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To appear in the Journal of Geophysical Research, 2002.

Subsurface geophysics of the Phlegrean Fields: New insights fromdownhole measurements

Alain RabauteLaboratoire de Geologie, UMR 8538, Ecole Normale Superieure, Paris, France

Beatrice YvenInstitut de Physique du Globe de Paris, CNRS-ESA 7046, Universite Paris 7, France

Walter CheliniAGIP S.p.A, Formation Evaluation Dpt., San Donato Milanese, Italy

Maria ZamoraInstitut de Physique du Globe de Paris, CNRS-ESA 7046, Universite Paris 7, France

Abstract

The volcanic complex of Phlegrean Fields, located north-west of Naples (Italy), has been the siteof deep geothermal exploration in the 80’s. Several wells were drilled by an Agip-Enel jointventure, with downhole continuous physical properties acquired in each well. The main purposeof this study is to map and describe the spatial variations of the volcanic deposits, in terms oftheir nature, thickness and in situ physical properties. We apply fuzzy clustering classification ofthe well-logging data available in the wells cored in the San Vito area. Fuzzy set theory providesan approach that quantitatively assigns individuals to physically continuous classes. The optimalnumber of classes is found by minimization of three mathematical functions, thus reducingsubjectivity. The resulting classifications are found (i) to reflect the main lithologies in the SanVito plain, (ii) to provide more detail on the geological stratigraphy —allowing a more precisevolcanic history— and (iii) to differenciate between transition zones and interbedded well-defineddeposits. In addition to discriminating between lithologies that have different physicalproperties, this study gives information on the degree of homogeneity of each lithologic unit, andthe range of variation for the measured properties. Finally, using the physical classification ofthe deposits, we are able to propose a detailed 2-D compressional acoustic velocity structure ofthe studied area.

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1. Introduction

The Phlegrean Fields is a quaternary volcanic andhydrothermal system, located 10 km North-West ofNaples (Italy). A 12 km-wide caldera constitutesthe main volcano-tectonic feature of the area, in-side which the volcanic, seismic and fumerollic activ-ities are confined. The eruptive and unrest phenom-ena mechanisms of this densely inhabitated area —affected by two recent episodes of strong ground upliftand seismic crises in 1969–1972 and 1982–1984— hasbeen thoroughly studied, and its volcanic hazard as-sessed. These studies have been largely supported bythe Agip-Enel (Italian national petroleum and elec-tricity companies) joint venture, which investigatedthe economical interest of geothermal activity in thePhlegrean Fields. Two main contributions arose fromthis geothermal research [AGIP report, 1987]: (i) thesurface geological and geophysical surveys provideddetailed geologic, geoelectric, gravimetric and mag-netometric maps and (ii) the result of the explorationdrilling helped to reconstruct the eruptive history andthe lithostratigraphic sequence of the explored areas.

However, although the geological structure of thesubsurface of the Phlegrean Fields is well described,little is known of the geophysical properties of thevolcanic deposits in depth [Zamora et al., 1994; DiMaio et al., 2000; Yven, 2001]. This is partly the rea-son why there are still difficulties and uncertaintiesin explaining and modeling the mechanical responseaccompanying the unrest episodes, the knowledge ofthe physical properties of the surface and subsurfaceformations of an active volcanic system being essen-tial to define a detailed and representative geophysicalmodel of it.

Well-logging techniques are currently applied insedimentary areas, where they provide fundamentalinformations on rock and fluid properties. By cross-correlation between boreholes, they allow to definethe structure of the studied area. As their use in vol-canic environments is uncommon, the data obtainedby Agip in the wells provides a unique opportunity toinvestigate the in situ physical properties of the mainvolcanic deposits.

The present study focuses on the in situ well-logging physical properties acquired in the San Vitoplain, located 3 km north of the city of Pozzuole (seeFigure 1). The two studied wells, San Vito 1 (SV-1)and San Vito 3 (SV-3), cut respectively 2 360 and3 040 metres of volcanic deposits and sedimentaryrocks. They show a different geological history: SV-1

is located inside a collapse structure, due to the Gauroeruption area some 10,500 years ago, while SV-3 isoutside. Furthermore, SV-1 is much closer than SV-3to the center of the area where the recent ground de-formations and seismic activity occurred. It is there-fore interesting and useful to study their differencesin physical properties. The downhole measurementsare analysed using fuzzy classification to give new in-sights on the different volcanic deposits in terms oftheir average in situ physical properties. As a resultof this study, a detailed compressional acoustic wavevelocities 2-D structure of the San Vito area is pro-posed.

