Application of a streamer resistivity survey in a shallowbrackish-water reservoir

Sung-Ho Song1 In-Ky Cho2,3

1Rural Research Institute, Korea Rural Community Corporation, Ansan 425-170, Korea.2Department of Geophysics, Kangwon National University, Chuncheon, Kangwondo 200-701, Korea.3Corresponding author. Email: choik@kangwon.ac.kr

Abstract. Todelineate the resistivity structure of sub-bottom sediments in a shallowbrackish-water reservoir in thewesterncoastal area ofKorea,we carried out a streamer resistivity survey using a dipole–dipole array. First, throughnumerical testing,we confirmed that the resistivity method with a dipole–dipole array could be applied in a shallow marine environment,when the resistivity contrast betweenwater and the underlying sediments ranges from a factor of 3 to 5.Also, inversionwith awater layer explicitly included is more effective than the conventional inversion method in resolving power, which weconfirmed by observing that the inversion results for synthetic datasets matched better when a water layer was included inthe inversion procedure.

After constructing a data acquisition system composed of a resistivity meter, GPS, and echo sounder, and developingdata processing software, we conducted a streamer resistivity survey and inverted the data obtained to identify thehydrogeological sequences and sediment characteristics at the bottom of the shallow brackish-water reservoir. Drill logsidentified three sediment layers, including silty sand, fine sand, and mixed sand. The resistivity distributions from inversionmatched the resistivity rangesmeasured onmaterials obtained by sampling near the drilling points.We constructed a contourmap of the top of the mixed-sand layer, using semivariogram analysis. Comparing these results with the drilling results,the depth to each layer, and the measured and estimated resistivity range of the materials, also corresponded to resistivityprofile. From this study, we are assured that the streamer resistivity method would be a useful tool for surveying shallowbrackish-water reservoirs.

Key words: brackish-water reservoir, inversion, semivariogram, streamer resistivity survey.

Introduction

The resistivity method has been used on land for more than acentury. Although it was developed for subsurface resourcesexploration, nowadays it is used extensively for numerousgeotechnical and environmental applications. Recently, it hasbegun to be used at sea (Snyder et al., 2002). As is well known,the main problem in marine resistivity surveying is that theseawater is extremely conductive, much more conductive thanthe geological materials at or below the seafloor. Seawaterconductivity is strongly dependent on salinity and temperature.The uppermost sediments under the sea are usually watersaturated and have resistivities of the order of 1–10W.m. Themost obvious difficulty in such a conductive area is that currentis channelled through the more conductive seawater, limiting theamount of current available for penetration into the underlyingsediments. In addition, it is generally difficult to obtainhigh-quality resistivity data in regions of very low electricalresistivity, because the potential differences may be too small tomeasure. Nevertheless, the marine resistivity method has recentlybeen developed for various geotechnical and environmentalapplications.

In the shallow marine environment, the seismic reflectionmethod, although expensive, has the advantage of providingdetailed structural information. However, lithologically, itsability to distinguish between silt, sand, and gravel is quiteweak. However, the marine resistivity method is easy to use andinexpensive compared to the seismic method, and it can provide

useful information for differentiating silt from sand or gravel.There have been several reports of resistivity surveys conductedon or under fresh water. Baumgartner and Christensen (1998)presented a resistivity method using an array called the ‘fishingrod’ to determine the resistivity of a lake bottom.Yanget al. (2002)illustrated a resistivity imaging technique at the water surface, todelineate lake-bottom structure. Kim et al. (2002) also provided aresistivity method to image the geoelectrical structure under ariver or lake bottom. In the shallow marine environment, Snyderet al. (2002) described an instrument system for performingcontinuous resistivity profiling using an electrode streamer.Graham (2002) also discussed the applicability and limitationsof the towed direct current method in the marine environment.

Here we have applied a streamer resistivity method to thesurvey of a shallow brackish-water reservoir on the west coast ofKorea. Through numerical modelling and inversion, we firststudied the performance of a streamer resistivity method whichuses a dipole–dipole array, in shallow sea water up to 5m ormore in depth, and developed data processing software to dealwith a large amount of data automatically. We then constructed amarine resistivity data acquisition system, which included aresistivity meter, GPS, and echo sounder. Finally, we acquiredstreamer resistivity data in a shallow brackish-water reservoir,and obtained two dimensional (2D) resistivity sections byinversion that included an explicit water layer. The resultingmodel was compared with some exploratory drilling results forfurther interpretation.

