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Journal of Structural Geology 49 (2013) 35e49

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Journal of Structural Geology

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Microfabric and anisotropy of elastic waves in sandstone e Anobservation using high-resolution X-ray microtomography

Wolf-Achim Kahl a,b,*, Robert Hinkes b, Volker Feeser b, Astrid Holzheid b

aDepartment of Geosciences, University of Bremen, Klagenfurter Straße (GEO), 28359 Bremen, Germanyb Institut für Geowissenschaften, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Straße 10, 24118 Kiel, Germany

a r t i c l e i n f o

Article history:Received 13 February 2012Received in revised form23 November 2012Accepted 10 January 2013Available online 28 January 2013

Keywords:X-ray microtomographySandstoneAnisotropyTortuosityElastic waves3D multi anvil pressure apparatusGeomechanics

* Corresponding author. Department of Geosciencegenfurter Straße (GEO), 28359 Bremen, Germany.

E-mail address: wakahl@uni-bremen.de (W.-A. Ka

0191-8141/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.jsg.2013.01.006

a b s t r a c t

Petrophysical experiments, using acoustic velocities to characterise anisotropies of mechanical behaviourof rocks are of essential relevance to understand the geomechanical behaviour of sandstone reservoirsunder changing stress fields. Here, we present high-resolution X-ray microtomography (m-CT) as a sup-plementary research tool to interpret anisotropic ultrasound velocities in sandstones with variation ofisotopic stress.

Specimens of two Lower Cretaceous sandstones (localities Bentheim and Obernkirchen, both Ger-many) have been used in petrophysical laboratory experiments under dry conditions to study ultrasonicsound velocities (frequency of signal input 1 MHz). Subsequently, oriented micro-plugs drilled from thesandstone samples were investigated using high-resolution X-ray microtomography. By means of imageprocessing of the reconstructed scan images, geometric attributes such as mean structural thickness,orientation and tortuosity were evaluated from the m-CT data for both pore space and grain skeleton. Ourobservations clearly indicate the different roles of pore space and grain skeleton in regard to thepropagation of ultrasonic waves: because the pores do not transmit the waves, it was sufficient toinvestigate the average thickness of this fabric element. In contrast, as the ultrasonic waves traverse therock via the adjacent grains, it was necessary to survey the actual travel lengths of seismic waves in thesandstone grain skeleton.

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1. Introduction

Sandstone aquifers are considered to be potential reservoirs forthe storage of industrial fluids and gases or the geological seques-tration of industrial carbon dioxide (Bachu, 2008). On reservoirscale, stiffness and strength of deep rock formations, bedding,fractures and cleavages create important boundary conditionsduring and after injection of fluids (e.g., supercritical CO2; Dautriatet al., 2009). On the pore scale, besides porosity also microcracks aswell as textural and compositional anisotropy of the grain phase areof basic importance for the understanding of anisotropic patterns ofthe sandstone (Louis et al., 2009; Ruedrich and Siegesmund, 2007;Armstrong et al., 1994). Several petrophysical studies revealedanisotropic patterns under defined isotropic conditions at the lab-oratory scale (e.g., Kern et al., 2008; Song et al., 2003). Despite thequite homogeneous appearance of the sandstones, experimental

s, University of Bremen, Kla-

hl).

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investigations of elastic and acoustic properties indicate distinctheterogeneous mechanical and seismic behaviour. These anisot-ropies show a strong dependence upon the orientations of thespecimens with respect to the main structural directions linked totheir sedimentary origin and due to their stress and strain history(e.g., Kern et al., 2008; Dvorkin and Gutierrez, 2002; Hrouda et al.,1993; Siegesmund et al., 1989). Obviously, the understanding of theboundary conditions governing the seismic behaviour on the scaleof the sandstone microfabric is essential. In sandstones, significantanisotropy of mechanical behaviour can originate from e.g., sedi-mentary bedding structures, preferred orientation or arrangementof mineral grains, and (partial) cementation of the pore space.During the operating phase of a reservoir, the stress field willchange, that may create new fractures or reactivating existing faults(Rutqvist et al., 2007).

To survey the microfabric of potential reservoir rocks, severalstudies employ microanalytical methods like optical or scanningelectron microscopy of thin sections or small chunks of repre-sentative samples of potential reservoir rocks (e.g., Peters, 2009;Benson et al., 2005; Vajdova et al., 2004; Saidi et al., 2003). Morerecently, microtomography on micro-plugs has been applied (Louis

W.-A. Kahl et al. / Journal of Structural Geology 49 (2013) 35e4936

et al., 2006, 2007; Dautriat et al., 2009) to establish the effects of themicrofabric on mechanical and seismic properties (e.g., Lo et al.,1986; Benson et al., 2005). Within the last decade, the resolutionof the X-ray micro-CT technique improved drastically. Hence thehigh-resolution X-ray micro-CT method is now capable to fill thegap between conventional medical CT systems (or comparablesetups, e.g., David et al., 2011), that allow to image dm-sized sam-ples with a resolution in the order of 1 mm, and high-resolutionmicrotomography using synchrotron X-ray sources that achievesa resolution in the order of 1 mm on mm-sized samples (Arns et al.,2004; Renard et al., 2004; Lindquist et al., 2000). These de-velopments made it possible to use micro-CT techniques in quan-titative mineralogical, petrophysical and diagenetic studies (VanMarcke et al., 2010; Long et al., 2009; Louis et al., 2009;Remeysen and Swennen, 2008; Noiriel et al., 2005).

In this paper we present high-resolution X-ray micro-tomography as a supplementary research tool to interpret aniso-tropic ultrasonic velocities in sandstones with the variation ofisotropic stress. We attempt to locate the anisotropic structuraldirections in the reconstruction volume of the X-ray micro-tomography scans. The three main seismic directions of theinvestigated samples are derived from ultrasonic measurementsusing compressional wave velocities (P-waves). Although thepropagation of elastic waves in dry samples is restricted to the grainphase, both, abundance and distribution of the pores also have animpact on the wave velocities. Therefore, the microfabric featuresof grain skeleton as well as pore space have been investigated.

2. Materials and methods

Specimens of two Lower Cretaceous sandstones have beenstudied in a 3D multi-anvil pressure apparatus for cubic samples.The dry samples were subjected to isotropic stresses up to 100 MPaat a temperature of 20 �C to map seismic behaviour (P-wave ve-locity) with respect to the sandstone fabric.

To relate the velocity anisotropies to the sandstone fabric, smalloriented cores were drilled from the sample cube subsequent to thepetrophysical studies. At ambient pressure these cores were scan-ned using the SkyScan1172 high-resolution micro-CT scanner. Bymeans of computer-aided image processing, important parametersfor reservoir rock characterisation such as porosity and pore sizedistribution were assessed and the results were compared withstandard petrographic techniques like density determination (im-mersion weighing) and thin section microscopy. Finally, the rele-vance of fabric features on the observed seismic anisotropies wasinvestigated.

2.1. Sandstone rock samples

The sedimentary rock samples used in this work are twosandstones of the Lower Cretaceous from the Valangin and Weal-den formations of the North German Basin in Germany (localitiesBentheim (52�1801100N 7�0903500E) and Obernkirchen (52�160000N9�120000E), respectively). Because of characteristic properties con-cerning permeability and porosity, both sandstones are often usedfor petrophysical laboratory studies (Dautriat et al., 2009; Ruedrichand Siegesmund, 2007; Benson et al., 2005; Louis et al., 2003; Puschand Meyn, 2001) and for numerical flow simulation in porousmedia (Øren et al., 1998; Harting et al., 2005; Ovaysi and Piri, 2012).

