Statistical and Geostatistical Study of Rn and Hydrocarbon Components Of

2016 | 69/2 | 255–268 | 15 Figs. | 3 Tabs. | www.geologia-croatica Journal of the Croatian Geological Survey and the Croatian Geological Society

Statistical and geostatistical study of Rn and hydrocarbon components of a soil gas monitoring system: an application to surface hydrocarbon exploration Janos Geiger1, Noémi Jakab1, Bálint Csökmei1, Zsolt Horváth2 and Balázs Gellért2

1 University of Szeged, Department of Geology and Paleontology; (corresponding author: [email protected], [email protected], [email protected]) 2 MOL Hungary; ([email protected], [email protected]) doi: 10.4154/gc.2016.20

Abstract Article history: This work addresses three topics: (1) the study of the joint areal distribution of the Rn and hy- Manuscript received October 31, 2015 drocarbon components of soil gases over a large region overlying some known hydrocarbon Revised manuscript accepted April 17, 2016 reservoirs in the southern part of Hungary; (2) the relationships between the positive anomalies Available online June 28, 2016 of Rn and hydrocarbon components of soil gases to the existing reservoirs; (3) suggestions for new targets for surface hydrocarbon exploration based on the results. Given the very low correlation coefficients between the Rn and hydrocarbon components of the soil gases, factor

analysis was used to reveal a background process controlling the common migration of hydrocarbon and Rn components. The lateral distribution of the factor scores were studied using sequential Gaussian distribution. The E-type grid generated from 100 realizations indicated seve ral positive anomalies at the surface. Indications with a larger than 0.7 probability were kept for further analysis. Seismic sections of a 3D survey support the comparison of the surface locations of these anomalies and the surface projections of the known reservoirs. The results proved the connection between the known reservoirs and the Rn and HC components of soil gases. From the positive verification, regions with a high probability positive anomaly of factor scores, Keywords: Rn monitoring, hydrocarbon reservoirs, factor analysis, sequential Gaussian but without any reservoir counterparts may be suggested as targets for further surface hydro- simulation carbon exploration.

1. INTRODUCTION However, most of the existing applications rely only on de Surface geochemical techniques have been used to explore for tecting either direct or indirect indicators. On the ground, not hydrocarbons ever since the late 1920s. These techniques look surprisingly, the geostatistical analysis deals with these sources for the presence and effects of minute levels of hydrocarbons that of information separately. CIOTOLI et al. (2007) studied the spa migrate through the imperfect seals that cover every reservoir tial character of a soil gas monitoring system; OLIVIER & and migrate either as macroseepage via faults or as microseepage KHARYAT (1999), BUTTAFUOCO et al. (2007) dealt with the vertically through the reservoir overburden (COLEMAN et al., geostatistics of Rn-monitoring systems; MALDONATO & 1977, KLUSMAN, 1993, WRIGLEY et al., 2012). Direct and in CAMPBELL (1992) or, recently, CASTILLO et al. (2015) used direct hydrocarbon indicators can be measured using these me geostatistical tools in the spatial analysis of the hydrocarbon com thods. Hydrocarbons measured on the surface are regarded as ponents of soil gases. Only a few papers have dealt with a geosta direct indicators, meanwhile the results of alternations induced tistically supported integrated interpretation of the Rn and hy by presence of hydrocarbons can be considered as indirect indi drocarbon components of soil gases. cators. Soil gases pertain to direct indicators, and radon measure The aims of this study were to (1) determine the common ments, which show anomalously high values at the surface due areal distribution of the Rn and hydrocarbon components of soil to enrichment in uranium induced by the presence of migrating gases in a large region above some known hydrocarbon reservoirs hydrocarbons, belong to indirect indicators. in the southern part of Hungary (Fig.1); (2) relate positive anom Radiometric mapping, as a petroleum exploration tool, began alies of Rn and hydrocarbon components of soil gases to the ex at the end of 1920s (MORSE et al., 1982; MORSE & ZINKE, isting reservoirs, and (3) to suggest new targets for the surface 1995). PIRSON found „halos” of high radiation in a petroleum hydrocarbon exploration on the basis of the results. basin in Texas, noting that each halo countered definable regions of lower gamma flux (PIRSON, 1969). Since then, several papers The studied area is located in the Southwestern part of Hun have reported on successful HC exploration strategies using ra gary, close to the Croatian border. In this region, six known hy diometric mapping. PALACIOS et al. (2013) demonstrated posi drocarbon reservoirs occur, including from North to South: tive radon anomalies around abandoned gas wells, LI et al. (2006), Berzence, Somogyudvarhely, Vízvár-Nord, Vízvár, Heresznye DYCK & JONASSON (2000), GHAGREMANI (1985) used and Görgeteg-Babócsa (Fig. 1). They were developed in the Szol Rn-anomalies as one of the indicators of hydrocarbon leaks from nok, Algyő and Újfalu Formations of the Miocene sequences. The the subsoil. LANDRUM et al. (1989) and PATRICK et al. (2011) studied area was also surveyed by 3D seismic survey, the results highlighted more emissive zones that could be related either to of which were used in the latter part of this paper to compare and main faults or to secondary fractures acting as migration pathways. validate the findings of the geostatistical analyses. Geologia Croatica developed above the HC reservoirs, initialize such geochemicalsuch initialize developed aboveHCreservoirs, the connected to the deep HC reservoirs. Rather, “geochemical cells”, by PIRSON as reported (1969). ahalo as precipitation appears pitate atzoneThis the boundary. preci will zone reducing the into transit to attempting uranium lower itthan would have been with no hydrocarbon present. The becomes concentration uranium the Consequently, stops. ment zone, its this upward into moveenters uranium oxidized When accumulations. (HC) hydrocarbon the overlying zones in ment carbons migrating upward induce a chemically reducing environ lowweightmolecularhydro oftime, passage the with process, bas was theory Their „halo”. radiological the of formation the for of the halo. boundary „halo”, the the form lowwhilewithin exist emissions up to the surface. In their view, relatively high gamma emissions tion fluidsfrom the deep pool, along some hypothetical pathways, geny. They thought that radionuclides were transported by forma carbon pools provided the sources of radionuclides and their pro 1973, SAUNDERS et al., 1993) proposed that deep seated hydro (e.g. authors Somewide.HEEMSTRA, ARMSTRONG& very is reservoirs hydrocarbon above measured signals radiometric to make muchpected more of flux. a to contribution the gamma of that whereas cm, of average the traveldistance environment, physical same the available are under isotopeof each quantities for 55seconds only is it while half their in ( isotopes 226 the subsurface HC basic The geochemical theory 256 Figure 1. Ra. Radon (Rn) can appear in two decay in different (Rn) series:appear Radon can Ra. ed on Laubmeyer’son ed this In migration. gas of concept vertical The The theories say that the radiation anomalies are not directly MORSE & (1995)ZINKE provided an elegant interpretation of geochemicalbackground the that explains literature The (Ra)Although radium in both appears decay series, the two (2) (1) The parent Study area. 238 232 222 U Th Th - Ra and and Ra lives. The half liveof half lives. The ® ® - elements of radon from are supposed to migrate 224 226 - reservoir. Essentially, they are 220 Ra Ra Ra Ra 220 Ra) are not identical: their difference lies Ra)notdifference identical: are their Ra is only 1 cm. That is whyis That cm. 1onlyis Ra ® ® 220 222 Rn Rn 220 Ra (from Ra 222 Ra (from Ra 232 222 Th). When equal equal Th).When Ra is around 100 around is Ra 238 238 U) is 38 days, is U) U, 222 230 Ra is exis Ra Th Th and decay, givecan effective about anomalies. these information formation fluids.Radon, as the most mobile member ofuranium- changes which cause the adsorption of the uranium content of the about anomalies. these uranium of member bile the most mo as Radon, fluids. formation contentonto the nium such geochemical changes which cause the adsorption of the ura Rather, “geo reservoirs. HC deep the to connected directly not are is belowsurface 10 m (VÁRHEGYI et al., 2008). water. There is no chance of underground indication Rn if detecting the water of surface the above down slows processes tion model transport of Rn assume high water The saturation. migra mentation the geochemical cell and the microseepage connected transport model of migration Rn (VÁRHEGYI microseepage et al., 2008). the In this imple and cell geochemical pothesized hyofcombination the shows 2. this Figure of radon. migration ® selective ofadsorption the dissolvedat the uranium redox chemicalcell reservoir HC mechanism: transport simplified lowing lying above the HC the fol layers. only initializes reservoir The radioactive elements is not the HC reservoir, but the rock bodies be formations the from radionuclides carry which accumulations of formation fluidand gas canbe connectedto the subsurface HC agent. water a in microseepage via migrate can which process, this elementof tracing a only is Radon process. long the only that tion of ionic geochemical constituents. It is very important to note the (subsurface) reservoir and the surface. It initializes the migra developsbetween charge electric inverse ofcloud the with cell givenTEDESCOby (1995). Tedesco’s In geochemicalare theory, a measurements radiological surface the and reservoirs face subsur the between relationshipfor the completetheories most non tween tween the and reservoirs the In surface. this case the source of uranium - In In summary, it can be concluded that the radiation anomalies VÁRHEGYI et al. (2008) migrations that vertical supposed the (1982)explained MALMQVIST & KRISTIANSSON diffusive transport diffusive oftransport Rn by carrier chemical cells” developed above the HC reservoirs initialize - radium radium and radium ® change of redox conditions near the surface changeof surface the redox conditionsnear - lived parent elements of Rn take part in this this in part take Rn of elements parent lived - decay, can give effective information information effective give can decay, - radon radon transformation - gas One transport. of the - saturated permeable permeable saturated Geologia Croatica 69/2 Croatica Geologia ® upward ® - fronts fronts geo ® Geologia Croatica

