The problem of identifying and quantifying the brittle deformation of carbonate reservoirs both in the United Arab Emirates (UAE) and elsewhere is addressed. Naturally occurring fractures may substantially increase or decrease the permeability and porosity of reservoirs, and therefore knowledge of location, orientation, density and connectivity of fractures is required to optimise hydrocarbon production. A rock containing parallel fractures can be seismically anisotropic, provided the vertical and horizontal extent and spacing of the fractures is small compared to the seismic wavelength. Seismic anisotropy may be detectable from attributes of pre-stack 3-D seismic data including reflection amplitude variation with offset and azimuth (AVOA). However, in carbonates seismic-velocity anisotropy can result from many different factors, including present-day horizontal stress anisotropy, sedimentological features such as clinoforms, and geological structure. We present a methodology for determining whether a proposed reservoir-fracture model is consistent with the observed seismic data. The approach includes modelling the seismic anisotropy where an essential input parameter is the compliance of the fractures. Since so little is known about this key parameter, we determine an upper bound to fracture compliance from well data and existing laboratory and field data and consequently obtain an upper bound to the seismic anisotropy that might be detected. We apply our method to data from an onshore carbonate oilfield in Abu Dhabi, United Arab Emirates, where analysis of core, log and 3-D post-stack seismic data indicates that open or partially open fractures may be pervasive and could have a dominant influence on reservoir production. Due to poor AVOA data quality our results are inconclusive. However, this case study is a demonstration of the methodology that could be applied elsewhere.

The detection of subsurface fractures and the estimation of fracture parameters from outcrops, cores, well logs and seismic data are of great importance in a wide variety of geological disciplines. In particular, the importance of identifying and quantifying the brittle deformation of hydrocarbon-producing carbonate reservoirs both in Abu Dhabi, United Arab Emirates (UAE), and elsewhere is widely recognised (Abdalla et al., 2000; Gouth et al., 2007; Holland et al., 2009a, b; Owusu and Nebrija, 2007; Roberts et al., 2001; Shibasaki, 2007). Johnson et al. (2005) have pointed out that the large volume of relatively undeformed rock located between faults and fault zones are likely to contain significant sub-seismic fracture populations. Such naturally occurring sub-seismic faults and fractures may increase or decrease the porosity and permeability of reservoirs, and therefore knowledge of location, orientation, density and connectivity of fractures is required for optimising production and recovery factor.

Subsurface fractures are notoriously difficult to study. Until horizontal drilling and the use of image logs became more common, it was unavoidable that fracture populations were grossly under-sampled. Lineaments in 3-D seismic data that may be due to faults and fault zones are detectable using attribute analysis techniques such as coherency, edge detection and oriented curvature. A rock containing aligned fractures can be seismically anisotropic, provided the vertical and lateral extent and spacing of the fractures is small compared to the seismic wavelength. This is detectable from normal move-out (NMO) velocity variation with azimuth, amplitude variation with offset and azimuth (AVOA) or by performing offset VSP surveys for a range of azimuths. The identification of the distribution and orientation of fluid or gas filled fractures by the use of AVOA analysis is now a well-established procedure (Gray and Head, 2000; Gray et al., 2002; Hall and Kendall, 2003; Holmes and Thomsen, 2002; Lynn et al., 1995; MacBeth et al., 1999; Thomsen, 1988).

However, interpretation of seismic lineaments and seismic anisotropy in relation to reservoir permeability should be undertaken with the greatest caution. There is no certainty that a seismic lineament is necessarily a fault/fracture zone or whether an observable fault is sealed or potentially hydraulically conductive. By comparing field observations with geometric modelling results Bergbauer (2006) has shown that normal surface curvature cannot be reliably used as a proxy for fractures prediction. Seismic velocity anisotropy can result from many different factors, present-day horizontal stress anisotropy, sedimentological features such as clinoforms, and oriented fractures. Apparent azimuthal NMO velocity anisotropy can also result from structural dips. The absence of seismic anisotropy can also be misleading. Hydraulically conductive aligned fracture sets might exist but the compliance of the fractures can be very small and hence the seismic anisotropy effect could be too small to measure. Alternatively, a number of different fracture sets might exist with different strike directions such that the vector summation of all the sets results in zero or small seismic velocity anisotropy. The intersection of fracture sets with different strike results in high inter-connectivity of the fractures and hence enhanced permeability or greatly reduced permeability, depending on the hydraulic properties of the fracture sets. In many instances mixed hydraulic fracture properties exist in a reservoir and therefore permeability prediction from seismic alone is not possible at this stage.

