INTRODUCTION

A key factor needed for the use of seismic-wave velocities in hydrocarbon exploration and reservoir characterization is an understanding of what seismic waves can tell about the intrinsic parameters (composition, texture, fluid saturation) and extrinsic parameters (state of stress, temperature, pore pressure) of rocks in situ. Many theoretical models of wave propagation in porous media have been proposed (Gassman, 1951; Biot, 1956; Geertsma, 1961; Geertsma and Smit, 1961; Kuster and Toksoz, 1974), but a theory capable of accounting for the variety of experimental studies still does not exist. However, experimental studies suggest that relatively simple relations between seismic velocities and such important rock parameters as porosity and clay content do exist (Wyllie et al., 1956, 19 8; Raymer et al., 1980; Tosaya and Nur, 1982; Kowallis et al., 1984; Han et al., 1986). An advantage of these relations is their independence of rock frame elastic moduli or pore aspect ratio needed for most theoretical models. A shortcoming of these relations is that they neglect parameters such as mineralogy, structural position of clay, and pore size and shape distribution. These parameters are most closely linked to the original composition, depositional environment, and diagenesis of clastic sedimentary rocks (Blatt, 1982; Greensmith, 1989), which are of great and growing importance in oil exploration and production.

The particular problem of clay location was theoretically modeled by Minear (1982), who showed that clay suspended in the pores of sandstone has only a small effect on velocities, whereas both structural and laminar clay result in a dramatic velocity reduction. In contrast, based on an experimental and observational study of a limited collection of sandstones, siltstones, and shales, Tosaya and Nur (1982) concluded that only the overall amount of clay is important in estimating porosity using compressional velocity. This was later

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refined by Han et al. (1986) on a much more extensive database.

Marion (1990) conducted velocity measurements in sand-kaolinite mixtures at high confining pressure. Those measurements suggest that there exists a threshold in clay content from shaly sand to sandy shale beyond which the sand grains cease to be connected, and the clay becomes the continuous matrix. Sand porosities (phi) of 34% and 39% were taken as the threshold values at 40 MPa and ambient pressure, respectively. For shaly sand, a modified Gassman's equation (1951) was used as a velocity-porosity transform; for sandy shale, Wood's relation (1941) was shown to best fit the data. An attempt was also made to extrapolate the model to consolidated sedimentary rocks.

In this paper, we develop a petrophysical classification of siliciclastics and demonstrate that a detailed petrographic study of rocks is of paramount importance in any experimental work. We also show that careful combination of petrographic observations with measurements can yield an accurate statistical model relating seismic velocities to intrinsic parameters of sedimentary rocks and, further, with their depositional environment and diagenesis. Our database covers a variety of petrographic groups of siliciclastics and spans a wide range of diagenetic grades. It includes data by Han et al. (1986) and our own additional experimental data on shales. Each laboratory specimen was characterized by a petrographic thin-section analysis. Clay content was determined by point counting, correc ed for microscopic clay porosity using helium porosimetry. Clay mineralogy was determined from x-ray diffraction data, so that clay content basically includes only clay minerals, rather than just particles of subsilt size. The measurement techniques of ultrasonic velocities (pulse transmission at 1 MHz central frequency for P-waves and 0.6 MHz central frequency for S-waves), helium porosity, and clay content were described earlier by Han et al. (1986). In addition, we used recently acquired data on Klinkenberg-corrected gas permeability at 30 MPa and irreducible water saturation (S[wi]) using the centrifuge method, which also yielded the effective porosity of each sample as phi[ef] = phi(1 - S[wi]). After oven drying at 110 degrees C for dry velocity measurements, the samples were brine aturated first using capillary forces and then fully saturated under pressure of 10 MPa.

PETROPHYSICAL CLASSIFICATION AND
POROSITY ANALYSIS OF
CLASTIC SEDIMENTS AND ROCKS

Petrographic Classification and
Grain Size Effect on Porosity

The petrographic classification scheme adopted in this paper, shown in Figure 1, subdivides sandstones on the basis of their original mineral content and their textural attributes (Greensmith, 1989). Secondary cement is not taken into account in this classification, whereas the original matrix normally comprised of clay minerals plays an important role. Sandstones bearing less than 15% matrix are referred to as arenites, with further subdivision according to grain mineralogy; those with 15% or more matrix will be referred to as wackes. It is also important to emphasize the textural difference between arenites and wackes. In particular, many quartz and feldspar grains forming wacke sediments have been deposited with linings of adsorbed clay particles. This gives rise to a specific text ral pattern that is characterized by a substantially reduced number of grain-to-grain contacts and is retained during the early stages of diagenesis.

