1 Introduction

Elastic properties of rocks and their pressure and saturation dependence are of interest in many areas including reservoir geomechanics; civil, mining and petroleum engineering; fault zone characterization; etc. Elastic properties include elastic parameters such as Poisson’s ratio, Young’s modulus, bulk modulus, and shear modulus. Each parameter describes the elastic deformation of a rock in a different manner. The elastic properties can be calculated statically, where stress is applied to deform the rock slowly and the resultant strain is measured. They can also be determined by inverting P- and S-wave velocities measurements, referred to as the dynamic properties. However, the two types of elastic properties are different. The difference between the static and dynamic elastic properties are caused by factors such as the presence of microfractures, stress induced anisotropy, the magnitude of the strain amplitude applied, the frequency at which the moduli is determined, the saturation state, and the type of pore fluid (Adam & Batzle, 2008; Adelinet et al. 2010; Batzle et al. 2001, 2006; Blake & Faulkner, 2016; Hammond et al. 1979; Jizba, 1991; Müller et al. 2010; Tutuncu et al. 1998a, b).

The static elastic properties are required in computing or modelling the deformation of rock when it is stressed. Hence, relationships need to be established to convert the dynamic elastic properties to static ones. Here, we will focus on the relationship between static and dynamic bulk moduli. The bulk modulus generally describes the resistance of the rock to hydrostatic compression. The inverse of bulk modulus gives the compressibility. Simmons and Brace (1965) found that the static to dynamic bulk modulus ratio (Kstatic/Kdynamic) of granites, quartzite and limestone is approximately 0.5 at atmospheric pressure and close to 1 at confining pressures of 300 MPa and above. Cheng and Johnston (1981) found that Kstatic/Kdynamic of dry oil shale samples is approximately 0.7 and remains fairly constant up to confining pressures of 200 MPa. Jizba and Nur (1990) found a linear  relationship between the static and dynamic bulk moduli (Kstatic and Kdynamic) for dry tight gas sandstones sample:

$$K_{{{\text{static}}}} = { 1}.{293}K_{{{\text{dynamic}}}} {-}{ 11}.{634}$$
(1)

Bakhorji and Schmitt (2010) found a consistent trend of the static to dynamic ratio of dry and water saturated carbonate samples to approximately 0.5. Adelinet et al. (2010) found a systematic small difference between static and dynamic bulk moduli of dry Basalt samples pressurized up to 200 MPa. Yan et al. (2017) found that the dynamic bulk modulus is approximately equal to the static bulk modulus when the pore stiffness of dry and water saturated sandstone is greater than 6 GPa.

The relationship that relates dynamic to static bulk modulus for argillites is non-existent in the literature. Argillites are indurated mudstones that have relatively high strength and low permeability. These rocks are often used in civil engineering projects, are unconventional petroleum reservoirs granted that the organic content is high, and serve as waste repository. In this study, the static and dynamic bulk moduli of Naparima Hill Formation argillites were measured simultaneously under both wet (fully water saturated) and dry (atmospheric) conditions as a function of effective pressure (confining pressure minus pore pressure) up to 130 MPa. The aim of this work is to determine if a relationship exists between the static and dynamic bulk moduli for argillites. If a relationship does exist, we want to explore if it is dependent on saturation state and effective pressure (equivalent to burial depth).

2 Methodology

2.1 Sample Description and Preparation

Experiments were carried out on rock samples that were retrieved from seven different outcrop locations (referred to as NHS1, NHS3, NHS4, NHS7, NHS10, NHS13 and NHS14) of the Naparima Hill Formation, Trinidad (Fig. 1). The lithology of the Naparima Hill Formation has been described as organic-rich argillites (Pindell & Kennan, 2009) and the lithofacies considered similar to the siliceous argillites found within the Monterrey Formation in California, USA. The porosity and permeability of these argillites ranged from 6 to 31% and 10–20 to 10–18 m2, respectively (Iyare et al. 2020). Petrographic investigation conducted by Iyare et al. (2020) on the studied outcrop samples showed that the samples are primarily quartz, with calcite present as a secondary mineral and cement. Clay minerals (e.g. illite and kaolinite) are also present, but are in small quantity (Fig. 2a). The thin section analysis of the outcrop samples revealed four lithofacies associations: Lithofacies a (location NHS7) is mainly an oil stained, siliceous calcareous mudstone (Fig. 2b); Lithofacies b (locations NHS1, NHS3, NHS4 and NHS14) is mainly a calcite cemented, calcareous mudstone interbedded with black chert (Fig. 2c–f); Lithofacies c (location NHS13) is mainly an oil-filled, carbonate rich mudstone with nodular chert (Fig. 2g) and Lithofacies d (location NHS10) is mainly a poorly sorted, siliceous mudstone (Fig. 2h).