It is commonly assumed that if the fracture orientation deduced from the seismic anisotropy matches the dominant orientation of a set of fractures observed in a borehole, the correct link between cause and effect has been identified. Reservoir fluid-flow models are then based on the fracture distribution supposedly determined from the regional seismic data. However, real reservoirs will contain fractures with a wide range of scales, varying spatial distributions and varying hydraulic properties and the seismic wave is responding to some spatial average property of the rocks. In carbonate reservoirs, multi-stage diagenetic histories can create complex pore networks ranging in scale from micropores to megakarst. Given all these inherent uncertainties, it is important to apply some quantitative check that the ‘open’ hydraulically conductive fractures, believed to contribute substantially to the reservoir permeability, are actually having any observable influence on the seismic waves and that the proposed reservoir fracture model is at least consistent with the observed seismic data.

Figure 1 illustrates two possible approaches. The first initially involves the construction of a reservoir macro-fracture model, or discrete fracture network model, normally resulting from detailed interpretation and attribute analysis of 3-D seismic data combined with well log data. An example of this procedure is described in Barr et al. (2007). It is then necessary to specify the compliance of the individual fractures as a prerequisite for seismic wave numerical modelling. The modelled seismic data are then compared with field data, which would normally consist of azimuthal variations of NMO velocity or amplitude variations with offset and azimuth, leading to the verification or possible refinement of the reservoir model. The second approach is computationally much simpler. If the fractures of interest are assumed to be small relative to the seismic wavelength, then the entire reservoir can be represented as an equivalent medium with an overall fracture compliance which is additive to the compliance of the unfractured rock. Synthetic seismic data, to be compared with the field data, are then obtained for this analytical model, as described in more detail below.

The key step in both these approaches is the selection of the discrete fracture compliances, with units of m/Pa, or the equivalent-media compliance, with units of 1/Pa. Unfortunately, there are very few values of these parameters in the open literature and they are difficult to determine. An example of the application of the first approach is described by Will et al. (2005) who admit that their choice of value of fracture compliance is very uncertain. A recent example of the second approach is described in Sengupta et al. (2009). They obtain values of equivalent-media fracture compliance from borehole image and sonic logs, following a method described by Prioul et al. (2007). However, they are concerned that values obtained on the scale of well logs may not be valid at the scale of seismic wavelengths and feel compelled to introduce an upscaling factor which is also very poorly constrained. The very sparse data relating to the spatial scaling of fracture compliance has been reviewed by Worthington and Lubbe (2007) and Worthington (2007).

In this study, we apply the second, equivalent-media modelling approach to an onshore fractured reservoir in Abu Dhabi, using a methodology proposed by Worthington (2008) to obtain an upper bound to the seismic anisotropy observed in the surface seismic data that could have resulted from open fractures within the reservoir. If the observed seismic anisotropy is significantly larger than this maximum value, then one should be very cautious about assuming that the seismic data are providing any useful information about reservoir fracture distribution. Such a result would suggest that some other factors are having a major influence on the seismic velocities and amplitudes.

We concede that the available data from this field are not sufficient for the result to be definitive. However, the study is an illustration of what could be achieved in the future in this or in other fields if data were systematically acquired with our proposed methodology in mind.

A key step in either of the procedures outlined in the introduction is the choice of normal and shear fracture compliance. We have pointed out that current knowledge about these parameters is extremely limited. In consequence, our approach is only to estimate an upper bound to the parameter values. Our assertion is that there is much less uncertainty in an upper bound compared to the uncertainties associated with any specific value of fracture compliance that one would otherwise have to select. Conclusions that can be drawn from the results are more limited but are much more robust. Some of the arguments that follow have already appeared in Worthington (2008) but are included here for completeness.