Both sandstones are almost pure quartz sandstones (>95%quartz) with rare feldspar and kaolinite, exhibiting a grain-supported fabric. The main fabric components are detrital quartzgrains, (in places skeletal) feldspar and accessory heavy minerals.According to Ruedrich and Siegesmund (2007), the two rocksrepresent beach sediments. Bentheim sandstone is moderately

sorted and consists of rounded grains in the range of 100e300 mm.Obernkirchen sandstone is well sorted and comprised of angulargrains in the range of 100e200 mm. Both sandstones display dis-tinct petrophysical properties: Bentheim sandstone exhibits highporosity (>20%: Baud et al., 2004, 2005: 22.8%; Baud et al., 2005:24.5%; Benson et al., 2005: 23.7%; Dautriat et al., 2009: 23.8e24.4%;David et al., 2011: 22%; Morales Demarco et al., 2007: 23.33%; Puschand Meyn, 2001: 24%; Ruedrich and Siegesmund, 2007: 24.8%) andexceptional large permeabilities between 1 and 2 Darcy, whereasmost specimens of Obernkirchen sandstone studied in the liter-ature showmedium to high porosity (between 10 and 20%: MoralesDemarco et al., 2007: 26.43%; Pusch andMeyn, 2001: 17%; Ruedrichand Siegesmund, 2007: 17.7%; Ruedrich et al., 2011: 19.9%) and lowpermeabilities between 1 and 10 mD.

The samples used for the investigations of this study were takenfrom large blocks (100 � 100 � 10 cm, provided by Obernkirchenand Bentheim quarries) cut parallel to bedding. As demanded bythe different analyzing methods, distinct types of samples havebeen prepared from these blocks, all oriented with respect to theformer sedimentation surface: large cylindrical cores for densitydetermination, co-preparation of large cubes for thin sections andcubic samples for the acoustic experiments, and cylindrical micro-plugs for the m-CT survey, drilled from the cubic samples after theiruse in the acoustic experiments. In all cases, the samples could beprepared in reference to the former sedimentation surface, witha mutual perpendicular reference coordinate system (X, Y, Z) beingchosen: with the structural Z-direction being perpendicular, both Xand Y, lying within the bedding plane, have been determinedseismically.

2.2. Porosity determination by water uptake experiments

Characterisation of the accessible porosity on the bulk scale wasperformed in the course of density determination by buoyancyweighing of cylindrical sandstone plugs (Ø and height: 50 mm;medium: water) and by determination of dry and saturatedmasses.Saturation was achieved by using a vacuum (underpressured by1 bar).

2.3. Thin section microscopy and 2D image analysis of porosity androck fabric

In the course of the preparation of the sample cubes for theacoustic measurements (see the following section), five orientedthin sections were cut parallel to the three main structural di-rections X, Y and Z (for details see Kern et al., 1997) for both sand-stone samples. In the course of thin section preparation, the openpore space was filled by a coloured resin. Determination of poros-ities and pore as well as grain size distributions were done by 2Dimage analysis of photomicrographs from the petrographic micro-scope, employing the software AxioVision (Rel. 4.8) by Carl Zeiss.Within this software, boundaries between grain and pore spacewere redrawn manually. Subsequently, surface areas of the con-nected pore space and grain phase regions were determined andrecalculated to structural thickness as diameters of the areaequivalent circles.

2.4. Petrophysical studies of acoustic anisotropies

The petrophysical experiments were done in a multi-anvilpressure apparatus at the Institut für Geowissenschaften, Uni-versität Kiel (Germany), allowing simultaneous measurements ofcompressional (Vp) and orthogonally polarised shear wave veloc-ities (Vs1, Vs2) in the three structural directions X, Y, and Z asa function of temperature in general up to 750 �C and pressure

Table 1Results of the porosity determination of Obernkirchen and Bentheim sandstonesfrom various methods.

Locality\Porosity(vol.%)

Densitydetermination(water uptake)

Imageanalysis(thinsections)a

Image analysis 3D(volumetric m-CTpore space models)

Obernkirchen 14e16 13.5e15.3 14.0 (closedporosity: 3.3; HRb);15.8 (closedporosity 3.6; MRb)

Bentheim 22e24 21.5e24.2 23.1 (closedporosity: <0.1; HR);21.0 (closedporosity: <0.2; MR)

a 15 thin sections per sample.b HR: high-resolution scan (2.86 mm per voxel); MR: medium-resolution scan

(6.76 mm per voxel).

W.-A. Kahl et al. / Journal of Structural Geology 49 (2013) 35e49 37

conditions up to 600MPa (for details see Kern et al., 1997). Since the3D multi-anvil pressure apparatus is not equipped with injectionunits, the followingmeasurements were done on dry cubic sampleswith 43 mm edge length. For experimental setup the implementedpistons, one pair for each direction, conducted to increase anddecrease pressure with respect to the sample material in well-balanced steps up to 100 MPa maximum at which seismic mea-surements were done to record data within repeated loading andunloading processes at stepwise steady state conditions. To avoidfailure of the quartz-dominated fabric due to thermal expansion,the temperature was kept at 20 �C. Due to the isothermal exper-imental boundary conditions, the elastic properties of the materialcan be determined. The seismic record is composed of nine veloc-ities, dependent on the three pairs of pistons for X, Y, and Z: three P-wave velocities and six S-wave velocities. Splitting of shear waves isobtained for each direction by two sets of the orthogonally polar-ised transducers, thus two sets of S-wave data are yielded for eachdirection. We used the ultrasonic pulse transmission technique forthe velocity measurements with transducers operating at 1 MHzfor P- and S-waves, respectively. Length and resulting volumechanges of the sample cube, due to changes of principal stress, areobtained by measuring the piston displacements.

For the seismic measurements sample cubes (43 mm on edges)were taken from large sandstone blocks and cut perpendicular tothe bedding. The correlation between ultrasonic wave velocityanisotropy and sandstone microfabric has been investigated usingthe P-wave data. A mutual perpendicular reference coordinatesystem (X, Y, Z, see above Section 2.1) for the investigations waschosen with seismically detected directions X and Y lying in the Z-plane parallel to sedimentary bedding.

2.5. X-ray microtomography method (m-CT)

Subsequent to the petrophysical studies, micro-plugs of 10 mmdiameter were drilled from the sample cubes parallel to the Z-di-rection. The X-ray microtomography scans of the sandstone coreswere done using the SkyScan1172 system (SkyScan, Belgium) at theInstitut für Geowissenschaften, Christian-Albrechts-UniversitätKiel, Germany. The SkyScan1172 is a tabletop unit for high-resolu-tion scans suitable for samples sized up to 35 mm in diameter andca. 55 mm in height. The cylindrical rock samples were scannedwith a beam energy of 100 kV, a flux of 100 mA, a copperealuminium filter, and using a 360� rotation with a step size of0.6�. High-resolution scans (detector at 2.86 mm per pixel) wereperformed for pore size, grain size and porosity determination.Medium-resolution scans in the oversized scan mode (5 connectedscans, 6.76 mm per pixel) were employed to determine the struc-tural thickness, porosity, and for large volume mean interceptlength (MIL) investigations (see Section 3.3 below). The tortuosityof possible pathways of the ultrasonic waves through the grainfraction was inspected using the 2.86 mm voxets (3-dimensionalregular grid) for Obernkirchen sandstone and the 6.76 mm voxetsfor Bentheim (see Section 3.5). Reconstruction of the spatial infor-mation on the linear attenuation coefficient in the sandstonesamples was done using the SkyScan software NRecon running ona cluster of 3 networked PCs. The program uses a modified Feld-kamp algorithm (Feldkamp et al., 1984). For each sample,a 990 � 990 matrix of up to 950 (or more) slices per stack isavailable.