The adopted classification disregards compaction, diagenesis, and grain size of rocks; hence, both petrographic groups of sandstones include unconsolidated sediments and their lithified equivalents with a range of median grain sizes from 0.06 to 2 mm. Perhaps this explains why this petrographic scheme is not widely accepted. Nonetheless, we have chosen to use this scheme because the effects of compaction and diagenesis could be traced independently based on quantitative petrophysical data, as will be shown later.

The effect of grain size on porosity is large in unconsolidated sediments (Fuchtbauer, 1974; Kobranova, 1986). In Holocene shallow marine sediments of the North Sea (Fuchtbauer and Reineck, 1963), an inverse relation exists between depositional porosity and median grain diameter (Figure 2a). It is noteworthy that the clay content in fine-grained sand (0.12-0.25 mm) with porosity of about 40% was below 5%, and that clay

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content increased as grain size decreased. Furthermore, sediments with the median grain diameter of about 0.06 mm, which is a border value between sands and muds, have a porosity of about 55% and clay content of 15%. The latter value suggests the affinity of the sands in that experiment to arenites.

Figure 2b shows experimental results for grain-size effects on porosity in well-sorted aggregates of different minerals (Kobranova, 1986). The upper and lower bars for each grain size correspond to the loose pack and pressure-compacted porosity values, respectively. Similar trends are seen also for the aggregates of rounded quartz and angular quartz and feldspar. In contrast, the trend for muscovite particles is for the porosity to increase with grain size due to the "card house" structure of their aggregates. This structure is usually invoked to explain the high porosity of muds, which occasionally reaches 80% (van Olphen, 1977; Engelhardt, 1977). Superimposing the North Sea sand data of Figure 2a on the experimental data of Figure 2b (Figure 2c) suggests that very fine-grained (0.06 0.12 mm) angular arenaceous sediments may have depositional porosity of more than 50%, whereas the porosity of fine-grained to medium-grained sands is around 40%.

Petrophysical Classification of Rocks

The data above suggest that the depositional porosity of well-sorted grain-supported arenaceous sands may vary at least in the range from 37 to 55%. Furthermore, detailed thin-section analysis of our database of clastic sedimentary rocks shows that the clay-volume threshold separating grain-supported from predominantly matrix-supported sandstones is only 15-18% (Figure 3). This threshold coincides with the diagenesis-independent, textural boundary between arenites and wackes as petrographically defined above. This observation allows us to trace the effects of diagenesis on physical properties of rocks separately for grain-supported arenites (Figure 4) and for matrix-supported wackes and sandy shales (Figure 5). The transition from wackes and sandy shales is not well defined in the pet ographic literature. Based on our database, we

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define this transition at 35% clay, where occasional grain-to-grain contacts seen in some wackes almost entirely disappear (Figure 5c). Finally, arenites can be subdivided into clean arenites (less than 2-3% clay) and arenites with larger amounts of lithic and feldspar grains, which are chemically unstable and thus tend to transform in the process of diagenesis into clay minerals that normally make up less than 15% of the rock volume (Figure 4c). Although the latter group of arenites petrophysically also includes arkosic sandstones, the term arenite is retained for the entire group. The final petrophysical classification of our database is shown in Figure 3.

Even though our petrophysical classification captures most of the basic petrographic features, there remain some inadequacies. For example, some feldspar-rich arkosic or lithic sandstones, which are arenites in the petrographic sense, may fall into the category of wackes as a petrophysical group if the majority of feldspar and lithic grains is transformed into pseudomorphic clay aggregates, giving rise to an apparently matrix-supported structure containing mechanically separated quartz fragments.