) k j ( in 257 (1) ) geo - is the is − ) k ( spectro Rn Ai s . Note that Note .

= …

( 1,2, , ) ) . Finally, Finally, . th k ( j j J Ra concentration theof Rn concentration. How ) k ( 226 222 sets with homogeneous soil soil homogeneous with sets s − ), UeRn (uranium equivalent equivalent (uranium UeRn ), 3 ) = … is the average, and average, the is K k ) j ( = … . . Then everages and variances k ( ( 1,2 , group Rn Mean , 1,2, , th k k k K S k K Ra difference is positive, otherwise it it otherwise positive, is difference Ra ) Mean k j ( , , ) = … − = , 1,2, , k Rn Ai S k K = … is the Rn content of the sample, sample, the of Rncontent the is can have positive and negative values. negative and positive canhave j k ( 1,2 , ) k j ( th variability was of primary variabilityof was importance. - Rn k k K The uranium equivalent of the measured Rn concentration in grouped were samples The − Rn concentration. When the migration adds Rn to the “regu Rn Ai 3. FIELD DATA COLLECTION ANDITS COLLECTION DATA FIELD 3. DESCRIPTIVESTATISTICS (pro C3 The geochemistry suggested that the(ethane), only C2 pane), nC4 (normal butane) and nC5 (normal pentane) compo worthin statisticalthekeeping gases were HC the of nents statistical modeling, since they could be expected to be deepof contrast,In ppb. in expressed were components these Allorigin. mo radiological the in calculated or measuredparameters the all Rn follows: as were They analyses. the in involved were nitoring kBq/m in gas, soil of content (radon (UeRn) was defined as the concentration of the parent element of element parent the of concentration the as defined was (UeRn) Rn in the soil. It was directly measured using gamma- metry. Under general conditions, the “standardized” asa determined was sample each value: for where group in content Rn the of variance soil soil environment is the origin the of “regular”this decrease or increase can processes migration ever, 222 Rnthis- concentration, lar” geochemistry soil characteristicsof local The negative. or zero is concen Rn the affect significantly can properties physical its and tration. The effects theseof features on the local Rn concentra tion larger can be thanmuch even the those migrationof proce sses. That is why correction of the measured concentrations to soil the characteristics, set, each for calculated were method - corrected -