As a result of the reconstruction procedure, each image consistsof isometric voxels (volumetric pixels) and has a certain thicknessdepending on the detector resolution. Thus, a stack of imagescontains true volumetric information. The information about thevaried X-ray absorption is encoded as grey values in the black-and-white images. Segmentation and binarisation (i.e. the recognition

of different fabric compounds by assigning grey values), imageanalysis and volume rendering were done using the SkyScan soft-ware CTAn and CTVox. To investigate possible tortuos pathways ofelastic waves through the sandstone’s grain framework, two plug-ins for the multi-platform free image processing package Fiji,Simple Neurite Tracer (written by Mark Longair) and 3D Viewer(see Schmid et al., 2010, for details), have been employed. Thefractal dimension of pore space and grain phase was calculatedusing the Kolmogorov “box counting” method (for details seeChappard et al., 2001). Within the SkyScan software CTAn, it iscalculated in both 2D and 3D. According to the software descrip-tion, in the course of the 3D calculation of the fractal dimension, thevolume is divided into an array of equal cubes, and the number ofcubes containing part of the object surface is counted. This isrepeated over a range of cube sizes such as 2e100 pixels. Thenumbers of cubes containing surface are plotted against the cubelength in a logelog plot, and the fractal dimension is obtained fromthe slope of the least squares regression.

3. Results

In order to investigate the source of the marked directionalanisotropies of ultrasound velocities observed in reservoir sand-stones, the rockmicrofabric was investigatedwith respect to fabric-related entities such as porosity, abundance and size distribution ofthe pores and grains, and tortuosity of the grain skeleton. To pro-vide a comparison of the microstructural characteristic obtained byimage analysis of both m-CT reconstruction volumes and thin sec-tion photomicrographs, we first compile the results of the porositydetermination as well as the size distributions of pore space andgrain phase from various Bentheim and Obernkirchen sandstonesamples. Subsequently, we present the results of a morphometricanalysis of the microfabric of two sandstone samples thatpreviously have been used in petrophysical studies of seismicanisotropies.

3.1. Characterisation of petrophysical rock properties by imageanalysis e a comparison of methods

3.1.1. PorosityThe fabric of clastic sediments such as detrital sandstones can

vary considerably on the cm-scale in response to sedimentary and/or diagenetic processes. However, we use the porosities derivedfrom the buoyancy weighing measurements to serve as a “bench-mark” for the accuracy of the datasets derived by image analysis ofthin section photomicrographs and m-CT reconstruction volumes,which are displayed in Table 1. The investigated samples of

W.-A. Kahl et al. / Journal of Structural Geology 49 (2013) 35e4938

Bentheim sandstone show a porosity between 22 and 24%,Obernkirchen samples scatter between 14 and 16%. It has beenobserved that Obernkirchen sandstone samples needed consid-erably longer time to reach saturation than Bentheim sandstonesamples.

Porosities determined from image analysis of thin section pho-tomicrographs (five thin sections per orientation, cut perpendicularto the X-, Y-, and Z-directions of the cubic sandstone samples, seeSection 2.1), based on the area percent determination of the man-ually redrawn boundaries of coloured resin in the pore space (seeFig. 1A and B), yielded values between 21.5 and 24.2% for Bentheimsandstone, and porosities between 13.5 and 15.3% for Obernkirchensandstone (see Table 1).

Fig. 1. Thin section photomicrographs and m-CT images of Obernkirchen (A, C, E) and Bedisplaying blue resin as pore space filling and the redrawn grain boundaries (in red), usedimages (2.86 mm per voxel). The characteristic fabric elements of both sandstones are welskeletal) and rutile and zircon as accessory minerals. (E) and (F) show the segmented and biinterpretation of the references to colour in this figure legend, the reader is referred to the

The true volumetric reconstruction of sandstone fabric by m-CT,which is basically a volumetric characterisation of the materialdensity arrangement within the samples, allows detailed inspec-tion of the fabric of the sandstones on micrometer scale in 2D andas well as in 3D. Each voxel represents the mean linear attenuationcoefficient for X-rays of the corresponding volume of the sampleand depends on the energy of the X-rays and on density and atomicnumber of the scanned material. In the reconstructed images, areasof high attenuation (e.g., accessory minerals, feldspar) are encodedin light grey values, whereas areas of low X-ray absorptionare colour-coded in dark grey (clay minerals as pore fillings) orblack (voids). The reconstructed images of Bentheim and Obern-kirchen sandstones are shown in Fig. 1C and D, respectively. The

ntheim (B, D, F) sandstones. (A) and (B) Photomicrographs of the rock thin sections,for image analysis of pore sizes from the thin sections. (C) to (D) High-resolution m-CTl recognized: quartz (C: dark grey; D: grey) and rare feldspar (D: light grey; in placesnarised pore space, pores are colour-coded corresponding to different size classes. (Forweb version of this article.)

W.-A. Kahl et al. / Journal of Structural Geology 49 (2013) 35e49 39

characteristic fabric features of the Bentheim sandstone are wellrecognised: fine to medium grained and rounded to subroundedquartz and rare feldspar (in places skeletal) with kaolinite as porefillings and rutile and zircon as accessory minerals. The Obern-kirchen sandstone exhibits subangular fine-grained quartz andaccessory minerals with little clay mineral content and noticeablenarrower pores. Besides the network of connecting pores, bothsandstones exhibit grain sized cavities that may result from thedissolution of feldspar. The latter process may account for the rareoccurrence of feldspar, which is often skeletal. In places, small areasof clustered grains occur.

Porosities determined from image analysis of m-CT the seg-mented and binarised reconstruction volumes (e. g., Fig. 1E and Fdisplays the segmented pore space which is colour-coded corre-sponding to different size classes) of both sandstones have beenobtained from both high-resolution (HR: 2.86 mm/voxel) and me-dium-resolution (MR: 6.76 mm/voxel) scans of the 10 mm micro-plugs: Obernkirchen 14.0% (closed porosity: 3.3%; HR) and 15.8%

Fig. 2. Pore and grain size distribution of Obernkirchen and Bentheim sandstones. (A, B) Porvarious methods: image analysis of thin sections (with redrawn grain boundaries in red) by dslices by the area equivalent circle method (grey curves); image analysis of the whole m-CTIllustration of the systematic differences between 3D maximal spheres (whole image volusection and individual slice). Upper image: slice of the pore space of Bentheim sandstone widashed circles indicates the maximum circles for different sites. Lower left: The two circles rresulting pore width. (D) Structural thickness distribution of pore space and grain phase ofimage volume by the maximal spheres (3D) method, for both high-resolution and medium-rreader is referred to the web version of this article.)

(closed porosity 3.6%; MR), and Bentheim 23.1% (closed porosity:<0.1%; HR) and 21.0% (closed porosity: <0.2%; MR). Althoughaffected by the scan resolution, it can be seen that Obernkirchensandstone exhibits a considerable fraction of closed porosity, whichmight be responsible e in combination with the overall largernumber of small pores for the slow saturation process observed forObernkirchen sandstone.

3.1.2. Pore and grain size distributionsThe pore size distribution of the sandstone samples, derived by

2D image analysis of thin section photomicrographs with redrawngrain boundaries, is based on the diameters of equivalent areacircles that have been determined from the connected regions ofcoloured resin within the pore space. Obernkirchen sandstonedisplays a spectrum of pore sizes that is distributed between 50 and150 mmwith a peak at 60 mm (Fig. 2A). Bentheim sandstone exhibitsa wide range of pore sizes: with the most observed diameterswithin the range of 50e200 mm, still a high fraction of pores show

e size distribution in Obernkirchen (A) and Bentheim (B) sandstones, as determined byiameters of area equivalent circles (thin black curves); image analysis of individual m-CTvolume by morphometry using the maximal spheres method (bold black curves). (C)me, 2D representation: dashed circles) and 2D area equivalent circles methods (thinth colour coding of different area intervals. Lower right, magnified view of a large pore:epresent the systematic differences of the two methods concerning the meaning of theObernkirchen and Bentheim sandstones, as determined by morphometry of the wholeesolution scans. (For interpretation of the references to colour in this figure legend, the

W.-A. Kahl et al. / Journal of Structural Geology 49 (2013) 35e4940

larger diameters (Fig. 2B). The grain size distribution has not beeninvestigated quantitatively by image analysis of petrographicphotomicrographs.

