric arrays II. Nonlinear and focussed arrays

Acta Geod. Geoph. Hung., Vol. 43(4), pp. 439–447 (2008)DOI: 10.1556/AGeod.43.2008.4.5PARAMETER SENSITIVITY MAPS OF SURFACEGEOELECTRIC ARRAYSII. NONLINEAR AND FOCUSSED ARRAYSS Szalai and L SzarkaGeodetic and Geophysical Research Institute of the Hungarian Academy of Sciences,POB 5, H-9401 Sopron, Hungary, e-mail: szalai@ggki.hu; szarka@ggki.hu[Manuscript received January 15, 2008; accepted March 17, 2008]In this paper we present, at ﬁrst time in a geophysical journal, parameter sensitiv-ity maps of nonlinear and focussed electrode arrays. We present them as anomaliesdue to electric dipoles forming on opposing surfaces of an elementary cube within thesubsurface at three diﬀerent depths, and not only the total eﬀect of the dipole, butalso of its components are shown. Parameter sensitivity maps of non-linear arrays,compared to those of linear arrays, have in general 1. more equal sensitivity valuesin x and y directions, 2. more chances for antisymmetry axes, 3. smoother lateraldistribution of sensitivity values. We recommend a systematic use of parameter sen-sitivity maps in geoelectric prospecting, both in planning and interpretation of ﬁeldmeasurements.Keywords: geoelectric arrays; parameter sensitivity; surface geoelectric methodsIntroductionIn the ﬁrst part of the paper (Szalai and Szarka 2008) we discussed the devel-opment of parameter sensitivity studies and techniques of calculation of parametersensitivity maps. Parameter sensitivity maps were presented for 14 linear arrays.Although some of the results had already been known, this paper, together withthe accompanying one (Szalai and Szarka 2008) is their ﬁrst complete presentationof parameter sensitivity maps of surface geoelectric arrays. In this second part, pa-rameter sensitivity maps of 7 nonlinear and 3 focussed arrays are discussed. Thereare more nonlinear and focussed arrays, but not all of them dispose with parametersensitivity maps.1217-8977/$ 20.00 c©2008 Akade´miai Kiado´, Budapest440 S SZALAI and L SZARKATable I. Electrode co-ordinates of nonlinear and focussed arrays for the computation of parametersensitivity mapsNumber of Type of Number of Name of A B M Nelectrodes the array the array the array x y x y x y x y15Dipoleequatorial0 0.05 0 –0.05 1 0.05 1 –0.0516Dipole axialnull0 0 0.1 0 1 0.05 1 –0.0517Dipoleparallel 54◦ 0 0 0.0058 –.0081 1 0 1.0058 –.0081Four Nonlinear 18 Square-α 0.2 –0.3 0.8 –0.3 0.2 0.3 0.8 0.3electrodes arrays 19 Square-γ 0 0 1 0 0.5 0.5 0.5 –0.520Schlumbergernull0 0 1 0 0.5 0.125 0.5 –0.12521Three-electrodenull0 0 inf 0 1 0.125 1 –0.125More than Linear 22 Unipole-α 0 0 1∗ 0 0.33 0 0.67 0four arrays 23 Unipole-β 0 0 0.33∗ 0 0.67 0 1 0electrodes 24 Unipole-γ 0 0 0.67∗ 0 0.33 0 1 0∗Means identical signs (current directions) of the two current electrodes. The numbering expresses acontinuity with linear, non-focussed arrays (Szalai and Szarka 2008)Parameter sensitivity maps of surface nonlinear and focussed arraysIn Figures 1–10 parameter sensitivity maps of seven nonlinear and three focussedarrays are shown. The array names and the corresponding electrode co-ordinatesare listed in Table I.In Fig. 1, the parameter sensitivity maps of the dipole-equatorial array is shown.Only the total eﬀect was published before (Hursa´n 1996). We present parametersensitivity maps of two further nonlinear dipole-dipole arrays: the dipole axial nullarray (in Fig. 2, Szalai et al. 2002), and the 54◦ parallel dipole array (Fig. 3). In Figs4 and 5 two variants of the square array are shown. In Fig. 6. the Schlumbergernull array (Szalai et al. 2002), in Fig. 7 the three-electrode null array (Szalai etal. 2002) are shown. In Figs 8–10 three focussed arrays: the unipole-α, -β and -γarrays are presented.Main features of parameter sensitivity mapsIn case of nongradient-like nonlinear arrays (Figs 4–5) and two dipole-dipolenonlinear arrays (Figs 1, 3) the role of y component becomes signiﬁcant. It maybe even more signiﬁcant than the role of x component! In case of linear focussedarrays (Figs 8–10) the x component remains dominant, but here the role of the zcomponent will be larger than in other cases.In most of the maps (in any depth and with any components) there are alsonegative zones. The zero isolines, separating the zones of positive and negativeparameter sensitivity values, have characteristic shapes. For example in case ofmost of the null arrays (Figs 2, 5, 6, 7, 8) they are linear.Acta Geod. Geoph. Hung. 43, 2008PARAMETER SENSITIVITY MAPS, PART II 441Fig. 1. Parameter-sensitivity map series of the dipole-equatorial array (No. 15 in Table I), with thecurrent electrode (stars) and potential electrode (circles) positions. x, y, z components illustratethe eﬀect of electrical charges accumulated at the corresponding opposite cube faces, while “total”means their superposed eﬀect. The maps were made at three various depths/characteristic lengthvalues (0.1, 0.2 and 0.3)The unipole