Fig. 1
figure 1

The study area (a). (b) provides a zoom-in on the study area. (c–i) show the locations of where the Naparima Hill Formation outcrop was sampled

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Fig. 2
figure 2

modified from Iyare et al. 2020). Note: (Qz) Quartz; (Cm) Chert matrix, (Op) Oil particle; (Os) Oil stain; (Ca) Calcite filled fracture; (CQ) Calcite-Quartz matrix;(Nc) Nodular chert (Fo) Oil filled fracture; (Fm) Foraminifera; (Bc) Bioclasts

X-ray diffraction (XRD) (a) and Photomicrographs (b–h) of the studied outcrop locations within the Naparima Hill Formation (

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A significant amount of the outcrop surface was removed from each location to retrieve fresh in-situ block samples. The outcrops are resistant to weathering due to their dense textures and high silica content (Fig. 2). Cylindrical specimens of 20 mm diameter were cored perpendicular to the bedding of the outcrops (see Fig. 3 for specimen preparation). The lengths of the specimens were between 50 and 55 mm and the ends were squared (± 0.02 mm) in accordance with ASTM D7012 (2014) and ASTM D4543 (2019) suggested methods. The oil within the specimens was then removed using toluene in the soxhlet extractor method, which increases the porosity and surface area (Gupta et al. 2017). Strain gauges (axial and radial) were attached to the centre of the specimens and then the specimens were placed in PVC jacket. The electrical connections of the strain gauges were fed out through small holes in the jacket, which were then sealed by an epoxy adhesive.

Fig. 3
figure 3

Preparation of sample. a Plugging machine to extract 20 mm diameter plugs. b Saw to trim the ends of the plug to the required length (50–55 mm). c Precision-end grinder to square ends of plugs to ± 0.02 mm. d Intact samples from the seven outcrop locations. e Typical prepared sample (sample from NHS10 is shown in this example) placed inside PVC jacket. Electrical wires are attached to the terminals of the axial and radial strain gauges and fed through hole in jacket. The hole is then sealed with a compliant epoxy resin

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2.2 Experimental Procedure

Static and dynamic measurements were conducted using a servo-controlled triaxial apparatus that is installed at the Geomechanics Laboratory, University of West Indies (Fig. 4). Blake and Faulkner (2016) provided more details on the apparatus. The apparatus has the capability to measure P- and S-wave velocities at 1.5 MHz under confining and pore pressures as high as 200 MPa. Experiments were carried out on dry and saturated specimens at effective pressures (confining pressure minus pore pressure) up to 130 MPa. To ensure that the specimens were completely dried, they were placed in an oven at 50 °C for seven days. For saturated tests, the specimens were placed in a bath of de-ionized water under vacuum. The specimens are then removed from the water bath and placed in the triaxial apparatus where de-ionized water was pumped, at a pressure of 10 MPa, into the specimens from both ends of the specimen, using the upstream and downstream pore pressure connections. The pore pressure controller was used to apply this constant pressure and to ensure that the pressure was equilibrated within the specimen pressure, which took hours to achieve due to the low permeability of the specimens. Confining pressure was applied to the specimens using the confining pressure pump and controller (Fig. 4b). The PVC jacket in which the specimens were placed, separated the confining fluid from the pore fluid.

Fig. 4
figure 4

Triaxial apparatus. a Front view showing pore pressure generator, controllers, and ultrasonic system (switchbox, oscilloscope and pulser/receiver). b Inside view showing confining and pore pressure controller systems, confining pressure generator, and pressure vessel with heaters. c Seismic sample showing confining pressure pipe (Cpp), upstream pore pressure pipe (Uppp), downstream pore pressure pipe (Dppp), plugged cylindrical sample, strain gauge and P- and S-wave piezoceramic connecting wires. The red stars indicate the locations of where the P- and S-wave piezoelectric ceramics are housed. The seismic sample assemble is placed inside the pressure vessel

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The axial and radial strain gauges that were attached to the specimens were used to monitor the deformation within the specimens when they were subjected to increasing effective pressures. The strain gauges were connected in a Wheatstone bridge configuration using a strain gauge amplifier. The output of the axial and radial strain gauges are identical, and were used to determine the static bulk properties. The static bulk modulus was determined by differentiating the volumetric strain (axial or radial strain multiplied by 3) vs effective pressure curve at 10, 30, 50, 70, 90, 110 and 130 MPa effective pressure (Cheng & Johnston, 1981) (Fig. 5a).