Scaling of Fracture Compliance

Any estimate of in-situ fracture compliance inevitably involves some model of how compliance scales with fracture size combined with a model of the sub-surface fracture distribution. One can then upscale values obtained from the laboratory or from well logs or near-surface field experiments.

The arguments differ depending on whether one is considering the specific compliance of individual fractures or the equivalent-media compliance of an entire region. We begin by considering the compliance of individual fractures.

A fracture can be thought of as two uneven surfaces in partial contact, with the fracture surface consisting of welded areas and open areas. Weld points increase the strength or resistance to closure of the fracture. As Marrett et al. (2007) have described, fracture strength can also be enhanced by partial cementation. So a single fracture will behave elastically like a series of smaller fractures or segments separated by weld points and the overall compliance of the fracture will not be greater than the maximum compliance of the individual segments. Using the expression for the normal compliance of a dry, circular crack from Sayers and Kachanov (1995), Worthington (2008) proposed a simple means of estimating maximum possible normal compliance of a fracture as a function of effective closure stress and mean fracture aperture.

The normal compliance Bn of a circular, dry fracture of diameter L is;


where υ is the Poisson’s ratio and E the elastic modulus of the rock matrix (Grechka and Kachanov, 2006). Dry in this context means that the theory does not take into account the effect of the compressibility of any liquid or gaseous fracture fill. So this is a useful equation since we are interested in a maximum compliance. The fracture will close as stress normal to the fracture increases and will be completely closed when applied normal stress equals b/Bn, where b is the fracture width (aperture). Hence, the stress normal to the fracture above which the fracture will be closed, σc, is;


where α = b/L, the aspect ratio of the fracture.

For a given mean fracture aperture and effective pressure at a specified reservoir depth, one can use equation (2) to determine a maximum fracture length above which a fracture would be closed. The normal compliance of this fracture is then obtained from equation (1). This is the maximum compliance of fractures at the specified reservoir depth. Fracture roughness amplitude is known to be roughly proportional to the roughness wavelength (Power et al., 1987), so one might expect surface roughness amplitude and hence mean fracture aperture to increase with fracture size. However, in reality, most natural fracture surfaces in the earth have surface topography which is correlated on some scale but uncorrelated at a smaller scale. The uncorrelated component of the topography of natural fracture surfaces, or effective roughness, is generally much less than the actual fracture surface roughness because it depends only on the uncorrelated, small-scale part of the fracture surfaces (Hillis, 1998). Nelson (2001) provides a compilation of published aperture data which shows maximum aperture of 1 mm or less for in-situ fractures at reservoir depths. Using equations (1) and (2) one obtains an absolute maximum normal fracture compliance of approximately 10−11 m/Pa at normal reservoir depths.

The possibility of a fracture compliance upper limit of this magnitude is consistent with existing experimental data. Few values of dynamic fracture compliance have been published, and the total data volume is much enhanced if static compliance data are also included. With regard to normal fracture compliance, it is logical to assume that static and dynamic experiments are measuring the same rock property albeit at zero frequency and some finite frequency, respectively. Pyrak-Nolte et al. (1987) provide a rare example of static and dynamic measurements on the same samples and show that static compliance is consistently greater than dynamic compliance. Given the unlimited time of a static experiment, a normal applied stress will induce as much closure as is possible for any particular fracture dimensions and rock properties. Whereas only partial closure might occur within one cycle of a dynamic experiment due to time variant anelastic processes. Thus static measurements can be viewed as a conservative upper bound on the values of normal dynamic fracture compliance.