Effects of Diagenesis on
Porosity and Texture of Rocks

We next analyzed the diagenetically driven porosity reduction separately for each of the petrophysical groups. Figure 3 shows all our laboratory data, as well

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as the results of Yin et al. (1988) for brine-saturated sand-kaolinite mixtures at a confining pressure of 50 MPa (corresponding to a depth of 3.5-4 km), which are added to the consolidated rock data for comparison. The data for unconsolidated materials present an upper bound to the porosity distribution with clay content in consolidated rocks. The apparent porosity reduction with the increase in clay content can be a result of diagenesis including early mechanical compaction due to grain rearrangement and later chemical processes of pressure solution and cementation and phase transformation. Therefore, the upper bound for porosity in Figure 3 corresponds to the initial stage of sediment diagenesis, where mechanical compaction is completed but chemical diagenesis has not yet begun.

In contrast to the arenites, the mechanical compaction of wackes and sandy shales due to the low stiffness of clay is a function of the mean effective stress (Fuchtbauer, 1974; Engelhardt, 1977). This process is normally accompanied by clay mineral phase transformations (e.g., smectite-illite transition) and quartz dissolution, which is enhanced by clay seams separating closely spaced grains. Thus, in wackes and sandy shales, the processes of mechanical and chemical diagenesis are complementary to each other at depth. The photomicrographs in Figure 5 represent a sequence of these lithologies that has undergone porosity reduction from 30% (Figure 5a) to 2.9% (Figure 5c) as a result of a progressive diagenesis. This dramatic porosity reduction due to matrix compaction was accompanied by clay mineral phase transformation from smectite to illite. Despite marked compaction the original quartz and feldspar grains in wackes essentially remain separated (Figure 5b), i.e., matrix supported.

The differences in porosity structure between grain-supported and matrix-supported rocks is better illustrated in photomicrographs shown in Figure 6, which are in fact magnified views of Figures 4b and 5b. The syntaxial quartz overgrowths filling an original pore between three adjacent quartz grains of a clean arenite in Figure 6a (Beaver sandstone) are clearly distinct from the original grains and form a new, much smaller pore with a nearly triangular cross section. The contacts between overgrowths must have been welded and highly stressed at depth, as can be inferred from numerous stress-induced microcracks splaying from the corners of newly formed pores (Figure 6b). However, many of these contacts should have broken apart due to the uplift and cooling, and thus contain low-aspect-r tio contact microcracks. These microcracks are clearly detected by a sharp increase in both P-wave and S-wave velocities with confining pressure in dry samples of many crystalline and low-porosity sedimentary rocks (Nur and Simmons, 1970; Vernik and Nur, 1992). In fact, a similar mechanism of porosity reduction and formation of extended grain contacts is characteristic of all arenites in our collection. In contrast, the porosity of a wacke in Figure 6c (Gulf Coast sandstone from a depth of 3.78 km) can not be optically distinguished from the clay matrix, which tends to insulate even sand grains that have been highly pressed against each other.

ANALYSIS OF ULTRASONIC VELOCITIES
VS. POROSITY RELATIONS

Effects of Lithology and Clay Content

The velocity versus porosity relationship is considered here for brine-saturated rocks at 40 MPa effective pressure (corresponding to a depth of about 3 km for hydropressured conditions) when most cooling or stress-relief induced microcracks should be closed. In terms of seismic-wave propagation, the rock under such conditions is believed to correspond to its in situ state in a wide range of depths because of dramatically reduced pressure sensitivity of velocities when most microcracks are closed. The P-wave velocity vs. porosity plot for our data without lithological discrimination is shown in Figure 7a. Overall, the time-average equation (Wyllie et al., 1956) based on velocities in quartz and water fits the data, but the scattering of the data is tremendous, making the model general y inadequate for either porosity or lithology prediction.