2. Geological settings

The Phlegrean Fields is an active volcanic arealocated inside the deep and large tectonic grabenthat forms the Campanian plain. The volcanic ac-tivity of the Phlegrean Fields began probably before50,000 years B.P. [Rosi and Sbrana, 1987]. However,the first widespread emitted products are related tothe impressive eruption of pyroclastic rocks, knownas the Campanian Ignimbrite, which occured around37,000 years ago. The pre-caldera activity was at firstsubmarine, with deposits of trachytic and latitic lavasinterbedded with tuffs, tuffites and quaternary silt-stones and sandstones. The activity became more andmore subaerial and ended with the Campanian Ign-imbrite episod, provoking the collapse of the caldera,which was then filled with water. Until 10,500 B.P.,the activity is again submarine and is characterizedby chaotic tuffites deposits intercalated with thin bedsof trachytic to latitic lavas. The activity culminatesbetween 14,000 and 10,500 B.P. with the eruptionof the Neapolitan Yellow Tuffs, emitted from severaleruptive centres confined inside the caldera [Rittmannet al., 1950; Rosi et al., 1983]. Several major col-lapses resulted from this episod. One of them appearsclearly in the lithostratigraphy cross-section betweenSan Vito 1 and 3 wells (Figure 1). The last periodis mostly subaerial and is divided into two main ac-tive phases separated by a long repose period of 3 500years. A detailed history of the volcanic activity of thePhlegrean Fields can be found in Rosi et al. [1983],Rosi and Sbrana [1987], Orsi et al. [1996] and in DiVito et al. [1999].

The regional stratigraphy of the Phlegrean Fields—based on petrography and on radiometric ages of atleast 150 sections coming from the geothermal wellsdrilled in the Mofete and San Vito areas— has been

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mainly described by Rosi et al., [1983]. Figure 1 il-lustrates the stratigraphy of the San Vito area. Thepresence of chaotic tuffs layer are prevalent on thelava dome and lava flows in San Vito.

3. Downhole measurements

Three types of physical properties were recorded inthe wells:

• Electrical resistivity, measured at different lat-eral depths of investigation. The electricalresistivity measurements were obtained usingthe dual laterolog tool. The shallow Laterolog(LLs) measures the resistivity of the zone in-vaded by the mud, in case of a permeable for-mation. The deep Laterolog (LLd) measuresthe resistivity of the non-invaded zone. Whenthe formation is not permeable LLs and LLd areequivalent.

• Compressional acoustic wave slowness (DT), itsreciprocal being the velocity of the compres-sional wave.

• Bulk natural gamma radioactivity (GR), that isvery sensitive to Th-, U- and K-bearing miner-als, such as K-feldspars, clay minerals such asillite or kaolinite, but also micas (biotite) andheavy minerals (zircon, monazite, apatite).

The intrinsic vertical resolution of the tools usedfor the measurements is directly dependent on thetool configuration. The theoretical value has been as-sessed through measurements in reference holes: it is20–31 cm for the measure of the natural radioactivity,61 cm for the different resistivity measurements, andaround 1 m for the acoustic slowness.

Details on logging techniques can be found in clas-sical textbooks such as Serra [1984], Hearst and Nel-son [1985] and Ellis [1987], and in the collection ofpapers published by Hurst et al. [1990, 1992] andHarvey and Lovell [1998].

Due to the important depth reached, logging op-erations in each well were carried out through mul-tiple runs, each of them covering a fraction of theborehole. Depth overlaps between successive runsin a single hole allowed successful splicing, in orderto obtain the most complete data coverage. As theresult of the geothermal gradient of the San Vitoarea (150◦C/km), recording was often stopped be-fore the bottom of the hole was reached. Table 1

shows the type of measurement, the physical proper-ties measured for each borehole, and the initial andfinal depths.

The variables used in the fuzzy classification are(1) the compressional acoustic wave slowness (DT),(2) the bulk natural gamma radioactivity (GR), (3)the logarithm of the deep resistivity, and (4) the ra-tio of the deep resistivity over the shallow resistivity(LLd/LLs), which informs on the mud invasion and,indirectly, on the permeability and the water satura-tion of the formation.

When one was available, we checked on the repeatsection for precision of the measurement. An exampleof such comparison is shown in Figure 2. We see thatthere is a fairly good agreement between the actualmeasurement and the repeat section. The accuracyof the measurement was checked through calibrationpatterns given at the end of each logging run record.All resistivity data were filtered using a lowpass filterin an attempt to remove high frequency noise.

4. Fuzzy (continuous) classification

Classification is a simple way of reducing a data set,composed of a large number of observations made onseveral variables, to a few number of classes (clusters)having more or less distinct properties. In our case, itis useful to discriminate between the different litholo-gies encountered in a borehole from the propertiesmeasured by logging techniques. It has been shown[Lofts, 1993; Rabaute et al., 1997] that a classical clus-tering algorithm, such as the k-means algorithm [Mc-Queen, 1967; Forgy, 1965], can be used to infer a log-derived lithostratigraphy, helping to overcome pooror no core recovery. However, in the case study pre-sented here, the geological units suffered from strongdiagenesis due to fluid circulation and high tempera-ture and pressure conditions. These transformationsaffected the entire formation, but with different de-gree from place to place. The boundaries betweenthe different units, and the behaviour of the physicalproperties inside one unit, are therefore sought to begradual instead of abrupt. Classication into mutu-ally exclusive classes with rigidly defined boundaries,that is, “hard” or discontinuous classification, may beunsuitable here. Fuzzy set theory provides the con-tinuous approach we need.