CSIRO PUBLISHING

www.publish.csiro.au/journals/eg Exploration Geophysics, 2009, 40, 206–213

� ASEG 2009 10.1071/EG08126 0812-3985/09/020206

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Theoretical considerations

Electrode configurations

In marine resistivity surveys, we can use most of the electrodearrays that can be used on land. Also, both floating andunderwater electrode systems are possible. A floating electrodesystem is much cheaper andmore convenient than an underwaterelectrode system, whereas an underwater electrode system isbetter in resolving power. Because the choice of electrodearray affects both depth of penetration and resolution, theelectrode array should be carefully chosen to get the desireddepth of investigation and resolution.

For resolution of horizontally layered structure, the Wennerand Schlumberger arrays have been preferred. They are suitablefor depth soundingwhen expansion of the outer electrode spacingover several decades is possible. To use the Schlumberger orWenner array inmarine resistivity surveys, a reverse array shouldbeused,where the location of current andpotential electrode pairsis interchanged. For example, the reverse Schlumberger arrayconsists of one pair of current electrodes, located at the centre ofthe array, and several pairs of potential electrodes symmetricallyarranged and logarithmically spaced (Graham, 2002). Bycontrast, the dipole–dipole array is more suitable for profilingbecause it is superior in horizontal resolution. The main purposeof this survey is to rapidly get the 2D resistivity distribution ofthe underlying sediments. Thus, profiling and sounding shouldbe done simultaneously. We assumed that the thickness of seabottom sediments could show a great horizontal variation, andthat the resistivity of the sediments themselves may be nothomogeneous. In such a case, the dipole–dipole array, havingbetter horizontal resolution, looks a better choice than theSchlumberger or Wenner array. Thus we used a dipole–dipolearray on the streamer cable.

However, the weak signal strength observed with adipole–dipole array leads to shallow depth of penetration.Moreover, the signal strength is much smaller in the marineenvironment because of very conductive seawater, furtherlimiting penetration of current into the underlying sediments.This is a main drawback of the dipole–dipole array, especially inshallow marine environment.

Resolving power of streamer resistivity method

As mentioned above, streamer resistivity method usingdipole–dipole array has very weak signal strength in extremelyconductive seawater environment, which makes depth ofinvestigation decrease and resolution become poor. Therefore,it should be examined that the streamer resistivity methodwith dipole–dipole array can resolve sub-bottom sediments inshallow marine environment. Using departure curve analysis,Snyder et al. (2002) demonstrated that the true resistivityof sub-bottom sediments could be estimated from dipole–dipole resistivity data if some conditions are satisfied. For thesake of completeness, we will explain Snyder’s analysiscomprehensively in this section.

In order to confirm the applicability of streamer resistivitysurvey using dipole–dipole array in extremely conductiveseawater, we analysed departure curves computed for adipole–dipole array deployed at the surface of a two-layeredearth, for n-spacings ranging from 1 to 8. Figure 1a and b showsets of these curves computed for n= 1 and n= 6, respectively.From Figure 1a, we can see that as water depth reaches the dipolelength, apparent resistivity converges to the resistivity of waterwhen n= 1. Apparent resistivity, however, becomes close to theresistivity of lower layer if the water is very shallow compared tothe dipole length. For the case n= 6 in Figure 1b, apparent

resistivity approaches the resistivity of the lower layer whenthe water is very shallow, while it seems difficult to find theresistivity of the lower layer when the water depth is larger thanthe dipole length. In particular, apparent resistivity is more than75% of the resistivity of the lower layer when the resistivitycontrast between the upper and lower layers is 3–5, for shallowwater depths.

Figure 2 showsdeparture curves computed for a dipole–dipolearray deployed at the surface of a two-layered earth, forn-spacings ranging from 1 to 8, when the resistivity ratiobetween lower and upper layers is 4. Apparent resistivityvalues approach the resistivity of the lower layer, regardless ofn-spacing, if the water depth is shallow. However, when thedepth to the lower layer is larger, apparent resistivity is close tothe resistivity of the upper layer when the n-spacing is small,while it approaches the resistivity of the lower layer with anincrease of n-spacing.