Ra), and the so called soil called so andthe Ra), Rn concentration of soil gas soil of concentration Rn 222 Rn concentration. They were the uraniumthe Rnwere Theyconcentration. Rn concentration (UeRn), the difference bedifferencethe (UeRn), Rnconcentration Ra(Rn - 222 222 226 Ai) content. Ai) Rnand A geochemical model of the radiation anomaly above hydrocarbon reservoirs VÁRHEGYI et al., 2008. al., et VÁRHEGYI reservoirs hydrocarbon above anomaly radiation the of model geochemical A 222 The critical point in the applicability of the research the of applicability the in point critical The chromatographic measurement. The headspace the of glass - Rn(Rn - tween 222 toring locations, three other properties were measured and cal the besides culated the of equivalent The samples were taken in a regular surface grid where the nodes nodes the where grid surface regular a in taken were samples The were 250 m apart. The change of background Ra radiation was moni the In process. registrations basic called so the by followed geostatisticalanalysis. the of Analysis 2.2. how the concentrations of hydrocarbon components decreased in decreased components hydrocarbon of concentrations the how labo the in analyzed were samples soil “artificial” “natural”and the measured only (HC), From hydrocarbon components ratory. C2, C3, nC4 and nC5 are in involved the further statistical and C1, C2, C1, C3, nC4, iC4, nC5 and iC5 (methane, ethane, propane, normal butane and isobutane, normal pentane and isopentane) were measured. assessTo the reliability of the measurements, container was sampled by syringe through the membrane and the and membrane the throughsyringe by sampled was container gas-chromatograph a into injected was syringethe in sample gas thiswith anWith apparatus,FID detector. hydrocarbons simple container of 20 ml volume, and sealed by a rubber membrane. This minutes20 glassware prior for towas °C then heated 85 at gas During the radon-monitoring field measurements, a specified mass g on (12 of soil average) was taken for the headspace gas glass a into placed were samples The analysis. gas soil of method 2. SOIL GAS AND RADIOLOGICALAND 2.SOILGAS MEASUREMENTS measurements gas Soil 2.1. based on radon detection is the differentiation of the deep origindeep the of differentiation the is detection radon on based de have (2008) al. et VÁRHEGYI radiation. background the and measuring for method a this. veloped Figure 2. 2. Figure Geiger et al.: Statistical Geigeral.: geostatisticalet and hydrocarbonand Rn of monitoringstudycomponents gas soil... a system of Geologia Croatica KHARYAT, 1999). Point (3) suggested the use of a stochastic & stochastic a of use OLIVIER the 1976; (3)suggested KHARYAT,1999). Point al., et (JÖRESKOG components Rn and tool could be expected to reveal the connections between the HC data. the measured in pected ex be could uncertainty (3) high analysis; quite the in targeted their pairwise relations, the pattern of their inter HC and of components; Rn (2) of forcing instead analysis the of consequences: (1) it was not possible to make a direct comparison important (among fact others)three This had periods. sampling types, and the temperature and humidity differences between the of heterogeneouswere consequences soil the results very These Table 2. 0.04. best, at were, components HC and Rn the between tions cant, but the coefficientsdeterministic ( carbon components in Table 2 (coloured light grey) were signifi situ” “in generated (Table 1). those to added were content Rn migrated the where sites pling - Rn of the maximum migrated into the However,surroundings. the high positive value indicating that there were sampling locations from where the Rn Table 1. beforefunction calculation of Table in the statistics 1. log10a by transformed were values original their distributions, Since the hydrocarbon components had very skewed probability Tablecharacteristics. analyses. statistical 1. general shows their (Fig. geomathematical of1). the measured target the were They there were only 538 in which all could the parameters have been However, them among analyzed. were altogether 2441samples by dimensionless). the soil corrected environments, kBq/m in components, Ra and Rn ppm), in content, Rn the of 258 Log(nC5) (ppb) Log(nC4) (ppb) Log(C3) (ppb) Log(C2) (ppb) Rn-Ai (dimensionless) Rn-Ra (kBq/m Rn (kBq/m Variables Log(nC5) Log(nC4) Log(C3) Log(C2) Rn-Ai Rn-Ra Rn Variables In the sampling process of soil gas and radon and gas soil of process sampling the In Point (2) meant that a factor analysis as a data integration integration data a as analysis factor a that (2)meant Point hydro and radon the between coefficients correlation The The minimum value of Rn Descriptive statistics of the variables analyzed. Correlation coefficients between the variables. 3 ) 3 ) 1.00 Rn Valid N 538 538 538 538 538 538 538 Rn-Ra 1.00 0.77 Ra property indicated that there werethere that indicated sam property Ra Mean 35.39 –0.21 –0.88 0.07 0.26 0.90 0.02 Rn-Ai 1.00 0.73 0.78 Correlations (N=538) - 3 Ra, Ra, in Table 1, has a negative sign - Rn ), and - Median Ra (the difference between Rn Rn between difference (the Ra 30.38 –0.15 –0.24 –5.34 0.24 0.90 0.11 Log(C2) –0.02 –0.01 –0.17 1.00 r Minimum 2 –81.76 ) of the highest correla –0.95 –1.04 –0.74 –0.67 –3.86 Ai (Rn measurements measurements (Rn Ai Log(C3) 1.00 –0.06 –0.03 –0.12 1.00 0.75 - Maximum correlations was 145.30 176.50 Log(nC4) 1.98 2.78 2.56 2.68 2.89 1.00 0.63 0.47 0.01 0.04 0.02 monitoring, -monitoring, Deviation Standard Log(nC5) –0.01 23.13 24.95 1.00 0.49 0.55 0.46 0.05 0.02 0.37 0.31 0.35 0.41 1.00 The main applications of factor analytical techniques are to re to are techniques analytical factor ofapplications main The Factor analyses are very effective tools of linear data integration. 3.2. Factor analysis at depth. components could suggest HC structures co the where regions those of bility probathe indicate study. to to (3) was goal final important The pling, the of spatial uncertainty the geostatistical model was also sam scattered the of (2)Because tools. geostatistical by lyzed ana and variables spatial continuous as regarded be could they gases, hydrocarbon and Rn of migration joint the in processes HC Rn the affecting processes background the of marizations principles. (1) three weresum compact as regarded factors The revealed spatial connections their (Fig. 3). and integrated are data seismic surface fieldwhichand in steps workflowThe analysis and ofgeostatistical shows statistical the modeling 3.1. Methods used in the statistical and geostatistical geneities (MUCSI et al., 2013). whiletistical characteristics emphasizing the small scale hetero ap proach does giveThis the best estimation, but tends to distribution. honour the sta spatial the of analysis the in simulation Figure 3. (EFA) we tried to uncover complex by patterns exploring the da Factor Analysis Exploratory called so this In method. detection lity. Here, we used this technique in the latter sense, as a structure dimensiona data reduce to is, that variables, between tionships rela the in structure detect to of and variablesnumber the duce - components. Because factors represented continuous spatial The statistical and geostatistical analyses were based on on based were analyses geostatistical and statistical The Workflow of analysis strategy. - variability of Rn of variability Geologia Croatica 69/2 Croatica Geologia - and HC and - and and Geologia Croatica is 259 (4) (3) h , which is )