Figure 2 shows laboratory and field estimates of normal fracture compliance taken from the literature. In some instances data have been simplified. For example, over one hundred values for a range of fracture widths from 0.07 to 0.3 m from Zangerl et al. (2008) are represented by just two points, a maximum and minimum value at a mean fracture length of 0.1 m. Static values are plotted in blue and dynamic values in red. The cluster of dynamic values at approximately 5 cm fracture length is laboratory data for a range of confining pressures from 5 to 85 MPa. The data in Figure 2 are indicative of an upper bound for normal compliance at meso-scale fracture lengths of approximately 10−11 mPa−1 with the likelihood, based on the results of Pyrak-Nolte et al. (1987), that this estimate is a factor of three or four too high. So fracture models that predict a continuous increase in normal compliance with fracture size are not consistent with existing data.

A value of shear (Bt) compliance is also required for the modelling. There are no published dynamic shear compliance data for fracture lengths greater than approximately 5 cm. Static shear compliances are within a range from 10−10 to 10−6 m Pa−1 for block sizes from 0.1 to 30 m and increase with increasing block size (Barton, 2006). There is no evidence that dynamic shear compliance is even remotely close to these static values in crustal rocks (Barton, 2006). Measured values of Bn/Bt for dry rocks fall within the range 0.3–1.0 (Lubbe et al., 2008) which suggests that the upper limit for normal and shear compliance are likely to be quite similar.

Estimating an upper bound for equivalent-media compliance is problematic because it is dependent on both the fracture compliance and the spatial distribution of the fractures. If a population of fractures can be approximated as a set of continuous, parallel fracture planes spaced L metres apart, then the equivalent-media fracture compliance,


where Bn,t is the normal or shear compliance of the individual fracture planes with units of m/Pa. This is an extremely simplistic model of fracture distribution. Nevertheless, equation (3) indicates that the same equivalent-media compliance could result from widely separated fractures of high compliance or closely separated fractures with lower compliance. So it is necessary to depend upon a model of how fracture distribution might vary with fracture size. Budiansky and O’Connell (1976) developed an expression for the crack density, ε, of a random distribution of elliptical, dry cracks;


where N is the number of cracks per unit volume, A is the area of the crack and P is the perimeter of the crack. For circular cracks, this reduces to ε=Na3 where a is the crack radius.

Larger cracks, or fractures or joints, are likely to be bed-limited in height while being much longer in length. In which case, it is straightforward to show that equation (4) becomes


where η is the joint or fracture density, h is the layer thickness and s is the joint or fracture spacing within the layer (Thomsen, 2002). There is a typographical error in equation (5) as originally published (Thomsen, 2010, personal communication). Since it is widely observed that joint spacing is proportional to bed thickness in sedimentary rocks (Narr and Suppe, 1991) it follows that joint density is approximately constant for all scales of jointing. If joint density is scale invariant, it follows from equivalent-media theory that equivalent-media compliance will also be scale invariant (Hall and Kendall, 2000). Hence, a value of equivalent-media compliance deduced from image and sonic logs (Prioul et al., 2007) can logically be applied to the whole reservoir.

This study uses data from a carbonate onshore oilfield located southwest of Abu Dhabi city. The field is producing from the Upper Cretaceous (Maastrichtian) Simsima Formation. The Simsima Formation was deposited on an actively growing palaeo-high in a shallow-marine environment (Hozayen et al., 2008).

The Simsima reservoir is capped by the basal shale member of the Umm Er Radhuma Formation (Palaeocene in age) and overlies the crest of the partly eroded former structure of the Aruma Group. The Simsima structure is a simple, elongated anticline, plunging in the NE and SW directions. The flanks dip at 4° to 8°. The anticline started to form during the Late Cretaceous as a result of the obduction of the Semail Ophiolite and growth continued during Early to Mid Tertiary times as a result of Zagros subduction.

The significance of the fractures in the Simsima reservoir was not recognised during the early development of the field. However, large variations in well productivity were observed between some wells that could not be explained by variations in matrix permeability alone. After detailed analyses of core data and FMI/FMS (Formation Micro Imager/Formation Micro Scanner) logs, it was recognised that the Simsima reservoir is highly fractured. The majority of the fractures are open although a few of them are sealed with calcite cement. Recently drilled horizontal wells have confirmed that the fractures are an important element in reservoir performance. Enhanced production rates were observed when horizontal wells were oriented perpendicular to the fracture trend.