Fig. 5
figure 5

Example of strain data as a function of effective pressure (a), and P- and S-wave arrivals at 10 MPa effective pressure (b, c) from location NHS4 (lithofacies b), under dry conditions. The red circles on the volumetric strain curve indicate the effective pressure at which P- and S-wave data were recorded. The P-wave arrived at 19.71 μs and the S-wave arrived at 34.02 μs

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Dynamic elastic properties were calculated by the inversion of P- and S-wave velocities. P- and S-wave piezoelectric ceramics (PZT-5A) placed in the top and bottom loading platens (Fig. 4c) were used to generate P- or S-wave at one end of the specimen and received the P- or S-wave at the other end. Backing material made from sintered stainless steel of 0.5 μm pore size and 0.125 inch thick was placed on the piezoelectric ceramics. A pulser/receiver (JSR DPR300 Pulser/Receiver) was used for the excitation and amplification of the received signals. A digital oscilloscope with high time-based accuracy (Tektronix MDO3034) was employed to display and record the amplified ultrasonic waves. For accurate and reliable P- and S-wave measurements, ASTM D2845-08 (2008) was adhered to, which significantly reduced the P to S-waves and S- to P-waves converted waves that usually obscure the S-wave arrival. The P- and S-wave arrivals are very clear and can be easily picked (Fig. 5b, c). The effective pressure was held constant for ~ 10 s at 10, 30, 50, 70, 90, 110 and 130 MPa, to record the velocity data. P- and S- wave velocities were calculated by dividing the specimen’s length (L) by the P- and S-waves travel time (t):

$${V}_{p}{ or V}_{s}=L/t$$
(2)

where Vp is the P-wave velocity and Vs is the S-wave velocity. The specimen length changes with increasing effective pressure, which is determined by the axial strain gauge. The corrected specimen length is used in the velocity calculations. By assuming the specimens are isotropic, the dynamic bulk modulus, Kdynamic, can be estimated from the P- and S-wave velocities using the well-known relationships for isotropic materials (e.g. Cheng & Johnston, 1981):

$${K}_{dynamic}=\rho \left({{V}_{p}}^{2}-\frac{4}{3}{{V}_{s}}^{2}\right)$$
(3)

where ρ is the density of the specimen. A detailed analysis of isotropy assumption is presented in the “Discussion” section. The change in the specimen’s density, calculated from the static volumetric strain data and porosity data from Iyare et al. (2020), was accounted for in the calculations.

3 Results

Figure 6 shows P- and S- wave velocities and density as a function of effective pressure for both dry and saturated conditions from which dynamic bulk moduli are calculated. The P- and S-wave velocities and density increase slightly with increasing effective pressure. Specimens from locations NHS7 and NHS10, (soft rocks from lithofacies a and d) experience a greater rate of velocity increase. Saturation of the specimens causes the P- and S-wave velocities to decrease, with the exception of the specimen from NHS7, where the P-wave velocity slightly increases. The decrease in the S-wave velocity is greater than the decrease in the P-wave velocity. As the effective pressure increases, the reduction in velocities lessens. The increase in P-wave velocity for the specimen from NHS7 also lessens with increasing effective pressure. At 10 MPa effective pressure, the P- and S-wave arrival could not be identified for specimen from NHS7 when it was saturated because the waveform was attenuated and within noise, hence the velocities were not determined. Similarly, the S-wave velocity of the specimen from NHS10 at 10 MPa effective pressure was not determined. The density of the specimens significantly increases when saturated.