h 2 (    g

) ≥ i ( − + ) i i negativity of negativity the of variance of 0 ( ) z u z u h   ( ) i 1 ( = . i ∑ N h i ) ) 0 ( L = i ( i ∑ 1 g h N h = 2 ) h b g h with b = ( ) g h (  is the number of data pairs for a given distance. given data a pairs numbertheof for is g ) required by prediction algorithms and also to smooth smooth to also andalgorithms prediction requiredby ( is the sill positive or slope of the corresponding basic h i N h b ed in terms of the dissimilarity (instead of similarity) be Typically, two or more permissible models must be combined combined be must models permissible more or two Typically, The variogram map (sometimes called variogram surface) The way in which the permissible models are chosen and The main purpose of the variogram calculation is partly to the amount of the effect of the actual factor exercised in each ob each in exercised actualfactor the of effect the of amount the scores factor of distribution areal the Consequently, (sample). ject could be expected to show the arealhydrocarbon variabilitythe and Rn of the of ‘hidden’ migration joint the controlling process gases. soil of components tools Geostatistical 3.3. Variography 3.3.1. In the geostatistical literature, spatial patterns are usually scribde separationdistance.Thethe function a of observationsastween average dissimilarity between data separated by a vector experimental and fitted themodel. However, toolof variogram map can also be thisfor applied purpose. By comparison the of variogram of that and dataoriginal from coming variogram map evaluated. be can variogrammodels the of goodness the models, declustering Cell 3.3.2. random regularnor neither show studythis in points sample The spatial distribution over the region This(Fig. 1). kind of ‘sam pling’ is said to be preferential. This situation means that available samples are the quite far from statistical representativity. neither the summaryConsequently, statistics the of data set nor out sample fluctuations. sample out The difficulty is conditionally that only definite negative functionscan be considered assemivariogram models, in order to ensure the - non toknown are models few a only practice,In error. prediction the DEUTSCH JOURNEL,1998, & DEUTSCH (e.g. permissible be 1997). GOOVAERTS, or 2002 Combinations semivariogram. experimental the of shape the fit to contribution the as long as permissible are models permissible of each of that basic is model positive, is the nested is model writ tenas: where semivariogram model direc of number variogram a thein calculating of idea thetakes map, a on values variogram the posting by created be can It tions. where the center of the2002). DEUTSCH, or 1989 map is the ISAAKSSRIVASTAVA, & lag distance of zero (e.g. their parameters (range, sill) are estimated is still controversial (MCBRATNEY & WEBSTER, 1986; GOOVAERTS, 1997). There are several ways to check the goodness-of-fitof the per missible model. It can be done per or view, using some criteria based on minimizing the least square differences between the measured by the experimental semivariogram the squared of as differencecomputed half the average between every data pair: of components the where analyze the and directionalpartly heterogeneity, to transfer this information to krigingexperimen the of or simulationvalues the procedures. to fitted be Therefore, must function a continuous pos any for values semivariogram deduce to as so variograms tal lag sible - ) m of of (2) is the … j , 1985). , e = , , , 2 1 2 FFF 0.7 0.49) MCDONALD

1) to 1. Loadings to close 1. 1) ( - p , that will account for the cor the willthatfor account , … p , the squared factor loading is the the is loading factor squared the , r 1 = m , , , i ∑ 1 2 XXX = ⋅ + are the factor loadings, and common ‘latent’ common factors ‘latent’ ( j ji i j

) X a F e m = … ( 2, 1, , ji a i m Here the main goal was to reveal such a factor in which both which in factor a such reveal to was goal main the Here One of the most ways to convenient interpret the results of Generally, a factor analysis decomposes the modified corremodified the decomposes analysis factor a Generally, The model assumes that each observed variable is a linear 1) or 1 indicate that the factor strongly affects the variable. In variable. the affects strongly factor the that indicate 1 or 1) - off for the definition of a high factor score was 0.5. For each sam each For 0.5. was score factor high a of definition the for off represent scores Factor calculated. also were scores factor the ple values of values the of extracted factors were larger thanThe rationale 1. should factor defined the of variance the that was criterion this of cut The standardized each variable. of that as large as least at be realized. In this algorithm the communality was approached by the multiple correlation coefficients, andwe used the centroid to method extract(THURSTONE, the 1931) factors. The eigen the Rn and all the hydrocarbon components appear with high positive factor loadings. After several trials a special factoring been have requirements these which in discovered was algorithm factor space are called factor scores. Computing factor scores fa scores factor Computing scores. factor called are space factor be may scores factor Also, outliers. factor for search the cilitates modeling. in usedsubsequent asvariables Factor analysis can also be viewed as a transformation of thebyoriginal originalthe into space an sample (defined variables) orthogonal space definedby factors. the coordinatesThe of this ever, some researchers, particularly for exploratory purposes, use purposes, exploratory for particularly researchers, some ever, other the central for for factor and 0.25 as 0.4 such level lower a factors. In any event, factor loadings must be interpreted in the 2002). arbitrary (STEVENS, by not theory, levels cutoff of light loadings should be 0.7 or higher. The rationale of this statement is is statement this of rationale The higher. or 0.7 be should loadings corresponds level to one halfabout that ( the 0.7 How factor. the by explained being indicator the variancein the to ( to is decision important first the loadings factor of interpretation the that saying thumb of rule a is There loadings. high the identify to factors. They represent to what extent a variable is explained by a by explained is variable a extent what to represent They factors. Pearson’s to Analogous factor. explained variable variance in particularthe indicator of percent Loadings by the can factor. range from ( factor analysis is the interpretation of factor loadings. The factor The loadings. factor interpretationof the is analysis factor and variables the between coefficients correlation the are loadings munalities are smaller Inthan this1). way factor analysis gives enough room to take measurement error and measuring uncer tainty intoconsideration. may also have error also have may variance. The estimated proportionvari of error of free be to assumed is (communality) variable the of ance the is matrix.It the in variables other with shared is and variance in variable variance common a with all others (com of together ments (they equal to 1) of the correlation matrix of are replaced equalby to 1) (they ments the prior communality estimates. It means that this technique it since variable each variance of whole the decompose not does specific or factor. or specific unique matrix.lation The is modification original that the ele diagonal where function these of factors together with a residual variance. This intends reproducemaximumtheto model correlations. to be discovered in to the be discovered dataset, to is find and the small goal the factors,common of number est variables, the of relations taset and is testingused when 2006). predictions EFA (CHILD, variables influencing factors of number the of discover to is aim hypothesis the basic A together’. ‘go variables which analyze to and is that thereEFA are Geiger et al.: Statistical Geigeral.: geostatisticalet and hydrocarbonand Rn of monitoringstudycomponents gas soil... a system of Geologia Croatica tual fraction of true values falling within symmetric probability symmetric values within of falling fraction true tual and precision viewhis In accuracy were onbased the ac terms. ment (significant figures) of a measurement or computedresult. refinePrecisionorrepeatability therefers standard. tothe to or excellence of the data or computed results, e.g. conformity ultimate therefers toprecision.to general,andaccuracy In curacy truth The goodness of a probabilistic model may be checked by its ac 3.3.4. Goodness of the probabilistic model (simulation) the original tify back are scores normal simulated the and space normal the in performed then is simulation The of the involves transform prior a drawing process. Sequential Gaussian simulation (sGs) typically Other realizations are obtained by repeating the entire sequential locations. visited previously at simulated values all to also but del, each ccdf is made conditional not only to the original the of reproduction To sequence.ensure then sampling it at each of the nodesgrid visited along a random (ccdf): mulative function distribution 1988; cu conditional ALABERT the modeling to 1990;MALVIC, amount 2008) & GÓMEZ 1990; (JOURNEL ISAAKS, simulations Sequential nodes grid 3.3.3. Sequential Gaussian Simulation the declusteredinverse in mean situation (DEUTSCH, 1989). high in clustered are data when chosen be should mean declustered lowest the with size cell versus mean size for a range of cell sizes. From plot this the declustered the by plotting recognized be can sample points the case itlatter is clustered other with locations. the In weighted. under being is location corresponding the that ple space is being over weighted, and a weight less 1 than shows isolatedlocations. 1 impliessam the A that weight than greater each cell. in Hence, to weights data these give more importance each cell within falling number the and datum one least at contain that cells over system the we method. study the latter used DEUTSCH, 1989; GOOVAERTS, 1997; cell GEIGER, 2012). called In this & so the (ISAAKS method polygonal SRIVASTAVA, the 1989; solutions: GOOVAERTS, 1997; used GEIGER, 2012) and monly data for amounts situation rangements needed the application of stochastic simulations, the of interest (DEUTSCH, 2002). Since the “very the sample distribution being representative of the entire volume the process. These methods rely on the assumption “intrinsic” of in fail algorithms simulation default, by clustering preferential representative for volume the entire of interest. be may attributes measured the of histograms the of shape the 260 The cell-declustering approach calls for definition of a grid grid for calls definition approacha of cell-declustering The Although most contouring or mapping algorithms adjust this DEUTSCH (1997) proposed specific definitions for these these for definitions specific proposed (1997) DEUTSCH at z attribute continuous the of simulation the Consider fordeclustering size cell “best” the implementations the In of number the to proportional inversely are weights These rbZuznu n z u Z Prob u n z u F u i , ( conditional to the data set data the to conditional i i , A | ; z area of interest and counting the number number the counting of and area interest - - n j w histogram. elseig prah JUNL 1983; (JOURNEL, approach declustering ( j = = b ) ) n B . Then .the weights Then as: defined are = - 1 ⋅ - valued areas or the size with largest largest with size the or areas valued - “declustering”. There are two com two are There “declustering”. ENNE & SRIVASTAVA, & HERNÁNDEZ b ,,, 1,2, , z - { transformed in order to iden to order in transformed - data into normal score data. data. score normal into data ( i ,  ) ≤ z { - n i u z semivariogram mo semivariogram ( |