In Figures 7b and 8, the P-wave velocity vs. porosity and S-wave velocity vs. porosity relationships are established separately for each of the four petrophysical groups described above. The correlation coefficients (R in Figures 7b and 8), which range from 0.97 to 1.0, emphasize the validity of the developed petrophysical

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classification. Moreover, the intercept in each equation is very close to the P-wave velocity and S-wave velocity in zero-porosity mineralogical equivalents of the particular groups. Specifically, 6.04 (clean arenite) corresponds to the P-wave velocity in quartzite, 5.57 (altered arenite) to that in a weathered granite, and 4.99 and 4.90 (wacke and sandy shale, respectively) to a slate (Lo et al., 1986; Vernik and Nur, 1992). Similarly strong correlation and physical meaning of the intercepts is typical of the linear fits to the S-wave velocity vs. porosity data (Figure 8). The linear regression lines of P-wave velocity and, especially, S-wave velocity tend to converge with decreasing porosity in wackes and sandy shales due to the much steeper gradients of these lines (0.84-0.91) for hales.

Since the petrophysical classification of rocks that we suggest is based on both overall quantity and structural position of clay, the apparent contradiction between modeling results of Minear (1982) and experimental data of Tosaya and Nur (1982), Kowallis et al. (1984), and Han et al. (1986) on the effect of clay on velocities can be understood and reconciled. In Figure 9, P-wave velocity is plotted versus clay volume for arenites, wackes, and sandy shales with superimposed isoporosity lines from 0 to 30%. Although there is a definite trend for velocity reduction with increasing clay content within broad bands (7.5%) of approximately equal porosity, any strong correlation within each of the petrophysical groups does not exist. This becomes obvious if we connect data points with equal porosity (within 1% absolute) separately for arenites, wackes, and sandy shales (Figure 9). In particular, for arenites, four out of six connections indicate no significant decrease and even increase in P-wave velocity when clay content increases. These observations stress the importance of structural position of clay, as implied in Minear's model (1982) and neglected in empirical equations of the type V = A + Bphi + Cc (Han et al., 1986), where V is the velocity, A, B, and C are constants, phi is porosity, and c is the clay content.

Trends of Incipient
Lithification and Diagenesis

It can be shown using thin-section analyses and x-ray diffraction data that the established relationships between velocities and porosity for each group of rocks essentially reflect trends of their chemical diagenesis including pressure solution and quartz cementation. Furthermore, the steeper gradients of the velocity increase with decreasing porosity in sandy shales compared to arenites (Figures 7b, 8) may be interpreted in terms of different mechanisms and chemical processes acting during diagenesis in these two rock types. Specifically, these processes include phase transformations accompanied by mechanical compaction in shales, and quartz cementation in all kinds of arenites. Plotting the data for these groups separately on the P-wave velocity vs.

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porosity diagram and adding the data points of the Ottawa sand and sand-kaolinite mixtures with the same range of clay content and at the same effective pressure of 40 MPa indicate that the linear trend of chemical diagenesis breaks down and is dramatically deflected at the transition to unconsolidated sediments (Figure 10). The process of incipient lithification consisting of the development of intergrain (interparticle) bonds and responsible for the sediment-to-rock transition apparently results in a sharp increase in velocity while the porosity reduction is much less pronounced. This effect is apparently better manifest in originally clay-rich lithologies.

To better understand the cause of this phenomenon, we calculated, and plotted in Figure 11, the bulk modulus and shear modulus versus porosity for clean arenites, arenites, and sandy shales. The following formulas were used.

(Equation; SEE PAGE IMAGE)

and
(Equation; SEE PAGE IMAGE)

where G is the shear modulus, K[w] is the bulk modulus of water saturated rocks, rho is dry bulk density, rho[w] is saturated bulk density, V[P] is compressional-wave velocity, and V[S] is shear-wave velocity.

Although no deflection in the linear relations with porosity was found for the bulk modulus, the deflection was revealed for the shear modulus, at least for arenites and shales. This suggests that the increase in the shear modulus rather than the bulk compressibility is responsible for the sharp velocity increase (and a dramatic drop in Poisson's ratio, as was observed in situ by Hamilton, 1979) during the incipient lithification.