Existing Fracture Model of Simsima Reservoir

There have been extensive investigations of the fault and fracture distribution within the Simsima reservoir (BEICIP-FRANLAB, 1999, 2002). These have included core and FMI log analysis of 27 wells, data from a limited number of DSI (Dipole shear sonic imager) logs and curvature analysis of the 1992/1993 3-D seismic data from the top Simsima reservoir. Curvature analysis showed lineaments with high positive curvature values oriented in two main directions: N40°E and N70°E (BEICIP-FRANLAB, 2002). They are interpreted as fracture swarms or as sub-seismic faults with very few fractures outside the clusters. Based on a combination of the curvature analysis and information from the well data, the width of these fractured zones has been estimated to range from 50–100 m and to be spaced 100–400 m apart.

Fracture densities measured from the core and FMI data within the fractured zones are 2–3 fractures per metre with a maximum value of 5 fractures per metre. Using the lineament network and the positive areas of curvature, a stochastic 3-D network of sub-seismic faults (fracture model) was generated and was then used in a dynamic simulation (BEICIP-FRANLAB, 2002). If such fracture swarms exist in the reservoir, then they are expected to have an influence on fluid flow in the Simsima reservoir and to greatly enhance production. Furthermore, seismic anisotropy will only be observed if the fracture size and fracture spacing is small relative to the seismic wavelength; at least ten fractures per wavelength is a rough guide. The dominant wavelength of the surface seismic data is ca. 60 m. So a patchy distribution of seismic anisotropy attributes is to be expected, depending on whether the CMP bins fall within or between the fractured zones.

Dipole Shear Sonic Image (DSI) Logs

Stoneley wave (or tube wave) reflectivity is sensitive to open fractures (Hornby et al., 1989). As the waves travel along the borehole and meet an open fracture a large-amplitude arrival is reflected from the fracture. This produces chevron disturbance patterns whose apex is at the intersection of the fracture plane and the borehole wall.

Dipole Shear Sonic Imager (DSI) data were acquired in wells X-31, X-25 and X-11 to identify open fractures. The DSI data revealed a number of zones of between 5 and 40 m width with shear wave anisotropy of 4% to 16% (Ahmad, 1998). However, these three DSI logs are the only available data of seismic anisotropy associated with the fracture zones. Ideally, there should be many more measurements in many more wells. The interpretation of the DSI data from these wells is as follows:

Well X-31: The DSI was run in Well X-31 in a deviated and horizontal hole, drilled through Umm Er Radhuma Formation and Simsima reservoir. Chevron patterns of Stoneley waves were observed at many places (Figure 3a). Most of the patterns are attributed to acoustic boundaries due to lithological changes or a washed-out hole. However, for a few events over the interval 4,356–4,382 ft, the Chevron patterns, energy loss and shear-wave splitting were interpreted to indicate the presence of fractures trending N20°E. Shear anisotropy of up to 16% has been estimated. This interpretation fits well with the electrical imagery (FMI) results shown in Figure 3b.

Well X-11: Chevron patterns in Stoneley waves, energy loss and shear splitting were observed within two zones (4,355–4,320 ft and 4,218–4188 ft). The shear anisotropy were found to be marginal (<5%) in the deviated hole and significant in the horizontal hole (up to 16%). The anisotropy dominant direction is N48°E with another component in the N30°E direction in the deviated hole. The anisotropy is interpreted to be caused by aligned fractures that are identified in the FMI logs in the deviated hole and due to horizontal stress in the horizontal hole over most of the interval.

Well X-25: DSI interpretation indicated few fractured intervals, which generally correspond to the fracture swarms identified on the FMI image logs. Shear anisotropy of <8% and up to 16% were observed in the deviated and horizontal holes, respectively. The anisotropy is linked to in-situ stress trending (N5°E).

Core Data

Cores from the reservoir zone in wells X-11, X-31 and the horizontal well X-25H have been analysed. Although individual open fractures can be identified (Figure 4), larger fractures are most likely to be within zones of poor core recovery. Consequently, core data provided an incomplete picture of the fracture distribution in the Simsima reservoir. Nevertheless, the core provided a check on the analysis of open-hole logs.