- i ( leaky” leaky” spatial ar ) ,2 , 1, 2, , i ) } … = , n b of data data of n n i u z data data ( B (5) (6) of i N } ) . 1 , , 1, 2, ,

… = probabilityupper values: The symmetric transformation. and variance mean, Gaussian the by defined or kriging dicator may be derived from a set of where (ccdf): conditional function cumulative distribution the for model a provide realizations These location. data each to bution is bymeasured the closeness of the offraction values true for all exceeds interval p the in falling values true of fraction the if intervals of varying with tions can be used for three main purposes: (1) purposes: im main the assessing for three used be can tions 1998). 1994;SRIVASTAVA,FORD, JOURNEL, & 1996;DEUTSCH RUTHER (GOTWAY & requirements computer the and for, metric), the amount and type of information that can be nonpara or(multiGaussianaccounted model function random underlying plished using a growing variety of techniques, which differ in the if seen only on a few simulated maps. Simulation can be accom of the simulated maps. Conversely, a feature is deemed uncertain on most seen if certain deemed are Spatial features uncertainty. spatial of model) a (actually measure quantitative and visual a the conditioning data. The set of alternative realizations provides reasonably match the same sample statistics and exactly identify all map.multiplethat generate mated Also, one can realizations esti smooth a than “realistic” more looks realization or model the hence data, the from inferred scattergram) semivariogram, (histogram, statistics of reproduction the allows it that is ging) (kri interpolation over simulation stochastic of advantage The 3.3.5. Analyses of uncertainty plot (DEUTSCH, 1997). accuracy an as to referred is plot This line. 45° the on or racy is to plot when accurate is ccdfs the generate to used algorithm tion symmetric is the proportion of locations where the true value falls within the x u i ( as: p p p p for all ) Next, anfunction indicatordefine Consider a range of symmetric values true the with associated probabilities The to leads simulation Stochastic According to SRIVASTAVA to According realiza (1996), geostatistical simula the accuracy, of definition earlier the to According averageThe of ∀ ≥ u n p ( in [0,1].in The precision of probability distri an accurate are calculated from the previous ccdf as x , i ( ) rbZuznu n z u Z Prob u n z u F p u PI p p is the set of n data at location i in in − . A grapcal way to check the assessment of accu of assessment the check to way grapcal A . ; ( x ( i i PI p [ ) | ; p 0,1 n p and p − = . ) low versus p and to see if all of points fall above      x ] ( , ;| ; 1, x x , 0, . ( = p u is defined bythe corresponding lowerand ( ) 1 i p u p fFuznupp p u n z u F if ; ) otherwise p − ) 2 = . A probability distribution is accurate = ) p over the n location L (

1 n ∑ realizations, calculated realizations, from in o up low i i i = n 1 { p ( upp L ( ( - i stochastic realizations at at realizations stochastic probability intervals ( ; = x i ) ) ) ( 1 ) p u ≤ u ∈ +

i 2 i ; . These local models ( Geologia Croatica 69/2 Croatica Geologia p | )

( at each location , u i u n z u F ) i } ( :