4.1. Hard classification

If one considers a set X of n data that one wantsto partition into p discontinuous classes, the result

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will be a n × p matrix of memberships M = (mik) ,where mik = 1 if data point i belongs to class k, andmik = 0 otherwise. The following conditions on Mapply:

p∑

k=1

mik = 1 , i = 1 . . . n (1)

n∑

i=1

mik > 0 , k = 1 . . . p (2)

mik ∈ {0, 1} , i = 1 . . . n ; k = 1 . . . p . (3)

The k-means algorithm minimizes the within-classsum-of-square errors function J(M, C) under condi-tions 1, 2 and 3:

J(M, C) =n∑

i=1

p∑

k=1

mik d2(xi, ck) , (4)

where C = (ckv) is a p×q matrix of class centroids ckv

of class k for the variable v, with v = 1 . . . q and q, thenumber of variables; xi = (xi1, . . . , xiq)T is the vec-tor representing individual i, and ck = (ck1, . . . , ckq)T

is the vector representing the centroid of class k.d2(xi, ck) is the square distance between xi and ck

according to a chosen definition of distance (notedd2

ik hereafter).

4.2. Fuzzy classification

Starting with the work by Zadeh [1965], Ruspini[1969, 1970] and Dunn [1974], several methods forconstructing continous classes have been developed,the most popular being the fuzzy k-means method[e.g., Bezdek, 1981; Bezdek et al. , 1984]. Fuzzy k-means is a direct generalization of hard k-means [Har-tigan, 1975], where the indicator function of conven-tional set theory, with value 0 or 1, is replaced by themembership function of fuzzy set theory, with valuesin the range 0 to 1.

Zadeh [1965] and Ruspini [1969] developed the the-ory of fuzzy sets by relaxing the all-or-nothing statusof the memberships so they are allowed to be partial,i.e., to take any value between and including 0 and 1.Condition 3 is then replaced by:

mik ∈ [0, 1], i = 1 . . . n; k = 1 . . . p (5)

leading to

JF (M, C) =n∑

i=1

p∑

k=1

m2ik d2

ik . (6)

Later, Dunn [1974] and Bezdek [1974] generalizedEq. 6 as

JG(M, C) =n∑

i=1

p∑

k=1

mφik d2

ik , (7)

where φ ∈ [1,∞} is the fuzzy exponent and controlsthe degree of fuzziness of the classification. With thesmallest meaningful value φ ≈ 1, the solution of Eq. 7is clearly a hard partition. Eq. 7 is termed the fuzzy k-means objective function, and is minimized to satisfyconditions 1, 2 and 5 [Bezdek, 1981; McBratney andde Gruijter, 1992].

5. Materials and methods

We used the program FUZME version 2.1 [Minasnyand McBratney, 2000], developed for the fuzzy clas-sification of soil, to classify the logging data acquiredin the two boreholes drilled in the San Vito area. Thedata have been separated into two distinct data sets(Table 2) according to the correspondance of depthand measured properties. Data Sets 1 and 2 corre-spond respectively to wells SV-1 and SV-3. The twowells have been separated in the classification becauseof the tectonic collapse that has affected the area fol-lowing the Gauro eruption. Well SV-3 is drilled onthe rim of the collapsing zone while well SV-1 is in-side the caldera, and their respective stratigraphiesare appreciably different [Rosi and Sbrana, 1987]. Wethen chose to process each well separately.

For the fuzzy analysis to be carried out, certainparameters need to be chosen for each data set. Theseare the distance measure (or metric), the number ofclasses and the value of the fuzzy exponent φ.

5.1. Choice of distance-dependent metric

The choice of the metric will help in driving theperformance of the fuzzy clustering to an optimum.The most frequently used metric is the Euclidian dis-tance

d2ik =

q∑

v=1

(xiv − ckv)2 = (xi − ck)T (xi − ck) , (8)

which gives equal weight to all the variables. There-fore, if one variable has much larger variance than theothers, the former will heavily determine the result.This is typically our case. For instance, the varianceof the acoustic slowness (DT) is much lower than theone of the natural radioactivity (GR). As this effect

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is undesirable, it can be suppressed by prior stan-dardization of the variables to zero mean and unitvariance, which is achieved through the use of theMahalanobis’ norm [Mahalanobis, 1930], defined by

d2ik = (xi − ck)T Σ−1 (xi − ck) , (9)

where Σ is the sample variance-covariance matrix ofthe data matrix X. Using this metric, not only dif-ferences in variance but also correlation between vari-ables are accounted for.

5.2. Degree of fuzziness

The degree of fuzziness is related to the internal de-gree of organisation (or disorganisation) of the dataset. It determines the extent to which the final classeswill be compact and separated. It is necessary tochoose carefully the value of φ, so it keeps a balancebetween substructures in the data set and continuous-ness between the classes. Some workers use a value of2 (Bezdek [1981]; DeGruijter and McBratney, [1988]).In our case, the classes are thought to have quite dis-tinct properties, that should allow a relatively easypartitioning. However, each logging measurement av-erages a rather large sampling interval, this implyingthat each data has an intrinsic uncertainty that is notalways within the variance of the class to which it be-longs. A large φ will enhance this “data fuzziness” tothe detriment of the inter-classes fuzziness. Based onthe work by Odeh et al. [1992] and McBratney and deGruijter [1992], we tried different values of φ between1.2 and 1.5 . The best compromise was φ = 1.25 , aslower values gave a too hard classification, and highervalues generated too much fuzziness between and in-side the classes.