Post-Stack Attribute Analysis of 3-D Seismic Data

Conventional structural and stratigraphic interpretation was carried out on a 3-D migrated seismic stack volume of the field. The data clearly show the anticlinal structure and the top and the base of the Simsima reservoir is clearly resolvable (Figure 5). The structural interpretation of the anticline indicates that the structural growth started during Late Cretaceous times as a result of the obduction of Semail Ophiolite. The onset of the deformation is clearly expressed by a well-defined angular uniformity at the base of the Laffan Formation, which rests on the Shilaif Formation. The structural growth of the anticline continued during deposition of the Simsima Formation resulting in a clearly defined thickness variation. For example, at the crest the Simsima Formation overlies directly on the Shilaif Formation and then progressively younger formations (Laffan, Halul and Fiqa) towards the flank of the structure. Furthermore, the 3-D seismic data show a number of NE-trending wrench faults cutting across the field. The density of the faults varies considerably and in the crestal area is relatively high. This may be related to structural deformation or lithological variation in the field.

The seismic data are tied to the available wells. Synthetic seismograms were generated from logs and compared to the seismic traces around the well (Figure 6). The top Simsima interface which lies at 730 milliseconds at the Well X-31, is a very strong and reliable event across the whole field. It represents an increase in acoustic impedance (a peak in the displays shown here) between relatively low velocity (Vp = ca. 2,900 m/s) sediments of the Umm Er Radhuma basal shales and the harder Simsima carbonates (Vp = ca. 4,000 m/s). The Base Simsima is a difficult horizon to pick. Being an unconformity, it can vary laterally from a soft to a hard interface according to the relative rock properties of the overlying and underlying sediments.

Post-stack attribute maps (e.g. amplitude, dip, curvature and ant tracking) were generated to highlight possible fault and fracture lineaments. Figure 7a shows the horizon-based curvature attribute of the top Simsima horizon. Figure 7b shows lineations identified in the top Simsima horizon using the ant-tracking process available in Petrel© software. The ant-track workflow included preparation of the seismic data with structural smoothing, followed by variance analysis to find and enhance fault structure from spatial discontinuity seismic attributes. Figure 7b shows a number of seismic lineaments that may be caused by subtle faulting or fractures. However, it is equally likely that they are due to other geological factors or even seismic acquisition footprint provided receiver lines are parallel to lineations.

Azimuthal Analysis of Pre-Stack Gathers

AVOA analysis of four pre-stack volumes (1 km x 1 km), located on the crest and flanks of the field, were carried out. The acquisition geometry of the 3-D seismic data was designed for optimal imaging of the Jurassic Arab sour gas carbonate reservoirs at around 3,000–3,500 m (10,000–11,500 ft and 1.5–1.8 seconds two-way travel time, TWTT) with up to 70 Hz and a nominal fold of 400. Therefore, at the Simsima level the data have low fold, small angular range, relatively poor signal-to-noise ratio and are partially contaminated by inter-bedded multiples. In addition, a non-true amplitude process (Coherent Noise Attenuation filter) was applied to the data. This process has inevitably affected the amplitudes and will impact on relative lateral amplitude AVOA variations. Consequently, the azimuth and offset at the Simsima level (ca. 0.8 second TWTT) is not ideal for AVOA analysis. Nevertheless, we performed AVOA analysis to illustrate the procedure that we are proposing.