) i i . . | ; n i u z ( i ( PI (10) ) (8). 1 , , 1, 2, , (7) (9) ) s). ) p … =

Geologia Croatica 261 0.341410 0.540717 0.652462 0.420220 0.389047 FACTOR 2 FACTOR –0.736023 –0.623170 –0.643253 Unrotated Factor Loadings Factor Unrotated 0.536540 0.570151 0.571089 0.526628 0.659843 0.545612 0.501242 0.314396 FACTOR 1 FACTOR Extraction: Principal factors (Centroid) factors Principal Extraction: The five traces of seismic sections. seismic of traces five The The result of factor analysis (high factor loadings are colored by light grey). light by colored are loadings factor (high analysis factor of result The The firstfactor correlated positively all theother variables vironment: humidity, soil type, season of measurements, etc. Rn Rn-Ra Rn-Ai Log(C2) Log(C3) Log(nC4) Log(nC5) Variance Total of Proportion Variables appearing in the probability map coincided with the subsurface pathway potential a be could system fault a such that or reservoirs the for common geochemical migration hydrocarbon of and pa Rn. of elements rent 4.RESULTS the meeting factors two only showed analysis factor of result The (un two The 1). than larger be eigenvalue the (let criterioninitial vari total the of 65% described 3. Table in shown factors rotated) variance: total the of proportions equal almost defined They ance. respectively. 34.1% and 31.5% complex a reflected it supposed we Therefore 1). Factor 3, (Table process increasing both the HC and the Rn components of soil gases. Consequently this factor was called a “Factor of migra con low Its looking were was for. we which what exactly tion”, de high the by explained be variancetotalcould the tributionto pendence of Rn components en on the very variable physicalOn the basis of the applied geochemical model this factor was surrounding regions, expectedoutline to surfacethe projections 3. Table Figure 4. 4. Figure lines three transects were created fromThese transects were compared with thethe corresponding seismic probability map. sections. This facilitated the checkingwhether the of structures

) . s ) ) (11) (12) + , two two , ( − cut off with each each with mean ; |

( i i ) i off. ( - score F u z n u off, we calculated calculated we off, - off in each grid node node grid each in off - = …

, 2, 1, , )

i i u i N ( 2 s 1 = N i ∑ off of these high factor scores were were scores factor high these of off ≤ - 1 N − = cut off U u was the standard deviation. The latter pro s locations of interest interest of locations ( Carlo risk analysis. The concept of space of calculated from the local ccdf from calculated local the - ) N i u ( Prob score Scores of Factor 2 s For the definition of cut-off of “high” scores, scores, “high” of cut-off of definition the For There is currently no theory that allows us to determineto uscurrently There theoryis no allows thatthe The uncertainty can be quantifiedby measures such as en have beenhave identified. Threesections were cut from3D theseis thesepoly Along 4. data mic Their set. traces in Fig. are shown seismic data sets, analysis of average amplitude and the interprethe and amplitude average of analysis sets, data seismic tation of some seismic attributes occurred.have As a result, all the known subsurface reservoirs and the most important faults expected to show the surface projections of the subsurface.the surfacethe of projections expected show to seismic 3D and results geostatistical Comparing 3.3.7. The 3D seismic covers almost the whole sampling area. In the In values. simulated 100 the from node grid each in probabilities were probabilities high by outlined regions map, probability this gave a larger number of regions on the map to be compared with compared be to map the on regions of number larger a gave cut proper the choosing After data. seismic the the approach, where vides an inflection pointof thenormal distribution.From these definitions two latter the was used in furthersince this analysis, approaches approaches were considered. The firstwas the box andwhisker the being second the 1977), (TUKEY, technique plot nodes. This thought needed two practical steps: (1) finding a cut- a finding (1) steps: practical two needed thought This nodes. describingmigration the factor the of scores “high” define to off this contouringcut of probability the (2) process; tion tion process interestof could be made in probable the region of cut the If scores. factor “high” cut this to belonging probability the known, grid in process migration the of possibility the characterize would large large enough number of realizations. The 100 equally probable values simulated in grid nodes provided the possibilitymigra the of thisthat said model geochemical accepted The derivation. lity distributions (ccdf) at each grid node via the calculation of stochastic realizations. Hence, calculation of any probability in quite straightforward is (7) grid have theat sense of we if nodes variance maps Probability 3.3.6. probabi cumulative conditional of generation the in results SGS are there where measure of spread. The uncertainty of a probabilistic model was model uncertaintyprobabilistic Thespread. a measureof of the in locations all of variance conditional average the as defined interest: areaof tropy, interquartile range, or variance. In this paper, the variance the paper, this In variance. or interquartile range, tropy, acceptancea as wide and simplicity its of becausepreferred was set of all possible outcomes if allset fairly sampled. of Thepossible characteriza tion of the space of uncertainty is rendered difficultby thefact realizations limited usuallya thatis only generated. numberof certainty could only be defined through the algorithm and con sists of all possible realizations that could be generated by the algorithm. 1994; SRIVASTAVA, 1994). Some authors believed that the space space the that believed authors Some 1994). SRIVASTAVA, 1994; of uncertainty must have been theoretically definedoutside the particular a useof algorithm. Others un stated that spacetheof pact of uncertainty; (2) reproducing the spatial variation; (3) per (3) variation; spatial the reproducing uncertainty; (2) of pact forming Monte uncertainty, and the associatedrealiequiprobability issue of of zation were discussed in detail in the 1990s (e.g. JOURNEL, Geiger et al.: Statistical Geigeral.: geostatisticalet and hydrocarbonand Rn of monitoringstudycomponents gas soil... a system of Geologia Croatica 262 scores of declustered normal Factor (B), 1 scores scores 1 (C). Factor clustered scores (A), frequency distribution of de Figure5. variogram model of (C). the of map Variogram (B), 1 Factor of Variogram models of the normal scores the normal scores of Factor 1 scores (A), 6. Figure Lateraldistribution of Factor 1 Empirical variogram map of map variogram Empirical Geologia Croatica 69/2 Croatica Geologia - Geologia Croatica 263 type estimation for Factor 1, was calcu was 1, Factor typefor estimation - ) ( average average of the Factor 1 scores and their variance - Accuracy plot of the simulation. the of plot Accuracy Figure 8. shows both the original and simulated Factor 1 E the nodes, gridIn The grid These laterally continuous regions of high Factor 1 scores curate, but not exact (Fig. 7). 7). (Fig. exact not curate, but al not did scores 1 theFactor Thescores. spatial dependence of could we examination visual By test. statistical any of use the low data input minimumthe decreasedthe simulation of the that say simula the acceptancethe affect of not this did Fortunately, set. tion, since lookingwere the we andthe for high for not positive scores. factor negative low fromlated backtransformedthe 9). normal (Fig. scores scores de were The ‘high’ respectively. and –0.072 were 0.192, variance. plus value expected the than larger being those as fined Box- the of than that set larger a produced thisdefinition fact,In Consequently it resulted in10). (Fig. plot higher possibilities in scores. 1 areathelateral the withoutlininghighFactor of lookingfor. were we targets the which were Figure 7. 7. Figure the checked simulation results by the accuracy 7) and (Fig. plot simulated and original of distributions the of comparison visual a simulation the of plot accuracy the in points Since 8). (Fig. scores ac was simulation the of result the line, 45° the above lie results + ⋅ ) (13) (