arrays (in Figs 8–10) have one symmetry axis, while the dipoleequatorial (Fig. 1) and the square-α (Fig. 4) arrays have two symmetry axes. Thedipole axial null array (Fig. 2), three three-electrode null (Fig. 7) and the unipole-α(Fig. 8) arrays have one antisymmetry axis, while the square-γ (Fig. 5) and theSchlumberger null (Fig. 6) arrays have two antisymmetry axes. They provide idealvectorial information about the subsurface. The symmetry properties follow fromthe original symmetry properties of the arrays. The antisymmetry axes indicatethat these arrays are unable to detect certain types of subsurface bodies in certainpositions (Szalai et al. 2002).The lateral distribution of sensitivity values is in general (with exception ofdipole-dipole arrays) smoother than in case of the most linear arrays. This featureis due to larger lateral interception of the electrodes.Acta Geod. Geoph. Hung. 43, 2008442 S SZALAI and L SZARKAFig. 2. Parameter-sensitivity map series of the dipole-axial null array (No. 16 in Table I). Notationsare the same as in Fig. 1ConclusionsWe have presented parameter sensitivity maps of altogether 10 nonlinear and fo-cussed geoelectric arrays. They are also results of simple analytical formula, as theparameter sensitivity maps of the 14 linear arrays, presented in the ﬁrst part of thispaper (Szalai and Szarka 2008). The parameter sensitivity values (namely their re-sponse to an elementary body in x, y, z position) can be now directly intercomparedfor 14+10 arrays.The physical source of anomaly (the electrical charges) at various cube facescan be separately studied. Separating e.g., the electrodes in y direction, the eﬀectof y component, while with focussing the eﬀect of the z component become larger.The ﬁrst case is favourable to get horizontal vectorial information, the second one isfavourable to get vertical information. The antisymmetry features make it possibleto apply the pure anomaly technique (Tarkhov 1957).A detailed study of parameter sensitivity maps helps in understanding thephysics of the resulting anomalies and basic features of various arrays. At thesame time, we should again underline that it is not necessary that an array havingfavourable parameter sensitivity maps over the elementary body, will have equallyfavourable properties over a multidimensional structure. In case of any given large-size multidimensional body the parameter sensitivity is worth studying by the re-sponse due to small changes in the parameters of the given model, as it is doneGyulai (1989).Acta Geod. Geoph. Hung. 43, 2008PARAMETER SENSITIVITY MAPS, PART II 443Fig. 3. Parameter-sensitivity map series of the parallel dipole 54◦ array (No. 17 in Table I).Notations are the same as in Fig. 1Fig. 4. Parameter-sensitivity map series of the square-α array (No. 18 in Table I). Notations arethe same as in Fig. 1Acta Geod. Geoph. Hung. 43, 2008444 S SZALAI and L SZARKAFig. 5. Parameter-sensitivity map series of the square-γ array (No. 19 in Table I). Notations arethe same as in Fig. 1Fig. 6. Parameter-sensitivity map series of the Schlumberger null array (No. 20 in Table I).Notations are the same as in Fig. 1Acta Geod. Geoph. Hung. 43, 2008PARAMETER SENSITIVITY MAPS, PART II 445Fig. 7. Parameter-sensitivity map series of the three-electrode null array (No. 21 in Table I).Notations are the same as in Fig. 1Fig. 8. Parameter-sensitivity map series of the unipole-α array (No. 22 in Table I). Notations arethe same as in Fig. 1Acta Geod. Geoph. Hung. 43, 2008446 S SZALAI and L SZARKAFig. 9. Parameter-sensitivity map series of the unipole-β array (No. 23 in Table I). Notations arethe same as in Fig. 1Fig. 10. Parameter-sensitivity map series of the unipole-γ array (No. 24 in Table I). Notationsare the same as in Fig. 1Acta Geod. Geoph. Hung. 43, 2008PARAMETER SENSITIVITY MAPS, PART II 447We are convinced, it is possible to bring together closer these two parametersensitivity approaches, since our method allows computing not only the responsedue to an elementary cube, but also the response due to larger bodies composed ofthe basic element. Such a study can be and should be done in the future.AcknowledgementsHungarian National Scientific Research Fund (projects K49604 and NI 61013); BolyaiJa´nos Research Scholarship of the Hungarian Academy of Sciences (Sa´ndor Szalai); A´kosGyulai and an anonymous referee, for their valuable comments.ReferencesGyulai 1989: Geophysical Transactions, 35, 209–225.Hursa´n G 1996: Magyar Geofizika, 37, No. 2, 106–117 (in Hungarian).Szalai S, Szarka L 2000: Geophysical Prospecting, 48, 871–885.Szalai S, Szarka L 2008: Acta Geod. Geoph. Hung. (present issue)Szalai S, Szarka L, Pra´cser E, Bosch F, Mu¨ller I, Turberg P 2002: Geophysics, 67,1769–1778.Tarkhov A G 1957: Bull. Izv. Akad. Sc. USSR, 8, 11.Acta Geod. Geoph. Hung. 43, 2008

PARAMETER SENSITIVITY MAPS OF SURFACE GEOELECTRIC ARRAYS II. NONLINEAR AND FOCUSSED ARRAYS

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