5.3. Optimal number of classes

An optimal number of classes should reflect sub-structures in the data set. It is determined fromprior knowledge of the data, and by using differentmathematical functions devised to assess the validityof the solution. We use three of these functions inthese study. The fuzziness performance index, notedF ′, estimates the degree of fuzziness generated by aspecified number of classes. It is defined as [Roubens,1982]

F ′ =1 − (p × F − 1)

F − 1, (10)

where F is the function [Bezdek, 1981]

F (M, p) =1n

n∑

i=1

p∑

k=1

(mφik)2 . (11)

As F ′ is a derivative of F (constrained as 0 ≤ F ′ ≤ 1)as shown in Eq. 10, minimization of F ′ indicates anoptimal number of fuzzy classes that best reflects theorganisation of the data set. As a consequence, F ′ = 1corresponds to maximum fuzziness, and F ′ = 0 tonon-fuzzy solution.

The Modified Partition Entropy, noted H ′, is de-fined as [Roubens, 1982]

H ′ =H

log p, (12)

where H is the entropy function

H = − 1n

n∑

i=1

p∑

k=1

mik log(mik) . (13)

To validate the optimal number of fuzzy classes, oneguesses that minimization of H (and hence H ′) equalsto maximizing the amount of information about thesubstructures in X that is generated by the fuzzy k-means algorithm. Despite the heuristic nature of theuse of these two validity functions, we will considerthem as good indicators when the algorithm consis-tently identifies substructures within X for a givenset of parameters {d, ck, φ}. For more definition andapplication of F ′ and H ′, one can refer to Odeh et al.[1992] and McBratney and Moore [1985].

The last function has been devised by Xie and Beni[1991] and noted S. It measures the overall averagecompactness and separation of a fuzzy k-partition. Itis defined as

S =JG(M, C)n ∗ (dmin)2

, (14)

where JG(M, C) is

JG(M, C) =n∑

i=1

p∑

k=1

mφikd2

ik , (15)

and (dmin)2 is the separation measurement, wheredmin is the minimum distance between cluster cen-troids, that is dmin = mini,j||ci − cj|| . In Eq. 14,the term JG(M, C)/n is called the compactness of thefuzzy partition of the data set. The function S is thendefined as the ratio of the compactness to the sepa-ration of the fuzzy partition. A smaller S indicatesa partition in which all the classes are overall morecompact and better separate to each other.

Using the same degree of fuzziness, φ = 1.25, weperformed the fuzzy k-means algorithm on the twodata sets for p = [2, 8]. The choice of the rangeof p is based on initial expectations, i.e., the range

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should span an approximate maximum number ofstructurally plausible classes that can be gauged fromthe data or based on a priori knowledge. Plotting F,H, and S helps in determining the optimal number ofclasses (Figure 3). For Data Set 1 and Data Set 2, Sshows the best organization of the fuzzy k-partitionfor 6 and 4 classes (S minimum), respectively, thatare also relative minima for F and H. The plots forF and H decrease further when p = 8, but we shalldiscard this value. It brings little improvement of Fand H, while S is deteriorating, and a higher numberof classes would complicate the interpretation of theclassification. For Data Sets 1 and 2, all three func-tions clearly show a similar minimum at respectively6 and 4 classes.

6. Results

The output of the fuzzy classification includes themembership for each data point in each class (given asprobabilities). A class gathers all data points whosemembership for this class is highest. A class k is char-acterized by its centroid, represented as a vector of co-ordinates (arithmetic mean) in the space of the vari-ables. The scatter of a variable around the mean isindicated by the standard deviation σ. Another out-put of the fuzzy classification is the confusion index ξi,which measures for each data point the degree of classoverlap in attribute space [Burrough and McDonnell,1998]. ξi is calculated as ξi = 1−(pi,kmax−pi,k2nd max),where pi,kmax and pi,k2nd max are respectively the high-est membership and the second highest membershipof data point i. ξi ranges from 0 (when the classesare well separated) to 1 (when they are not).

Table 2 shows the properties of the class centroidsand the corresponding standard deviations, for DataSets 1 and 2. Figures 4 and 5, respectively attributedto well SV-1 and SV-3, show, from left to right:the lithology —determined from cuttings description[Rosi et al., 1983]— the succession of the maximumclass memberships (MCM), and the distributions ofthe data per class for the variables used in the clas-sification. The meaning of a class will be commentedby considering (i) that a centroid is representative ofthe properties of the class it refers to, and (ii) that thestandard deviation indicates the degree of homogene-ity of the class. From the succession of the maximumclass memberships, we will define several “log-units”.A log-unit may include one or more classes and sepa-rates sharp differences in the occurrence of the classes.The results for Data Sets 1 and 2 are presented sep-

arately in the following sections.