Fig. 6
figure 6

P- (a, b) and S- wave velocities (c, d) and density (e, f) as a function of effective pressure, under dry and saturated conditions

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The static and dynamic bulk moduli vary for the different lithofacies, with specimens from lithofacies (c) and (a) having the highest and lowest bulk moduli, respectively (Figs. 7 and 8). Figure 6 shows the static and dynamic bulk moduli with varying effective pressures. We observed that the dynamic Bulk modulus is higher than those of the static in both dry and saturated conditions. For dry and hard lithofacies (specimen from NHS13), the static and dynamic bulk moduli are approximately equal. The bulk modulus increases with increasing effective pressure, which is more dominant for the dynamic bulk modulus. Saturation of the specimens caused the static bulk modulus to decrease and the dynamic bulk modulus to increase. Figure 8 shows Kstatic/Kdynamic as a function of effective pressure for dry and saturated specimens. Kstatic/Kdynamic ratio of specimens from lithofacies a and d, shows slight reduction with increasing effective pressure when the specimens are dry. Saturating these specimens, causes a significant decrease in the Kstatic/Kdynamic ratio, which increases with increasing effective pressure. Specimens from lithofacies b show slight decrease in Kstatic/Kdynamic ratio with increasing effective pressure for both dry and saturated conditions. There is no significant change in the Kstatic/Kdynamic ratio with increasing effective pressure for the specimen from lithofacies c. Under saturated conditions, specimens from lithofacies b and c also exhibit reduction in Kstatic/Kdynamic, but not as major as specimens from lithofacies a and d.

Fig. 7
figure 7

Comparison between static and dynamic bulk moduli at 10, 30. 50, 70, 90, 110 and 130 MPa effective pressure for dry and saturated conditions. Red line represents linear relationship. The static and dynamic error is less than 7 and 1%, respectively

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Fig. 8
figure 8

Kstatic/Kdynamic ratios as a function of effective pressure under dry and saturated conditions. The static and dynamic error is less than 7 and 1%, respectively

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Figure 7 also shows that linear relationships exist between the static and dynamic bulk moduli at varying effective pressures for both dry and saturated conditions. The linear relationships have high correlation of R2 value equal to 0.85 and greater. In the dry conditions, the gradient and intercept, of the linear relationship, increases and decreases, respectively, with increasing effective pressure (Fig. 9). When saturated, the gradient and intercept follow the same trend as the dry conditions, but the gradient is higher and the intercept is significantly lower.

Fig. 9
figure 9

Static and dynamic bulk moduli linear relationship as a function of effective pressure for dry and saturated conditions

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4 Discussion

In this study, we aimed to sample a minimum of three locations per lithofacies to quantify the heterogeneity, but the terrain, accessibility, and difficulties in retrieving samples limited the study to only a total of seven locations. However, we measured the static and dynamic bulk moduli simultaneously for each outcrop, which removes any heterogenetic effects that could possibly influence the difference between the static and dynamic measurements. Our results show that the dynamic bulk modulus is greater than the static bulk modulus, which is in agreement with previous studies (Adam & Batzle, 2008; Adelinet et al. 2010; Bakhorji & Schmitt, 2010; Batzle et al. 2006; Blake & Faulkner, 2016; Cheng & Johnston, 1981; Jizba & Nur, 1990; Simmons & Brace, 1965). Saturation causes the difference between the static and dynamic elastic properties to increase. This is because it reduces the static bulk modulus and increases the dynamic bulk modulus. Saturation causes the P- and S-wave velocities to decrease, but it also causes the density to increase (Fig. 6) because water fills the pore spaces and creates excess mass, which resulted in an increase in the dynamic bulk modulus. The porosity of the argillites plays an important role in the increase in the dynamic bulk modulus. When the pore spaces are saturated, a new term, the bulk modulus of the pore fluid (Kf), will be added to the bulk modulus of the rock frame (Kfr). The results due to saturation are similar to the results by Adelinet et al. (2010) and Blake and Faulkner (2016).

We measured the static and dynamic bulk moduli of soft and hard lithofacies, where the static bulk modulus ranged from 2.2 to 28.7 GPa and dynamic bulk modulus ranged from 3.2 to 31.9 GPa. A high bulk modulus implies that the rock is hard and resists hydrostatic compression. Table 1 shows the porosity and mineralogy composition of the argillites. The soft rocks (lithofacies a and d) have high porosity and mainly silica content, whereas the hard rocks (lithofacies b and c) have lower porosity and are dominated by silica and carbonate. The carbonate content in the lithofacies mainly acts to cement the argillites (Iyare et al. 2020), which causes the bulk modulus to be high. The difference between static and dynamic bulk moduli is reduced as the bulk moduli increase. Hence, the stiffer the rock, the closer the static bulk modulus to the dynamic bulk modulus (Wang, 2000). This explains the static and dynamic bulk moduli being approximately equal for the hard lithofacies (lithofacies c, specimen from NHS13).