From these analyses, we can confirm that the true resistivity ofsub-bottom sediments can be estimated from dipole–dipoleresistivity sounding data when the water depth is less than halfa dipole length, and the resistivity contrast between seawater andsediments is 3–5. Also, resistivity changes at a higher resistivitycontrasts are easily resolved at the larger n-spacing. In our surveyarea, average resistivities of seawater and sediments are around0.3 and 1.0W.m, respectively. Also, the depth to sub-bottom

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A streamer resistivity survey Exploration Geophysics 207

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sediments is less than 5m, except in some extraordinarily deepareas.Therefore,wecanbeassured that adipole–dipole resistivitysurvey is able to provide sufficient information to determine the1D resistivity distribution of sub-bottom sediments.

2D inversion considering a water layer

Although we found that the hydrogeological structure in themarine environment could be analysed from the variationtrends of vertical sounding data obtained using a dipole–dipolearray, we next examined whether a 2D inversion can provide aplausible result that matches well the true model. For this, wecarried out conventional inversion with 2D resistivity datasynthesised from the results of 1D modelling for two- andthree-layered models. Figure 3 shows sets of resistivityprofiles derived by 2D inversion for two- (Figure 3a) andthree-layer models (Figure 3b), respectively. It can be seenthat it is difficult to interpret the models quantitatively whenthe inversion blocks are inconsistent with the water layer,although the overall trend is consistent with the true model.

A conventional 2D inversion program will not allow us toincorporate a water layer. Conventional inversion blocks or cellsdo not match with the boundary between water and underlyingsediment layer, because the thickness of the inversion blocks isset to increase with depth. Also, the size of inversion blocks isnot detailed enough to sufficiently reflect the topography ofthe water bottom, and inversion blocks are always horizontal,compared with the undulating water bottom topography.Correspondingly, inversion error becomes larger in the case ofconventional inversion in a shallow marine environment with alarge topographical effect. To avoid this problem and get animproved subsurface resistivity image, inversion considering anexplicitly defined water layer is necessary. The detaileddescription of 2D inversion considering a water layer can befound at Kim et al. (2002).

For comparison, we conducted both conventional inversionwithout considering awater layer, and inversion including awaterlayer. In the two-layer model shown in Figure 3a, the result ofinversion including water layer is more consistent with the truemodel than that of conventional inversion.Although the inversionresult for the three-layer model shown in Figure 3b is somewhatdifferent from the true model, we can see that the result ofinversion including a water layer is more effective than theconventional inversion method.

Data acquisition system

A streamer resistivity survey requires various kinds of equipmentand operating systems such as the vessel, the streamer cablewith electrodes, multi-channel resistivity measuring equipment,GPS, bathymetry measuring equipment, a portable electricalconductivity meter, and data processing and interpretationsoftware. Figure 4 shows a block diagram of the streamerresistivity system that we have deployed to conduct shallowwater resistivity surveys. The streamer resistivity system is

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Fig. 3. Resistivity profiles obtained by 2D inversion for the data generatedfrom 1D modelling over (a) two- and (b) three-layer models.

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208 Exploration Geophysics S.-H. Song and I.-K. Cho

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composedof fourmain sub-systems: navigation, data acquisition,resistivity measurement, and streamer cable.

The navigation system consists of a differential GPS system,which is interfacedwith a digital echo sounder. This system storesgeographic position andwater depth at 1-s intervals in the systemcomputer with the corresponding GPS time. In the resistivitymeasurement sub-system, a multi-channel resistivity meter isused to measure the potential difference data at six to eightn-spacings simultaneously. The resistivity meter reads thepotential difference data periodically and stores it on thesystem computer, with the time of the reading. From the timesrecorded with the resistivity and navigation data, we can find thepositions of each electrode installed on the streamer cable. Thestreamer cable consists of an insulated multi-conductor cable,which hosts 11 electrodes. The electrodes and buoys areconstructed at every 10m along the cable. The two electrodesclosest to the boat are used as current electrodes and the othersas potential electrodes, as shown in Figure 4. The data acquisitionsub-system is a simple laptop computer to store both navigationand resistivity data. Although the navigation and resistivity dataare stored in different data files, we can merge them easily duringpost processing.