6.1. San Vito 1

In the first 260 metres (between 160 and 420 m)studied of the SV-1 well (Figure 4), only the class 3appears. This class is characterized by the highesttransit times (lowest acoustic velocities), showing abimodal distribution. The first peak of the distri-bution, holding most of the data, is centred around145 µs ft−1, while the second is at 210 µs ft−1. Thenatural radioactivity signature is very sharp arounda relative average value of 200 gAPI. This class is oneof the most resistive, showing a highly resistivity con-trast (superior to one) between the deep and shallowresistivities (see Table 2) —indicating that this for-mation is permeable.— By comparing with the lithos-tratigraphy, this class can be associated to the pyro-clastic incoherent deposits.

The next geological unit, described as the Gauro’syellow tuffs, corresponds to two successive classes,class 5 and then class 1. Their main difference is theresistivity contrast, superior to one in class 5, andinferior to one in class 1. They have similar deep re-sistivity and natural gamma-ray distributions. Theirdeep resistivity and transit time are significantly lowerthan the previous unit. Class 5 and class 1 have re-spective thicknesses of 220 and 270 m.

Class 6 is the main class between 910 and 1 650 mand corresponds to the tuffites deposit. Its proper-ties are well defined with moderate standard devia-tions. The transit time follows the decreasing trendobserved from the top of the section, and is centredat 92 µs ft−1. Its natural radioactivity distribution isshifted towards the lowest values of the entire hole(average of 168 gAPI). Its resistivity is higher thanthe one of the two previous classes, still it stays inthe same order of magnitude.

After 1 650 m, we observe a mixture of classes 6,4, 5 and 2. Class 2 appearance is rare and ratherbrief, showing the lowest and best defined transit timevalues (73±5 µs ft−1). Its bimodal deep resistivitysignature, with one peak centered around 20 ohm mand another peak at 180 ohm m, can be partly ex-plained by the vertical resolution limits of the resis-tivity tool (around 60 cm). Class 4 shows the sameacoustic slowness as that of class 6, but has a higherdeep resistivity and natural radioactivity, which bythe way is the highest and most scattered of the sec-tion (276±35 gAPI). The highest class diversity be-gins around 1800 m, corresponding to the beginningof the geological unit described as the chaotic tuffs,

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which indeed is composed of interlayered thin beds ofdifferent physical properties.

6.2. San Vito 3

As Rosi and Sbrana [1987] did not clearly definethe lithologies encountered during the first 800 m ofSV3, we will not relate, at this level, a class to aparticular lithology. In Figure 5, class 1 is the firstand only class to appears in SV-3 between the top and365 m. It is then mixed with class 2 from 365 to 600 m.Class 1 shows the highest transit time values, withan average well-constrained around 147µs ft−1. Thetransition with class 2 is gradual and is mainly char-acterized by a decrease of the deep resistivity by oneorder of magnitude. Class 2 shows also a lower andbroader transit time distribution. It is the sole classcharacterizing the interval between 600 and 800 m.

The transition between class 2 and 3 is 250 m thick,and seems to correspond to the chaotic tuffs unit de-fined by Rosi et al. [1983]. As in well SV-1, its averagephysical properties are difficult to determine.

Class 3, with rather well-constrained low transittime and high resistivity values, clearly correspondsto the lava deposits [Rosi et al., 1983]. The thick-ness of the lava dome can be precisely estimated at250 m. Figure 6 illustrates how it is possible to de-termine with accuracy its position in the stratigraphyand its own physical properties. The lava dome is lo-cated between 1 040 and 1 290 metres deep. It is a ho-mogeneous formation, characterized by a low transittime around 70µs ft−1, an average deep resistivity of17 ohm m and a natural radioactivity centred around400 gAPI, which corresponds to the second peak ofthe natural radioactivity distribution.

Following the presence of class 3 alone, the bot-tom part of SV-3 is composed of a succession of in-tercalated beds showing distinct physical properties,namely that of classes 2, 3 and 4. Their major dif-ference is the natural radioactivity, much higher inclass 4. Class 2 is visible at the top of this log-unit,but quickly becomes sparse. From the log curves, anincreasing downward trend is visible in class 4 for thenatural radioactivity and the deep resistivity. Thisunit will be documented with more detail in the dis-cussion part. For this well, the ratio LLd/LLs is al-ways greater than one, and, therefore, it was not usedas a discriminant parameter.

7. Discussion

Using the probabilistic character of this cluster-ing, that allows to differenciate intercalations of well-defined layers from mixed lithologies characterizingdisturbed transition zones, we discuss the physicalmeaning of each log-unit and attempt to correlate theresults found in each well of San Vito area.