) ( + ⋅ ) ( Exp h Gauss h Gauss h + ⋅ ) ( 0.63 0.26 .2000 0.14 .1400 0.03 .2400 Comparisons of original (A) and simulated (B) Factor 1 scores. 1 Factor (B) simulated and (A) original of Comparisons = + ⋅

transformed to the original 1 We score. the of Factor scale ) - Using Using the variogram model and declustering weights, 200 In this model, the short small scale heterogeneity had 1400 m 1400 had heterogeneity scale small short the model, this In Variogram maps calculated from the models honoured the The variogram maps calculated the for normal score trans The lateral distribution of Factor 1 scores appeared with high high with appeared scores 1 Factor of distribution lateral The The second factor showed a high positive correlation with all with correlation positive high a showed factor second The h

( g Figure 8. 8. Figure equally probable stochastic realizations were generated by se were scores normal simulated The simulation. Gaussian quential back geneity. However, the comparison However, of model and empiricalgeneity. vari range the beyond was information of loss this that proved ograms C). A, 6 (Fig. main anisotropic-characters of Factor 1 (Fig. 6, C). It can also be also can It C). 6, (Fig. 1 Factor anisotropic-charactersmain of hetero initial the of whole the cover not did models the that seen rogeneity. The nugget effect was very large (0.63 in (13)) expressing expressing (13)) in (0.63 large very was effect nugget The rogeneity. characte be cannotvariability spatial total the of 60% about that rizedlinear any geostatisticalby model. where the directions and the anisotropy ratios were 118°, 40°, 35°, 35°, 40°, 118°, were ratios anisotropy the and directions the where respectively. 50, and 40 0.76, and hete scale large the to belonged range of m 2400 while range, of

by the variogram map was modeled by a nested theoretical vario theoretical nested a by modeled was map variogram the by grammodel: formations of the Factor 1 scores showed a definite NE-SW con definite NE-SW a showed scores 1 Factor the of formations tinuity direction The 6 (Fig. A). empirical continuity expressed tistics of the frequency distribution. The frequency distribution pos high the toward skewed is data declustered the from derived origi of transformation score normal The B). 5, (Fig. figures itive C. 5, in Fig. shown is scores 1 Factor declustered nal positive values in the southern part of the studied area (Fig. 5, A). A). 5, (Fig. area studied the of partsouthern the in values positive requiredcell a locations sample the appearance clustered Theof sta descriptive representative more get to approach declustering ble 3, lowermost row) and is why Factor 2 was ignored at the next next the at ignored was 2 Factor why is and row) lowermost 3, ble modelling. of stage nents, which was low: inconsistentvery was factor withthis of the content assumed information the geochemicalEven process. (Ta itself by variability total the of 3% only explain to able was it of the of existing subsurface radon reservoirsanomaly” (“Positive 2). inFig. compo hydrocarbon with correlations negative Rnhigh theand Geiger et al.: Statistical Geigeral.: geostatisticalet and hydrocarbonand Rn of monitoringstudycomponents gas soil... a system of

+ ⋅ )

( Exp h Gauss h Gauss h 0.63 0.26 .2000 0.14 .1400 0.03 .2400 = + ⋅ ) h ( g Geologia Croatica standard deviation of the distribution. plot and ( Figure 10. Figure 9. est uncertainty coincided with a subregion of high Factor 1 scores. in surface Fig. 11B). This processing clearly shows that the high ofconditional(contourcontoursthe variance above3Dmap the ofE mapthestack very definite subregionwith high uncertainty. Fig. 11B showsthe a wastherelowwasmost of area, in the generaluncertainty the mation was derived (Fig. 11, A). This map E whichsuggestedthe modelstochasticfrom theof that uncertainty although 264 The map of conditional variance was used to characterize the e E-type estimation of Factor 1 scores from 200 stochastic realizations. + Comparison of the sets of “high Factor 1 scores defined by the Box- s ) techniques. - type estimation(3DFig. in type surface 11B) and e is the expected value of the distribution; - type esti type s is the The subsurface counterparts ofThe subsurface counterparts Vízvár lies. The probability of their appearance wasscores: more Somogyudvarhely, than 0.7 Vízvár (Fig. below accumulation carbon anomaly the (Fig.Berzence 14). vár hydrocarbon field, butthere was noknown equivalent hydro them Somogyudvarhely and Heresznye developed above the 14). Víz(Fig.Among anomalies Heresznye and Somogyudvarhely Berzence, the SE, to 0.7 NW than probability. from were, They anomalies of Factorcharacteristic with more 1 scores appearing Field.North anomaly to corresponding the locationsubsurface of the Vízvár tion of the Vízvár Field. The northern anomaly was a typical halo more 0.7than probability and matched with the posi subsurface (Heresznye scores 1 Factor of anomaly southern The transect. probability the in identified The lateral extension of Vízvár and Vízvár-North fieldscould be Figure 12, II demonstrates the seismic section along this transect. (Fig.13,I). scores 1Factor high of geometry halo typical most the surface projections of the seismic sections (Fig. 12,voirs. B,C Three transects andwere D).cut out from the probability grid along Thesewere expected toreflect the subsurface hydrocarbon reser nuous subregions of high probabilities could be easily recognized. ticrealizations (Fig. 12, A). thisOnmap, atleast sixlarger conti high scores, 0.120 (mean+variance) was derived from the stochas whereFactor 1scores were larger than the lower boundary of the The third transect also crossed three spots of high Factor1 ofhigh spots three crossed also transect third The The second (III to transect IV in Fig. 12) went three through al in Fig. an 13)(I-II identified we transect first the Along locations of probability the showing map probability The - anomaly in Fig. 13) appeared with with 13)Fig.appeared in anomaly - North and the Komlósd anoma - North North and Komlósd were Geologia Croatica 69/2 Croatica Geologia