The approach of the image analysis of the m-CT-derived recon-struction volumes has been twofold: (a) the whole stack of imageshas been analyzed as a continuous volume, and (b) each slice in thestack has been assessed individually. As the thickness of each slice(see Section 2.5) is within the range of the thickness of a thinsection, it contains comparable fabric information and was ana-lyzed using the “2D” methods (e.g., determining pore diametersfrom equivalent area circle diameters) similar to the procedure onthin section photomicrographs.

The inspection of the continuous image volume has been doneby computer-aided morphometry: grain phase (i.e. the fabriccompounds that were recognised by segmentation and subsequentbinarisation of the reconstructed scan images, see Section 2.5) andpore space thickness was evaluated by using the method ofweighted distances and medial axis extraction following Remy andThiel (2002). The resulting structural thickness distribution curvesare shown in Fig. 2A and B, respectively, for pore space, and inFig. 2D for pore space and grain phase. For Obernkirchen sandstone,the majority of the pores is between 20 and 70 mm, with a morepronounced skewness towards small diameters for the high-resolution scan. Bentheim sandstone displays the majority ofpores in the range of 30e100 mm. The mean volume-weightedthicknesses measured by the distance transform thicknessmethod (sphere fitting as described by Hildebrand and Ruegsegger,1997, reported for the high-resolution scan and the e not froma coinicident volume emedium-resolution scan, the latter given inparentheses) are: Obernkirchen grain phase thickness 95.3(86.7) mmand pore space 43.6 (48.7) mm, and Bentheim grain phasethickness 140.3 (161.7) mm and pore space 61.1 (75.1) mm.

Size distribution analyses of the fabric components of the in-dividual image slices have been performed based on the diametersof equivalent area circles, and not on structural thickness, becausethe former are morewidespread in 2D digital image analysis of thinsections (e.g., Klein and Reuschlé, 2003; Trautwein and Huenges,2005). Here, equivalent diameters are derived from countingnumber and area of pixels that belong to a pore, and the subsequentconversion into the diameter of a circle of the equivalent area (seeFig. 1E and F). To mimic the preparation procedure of the orientedthin sections that have been cut in the three main structural di-rections from the sandstone cubes, the image volumes of both high-and medium-resolution scans have been cut as stacks of “virtualthin sections” (up to 1500 per stack, see Fig. 2A and B) perpendic-ular to the X-, Y-, and Z-direction. Obernkirchen sandstone exhibitspore diameters between 20 and 180 mm with a marked bimodalmode displaying peaks at ca. 35 and 95 mm, respectively. Bentheimsandstone exhibits a spectrum of equivalent area circle diametersfrom 40 to almost 400 mm that peaks at 140 mm.

It is obvious from Fig. 2A and B, that the determination ofstructural thickness bymaximal spheres/circles using the whole 3Dimage stack leads to different (smaller) results than the calculationof pore radii and grain sizes for the individual slices using theequivalent circle area method. In part, these differing results can beattributed to the differences inherent in the calculationmethods, asis shown exemplary in Fig. 2C: since the equivalent area methodcounts all connected voxel regions, the diameter of the equivalentarea circle of the single turquois pore is 376.1 mm, which is muchlarger than the diameter of the biggest maximal sphere that can befitted to the pore body, 123.0 mm.

It is important to note, that with respect to the lower values ofobserved pore diameters, the outcome of the thin sectionmicroscopy-based image analysis is in agreement with the resultsof the 3D morphometric characterisation of the whole stack,

whereas concerning large pore diameters the results of the imageanalysis of the manually redrawn thin section photomicrographsare almost coincident with the outcome of the 2D m-CT imageanalysis for large pore diameter size classes except for their relativeportions of the porosity. Here, the higher relative portions of lowerdiameters might point to differences in positioning the boundarygrain/pore by (a) manual redrawing and (b) computed thresh-olding. On the one hand, the computer-aided determination ofgrain boundaries may detect relative more narrow pores, on theother hand the result might be biased by the occurrence of inclinedgrain boundaries relative to the optical path in the petrographicmicroscope: within a 25 mm thick thin section, an inclined grainboundary can reduce the thickness of the layer of coloured resin toinvisibility. However, in case of the 2.86 and 6.88 mm thick indi-vidual slices, there are still a few reconstruction images that willretain connected pores. Since the thinning out of the coloured resinto invisibility is not symmetric, each inclination of grain boundarieswill narrow the positioning of the pore walls to a certain degree.

3.2. Directional dependence of P-wave velocities as a function ofpressure

Fig. 3 displays the three P-wave velocities measured in thestructural directions X, Y, and Z as a function of pressure up to100 MPa. The velocityepressure relations display the well-knowninitial steep velocity increase with increasing confining pressure.The non-linear increase is due to progressive closure of micro-cracks, typically illustrating the pressure sensitivity of P-waves(Kern et al., 2008). Linear behaviour is approached above about40 MPa, marking the intrinsic behaviour of the compacted aggre-gate. In both sandstone types, Vp is highest parallel to the bedding(X- and Y-directions in the Z-plane) and lowest perpendicular to thebedding (parallel to the Z-direction). The significant differences ofP-wave velocities measured in the three structural directionsindicate strong velocity anisotropy. Obernkirchen sandstone showshigher velocities in all directions than Bentheim sandstone, withthe lowest Vp (parallel to the Z-direction) in Obernkirchen sand-stone being still faster than the highest Vp velocities in Bentheimsandstone (in the Z-plane).

3.3. Linking bulk anisotropic sound velocities to microstructuralanisotropy analysis of pore space and grain phase

For the correlation of the bulk seismic properties to the rockmicrofabric, the orientation of the main directions of seismic ve-locities needs to be located in the reconstruction volume. To ensurecorrect assignment of the main direction of seismic anisotropiesmeasured in the multi-anvil pressure apparatus, we positioned themicro-plug in the scanner with the seismic Z-direction upward andseismic X-direction to the right in the transmission image. In thereconstructed images, the structural directions X and Y lie withineach slice (to the right and upward, respectively), and the Z-di-rection points upward the stack.

In the microstructural context, the mean intercept length (MIL)analysis is a measuring tool for the isotropy of a structure (Harriganand Mann, 1984). Odgaard (1997) showed that MIL analysis can beused to infer the mechanical strength of cancellous bone. Accordingto the SkyScan CTAn software description, the mean interceptlength is found by sending a grid of scan lines over a large numberof 3D angles through a spherical 3D image volume of interest (VOI)containing binarised objects (Fig. 4A). It is the length of the scanline through the analyzed volume divided by the line’s number ofpasses through the solid phase. This method gives an accurateresult for the mean structural thickness, as long as the analyzedvolume contains a sufficient large number of objects. This is the

Fig. 3. P-wave velocities in the structural directions X, Y, and Z as a function of pressure up to 100 MPa, measured in the sample cubes of two sandstones. The slowest velocities wereobserved in the Z-direction, which is perpendicular to the bedding. The fastest and intermediate P-wave velocities have been observed in the X- and Y-direction within the beddingplane.

W.-A. Kahl et al. / Journal of Structural Geology 49 (2013) 35e49 41

case for the VOI of the reconstructed sandstones: the spherediameter in mm is the 59-fold (Obernkirchen) and the 38-fold(Bentheim), respectively, of the mean structural thickness of thegrain phase. An ellipsoid is fitted to the 3D distribution of MILsmeasured over the full range of 3D stereo-angles (see Fig. 4B). Thisellipsoid has 3 vectors which are orthogonal and describe thelongest orientation (E1), and the length (E2) and width (E3) of theellipsoid at right-angles to the longest orientation (see Fig. 4C).