The pre-stack data consisted of processed pre-migration CMP gathers with a bin size of 12.5 m x 12.5 m. For this study, very low structural dips at the reservoir level (<5°) and the absence of complex overburden allow the use of unmigrated data. Additional processing and conditioning were applied to the data including NMO correction and muting followed by azimuthal sectoring and conversion from the offset to angle domain using migration velocity. Four bi-directional azimuthal angle gathers were generated to reveal azimuthal variations. Superbinning (from 12.5 m x 12.5 m bins to 100 m x 100 m bins) of common midpoint gathers and stacking of offset bins in common-azimuth gathers was also applied to make offsets more regular between different azimuth sectors. Superbinning substantially suppressed the random noise and provided an average result which is good to identify major fracture direction. Figure 8 shows the AVOA extraction from the top Simsima interface for two superbin gathers located on the flank and crest of the field. Amplitude extractions of some superbin gathers give an indication of anisotropy. However, the majority of superbin gathers show very irregular amplitudes. For example, Figures 8a and 8b indicate that the average amplitudes of the 45° azimuth are higher than that of 135° azimuth. In contrast Figures 8c and 8d show very erratic amplitudes that are not consistent with even any plane-layered earth model, isotropic or anisotropic. We attribute this to limitations, with respect to AVOA analysis, in the acquisition and processing as discussed above.

As outlined in the introduction, our aim is to obtain an estimate of the maximum value of a specified seismic anisotropy attribute for the survey region. If existing field data estimates exceed this value then it is likely that factors other than aligned open fractures are influencing the results. A causative link between a seismic anisotropy attribute and fracture permeability is, therefore, not proven. Alternatively, if field data has yet to be acquired, then the predicted estimate might provide grounds for designing a future survey to ensure that, for example, AVOA can be effectively measured.

Following an approach described by Prioul et al. (2007), we determine the excess equivalent-media compliances associated with values of shear-wave velocity anisotropy obtained from the DSI logs. Figure 9 is a plot of shear-wave anisotropy as a function of equivalent-media shear compliance, calculated using the theory of Schoenberg and Sayers (1995). The red curves are bounds due to a variation of average velocity of +/− 500 m/s. The maximum value of shear-wave anisotropy obtained from the DSI log data was 16%. Velocity anisotropy of 16% results from a compliance of 2.0 × 10−11 Pa−1. We use a value of 0.3 for Zn,t based on the experimental results of Lubbe et al. (2008) to obtain an equivalent-media normal compliance of approximately 6.0 × 10−12 Pa−1.

A check on the plausibility of this estimate is obtained by calculating individual fracture compliances and comparing these with the laboratory and field data in Figure 2. Given that fracture spacing estimated from the well logs is approximately 0.3 m, we use equation 3 to obtain an individual normal fracture compliance of 2.0 × 10−12 m/Pa which is consistent with values that might be expected on the basis of existing laboratory and field estimates.

The BEICIP-FRANLAB (1999, 2002) fracture model includes two fracture sets with strikes of N40°E and N70°E and in some locations, these two sets coexist. Nichols et al. (1989) have developed the theory for the summation of the compliances of individual fracture sets. Two or more sets of fractures with differing strikes will, in general, result in an equivalent-medium compliance (or stiffness matrix) that has a complex symmetry. So it is convenient to decompose the matrix into a stiffness matrix for a canonically oriented transversely isotropic medium (whose properties can be readily understood) plus a perturbation representing the medium’s deviation from perfect symmetry plus a rotation to maximise the symmetry. This approach is described by Dellinger (2005).

Using the theory of Ruger (2002), we calculate the AVOA response of the top Simsima interface, assuming that the Umm Er Radhuma Formation is isotropic and the top Simsima carbonates are anisotropic with HTI symmetry due to sets of sub-vertical fractures. The two solid red curves in Figure 10 are the results, parallel and at right angles to the fracture strike, when the Simsima rocks contain one set of vertically aligned fractures with an equivalent-media compliance of 6.0×10−12 1/Pa. The blue curve is for isotropic Simsima rocks in which fractures are either sealed or absent.

The dashed red curves are obtained by assuming that two vertical fracture sets in the Simsima Formation have strikes that differ by 30° but the same equivalent-media compliance of 6.0×10−12 1/Pa. We sum the compliances of the two fracture sets using the method of Nichols et al. (1989). We then perturb the resulting stiffness matrix by 2.5% to obtain a matrix with perfect HTI symmetry, using the approach proposed by Dellinger (2005), which can then be used in the equations in Ruger (2002). We have no way of knowing whether these two fracture sets have the same compliance. So these curves simply provide one measure of uncertainty in the AVOA modelling.