The minimum speed of the vessel used in our survey is ~3 kn(1.5m/s). The resistivity meter reads eight channels of potentialdifference data every 7 swhen the stacking number is set at 1. Thismeans that eight resistivity measurements are acquired at ~10mintervals. Thus we can acquire 3–4 km of resistivity data per anhour, which is very rapid compared with a land survey.

Data processing

The first step in data processing is to get apparent resistivityvalues from the potential difference data. By assuming thatthe streamer cable will follow the ship’s track, we calculatedthe positions of the current and potential electrodes and thecorresponding apparent resistivity. Next, to obtain equallyspaced apparent resistivity data before performing theinversion, the values should be interpolated and re-sampledafter projecting the values onto a straight survey line. Thisprocess is done individually for each n-spacing. If we assumethat the number of apparent resistivity values is N, each apparentresistivity is given by a function of the location of the electrodesat each measuring time:

rna ¼ f ðrna1; rna2; . . . ; rnaN Þ: ð1ÞWhenperforming a dipole–dipole resistivity survey, themidpointbetween the current and potential dipoles may be used as theplotting point for the associated apparent resistivity value. Afterdetermining the plotting point for a particular n-spacing value, itshould be projected to a point on the straight survey line, by arotation of the coordinate system. If the Transverse Mercator(TM) coordinates (x – x0, y – y0) are rotated counterclockwisethrough an angle �, we get the following relations between thecomponents resolved in the original TM coordinate system(unprimed) and those resolved in the new rotated coordinatesystem (primed) (Figure 5):

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Although all of the apparent resistivity values are now projectedonto the straight survey line, they are not equally spaced, because

thevesselmoves alonga curved track and its speed is not constant.For inversion, the apparent resistivity values should be re-sampled to be equally spaced. Through interpolation and re-sampling, apparent resistivity data that can be directly used forinversion is produced.

It is very difficult to acquire data of a quality similar tothat achieved on land, because the stacking number should befixed to one to minimise the measuring time, and the contactbetween the electrodes and the water can be intermittently poordue to the motion of the vessel, and waves. Moreover, it ispractically impossible to process and edit data by handbecause the amount of survey data is enormous. Thus, it isnecessary to use a data processing program that automaticallyrejects unreliable data.

In dipole–dipole resistivity surveys, as the n-spacingincreases, the potential difference measured generallydecreases, regardless of subsurface structures. However,apparent resistivity values increase with increasing n-spacingbecause the resistivity of reservoir water is very low and that ofsub-bottom sediments is relatively high. From this perspective,during data processing, we first eliminated apparent resistivityvalues that decreased rapidly as the n-spacing increased. Wethen rejected apparent resistivity values for which the ratio of nto n+ 1-spacing apparent resistivities was less than 0.6–0.8. Theprocessed data were then inverted to a subsurface resistivitystructure using a 2D algorithm based on finite elementmodelling and Active Constraint Balancing (ACB) (Yi et al.,2003).

Field application

Hydrogeological setting

The survey area is located within a brackish-water reservoir in acoastal area of Korea. The construction of the reservoirembankment was finished in 2007. According to the maritimemaps of 1982 and 1994, made before the dyke construction, thetopography of the sea floor in the study area region is almost flat.The sea floor inside the dyke, however, has got remarkablyshallower, with expanding tidal flats due to trapping by thedyke of continuous sediment input from the rivers (Lee et al.,2006). Figure 6 is a bathymetric map of the survey area. The totalarea of this reservoir is ~401 km2 and water depth over much ofthe reservoir ranges from 1 to 10m. However, the water depthnear the embankment dyke, especially at the closing gap, reaches~40m because of erosion by the fast tidal current.

From the drilling data obtained at four representative drillholes during thegeological investigation, there aregenerally three

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Fig. 5. Notation for the rotation of coordinate system calculations.