In the literature there are several methods and approaches tocharacterise the anisotropy of porous materials in terms of fabrictensors in 2D and 3D (e.g., Gerik and Kruhl, 2009; Inglis andPietruszczak, 2003; Ketcham, 2005; Launeau and Robin, 2005). Inthe case of a spatial multiply interconnected grain phase that in-terpenetrates an as complex and likewise connected pore spacestructure in three dimensions, there are complex geometries to beassessed by the fabric descriptors. In particular, a grain phase thathas not been separated by artificial watershed transform toapproach “grain sizes” as used in this study (see Section 3.4) is verycomparable to the description of trabecular bone (see e.g., Ketchamand Ryan, 2004; Moreno et al., 2012). In this study, we chose themean intercept length analysis provided by the SkyScan software,because it can utilise the true 3D volume to compute a fit ellipsoid

Fig. 4. Illustration of the mean intercept len

from all 3D scan lines and not merely a mean of ellipses in a stackorientation.

Moreover, as wemeasure a bulk property that depends onmanyparameters, an arithmetic mean as provided by the MIL mightactually be a good approximation to a grain phase network madeup by cemented grains, which are deposited in a beach sediment,since we do not have any information about the crystal orienta-tions. In a texture without a preferred crystal orientation (as e.g.,could be present in a magmatic texture or mantle rocks) as a con-sequence of the depositional origin, we would expect a randomdistribution of grains with a low aspect ratio compared to texturesof magmatic origin.

To link the bulk seismic behaviour to microstructural aspects,we performed combined MIL analysis on four cubic VOIs of 6 mmedge length based on the grain phase as well as on the pore space(stack Obernkirchen: 3952 slices of images of 986 � 986 voxels;stack Bentheim: 3768 slices of 927 � 927 voxels). Although in drysamples the elastic waves propagate exclusively through the grainphase, abundance and distribution of the pores also imply impor-tant constraints on the wave velocities. Therefore, the mean inter-cept length of the grain phase as well as the pore space have beeninvestigated and are compiled in Table 2.

gth analysis (MIL). See text for details.

Table 2Directions of seismic P-wave velocity and MIL analysis results of grainskeleton and pore space in Obernkirchen and Bentheim sandstones.

Sandstone samplelocality characteristicP-wave velocity

Mean intercept length (mm)pore spacejgrain phase based MILanalysis pore space MIL ellipsoid vector

Obernkirchen 0.0740j0.5763Z, slowest E-vector 1, largestObernkirchen 0.0576j0.4577Y, intermediate E-vector 2, intermediateObernkirchen 0.0554j0.4410X, fastest E-vector 3, shortestBentheim 0.1197j0.5568Z, slowest E-vector 1, largestBentheim 0.1008j0.4711Y, intermediate E-vector 2, intermediateBentheim 0.0959j0.4491X, fastest E-vector 3, shortest

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At first we focus on the correlation between bulk seismicproperties, i.e. the characteristic P-wave velocities, and meanintercept lengths of the pore space. The P-wave velocities arenegatively correlated with the mean intercept lengths. The direc-tion of the largest mean intercept length in both oriented drill coresamples is parallel to the slowest observed seismic P-wave veloc-ities in the Z-direction (Obernkirchen MIL jjeigenvector E1:0.0740 mm, Bentheim MIL jjeigenvector E1: 0.1197 mm). Fur-thermore, the highest Vp velocities observed in the X- and Y-di-rections in the bedding plane of Obernkirchen sandstone as well asBentheim sandstone correlate with the smallest MILs found jjE3(0.0554 mm) and jjE2 (0.0576 mm) for Obernkirchen and thesmallest MILs found jjE3 (0.0959mm) andMIL jjE2 (0.1008mm) forBentheim. It is obvious that all three MILs of the Obernkirchensandstone (0.0554 mm, 0.0576 mm, 0.0740 mm) are smaller thanthe MILs observed for the Bentheim sample (0.0959 mm,0.1008 mm, 0.1197 mm). This is again corresponding to the overallhigher Vp velocities in the Obernkirchen sandstone compared tothe Bentheim sandstone. In summary, the analysis of the meanintercept length of the pore space has shown that (a) the relativesuccession of the elastic wave velocities observed in the threestructural directions X, Y, and Z correlates inversely with theincreasing mean pore width, and (b) that the orientations of theellipsoid vectors that describe the results of the MIL analysiscoincide with the orientations of these main directions. In Fig. 5Athe directions of the eigenvectors E1, E2, and E3 (see Table 2) of thepore space-based MIL analysis ellipsoid are plotted in a stereo-graphic projection. The orientations of the eigenvectors E1, E2, and

Fig. 5. Orientations of the P-wave velocities in the structural directions X, Y, and Z and eBentheim sandstones. (A) The eigenvectors of the pore space MIL ellipsoids are plotted in a sUniversität Bochum, 2003e2008). Eigenvector E3 denotes the shortest mean intercept lengtdirection) in the oriented drill cores is upward, which is the orientation of the direction withare parallel to the structural directions X and Y.

E3 as well as the orientations of the structural directions X, Y, and Zare visualised in the two reconstruction images of Obernkirchenand Bentheim sandstones (Fig. 5B and C, respectively). Both imagesdisplay the slices that contain the origin of the spherical 3D vol-umes, which were used for the mean intercept length analyses.

The investigation of correlation between characteristic P-wavevelocities and mean intercept lengths of the grain phase led to anunexpected observation (see Table 2): Within one single sandstone,P-wave velocities and MILs of the grain phase are again negativelycorrelated. The direction of the largest MIL in both oriented drillcore samples is parallel to the slowest observed seismic P-wavevelocities in Z-direction (Obernkirchen MIL jjE1: 0.5763 mm, Ben-theim MIL jjE1: 0.5568). The high velocities in Obernkirchen’s andBentheim’s X- and Y-directions are oriented parallel to the shortMILs jjE3 (0.4410 mm) and jjE2 (0.4577 mm) for Obernkirchensandstone and short MILs jjE3 (0.4491 mm) and jjE2 (0.4711 mm).The result of the mean intercept length analysis of the grain phaseis unexpected for two reasons: (a) the negative correlation betweenP-wave velocity and mean structural thickness of the grain phase isunexpected, as grain-bound P-waves should propagate fastestalong the direction with the largest, and not the smallest, meanthickness of the grain skeleton, and (b) the observation, that theresults of the mean intercept lengths of the grain phase in bothsamples are very comparable is unexpected, because both sand-stones exhibit significant differences in grain size and P-wave ve-locities. However, this supposedly enigmatic findings can beexplained by a thorough consideration of the meaning of theobserved MILs of the grain skeleton: the mean intercept length ofthe grain phase (ca. 500 mm) is much larger than the size of theindividual grains of both sandstones. Fig. 1C and D provides anexplanation for this: in the grain-supported sandstone skeleton themean distances of conjoined grains are similar in both samples.This is correctly reproduced by the measuring principle for the MILanalysis. However, the influence of pore space as well as grainphase for the propagation of ultrasonic waves is different. Thewavecannot pass into the pores: the direction of the pore space with thelargest mean intercept length imposes the largest detour on thewave path, resulting in the slowest wave velocity. Instead, the ul-trasonic waves traverse the rock via the adjacent grains. Theattenuation of seismic waves by a fabric consisting of large, roun-ded to subrounded grains containing wide cavities is very differentfrom the attenuation originating from small, subangular grainspossessing narrow pores. Therefore, to correlate the anisotropy ofultrasonic waves with the sandstone microfabric, the actual travellengths of possible paths of seismic waves in the sandstone grainphase has to be compared.

igenvectors E1, E2, and E3 shown in the reconstruction volume of Obernkirchen andtereographic projection (using Stereo32, rel. 1.0.1, by K. Röller and C. A. Trepmann, Ruhrh, E1 the largest. (B, C) The orientation of the slowest seismic velocity (the structural Z-the largest pore space MIL jjE1. In both sandstone samples, the eigenvectors E2 and E3

Fig. 6. Binarised images of the grain skeletons of Obernkirchen (A) and Bentheim (B) sandstone. Since the individual grains of the solid fabric component have not been separated inindividual grains by means of image manipulation methods (e.g., watershed transform), this binarised structure “as it is” might be a very representative analogue of the sandstonemicrofabric during the pressure experiment, when the microcracks are closed under the superimposed load pressure. Analysis of the fractal dimension has been made of bothinterpenetrating fabric compounds, pore space and grain phase, in 3D and in 2D (shown here for the grain phase, images are the same as in Fig. 1C and D).