Water Saturation Effects and Velocity Ratio

The problem of distinguishing between gas-saturated and fluid-saturated rocks using sonic and seismic data is quite complex and was addressed in many experimental works (King, 1966; Nur and Simmons, 1969; Gregory, 1976; Murphy, 1984). Our goal in this section is simply to demonstrate the differences in the ultrasonic P-velocity response in oven-dry versus brine-saturated

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arenites and shales at high confining pressure. The data for clean arenites and arenites including unconsolidated sediments essentially overlap, as shown in Figure 12a. The dry vs. saturated velocity relation is strong and obeys an exponential law. Even though the saturated velocity is always higher than the dry velocity, the difference between them for rocks in the porosity range from 24-26% to about 10% is on the order of 0.1 km s{-1}, i.e., not significant given the common accuracy of the sonic logs. This difference gradually increases to 0.2-0.3 km s{-1} in low porosity (<10%) sandstones, reaching its maximal value in some granites at the same effective pressure of 40 MPa. It is well known that microcracks are predominantly responsible for the P-wave velocity increase with satu ation in a variety of rocks (King, 1966; Nur and Simmons, 1969). Whereas the effective pressure of 40 MPa is sufficient to close these pores in high porosity arenites due to stress amplification at the grain contacts, this is progressively less likely to be the case for their low porosity equivalents and especially crystalline rocks.

The dry vs. saturated velocity dependence for sandy shales can also be approximated by an exponential law. The effect of saturation, however, is much stronger than for arenites of comparable porosity when the porosity is higher than about 10-12% (Figure 12b). For the lower porosity shales, the effect of saturation at high effective pressure is difficult to detect even using accurate ultrasonic measurements.

The velocity ratio V[p]/V[s] is frequently used for lithology discrimination (e.g., Tatham, 1982), and it was tempting to check the petrophysical classification adopted in this paper using the V[p]/V[s] vs. porosity diagram (Figure 13). The following major points should be made regarding this diagram: (1) the plot clearly separates grain-supported from matrix-supported lithologies,

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(2) the data points of matrix-supported rocks (wackes and sandy shales) overlap showing similar trends, (3) clean arenites can be distinguished from arenites (in fact, from altered arenites and arkoses), and (4) the trends for matrix-supported rocks can be approximated by linear functions, whereas second-order polynomials best describe the data corresponding to grain-supported rocks. Thus, the velocity ratio proves to be a useful additional parameter not only in

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distinguishing siliciclastics from carbonates (Tatham, 1982), but also for better lithology identification within siliciclastics.

ANALYSIS OF PERMEABILITY
VS. POROSITY RELATION

Having established a strong correlation between ultrasonic velocities and porosity for each petrophysical group separately, it seems straightforward to use the porosity as a bridge between velocities and permeability. The most problematic issue that normally tends to obscure any significant correlation between permeability and porosity in any population of data is the effect of subtle lithologic differences (e.g., the grain size) always encountered in geological formations.

The plot of gas permeability at 30 MPa vs. porosity for our data is shown in Figure 14. The best fit approximation to each of the petrophysical groups, except sandy shales for which there were not enough data, is a power law, with correlation dropping from clean arenites (R = 0.93) to clay-bearing lithologies (arenites at R = 0.42 and wackes at R = 0.23). This diminished correlation is a result of intermingling between some arenites and wackes in terms of permeability, as well as substantial scattering of the data. As detailed petrographic observations suggest, three data points of arenites having a relatively decreased permeability are characterized by minor amounts of authigenic clay coating grains and apparently plugging the pore throats of these rocks (Klimentos and McCann, 1990). In contrast, two wacke samples with a relatively increased permeability are characterized by a pronounced textural inhomogeneity and the presence of larger, microscopically identifiable pores. Apart from these accountable complications, the general trends of the permeability vs. porosity relationships suggest that at a given porosity the permeability considerably decreases in the sequence clean arenite/arenite/wacke/sandy shale.

To gain a better insight into the permeability vs. porosity relations in our database, measurements of irreducible water saturation (S[wi]) were undertaken using the centrifuge technique, and subsequently the effective porosity (phi[ef]) of the samples was calculated. The effective