7.1. San Vito 3

We attempt here to precise the stratigraphy of thefirst 800 m of SV-3 well, which are not clearly definedin the vertical cross-section represented in Figure 1.Making the correspondence of the classes found inthe SV-1 and 3 wells, we notice that class 3 in SV-1and class 1 in SV-3 have similar physical propertiesand correspond to the incoherent pyroclastic rocks.A 235 m-thick zone follows, composed mainly by amixture of classes 1 and 2. A clue to characterize thiszone is given by the confusion index ξ. Figure 7 showsthe memberships for classes 1 and 2, for the depthinterval 200–800 m, along with the confusion index.A high ξ characterizes the transition zone between365 and 600 m, while it is mostly null in the two well-defined surrounding intervals. This transition zonecorresponds probably to the mixed breccia describedby Rosi et al. [1983] and filling the rim of the collapsezone.

Class 6 of SV-1 has the closest physical propertiesof class 2 in SV-3. Its slightly higher P-wave velocityand deep resistivity are probably due to its greaterdepth of burial. In SV-1, the interval where class 6is prevalent (approximately between 900 and 1900 m,Figure 4), matches the chaotic tuffites deposits. Rosiet al. [1983] indicates that SV-3 crosses a rather thinlayer of chaotic tuffites (Figure 5). These two ob-servations agree to position the chaotic tuffites layerbetween 600 and 800 m in well SV-3.

A second transition zone, defined by the simultane-ous occurence of classes 2 and 3, is found between 800and 1 040 m. The memberships of classes 2 and 3 andthe confusion index ξ of this interval are representedin Figure 7 and can be divided into three parts. Thefirst 80 metres show a high confusion index and an un-defined mixture of the two classes. This interval canbe defined as a real transition zone. The following120 metres are made of well-characterized interbed-ded layers defined by class 2 or class 3. Inside eachlayer, ξ equals zero and the corresponding class mem-bership is maximum, while its boundaries display asharp increase of the confusion index. This interbed-

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ded layers zone corresponds well with the lower partof the chaotic tuffs deposit. The main differences be-tween the layers are their transit time and deep resis-tivity (see Figures 4 and 5). The last 20 metres are,as the previous transition zones, not representative ofa clear formation, and mark the transition betweenthe chaotic tuffs and the lava dome. From Figure 7,we see that, in the firts part of the dome, ξ variesbetween 0 and 0.9. These high confusion index zonesmay correspond to less homogeneous or more alteredparts inside the lava body.

From 1 290 m to the bottom of the well, the lastlog-unit is represented by a succession of classes 2, 3and 4. Between 1 290 and 1 560 m, the confusion in-dex is generally high and does not allow to clearly dis-criminate between deposits (Figure 8). After 1 560 m,class 2 almost disappears, and the layers are bet-ter defined, showing an intercalation with an aver-age thickness of 20 to 30 metres. The maximum ξpeaks define the transition between the layers and al-low to estimate the thickness of each layer. In thelast column of Figure 8, we tentatively interpretedthe succession of the class memberships. The pat-tern of the tuffs-tuffites-lavas layers was given whenthe confusion index was to high to differenciate eachdeposit. Although we attributed to class 3 the pat-tern of the lava, which has been previously clearlyidentified, this class can be, in this interval, inter-preted either as lavas layers or as indurated layersof pyroclastics rocks. We correlated class 4 to thevolcano-sedimentary complex intervals. The high nat-ural radioactivity of this formation may be related tothe severe hydrothermal alteration that has deeplytransformed the nature of the formation [Rosi andSbrana, 1987]. This thick unit, corresponding to thepre-caldera products, is only encountered at greaterdepth in well SV-1. This is certainly the reason whythe very high values of natural gamma-ray are neverreached in the distributions obtained in SV-1.

7.2. San Vito 1

In well SV-1, we observe that each change in de-posit is correlated with a different class. As a conse-quence, each class can be directly assigned to a vol-canic deposit. The additional partitioning inside theyellow tuffs does not bear a significant change in termsof physical properties between classes 5 and 1. Theseclasses show similar transit time, natural gamma-rayand deep resistivity distributions and have only dif-ferent LLd/LLs ratios. The boundary at 640 m marksactually the limit above which the LLd/LLs ratio is

superior to 1 (classes 3 and 5), and below which itis inferior to 1 (every other classes). The fact thatthe invaded and non-invaded zones have a similar re-sistivity (LLd/LLs=1) is often interpreted by the im-pervious character of the geological unit. This is thenprobably the case of class 5.

Below 910 m, the main class to appear is class 6which is sometimes cut by thin and rare layers belong-ing to classes 1 and 2 and by thicker layers of classes 4and 5. As observed in Figure 9, only the occurrencesof classes 2 and 4 below 1 600 m are associated withmaximum class memberships, thus leading to a zeroconfusion index. The last column of figure 9 showsthe deep resistivity log curve between 1 000 and 2 000metres, where each occurrence of class 2 is correlatedwith a more or less broad peak of the resistivity. Theresistivity around 20 ohm m belongs to the first fourlayers located at the top of the section. The resistivityaround 180 ohm m corresponds to the true resitivityof class 2.