A streamer resistivity survey Exploration Geophysics 209

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hydrogeological layers. The hydrogeological sequence identifiedin the study area is as follows: a silty sand layer, a sand layer, and amixed sand layer, as shown in Figure 7. The uppermost layer,which constitutes most of the surface of the sediments, is a siltysand layer generally classified as silt or silty loam according to theUSDA textural classification (USDI, 1974, see Figure 8). Thethickness of this silty sand layer ranges from 3.0 to 9.5m. Belowthe silty sand layer, a sand layer (sandy loam and loamy sand) isencountered. The thickness of this layer is between 6.0 and31.0m. The bottom layer is a mixed layer, composed of siltysand, fine sand, and coarse sand on top of bedrock, which isintruded by volcanic rocks.

Physical properties of sediments

Soil samples obtained from drill cores from the four boreholeswere classified on the basis of the diameter of the individualgrains (Friedman and Sanders, 1978). Figure 9 shows the grainsize distribution curves for eight samples from the four boreholes,with the depth of each sample indicated in the legend. Of thethree types of sediments that are shown in Figure 7, the silty sandlayer, with more than 60% of silt is found in samples B2 (4.5m),B4 (9.0m), andB6 (1.5m) in the upper part of the sequences. Finesand, with more than 80% of fine sand occurs in samples B2(10.5m), B3 (9.0m), and B4 (25.5m). Below the fine sand, themixed sand layer is encountered in samples B3 (31.5m) and B6(27.0m).

The ability of a saturated subsurface formation to conductelectrical current depends primarily on three factors: porosity,connectivity of pores, and the specific conductivity of thewater inthe pores (Telford et al., 1990). Pore water and its chemical

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Fig. 6. Location map of the study area, with water depth contours and four drill hole locationsshown. Dotted lines represent the dipole–dipole resistivity survey lines, and the solid line witharrows indicates the line of which the 2D inversion section is represented in Figure 10b.

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210 Exploration Geophysics S.-H. Song and I.-K. Cho

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characteristics are especially dominant factors influencingthe flow of the electric current because the formation materialsare in general resistant to electrical flow. To identify thehydrogeological sequences from the resistivities obtained byinversion, representative resistivities for each layer wereclassified (Table 1). The measured resistivity values forsediment samples vary from 1.1 to 1.8W.m, which is ~fourtimes higher than the average resistivity of the reservoir water,0.25W.m.Comparing themeasured resistivity from sampleswithestimated resistivity from inversion, we can classify the soilsamples into three groups based on the resistivity ranges. Thesilty sand layer resistivities range from 1.1 to 1.3W.m. The fine

sand layer and mixed sand layer resistivities range from 0.9 to1.1W.m and from 1.3 to 1.8W.m, respectively.

Streamer resistivity survey

Figure 10 shows the result of the streamer resistivity survey alonga segment within the 10th line among the 12 lines shown inFigure 6. The segment is 1 km long, and the water depth alongthe segment is around 5m. For the automatic data rejectionmentioned in the previous section, the ratio of n to n+ 1-spacing apparent resistivity values is set to 0.65. Figure 10ashows the apparent resistivity pseudo-section after editing.Figure 10b indicates the inversion result, using the ACBmethod to enhance the resolving power by controlling theLagrangian multiplier according to the subsurface model andmeasured data (Yi et al., 2003). We can see that inversion with awater layer is more reliable than conventional inversion. TheRMS error (9.8%) achieved by inversion with an explicit waterlayer is smaller than that (12%) achieved by conventionalinversion.

Figure 11 shows an enlarged image of the boxed area inFigure 10b, with the result of drill hole B3 (Figure 7) overlain.Resistivities in the 2D inversion section range from 0.5 to2.2W.m, excluding overestimated interpolation results.Comparing the inversion result with the drill log, we can seethat the inversion resistivity value at a depth of ~30m near B3ranges from 1.3 to 1.8W.m, which corresponds to the resistivityrange for mixed sand as described in Table 1.

Spatial distribution of inversion results and drilling data

To examine the spatial distribution of resistivity values withdepth, a kriging method was first used. However, kriginggenerally smoothes out local details of the spatial variation ofthe attribute, with small values being overestimated and largevalues being underestimated (Cressie, 1988). To construct acontour map without smoothing effects, a variogram analysiswas conducted. Semivariogram (or, traditionally, variogram)analysis is a tool used to analyse how data are spatially

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Table 1. Resistivities and their ranges for eachmaterial. Units areV.m.