Table 3Fractal dimensions in 3D and 2D (mean of all slices per stack order) of pore space andgrain skeleton of Obernkirchen and Bentheim sandstones.

Fabric component Stack order Obernkirchen sandstone Bentheim sandstone

3D 2D mean 3D 2D mean

Pore space Z (MRa) 2.29 1.32 2.42 1.50Y (MR) 1.35 1.51X (MR) 1.35 1.51Z (HRa) 2.35 1.49 2.58 1.68Y (HR) 1.54 1.69X (HR) 1.53 1.69

Grain phase Z (MR) 2.93 1.93 2.91 1.91Y (MR) 1.93 1.91X (MR) 1.93 1.91Z (HR) 2.94 1.94 2.90 1.91Y (HR) 1.94 1.92X (HR) 1.94 1.91

a HR: high-resolution scan (2.86 mm per voxel); MR: medium-resolution scan(6.76 mm per voxel).

W.-A. Kahl et al. / Journal of Structural Geology 49 (2013) 35e49 43

3.4. Fractal characterisation of pore space and grain phase

In the recent years, fractal analysis has been usedmore andmoreto characterise the self repeating patterns of geologic materials, e.g.,Kruhl and Nega (1996) studied the relationship between the fractaldimensions of sutured quartz grain boundaries and their formationtemperature from thin section images; Mamtani et al. (2012)quantified microcrack patterns in a quartzite using fractal geome-try-based methods from SEM images; Mahamud et al. (2003)determined the fractal dimension of the porous coal microfabricfrom mercury porosimetry and monitored the textural evolutionduring the oxidation process; Yao et al. (2009) investigated thepermeability of seepage-pores in coals by fractal characterisation ofmercury porosimetry data. Mostly on behalf of biomechanical andmedical m-CT or MR studies, also true volumetric 3D data is char-acterised with fractal analysis, e.g., Zioupos et al. (2006) employedfractal analysis to investigate, whether certain aspects of bonebehaviour are more governed at the architectural/compositionallevel, or at the molecular/biophysical level; Zhang et al. (2006)developed a 3D method that is accurate and sensitive in detectingage-related white matter structural changes in human brain.

To assess the multiply interconnected, mutually interpenetratingfabric phases of pore space and grainphase as awhole (see Fig. 6), theKolmogorov box countingmethodwas applied in 3D and 2Das shapecomplexity descriptor. For Obernkirchen sandstone, the fractaldimension of the true 3D binarised volume of the pore space (firstresult is the high-resolution scan, the result for the medium-resolution scan is given in parentheses, see Table 3) was deter-mined to be 2.35 (2.29), and for Obernkirchengrainphase 2.94 (2.93).The 3D volume fractal analysis of Bentheim sandstone yielded 2.58(2.42) for the pore space, and 2.90 (2.91) for the grain phase.

In addition, for each scan, the mean fractal dimension of allslices (in 2D), stacked in the three mutual perpendicular mainstructural directions, X, Y, and Z, has been determined.

It could be observed thate in case of the pore spacee it is alwaysthe stack ordered in the Z-direction that exhibits a slight lowerfractal dimension than the stack ordered in the X- and Y-direction

(first value: HR scan/second value: MR scan): Obernkirchen porespace 2D in Z (1.49/1.32), Y (1.54/1.35), X (1.53/1.35), Bentheim porespace 2D in Z (1.68/1.50), Y (1.69/1.51), X (1.69/1.51). In case of thegrain skeletons,most of the values in all three stack orders are equal,and almost identical for high- and medium-resolution scans:Obernkirchen grain phase in Z, Y, and X (1.94/1.93; 1.94/1.93; 1.94/1.93), Bentheim grain phase (1.91; 1.91; 1.92/1.91; 1.91; 1.91).

In general, it can be stated that the m-CT-derived values gainedfor the fractal dimension (FD) of the pore space in 3D and 2D arecomparable to the values of FD gained in other studies: Bartelset al. (2002) reported an FD number of 2.45 for the pore space ofBentheim sandstone derived from a validation of a numericalsimulation of induced permeability change in reservoir sandstoneby a core flooding laboratory experiment; Schlueter et al. (1997)obtained an FD number for sandstone pore space from a perime-ter-area power-law relationship from specimens of Berea sand-stone of 1.49. The increase in FD for the high-resolution scan incomparison to the medium-resolution scan show that the

Fig. 7. Determination of the tortuosity of possible pathways of elastic waves through the sandstone grain skeleton. (A) Data volume of Bentheim sandstone with structural di-rections and planes assigned. (BeD) Location of the slices used for tortuosity analyses, exhibiting grain fraction abundances identical, lower and higher, respectively, to the overall3D proportion of the grain phase percentage. (EeG) Outline of the relation of planes and directions used for the determination of tortuosity.

W.-A. Kahl et al. / Journal of Structural Geology 49 (2013) 35e4944

behaviour of the porous structure is of fractal nature. As a roughindication of the 3D FD numbers, coarser fabrics like the Bentheimpore space yield numbers closer to 3, and more rugged fabrics yieldsmaller numbers. Thus, the larger voids of the Bentheim pore spaceyield larger FD numbers, and the more serrated porous system ofObernkirchen sandstone with its smaller pore diameters exhibitsmaller fractal dimension numbers.

The 2D data show, not very pronounced but consistent,a smaller FD number for stacks parallel to the main fabric

directions X and Y, i.e. those m-CT images with one component inthe Z-direction (with the slowest seismic velocity). This couldindicate that in the Z-direction the pore space voids are slightlylarger and cause larger deviations of the wave paths through theconnected grain skeleton, thus yielding lower seismic velocitiesin these directions. For the grain skeleton, which was not sep-arated in individual grains by means of image manipulationmethods (e.g., watershed transform), the fractal dimensions arevery similar and close to 3. Thus both networks of the connected

Fig. 8. Tortuosity of the sandstone grain framework inferred from 2D slices. For theautomated search we employed the plug-in Simple Neurite Tracer (written by MarkLongair) for the multi-platform free image processing package Fiji. (A) shows the plug-in in the process of tracing the shortest path in X-direction between point “x” and point“x0”. The cyan lines represent the wave fronts emanating from both points. (B) displaysthe paths found in X- and Y-direction (purple horizontal and vertical lines). Thelocation of the starting and the end points was chosen following a rough grid of fivepaths in each direction per slice. (For interpretation of the references to color in thisfigure legend, the reader is referred to the web version of this article.)

W.-A. Kahl et al. / Journal of Structural Geology 49 (2013) 35e49 45

grain phase for both sandstones are possessing a comparableconnectivity, although the Obernkirchen FD number is slightlyhigher, presumably due to the smaller, subangular grains.

These overall findings may suggest, that the velocity anisot-ropies of the former beach sediments might be governed by theinterplay of grain size, grain geometry, and thereof resulting poresizes. A connected network of large, rounded grains as Bentheimsandstone has large pores that cause strong deviations of the actualwave paths. Such networks possess a lower number of grain con-tacts as networks made of smaller, subangular grains like Obern-kirchen sandstone. The larger grain size and e in relation to thegrain size e smaller cojoint grain boundaries between neighbour-ing grains cause stronger attenuation of the waves.