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porosity may be envisioned as porosity occupied by fluid mobile (at pressure gradients normally encountered in situ) in water-wet rocks. The effective porosity, therefore, better scales with permeability than total porosity. The plots of S[w]i and phi[e]f versus porosity illustrated in Figures 15 and 16 can be summarized as follows. The matrix-supported rocks (wackes and sandy shales) basically overlap and exhibit similar linear trends with generally higher irreducible water saturation and lower effective porosity compared to clean arenites and arenites. This is in agreement with petrographic observations of the pore size, which ranges from about 10 to 200 micrometers in grain-supported rocks and is generally indistinguishable (i.e., <1 micrometer) in matrix-supported ones (cf. Fig res 4-6). The S[wi] values in arenites are fairly close to those of clean arenites at high porosities, but the trend of arenites gradually deviates from that of clean arenites, approaching the trend of matrix-supported rocks when the porosity drops to about 5% (Figure 15). Such a behavior of arenites is consistent with their permeability trend that also approaches clean arenites at high porosity and tends to merge with the trend of wackes at low porosities. Finally, we note that the effective porosity vs. porosity trends of all rock groups considered converge to a point close to zero effective porosity when the porosity is still about 1-3%.

CONCLUSIONS

In this paper, we have focused on the effects of composition, texture, and degree of diagenesis on relations between ultrasonic velocity, porosity, and permeability of clastic sedimentary rocks using an extensive set of petrographic and petrophysical data. The petrophysical classification proposed here incorporates experimental rock physics data and detailed petrographic analyses of the rocks studied. The subdivision of what is generally known as siliciclastic sand-mud or sandstone-shale sequences into petrophysical groups is based primarily on such considerations as the presence of grain contacts, grain and clay matrix mineralogy, and content. Such subdivision significantly improves the

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empirical models establishing correlation of ultrasonic velocities with porosity. No attempt to physically model these relations was made in this paper. The depositional and diagenetic features as well as established petrophysical correlations and trends in each of the petrophysical groups can provide the necessary guidance in future modeling.

The principal point in the petrophysical classification of siliciclastics is establishing whether the rock is grain supported or matrix supported. Our observations agree well with the modern petrologic scheme in that rocks with 15% or more matrix, which is predominantly composed of original depositional material (mostly clay), are essentially matrix-supported sandstones termed wacke and should be distinguished from grain-supported arenaceous sandstones. Further subdivision, the validity of which was confirmed by strong velocity vs. porosity relations for each group, is based on the observation of structural position and overall amount of clay. In this manner we separate clean arenites (<2% clay) from arkosic and lithic arenites bearing either lithic or grain alteration clay, and wa kes from sandy shales with 35% or more matrix. Thus, the information on the exact clay content, as required by previously published statistical velocity-porosity transforms, is actually not necessary for reliable porosity estimates using seismic velocities, provided that the general lithologic information is available from independent sources (e.g., analyses of cuttings). Moreover, no significant correlation between clay content and velocity was found inside each petrophysical group. The textural and mineralogical difference between grain-supported and matrix-supported lithologies is further stressed by their different sensitivity to fluid saturation effects on ultrasonic velocities and the distinct trends of their velocity ratio.

Another important aspect that follows from our data analysis is the possibility of lithology prediction using seismic velocities. In order to do this, however, an independent source of porosity data is required (e.g., neutron, resistivity, or density logs). If porosity data is available, then the velocity-porosity transforms proposed here can be used to determine the petrophysical group from velocity and porosity constraints. Since the petrophysical classification is tied to the petrographic one, the geological interpretation of the logging data becomes much more straightforward and meaningful.

We also discussed porosity reduction in well-sorted arenaceous sediments from depositional porosity of 37-55% to about 25% due to the mechanical rearrangement of grains and further due to chemical diagenesis featuring interparticle bonding and dissolution-precipitation of the material. It was demonstrated that the onset of chemical diagenesis (incipient lithification) can be detected based on the dramatic increase in seismic velocities on the background of a very minor porosity reduction. This sharp velocity increase is related to the major increase in the shear modulus with only minor increase in the bulk modulus during sediment-to-rock transformation. The dependence of established linear trends of the velocities and elastic moduli on porosity were shown to reflect further porosity r duction due to the chemical diagenesis of rocks.

Finally, a relatively good correlation revealed between gas permeability and porosity for clean arenites was found to deteriorate in arenites due to the authigenic clay plugging the pore throats and especially in wackes due to their small-scale inhomogeneity. The statistical significance of some of these relationships was questioned; however, to a first order they can be used as a bridge for permeability derivation from seismic velocities, provided general information on lithology is available.