Materials Resistivity Range Remarks

Water 0.25 0.2–0.3 MeasuredSilty sand 1.2 1.1–1.3 EstimatedA

Fine sand 1.0 0.9–1.1 MeasuredMixed sand 1.5 1.3–1.8 EstimatedA

AValues of disturbed samples obtained from offshore.

A streamer resistivity survey Exploration Geophysics 211

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interconnected (Isaaks and Srivastava, 1989), and asemivariogram describes the variance distribution in the datathat results from difference in relative location.

In the results of the semivariogram analysis, the ‘nugget’ and‘sill’ values were 45.9 and 91.8, respectively (Table 2), whichshowed no significant values comparing to the length of surveylines. The small value of the nugget and sill parameters alsoindicates that interconnection between the interpreted values isquite high regardless of the locations of the survey lines.However, the ‘range’ parameter value of 8110 is too high, andit can be predicted that inversion including water depth is morereliable because the range parameter value tends to increase asmore and better data become available.

Figure 12 shows the contour map of the depth to the mixedlayer calculated with the semivariogram by using the

‘Exponential’ model which is generally combined with thenugget effect. The area in which the depth to the mixed layeris greater than 30m is mainly located from centre to the left(west) side of the study area and is generally deeper near theembankment dyke. This trend matched well with the trend ofsea-bottom elevation shown in Figure 6. Depths from the fourdrilling wells are nearly in accordance with the depth to mixedlayer. However, the depth to the mixed layer in the central part ofstudy area is less than 20m, which also coincides with the trendof sea bottom elevation.

Conclusions

Streamer resistivity surveys were conducted to evaluate theirapplicability in a brackish-water reservoir on the west coast ofKorea.

From numerical tests, we confirm that the streamer resistivitymethod using a dipole–dipole array can give sufficientinformation about sea-bottom sediments even when theelectrode array is on the water surface. Also, inversion with anexplicit water layer ismore effective than conventional inversion,because the inversion results for synthetic datasets obtained for

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B3

162000 163000

Fig. 12. The contour map of depth to the top of the mixed layer showing the greatest depth from the centre to theleft side. Open circles with a cross indicate the location of drill holes.

Table 2. Parameters of the semivariogram analysis using anexperimental model.

Layer Nugget Sill Range R2

Mixed sand 45.9 91.81 8,110 0.933

212 Exploration Geophysics S.-H. Song and I.-K. Cho

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two- and three-layer models matched better when a water layer isincluded in the inversion procedure. In addition, we developeddata processing software for marine resistivity surveys. Thesoftware automatically merges GPS locations, eight-channelpotential-difference data, and water depth profiles from anecho sounder. Then, apparent resistivity data are calculatedassuming a curved ship track. Moreover, the softwareautomatically rejects unreliable potential difference andapparent resistivity data by assuming that potential differencedecreases and apparent resistivity increases as n-spacingincreases. Finally, the software produces an apparentresistivity data file including water layer thickness values,which can be used directly for inversion.

Weconstructed adata acquisition system formarine resistivitysurveying, consisting of an eight-channel resistivitymeter, aGPSreceiver, and an echo sounder. Using the data acquisition systemand data processing software, we carried out streamer resistivitysurveys in a brackish-water reservoir. Then, we conducted 2Dinversion using the data obtained. The 2D inversion resultsindicated that the resistivity ranges of measured materialsreasonably matched a simple stratigraphic column near drillhole locations, and this was confirmed by the drilling data. Inaddition, a contour map of the depth to the mixed layer wasconstructed by using semivariogram analysis, and measuredresistivities for four columnar sections of drilling results werecompared with the estimated resistivities. From the contour map,weare assured that this approachwouldbeveryuseful todelineatethe resistivity structure ofbottomsediments in a shallowbrackish-water reservoir.

Acknowledgments

The research was partially supported by a grant (code number 3-3-3) fromSustainable Water Resources Research Centre of 21st Century FrontierResearch Programs. The authors also thank the Ministry for Food,Agriculture, Forestry and Fisheries for financial support, and are gratefulto Dr G. S. Lee, Miss M. K. Kang and Mr Y. I. Kim at the Rural ResearchInstitute for their assistance with data acquisition.

References

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Manuscript received 17 November 2008; revised manuscript received29 December 2008.

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