The black dots are the data taken directly from Figure 8a. Amplitudes are converted to reflection coefficients by scaling with the zero-offset amplitude and zero-offset reflection coefficient predicted from the AVOA analysis. The reflection coefficients are lower than would be expected for an isotropic model and are more consistent with the curves for the anisotropic Simsima carbonates. These data are consistent with, but do not prove, the hypothesis that AVOA analysis of 3-D seismic reflection data may provide information about hydraulically conducting fracture networks in the Simsima reservoir.

The study demonstrates that an upper limit to the compliance of fractures within a reservoir can be determined and, given the present lack of experimental data, is the most reliable and useful estimate to obtain. The value can then be used to determine an upper limit to the seismic velocity anisotropy that would result from any specified set of fractures. This then provides a level of confidence in interpreting seismic anisotropy as an indicator of the presence of fractures that contribute significantly to reservoir permeability.

Analysis of core, log and 3-D post-stack seismic data from the field indicates that open or partially open fractures may be pervasive and could have a dominant influence on reservoir production. Core data provide an incomplete picture of the fracture distribution since larger fractures are most likely to be within zones of poor core recovery. Nevertheless, the core data provided a check on the analysis of the well logs. DSI logs of three wells revealed shear-wave anisotropy of 4–16%. The anisotropy is attributed to fractures as confirmed by the FMI measurements over all the anisotropic zones. Seismic attributes from 3-D post-stack data revealed a number of lineations, which could be due to sets of aligned fractures. If so, the resulting seismic anisotropy would be patchy and laterally variable.

AVOA analysis was performed on a limited sub-set of the pre-stack 3-D seismic data. Results were inconclusive, mainly because the data acquisition and processing was not suitable for a successful AVOA analysis at the Simsima reservoir level. However, the AVOA modelling described in this paper is illustrative of a methodology that could be applied to new data acquired at the field site at other localities.

We would like to thank the Oil Sub-Committee (ADCO, ADMA-OPCO and ZADCO) for sponsoring this research work, ADNOC for providing the 3-D seismic data of the field, the project technical committee for their valuable feedback, support and contribution and we thank Marwan Haggag for his coordination of the project.

We would like also to acknowledge our colleague Hani Nehaid who contributed through the reprocessing of pre-stack data and analysis of AVOA data, and Professor Mike Searle who contributed through an outcrop analogue study of Jabal Rawdah (northern Oman mountains). Abdullatif Al-Shuhail and two anonymous reviewers greatly improved the manuscript. GeoArabia Designer Nestor Niño Buhay IV is thanked for designing the manuscript for press.

Mohammed Y. Ali has a BSc in Exploration Geology from Cardiff University, an MSc in Geophysics from Birmingham University, a Postgraduate Certificate in Education from UWCN, and a PhD in Marine Geophysics from Oxford University, UK. His current research projects are focused on exploration geophysics in the areas of passive seismic, seismic stratigraphy and reservoir characterization and modelling. Other research interests include basin analysis, crustal studies, and the structure of passive margins. Mohammed joined the Petroleum Institute in 2003 and currently he is an Associate Professor of Geophysics. He is a fellow of the Geological Society of London and a member of the SEG, EAGE and AGU.

Michael H. Worthington has a BSc in Applied Physics and an MSc in Geophysics from Durham University, UK, and a PhD in Geophysics from the Australian National University, Canberra. His current research is focused on seismic wave propagation in crustal rocks and specifically the relationship between seismic attributes and the petrophysical properties of the rocks. His work has included studies of seismic velocity anisotropy, seismic attenuation and most recently seismic wave propagation in fractured media and the compliance of fractures. Other research interests include the relationship between the electrical properties and seismic properties of rocks, particularly with regard to rock fracture parameters and hydraulic conductivity. Michael was a Lecturer in Geophysics at Oxford University from 1973 to 1985, Professor of Geophysics at Imperial College, London, from 1985 to 2001 and Professor of Geophysics, Oxford University from 2001 until the present. He is a fellow of the Geological Society of London and a member of the SEG and EAGE.