15). - - Geologia Croatica 265 The basis of the factor analysis approach was the lack of any of lack the was approach analysis factor the of basis The process, consequently we had to use probabilistic approaches. probabilistic haduseto we process,consequently strong correlation between the andHC Rn components. In fact, the application of factor analysis did not follow the traditional factors few used are firstinterpretation.in the the inwhich way, In this study we searched for “the” factor correlating with both the Rn and CH components. In this strategy accept,we that the by affected be could gases soil propertiesof HC and radiological phenom targeted the admittedthat also was It processes. several Rn gases) migration and of HC the joint expressing (factor enon The choice of stochastic simulation was supported was stochastic simulation facts: two of by Thechoice analy gas HC the of results ‘uncertain’ some out filtering after (1) ses, the remaining a verysamples showed scattered pattern; (2) direct not the factor scores were measurements the migration of 1 > 0.120). A: probability contours with the surface projections of seismic sections (I to VI). B, C and and C B, VI). to (I sections seismic of projections surface the with contours probability A: 0.120). > 1 Factor Factor ( Prob Babócsa Fields. The Miocene - North and Görgeteg - A: The uncertainty of the stochastic model by which the E-type estimation was derived (A); B: Stacked map of the E-type estimation (3D surface) and and surface) (3D estimation E-type the of map Stacked B: (A); derived was estimation E-type the which by model stochastic the of uncertainty The A: Map showing the lateral distribution of of distribution lateral the showing Map Secondly, that the regional appearance of this migration process could be analysed by the tools of stochastic simulations. simulations. stochastic of tools the by analysed be could process in the factor matrix of the studied components. The consequence The components. studied the matrixof factor the in thisof hypothesis was that the strength thisof process could be characterizedthis factor. of scores the by HC HC components of soil gas samples was based on two expecta migrationcommon the controlling process the that Firstly, tions. of these components could be recognized by a particular factor 5. DISCUSSIONANDCONCLUSION 5. and Rn the of analysis geostatistical and statistical presented The the Vízvár fault appearing below the Somogyudvarhely anomaly was re this anomaly. background of genetic gardedthe asbeing Figure 12. 12. Figure sections. seismic the of polygons surface the along created transects the are D the conditional variance (contour map above the 3D surface). 3D the above map (contour variance conditional the Figure 11. 11. Figure Geiger et al.: Statistical Geigeral.: geostatisticalet and hydrocarbonand Rn of monitoringstudycomponents gas soil... a system of Geologia Croatica Figure 14. Figure 13. 266 Correlation of the probability map of high Factor 1 scores and the subsurface hydrocarbon fields along the second transect. Correlation of the probability map of high Factor 1 scores and the subsurface hydrocarbon fields along the first transect. Geologia Croatica 69/2 Croatica Geologia Geologia Croatica 267 type grid - type estimation - type estimation of Factor 1 scores could could scores 1 Factor of estimation type - These results suggested that the research achieved its origi Theseits results suggested that researchthe achieved The probability maps showed the possibility of locating such such locating of possibility the showed maps probability The voirs on the map of the E the of map the on voirs be outlined with a significantlysmaller uncertaintyFig. 9, (Fig. 15). Fig. and 11 nal purpose: the connection between the known reservoirs and the in proven been have gases soil of components HC and Rn the studied area. This com verificationRn the only not seemsused it to literature,since berelevant the more of precise those than ponents alone, but also the C2–C5 hydrocarbon components of soil gases. Because of the positive verification, regions with a algorithm resulted in a unimodal distribudistribution,lateral general or theaverage the E show to accepted be could distributions areal The process. migration the of results the of tion of regions with high Factor 1 scores of the E roughly matched the surfacechar was matching rough thisuncertainty projections The of 9). and of 1 the(Figs. known fields distribu probability the variance of acterizedconditional the by highesttheun gridthe generatedUnfortunately, tions at nodes. certainty values are concentrated in the larger area of the1 Factor high of heterogeneity the Perhaps 11B). (Fig. scores 1 Factor less the for reason the were surrounding its and area this in scores accurateestimation results. 1 scores are regions, where Factor large in the thesense defi of this where regions the that showed results The above. given nition 0.7) > was probability the general (in probability large a had event res subsurfacehydrocarbon the with correlated clearly be could correla This 13–15). ervoirs(Figs. identified profiles seismic in tion produced a result positive even in the region where the and un 13 Fig. 1, Fig. in anomaly (Heresznye high very was certainty The probability counterparts 14). Fig. the of other known reser para like pattern which would have - Correlation of the probability map of high Factor 1 scores and the subsurface hydrocarbon fields along the third transect. third the along fields hydrocarbon subsurface the and scores 1 Factor high of map probability the of Correlation The 200 equally probable stochastic realizations honoured The spatial analysis of the factor scores highlighted some The loadings in Factor 1 showed exactly what we were look were we what exactly showed 1 Factor in loadings The simulation result was accurate, although the simulated set showed showed set simulated the although accurate, was result simulation Gaussian a Since input. the of that variabilitythan larger slightly necessitatedanapproach. indicator The 8). and 7 (Figs. set input the statisticalcharactersthe of well - non a of application the for calls outliers such of existence metric in simulation approach. Fortunately, this case the spatial outliers did not form any chain Under regular circumstances, these outliers should be filtered out. out. filtered be should outliers these circumstances, regular Under regarded were scores factor the since rule,this follow not did We the Also, process. background the strengththe of measuresof as basis of the available seismic survey. seismic available the of basis appeared score high a 5A, Figure in example, For outliers. spatial dots). blue and (green scores average among map) the on dot (red of of the Rn components did not change significantly. Thesephe resethe of phase water the characteristic be above may nomena rvoirs. Unfortunately this situation could not be on checked the belonging to the Rn and HC component were contradictory. This contradictory. were component HC and Rn the to belonging process could be characteristic above such regions, migration the where while down the slowed gases HC of migration vertical ing for: the higher the Rn content, the higher the CH content is ge basic the withharmony absolute in was Thisresult 3). (Table loadings factor of signs the 2, Factor In 2). (Fig. theory ochemical a factor. This was the main reason for (1) the application of only only of application the (1) This mainthe was for reason factor. a 1 Factor of analysis spatial the (2) and matrix factor unrotated the highcommunality. have not did it if even might might be not necessarily the dominant the process. purposeFor important only the such this thingstudy, existenceof the of was Figure 15. 15. Figure Geiger et al.: Statistical Geigeral.: geostatisticalet and hydrocarbonand Rn of monitoringstudycomponents gas soil... a system of Geologia Croatica JOURNEL, A.G. 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