3.5. Assessing the tortuosity of the grain-bound soundwaves’pathways through the grain framework

To link the bulk seismic behaviour to microstructural observa-tions of the grain phase, we inspected the tortuosity of possiblepathways (in 2D slices) of the elastic (seismic) waves through thegrain fraction of the sandstone. The data volumes, cuboids of 1007and 848 slices (Obernkirchen and Bentheim, respectively) of1000 � 1000 voxel images (Fig. 7A), have been oriented coinci-dently to the strain field applied in the 3D multi anvil pressureapparatus. Therefore we were able to investigate the elastic waves’pathways perpendicular to the former sedimentary bedding plane(the Z-direction, exhibiting the slowest elastic wave velocity) aswell as within the bedding parallel to the fastest and the inter-mediate velocities (X- and Y-directions, respectively, both lying inthe Z-plane). To determine wave paths in the Z-direction (per-pendicular to the Z-plane, see Fig. 7A), wemeasured path lengths inthe corresponding directions in images of the X- and the Y-plane(see Fig. 7F and G). To determine wave paths following the grainegrain contacts in Y-direction, the corresponding directions in thecohorts of the images of the Z- and the X-plane were surveyed(Fig. 7E and F). Eventually, the grain-bound paths in the X-directionwere inspected using the appropriate directions in the image stacksof the Y- and Z-planes.

In order to eliminate a possible bias caused by differing abun-dances of the grain fraction in the different slices, we chose levelsthat exhibit an abundance (I) identical to, (II) higher, and (III) lowerthan the overall 3D percentage of the grain phase (Obernkirchen:86.5 vol% grain fraction,13.5 vol%porosity; Bentheim:80.1 vol%grainfraction, 19.9 vol% porosity; see Fig. 7BeD for the location of thelevels).Within a given slice (17 of each plane cohort),five trajectorieswere evaluated in vertical and horizontal orientation, respectively.For the automated search we employed the plug-in Simple NeuriteTracer (written by Mark Longair) for the multi-platform free imageprocessing package Fiji. In Fig. 8A, the plug-in is shown in theprocessof tracing the shortest path in the X-direction between two points“x” and “x0”. The cyan lines represent the wave fronts emanatingfrom both points. In Fig. 8B, the purple vertical and horizontal linesrepresent the trajectories evaluated within this slice.

The path lengths of the shortest tortuous passages through thegrain framework found by the Simple Neurite Tracer Fiji plug-inwere correlated with the direct distance between the path’s start-ing and end points. The tortuosity (the ratio of path length to thestraight distance of the end points) was determined by the evalua-tion of 170 paths in each direction. To link the effect of tortuosity tothe observed velocities of elastic waves in sandstones, the consid-eration of the shortest pathe andnot the average of all observede isdecisive.

The analysis of the tortuosity of 510 trajectories for possiblepathways of elastic waves through the grain skeleton of Obern-kirchen and Bentheim sandstones (see Fig. 9A and C: Obernkirchen

sandstone and Fig. 9B and D: Bentheim sandstone) shows, that thehighest tortuosity value (1.057322) can be found parallel to thedirection of the lowest observed velocity of elastic (seismic) waves(parallel to the Z-direction), which is the orientation perpendicularto the former sedimentary bedding plane of the sandstone (the Z-plane). The tortuosity values observed in the two other orientationswithin the bedding plane are very similar (see Table 4), but smallercompared to the tortuosity value perpendicular to the Z-plane:1.050405 and 1.051487 in X- and Y-direction, respectively. Bothobservations, the similarity of the values in X- and Y-direction aswell as the clear difference to Z-direction, correlate with theobserved differences in the elastic wave velocities observed in 3Dmulti-anvil pressure apparatus for cubic samples.

4. Discussion

In both sandstones, the relative succession of the anisotropic P-wave velocities observed in the petrophysical experiments is linkedto the bedding structures. Fig. 10 summarises the main observa-tions and provides an overview of the ultrasonic wave velocityanisotropy and the microstructural anisotropy in Obernkirchen andBentheim sandstones. Obernkirchen sandstone shows higher bulkseismic P-wave velocities in all structural directions than Bentheimsandstone (Fig. 10A; see Section 3.2 for more detail). In both

Fig. 9. 2D tortuosity of possible seismic wave paths. Tortuosity of Obernkirchen (A, C) and Bentheim (B, D) sandstone in Z- and X-directions. The data, grouped by the relative grainfraction abundances of the selected slices, do not exhibit a dependence of the local slice porosity on the observed tortuosity. Symbols: triangles e high porosity levels; circles e

average porosity levels; squares e low porosity levels.

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sandstones, the relative succession of velocity values is associatedwith the bedding structures. The results of the pore space MILanalysis correlate well (inversely) with the bulk seismic properties(Fig. 10B; see Section 3.3). In contrast, the MIL results of the grainphase exhibit an unexpected pattern: Still showing the relativesuccession of the directional velocity dependence, the mean traveldistances of waves are similar in both samples in the structural X-,Y-, and Z-direction, respectively, and they are larger than thethickness of the single grains (Fig. 10C; see Sections 3.2 And 3.3).

The main orientations e and the relative values e of bulkanisotropic sound velocities show a correlation with the main di-rections of microstructural anisotropy of the sandstone pore space

Table 4Tortuosities of the shortest possible trajectories (2D) of elastic waves through thegrain skeleton of Obernkirchen and Bentheim sandstones.

Locality Z (perpendicularto sedimentary bedding)

Y (withinbeddingplane)

X (withinbeddingplane)

Obernkirchen 1.044805 1.044182 1.041437Bentheim 1.055012 1.051487 1.050405

in terms of mean intercept length. In this context the mean inter-cept length (MIL) describes the directional-dependent averagestructural thickness. As we measure a bulk property that isdependent on many factors, an arithmetic mean might still bea good approximation to a grain phase network made up bycemented grains, which are deposited in a beach sediment. Wecannot not make assumptions about crystal orientations e since itis not a texture with a preferred crystal orientation but a deposi-tional feature, we would expect a random distribution. Moreover,fractal analysis (Section 3.4) of the self-repeating patterns of porespace and grain phase fabric components suggested that the ve-locity anisotropies of the clastic sediments may be induced bycharacteristic differences in the connectivity (Odgaard, 1997) of thegrain skeletons that arise from the interplay of grain size, graingeometry, and hence resulting pore sizes in terms of varied num-bers of grain contacts and differing morphologies of cojoint grainboundaries.

Our data also show that the MIL analysis cannot be applied tothe grain skeleton: Despite the significant differences of grain sizeand P-wave velocities in both sandstones, themean travel distancesof waves are found to be similar in both sandstones e and found to

Fig. 10. Anisotropy of elastic waves and microstructural anisotropy in sandstone. (A) Bulk seismic P-wave velocities: Obernkirchen sandstone shows higher velocities in allstructural directions than Bentheim sandstone. In both sandstones, the relative succession of velocities is linked to the bedding structures. (B) Anisotropy of the mean interceptlength of the pore space, derived frommorphometry based on m-CT reconstruction images. The results of the pore space MIL analysis correlate well (inversely) with the bulk seismicproperties. (C) The MIL results of the grain phase exhibit an unexpected pattern: Still showing the relative succession of the directional velocity dependence, mean travel distancesof waves are similar in both samples in X, Y, and Z, respectively, and they are larger than the thickness of the single grains. (D) The tortuosity of possible wave paths through the grainphase correlates with the relative succession of the seismic velocities within and between the two sandstone samples.