Table 1 Porosity (Φ), and mineral compositions of the Naparima Hill outcrop locations (from Iyare et al. (2020))
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Empirical relationships between the static and dynamic bulk moduli are limited in the literature. We established a linear relationship with high correlation between the static and dynamic bulk moduli of argillites and quantified how this relationship changes as a function of effective pressure (equivalent to burial depth) and saturation state. Jizba and Nur (Jizba & Nur, 1990) also established a linear relationship between the static and dynamic bulk moduli for dry tight gas sandstones, at various confining pressures from 5 to 125 MPa. To get a direct comparison with the study done by Jiza and Nur (Jizba & Nur, 1990), we applied a linear fit (r2 = 0.93) to the present study's entire data (from 10 to 130 MPa effective pressure) for the dry conditions obtaining:

$${\text{K}}_{static} = \, 0.{\text{996K}}_{dynamic} { - 3}.{157}$$
(4)

This relationship is in agreement with the linear relationship proposed by Jizba and Nur (Jizba & Nur, 1990) (less than 3 GPa difference), within the dynamic range of 19–38 GPa (Fig. 10). As the agreement is for such a small range (dynamic bulk modulus of 19–38GPa), this suggests that the empirical relationships may be dependent on the rock type.

Fig. 10
figure 10

Relationship between the Static and dynamic bulk modulus from the literature and present study. The filled circles represent the present study entire dataset under dry conditions

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4.1 Effect of Microfractures and Effective Pressure on the Kstatic and Kdynamic.

The presence of microfractures affects the stiffness of the rock, reducing the bulk modulus. Microfracture also plays a key role in the difference between the static and dynamic elastic properties. Static elastic bulk modulus is affected by all the fractures, while the dynamic elastic bulk modulus is only affected by fractures that are in the path of the travelling P- and S-waves. If the microfractures are closed then the static and dynamic bulk moduli should be closer to each other (Blake & Faulkner, 2016; Cheng & Johnston, 1981; Simmons & Brace, 1965). Subjecting a rock to effective pressure closes fractures. A plot of velocity vs effective pressure can be used to clearly demonstrate closure of fractures and show the pressure at which all low aspect ratio microfractures are closed. The velocity increases rapidly in a non-linear manner below the fracture-closure pressure, and then increase approximately linearly as effective pressure increases (Birch, 1960; Blake et al. 2013; Kern, 1978). The linear increase may be due to high aspect ratio microfracture, microfractures with mismatched faces and or compaction of pores. High aspect ratio microfractures and microfractures with mismatched faces require very large effective pressures to close them completely. The velocity vs effective pressure plots seen in Fig. 6 have only linear increase in velocity. This suggests that mainly high aspect ratio microfracture and microfracture with mismatched faces are present in the argillites. This is corroborated with thin section analysis done by (Iyare et al. 2020) (Fig. 2).

Blake and Faulkner (2016) found that the increase of Kstatic/Kdynamic ratio with increasing effective pressure is dependent on the fracture density. Westerly granite samples were used in their study, which have low aspect ratio microfractures and microfractures with matched faces. These facture types are easier to close compared to the microfracture types in the present study. Blake and Faulkner (2016) found that the higher the fracture density, the lower the Kstatic/Kdynamic ratio at low effective pressures. The Kstatic/Kdynamic ratio converges towards 1 at higher pressure. The rate of increase of the Kstatic/Kdynamic ratio is high at low effective pressures, but decreases with increasing effective pressure. This suggests that the closing of microfractures increases the static bulk modulus much more than the dynamic bulk modulus. Figure 8 shows a general trend of Kstatic/Kdynamic ratios slightly decreasing with increasing effective pressure. This is most likely due to the low fracture density (Fig. 2) and compaction of the matrix (intrinsic properties), which result in a more dominant increase in the dynamic bulk modulus compared to the static bulk modulus.