In the deep resistivity log curve the occurence ofclass 2 alone corresponds to a mean value of 180 ohmm. More than beeing the most resistive, class 2 hasthe highest compressive velocities, and a high naturalradioactivity. These physical properties are typicalof the lavas encountered in SV-3 (class 3). Class 2may show lavas layers interbedding the pre-calderachaotic tuffs and the post-caldera chaotic tuffites, asdescribed in Rosi et al. [1983]. The thickness of theselava beds can be estimated with accuracy and are in-dicated in Figure 9. Class 4 occurrences are more dif-ficult to associate to a particular lithology. However,because of a higher natural radioactivity, its classmemberships and confusion index show that these oc-currences are clearly distinct from class 6 (Figure 9).This high radioactivity may come from the presence ofa particular secondary mineral holding a lot of potas-sium [like K-feldspar or illite; see Rosi et al., 1983].

7.3. 2-D velocity structure

Previous studies on the seismic velocity structureof the Phlegrean Fields are rare and the most signifi-cant are certainly the ones by Aster and Meyer [1988]and Aster et al. [1992]. These authors reconstructeda three-dimensional velocity structure in the centralCampi Flegrei caldera, using a three-dimensional si-multaneous inversion of P- and S-wave arrival timesof 228 well-located microearthquakes recorded fromFebruary to June 1984. The dimension of the inves-tigated area was 8 km along a East-West line, 6 kmalong a North-South line and 3 km in depth, centered

9

1 km north to the city of Pozzuoli.The study presented here differs from those of

Aster and Meyer [1988] by several points: (i) the lo-cation of the investigated area; (ii) the frequency usedto explore the geological formations (10 kHz for down-hole transit time measurements compared to 100 or200 Hz for seismic data); and (iii) the continuous char-acter of the well logging measurements (one measure-ment every half a foot), allowing to fully describe theinvestigated subsurface, and providing detailed infor-mation on the heterogeneity of the deposits, by oppo-sition to the resolution of the seismic velocity modelwhich depends on the ray-path density.

Figure 10 shows the 2-D acoustic velocity structureof the San Vito area, where are indicated the acousticvelocity representative of each unit and the depth ofeach interface. The P-wave velocities are calculatedby a weighting average of the transit time values ofthe centroids of the classes that are present in eachinterval. The weight is simply the relative amount ofdata belonging to each class in the interval.

Due to the collapse between SV-1 and 3, only thefirst unit shows similar P-wave velocities in the twowells. In the pyroclastic rocks, the velocity varies be-tween 2080 m s−1 at the surface, where the rocks areincoherent, and 3400 m s−1 where they have sufferedfrom hydrothermal alteration. The stronger valuesaround 4440 m s−1, belong to the lava body. SV-1 and3 show significant difference in their P-wave veloci-ties profiles. In SV-1, the velocities increase regularlywith depth from 2080 m s−1 at surface to 3400 m s−1

around 2.5 km depth. In SV-3, the acoustic velocitiesmodel is more heterogeneous. This is partly due to itslithostratigraphy, composed by pyroclastic rocks andlavas.

8. Conclusion

We applied a fuzzy classification technique on sev-eral well-logging data sets coming from two geother-mal wells drilled in the San Vito area. This techniqueenabled to partition the data sets into classes hav-ing the same physical properties and gave the aver-age physical properties and the degree of homogene-ity of each class. The additional concept of fuzzinesswith respect to the classical hard clustering, allowedto take into account the continuous character of thesubsurface geological and geophysical structures. Us-ing these valuable informations, we emphasized thegeophysical structure of the volcanic deposits of theSan Vito plain, which represents an area of recent

collapse within the oldest Phlegrean caldera.The fuzzy classes were found to closely reflect the

lithostratigraphy defined by Rosi et al. [1983] and de-scribed in detail by Rosi and Sbrana [1987]. The firstand shallow deposit of incoherent pyroclastic rockswas recognized, independently, in SV-1 and 3, whereit shows similar sharp distributions and average prop-erties. It is one of the most resistive layers (10-15ohm m), and it does not show any particular natu-ral gamma-ray signature. It has the lowest acousticvelocity of the whole section (centred on 2080 m s−1).

In SV-1, the thickness of the yellow tuffs has beenprecisely estimated at 490 metres. Its deep resistiv-ity distribution, mainly concentrated between 1 and2 ohm m, allows to discriminate this unit from the restof the formation. The acoustic velocities of the yellowtuffs are well defined, with values around 2810±90 ms−1.

In SV-3, a transition between two geological unitsor collapse zones —represented by a chaotic mixtureof deposits— could be differenciated from well-definedinterbedded deposits. Particularly, SV-3 cuts, be-tween 365 and 600 m, a mixed zone, correspondingprobably to the rim of the collapse structure.

Several lava beds belonging to the chaotic tuffs de-posit in the SV-1 have been clearly recognised, amongthe chaotic tuffs and tuffites deposits. Their thick-nesses have been estimated and vary from 4 to 18metres. The lava shows the highest P-wave veloci-ties associated with the smallest standard deviation(4245±160 m s−1). They have a high natural radioac-tivity around 250 gAPI. Their resistivity is one orderof magnitude higher that the rest of the formation.In SV-3, the thickness of the lava dome was preciselyestimated at 250 m.