W.-A. Kahl et al. / Journal of Structural Geology 49 (2013) 35e49 47

be larger than the thickness of the single grains. Still, the relativesuccession of the directional velocity dependence is preserved. Ourresults clearly indicate the different influence of pore space andgrain skeleton on the propagation of ultrasonic waves: Because thewave cannot pass into the pores, it is sufficient to assess the averagethickness of this fabric element (Section 3.3). In contrast, as theultrasonic waves traverse the rock via the adjacent grains, it isnecessary to survey the actual travel lengths of seismic waves in thesandstone grain skeleton (see Section 3.5). Since the ultrasonicwaves traverse the rock via the adjacent grains, the actual travellengths of seismic waves in the sandstone grain phase depend onthe connectivity of the grain skeleton e and not on its meanthickness. As found by image analysis of the reconstructed m-CTscans, the tortuosity of possiblewave paths through the grain phasecorrelates with the relative succession of the seismic velocitieswithin and between the two sandstone samples (Fig. 10D).

Some of our data are in fact counter-intuitive: although showingthe highest mean intercept length perpendicular to the bedding(parallel to the Z-direction), the fractal analysis pointed to higherroughness in this direction (and hence wider deviations of theseismic waves paths from this direction). This probably is resolvedby the finding of Trautwein (2005) on the preferential closing ofpores with a high aspect ratio and the development of extensionalvertical pores in uniaxial petrophysical experiments, which couldbe comparable to the stress regime active in diagenetic processes.

In this study, we were able to survey parts of sandstonemicrofabrics that were responsible for the directional anisotropicattenuation of seismic waves in a petrophysical experiment.Although we could achieve a marked directional correlation be-tween bulk seismic behaviour and the investigated rock micro-fabric, the morphometric characterisation of the fabric compoundscould only reproduce the relative succession of the P-wave veloc-ities observed in the corresponding directions, and not a complete

concordance concerning the ratios of the observed anisotropies. Inpart, this might be due to the fact that we were not able to surveythe microfabric of the complete cubic sample with the high-reso-lution of below 10 mm, which is a prerequisite for the detailedmorphometric investigation of the true 3D microfabric of thesandstone fabric. However, the accuracy of tracing the tortuosity ofpossible wave paths through the grain skeletonwith the free imageprocessing package Fiji will be improved by applying the softwareto the full 3D space rather than to 2D slices selected from the stack.Furthermore, the quantitative assessment of the contribution of theconnectivity within the grain skeleton could enhance the con-cordance with the observed compressional wave anisotropies.

Nevertheless, by applying high-resolution m-CT below the10 mm-range to the characterisation of sandstone fabric, we wereable to reproduce the different attenuation of seismic waves bya fabric consisting of large, rounded to subrounded grains con-taining wide cavities (Bentheim sandstone) and the very differentattenuation originating from small, subangular grains possessingnarrow pores with e sporadical present e fine-clustered patterns(Obernkirchen sandstone).

5. Conclusions

In this study, we presented microfocus X-ray m-CT as a supple-mentary research tool to investigate sandstone microfabric withrespect to its constituent fabric compounds. The high-resolutiondata of the m-CT image volumes yielded in this study (with 6.76and 2.86 mm per isometric voxel) permit profound assessment ofthe microfabric of pore space and grain phase. Since the m-CT-derived image volumes consist of individual image slices witha certain thickness (see Section 2.5) depending on detector reso-lution and reconstruction procedure, image analysis of the recon-struction volumes can be either analyzed as a continuous volume or

W.-A. Kahl et al. / Journal of Structural Geology 49 (2013) 35e4948

as individual “virtual thin sections”. Thus, the m-CT-derived datacan be inspected with quantitative image analysis methods usingtrue 3D and 2D methods (similar to the procedure on thin sectionphotomicrographs).

Our investigations shed light on the potential but also the lim-itations of high-resolution m-CT. On the one hand, we could gaininsights in the sandstone microfabric on the pore scale: due to thehigh-resolution of the scans it was possible to assess the tortuosityof grain-bound pathways as well as the microstructural anisotropyof the pore space directly by means of computer-aided quantitativeimage analysis. In this regard, we are convinced that the e incomparison to SEM still limited e resolution of the reconstructedimages of several mm is in fact a very representative analogue of thesandstone microfabric during the pressure experiment, when themicrocracks are closed under the superimposed load pressure. Inthe loaded state, the actual grain-to-grain contacts may be morefrequent and differently distributed as in the unloaded state, andthe pore size distributions might be altered to exhibit less portionsin the sub-micrometer range. However, due to the microfocus conebeam geometry of the X-rays, the high-resolution scan setup of thisstudy demands a certain maximum sample size for a high-resolution analysis. Hence, a cylindrical sub-sample (Ø 10 mm,height 43 mm) was prepared for the m-CT analysis from the sand-stone cubes (43 mm on edges). Thus, the complete spatial extend ofthe sandstone fabric that responded to the ultrasonic signals couldnot be assessed. Nevertheless, a substantial part of the sample wasaccessible to m-CT based image analysis. In contrast, in case of theprepared thin sections, a larger area could be surveyed, but neitherthin section has been part of the actual grain frame work thatrespond in the petrophysical experiments. In regard to the scanresolution, the ongoing development of microfocus X-ray tubes anddevices will continue to increasing voxel resolution also for largersample volumes. Currently, sample cubes like the one used in thisstudy may be scanned as a whole with ca. 50e60 mm per isometricvoxel, which would not have enough resolving power for theconsiderations of this study. Scanning of 20mmmicro-plugs drilledfrom the sample cubes would yield ca. 20 mm isometric voxel res-olution and would substantially enlarge the sampled subvolumeand thus increase the representativeness of the fabric analysis re-sults in respect to the sample cubes. However, this resolution couldbe sufficient for the fabric of Bentheim sandstone that consists oflarge grains and wide pores, but presumably not for the Obern-kirchen sample.

Therefore, supplementary to microscopic analysis, X-ray m-CT isa valuable research tool that has considerable potential to con-tribute to the interpretation of petrophysical experiments, evenwith full sample coverage yet to come. In particular, we would liketo stimulate the use high-resolution X-ray microtomography in thecourse of clarifying the important factors that govern the elasticand seismic behaviour on the scale of the sandstone microfabric.The image analysis procedures presented herewould have not beenas rewarding when applied to voxets with a lower resolution in therange of 50 mm or larger.

In the last decade, m-CT has proved its applicability for reservoircharacterisation in terms of the 3D-assessment of textural relationsof mineralogical phases as well as in the parameterisation of nu-merical flow simulations to quantify the hydraulic conductivity.Furthermore, this technique has been applied to document theresponse of the rock matrix in petrophysical experiments. A furtherstep would be to combine the findings related to the materialproperties of the sandstone grain matrix (which account for thepossible complexity of matrix permeability in reservoir rocks andfor internal deformation during diagenetic and tectonic episodes)with the fracture scale features that are surveyed by geophysicalmonitoring methods.

As underscored by our investigations, the use of m-CT in rockmechanical investigations can help to quantify the reservoirmicrofabric for a better understanding of the alteration of specificpore volume, stiffness, and strength in the course of reservoir rockcharacterisation. High-resolution m-CT below the 10 mm-range of-fers new perspectives for the consideration of boundary conditionsimposed by both grain phase and pore space that govern the bulkseismic behaviour of sandstones.

Acknowledgements

This study was funded by the German Federal Ministry of Ed-ucation and Research (BMBF), EnBW Energie Baden-WürttembergAG, E.ON Energie AG, E.ON Ruhrgas AG, RWE Dea AG, VattenfallEurope Technology Research GmbH, Wintershall Holding AG andStadtwerke Kiel AG as part of the CO2-MoPa joint project in theframework of the Special Programme GEOTECHNOLOGIEN.

We are grateful to Phil Salmon (SkyScan, Belgium) for hisenlightening discussions about the SkyScan software products andto Steffen Schächinger for his tenacity in evaluating the 2D equiv-alent area analysis results.

We thank Tom Blenkinsop and an anonymous reviewer for theirreviews which highly improved the paper.

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