4.2 Evaluation of the Anisotropy in the Argillites

The major assumption made in our analysis is isotropy. In general, most natural rocks are anisotropic, because of factors including foliation, oriented fracture networks and mineral preferred orientation. Assuming anisotropic rocks to be isotropic can lead to some degree of discrepancy in the analysis. To evaluate the anisotropy in the argillites, we measured P- and S-wave velocities on orthogonally plugged specimens that were taken from in-situ blocks, from each of the studied locations. Velocities were measured perpendicular (90°) to outcrop bedding, and parallel to outcrop bedding in the strike direction (0°—S) and dip direction (0°—D) (Table 2). The oil within these specimens were not removed, and the specimens were dried and subjected to effective pressures up to 130 MPa. The anisotropy of the argillites ranged between 2 and 27% (Table 2 and Fig. 11). An increase in the effective pressure caused the anisotropy to reduce, which may be mainly due to fracture closure and compaction of the rock leading to loss of porosity. This is evident as the reduction in the anisotropy is directly proportional to the porosity of the lithofacies. Figure 11 and Table 2 show that lithofacies a (31% porosity) has the greatest reduction in the anisotropy, followed by lithofacies d (21% porosity), c (18% porosity) and b (less than 16% porosity). The P- and S-wave anisotropies are less than 10% for the four sample locations within lithofacies b. For lithofacies a, the P-wave and S-wave anisotropies are 27 and 21%, respectively, at 10 MPa effective pressure and reduced to 17 and 13% at 130 MPa effective pressure. For lithofacies c and d, the P-wave anisotropy is less than 17%, whereas the S-wave anisotropy is less than 12%. It can be concluded that the results presented in this study have some degree of uncertainty, especially for lithofacies a, c, and d that displayed moderate anisotropy. However, the uncertainty is reduced for results calculated at higher effective pressures as the rocks become more isotropic with increasing effective pressure.

Table 2 P- and S-wave velocities anisotropies in the argillites (
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Fig. 11
figure 11

modified from Blake et al. (2020))

P-wave (a) and S-wave (b) anisotropies as a function of effective pressure in the argillites (

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It is better to assume that these argillites are transversely isotropic with the plane of transverse isotropy in the direction parallel to the bedding of the outcrop. This is because the P- and S-wave velocities are approximately equal in the strike and dip directions of the beds (Table 2). For a transversely isotropic rock, five independent materials parameters need to be determined which involves measuring: (1) the Young’s modulus in the direction parallel and perpendicular to the plane of transverse isotropy (outcrop bedding); (2) Poisson’s ratio in the direction parallel and perpendicular to the plane of transverse isotropy; and (3) shear modulus in the direction perpendicular to the plane of transverse isotropy. When a rock is isotropic, only two independent elastic constants are required to fully characterize the elasticity of the rock (for example, Young’s modulus and Poisson’s ratio), from which the other elastic constants can be easily calculated (for example, bulk modulus, shear modulus and Lame’s first parameter). Completely characterizing the static and dynamic elastic anisotropies of these argillites requires simultaneous static (stress–strain) and dynamic measurements (P- and S-wave velocities) on specimens that are plugged perpendicular, parallel, and 45° to the outcrop bedding (e.g. Amadei, 1996; Dewhurst & Siggins, 2006; Homand et al. 1993; Lo et al. 1986; Sone & Zoback, 2013). Sone and Zoback (2013) evaluated the error of assuming that a rock is isotropic rather than transversely isotropic for 16 different anisotropic shale samples and reported that the error in the Young’s modulus is within 5%. This suggests that the degree of uncertainty in our results, due to the assumption that the argillites are isotropic, is small, especially for argillites with low anisotropy.

5 Summary

The static and dynamic bulk moduli were measured simultaneously, at effective pressure up to 130 MPa, for dry and fluid-saturated organic-rich argillite specimens. We found that the dynamic bulk modulus is greater than the static bulk modulus. For dry and harder rocks (bulk modulus of approximately 28 GPa) both moduli are roughly equal. Saturation of the specimens increases the difference between the static and dynamic bulk moduli, which proves to be significant for weaker lithofacies.

Relationships that relate static to dynamic bulk modulus of argillites do not exist in the literature. We established a linear relationship between the static and dynamic bulk moduli and found that the relationship is dependent on the effective pressure (equivalent to burial depth) and saturation state. The few empirical relationships that exist in the literature are not in total agreement, which suggests that the relationships are dependent on the rock type. Hence, core or outcrop measurements for both the dynamic and static bulk moduli should be carried out to establish type locality and regional empirical relationships for the interested fields or reservoirs.