Acknowledgments.

This is a CNRS-INSU-PNRN contribution no. XXX(Theme risques volcaniques), and a EEC contribution ofthe Environmental and Climate Work programme (Vol-canic risk). IPG contribution no. XXXX.

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Beatrice Yven, Maria Zamora, Departement desGeomateriaux, IPGP, 4 Place Jussieu, 75252 Pariscedex 05. (e-mail: yven@ipgp.jussieu.fr), (e-mail:zamora@ipgp.jussieu.fr)

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Received December 9, 1998; revised November 30, 1999;accepted December 8, 1999.

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Figure 1. Lithostratigraphic cross section of the San Vito geothermal area (modified after Rosi et al. [1983]).

Figure 2. Repeated section of the total gamma-ray curve. The thin curve is the main log, the thick curve is therepeat measurement.

Figure 3. Determination of the optimal number of classes for each data set according to the minimum value ofthe fuzziness performance index (F ′) and of the modified partition entropy (H ′). 6 classes were taken for DataSets 1 and 4 classes for Data Set 2. The function S is also plotted against the number of classes and shows thesame minimum for Data Sets 1 and 2.

Figure 4. Results for well SV-1. From left to right: Stratigraphy defined by Rosi et al. [1983], maximumclasses membership (MCM) determined by the fuzzy classification, distribution of the physical properties: acousticslowness (DT), natural gamma-ray (GR), electrical deep resistivity (LLd) inside the six classes.

Figure 5. Results for well SV-3. From left to right: Stratigraphy defined by Rosi et al. [1983], maximumclasses membership (MCM) determined by the fuzzy classification, distribution of the physical properties: acousticslowness (DT), natural gamma-ray (GR), electrical deep resistivity (LLd) inside the six classes..

Figure 6. Thickness of the lava dome in SV-3. A constant low transit time (DT) and relatively high naturalradioactivity (GR) between 1040 and 1290 m show the precise boundaries of the lava dome identified by Rosi et al.[1983].

Figure 7. Information given by the confusion index (ξ) in SV-3. A high ξ indicates the transition zones (T.Z.),while it is low or zero in well-defined layers with distinct physical properties. C1, C2 and C3 indicate the classmemberships for classes 1, 2 and 3, respectively. In the last column the patterns are the same as in Figure 1.

Figure 8. The information brought by the fuzzy classification: Maximum class memberships (MCM) and theconfusion index (ξ) allows to describe precisely the stratigraphy of the thermometamorphic interval crossed bySV-3. We tentatively correlated class 3 to the tuffs-tuffites-lavas layers, and class 4 to the volcanosedimentarycomplex intervals. T.Z.: transition zone. In the last column the patterns are the same as in Figure 1.

Figure 9. Information given by the confusion index (ξ) in SV-1. Left to right: Maximum class memberships(MCM), class memberships for classes 2 (C2), 4 (C4) and 6 (C6) and high readings of the deep resistivity (LLd) ofclass 2. A high ξ indicates the transition zones, while it is low or zero in well-defined layers with distinct physicalproperties. Typically, the high readings in deep resistivity that corresponds to a zero ξ match probably the lavabeds described by Rosi et al. [1983]. We indicate their position (black rectangles) and estimated thickness.

Figure 10. 2-D compressional acoustic velocity structure of the San Vito area. The acoustic velocities arecalculated as the inverse of the transit time value of the centroid of the class. In case of an interbedded interval(several classes describing the interval), we used the average of the values of the centroids.

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Table 1. Physical properties measured downhole and corresponding intervals. DT is compres-sional acoustic slowness, LLd and LLs are deep and shallow depths resistivity and GR is totalnatural gamma radiation.

Hole SV-1 SV-3

Type of measurement electrical − nuclear − acousticalPhysical properties LLd, LLs − GR − DTIntervals 160-2153 m 204-2350 m

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Table 2. Centroids and standard deviation of the classes resulting from the fuzzy k-means analysis ofData Sets 1 and 2. The centroids are given as vectors ck,v where v is DT, GR, LLd and LLd/LLs, and kis the class number. σ is the standard deviation. Although log(LLd) is used in the analysis, we show theresistivity LLd instead for easier use in the discussion.

k ck,DT σ ck,GR σ ck,LLd σ ck,LLd/LLs σ(µs/ft) (gAPI) (ohm m)

Data Set 1: San Vito 1

1 111 9 207 14 1.8 0.8 0.80 0.082 73 5 248 24 97.0 113 0.93 0.273 143 8 194 7 15.0 6 1.57 0.214 88 8 276 35 5.3 2.6 0.82 0.105 106 13 189 18 2.2 2.1 1.07 0.136 92 8 168 21 3.2 1.6 0.83 0.09

Data Set 2: San Vito 3

1 147 16 152 27 9.6 5.9 1.36 0.382 110 21 172 66 2.1 1.0 1.16 0.163 69 7 235 92 19.6 17.6 1.42 0.254 79 20 586 140 20.9 39 1.63 0.42