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The correlations between the saturated and dry P-wave velocity of rocks

S. Kahraman *

Mining Engineering Department, Nigde University, Nigde, Turkey

Received 7 February 2007; received in revised form 31 May 2007; accepted 31 May 2007Available online 7 June 2007

Abstract

Sometimes engineers need to estimate the wet-rock P-wave velocity from the dry-rock P-wave velocity. An estimation equationembracing all rock classes will be useful for the rock engineers. To investigate the predictability of wet-rock P-wave velocity from thedry-rock P-wave velocity, P-wave velocity measurements were performed on 41 different rock types, 11 of which were igneous, 15 of which were sedimentary and 15 of which was metamorphic. In addition to the dry- and wet-rock P-wave velocity measurements, theP-wave velocity changing as a function of saturation degree was studied. Moreover, dry-rock S-wave velocity measurements were con-ducted. The test results were modeled using Gassmann’s and Wood’s theory and it was seen that the measured data did not fit thetheories. The unconformity is due to the fact that the theories are valid for high-porosity unconsolidated sediments at low frequencies.Gassmann’s equation was modified for the rocks except high-porosity unconsolidated sediments.

The dry- and wet-rock P-wave velocity values were evaluated using regression analysis. A strong linear correlation between thedry- and wet-rock P-wave velocities was found. Regression analyses were repeated for the rock classes and it was shown that correlationcoefficients were increased. Concluding remark is that the derived equations can be used for the prediction of wet-rock P-wave velocityfrom the dry-rock P-wave velocity. 2007 Elsevier B.V. All rights reserved.

Keywords: Wet-rock P-wave velocity; Dry-rock P-wave velocity; Regression analysis

1. Introduction

Ultrasonic measurement is one of the non-destructivegeophysical methods commonly used by engineers workingin various fields such as mining, geotechnical, civil, under-ground engineering as well as for oil, gas minerals explora-tions. This method can be applied both in the laboratory

and in the field. There are different application areas suchas the assessment of grouting [1,2], rockbolt reinforcement[3], the determining of blasting efficiencies in the rockmass [4], the prediction of rock mass deformation andstress [5,6], the determination of rock weathering degree[7], rock mass characterization [8,9] and the estimation of the extend of fracture zones developed around under-ground openings [10]. A number of study [11–16] investi-

gating ultrasonic propagation in fractured rock has beencarried out. Some researchers [17–19] used the P-wavevelocity for the estimation of weathering depth of buildingstones. Most researchers [20–27] studied the relationsbetween rock properties and sound velocity and found thatsound velocity is closely related with rock properties.

There are a number of factors that influence the sound

velocity of rocks. The important factors are rock type, tex-ture, density, grain size and shape, porosity, anisotropy,water content, stress and temperature. In addition to thesefactors, rock mass properties also influence the soundvelocity. Weathering and alteration zones, bedding planesand joint properties (roughness, filling material, water,dip and strike, etc.) have important influence on the soundvelocity.

Some researchers have investigated the effect of watercontent on the ultrasonic velocities. Wyllie et al. [28] inves-tigated the variation of velocity in sandstone as a function

0041-624X/$ - see front matter 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.ultras.2007.05.003

* Tel.: +90 388 2252264; fax: +90 388 2250112.E-mail address: [email protected]

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Available online at www.sciencedirect.com

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of water content. They showed that there is a markeddecrease in the P-wave velocity as the saturation is reducedfrom 100% to approximately 70%, between 70% and 10%the P-wave velocity is nearly constant and below 10% thevelocity is changeable. Wyllie et al. [29] clearly indicatedthat the velocity of fluid saturated rocks was dependent

on the ratio between the velocity of rock and the velocityof pore fluid. Thill and Bur [30] examined the influenceof saturation on pulse velocity in St. Cloud granodiorite.They found that a remarkable velocity changes can occureven in compact rock having only a minute amount of porosity. Nur and Simmons [31] measured the compres-sional wave velocity in a sample of Chelmsford granite, ini-tially saturated with water but allowed to dry in theatmosphere over a period of four days. They indicated thata rapid change of velocity occurred in the first a few hourseven though the porosity of the sample is only about 1%.Ramana and Venkatanarayana [32] studied the effect of water saturation on Kolar rocks. They showed that in gen-

eral both weight and velocity increased with increasingtime of saturation. Beyond 48 h the saturation curves tendsto be steady. Wang et al. [33] determined both compres-sional and shear wave velocities in Alpine gneiss along itsprinciple fabric directions under dry and saturated condi-tions. The compressional wave velocities in all three direc-tions increased remarkably as the sample was immersed inthe water, whereas the shear wave velocities indicated littlechange. The greatest change took place in the compres-sional waves in the direction perpendicular to the foliationof the rock. Gregory [34] investigated the influence of sat-uration by water, oil, gas, and mixtures of these fluids on

the densities, velocities, reflection coefficients, and elasticmodules of consolidated sedimentary rocks in the labora-tory by ultrasonic wave propagation methods. He foundthat fluid saturation effects on compressional wave velocityare much larger in low-porosity than in high-porosityrocks. Lama and Vutukuri [24] stated that the wetting of rocks usually leads to a rise in the P-wave velocities. Nor-mally, the wave velocity in more porous rocks completelysaturated with water is lower than in slightly porous rocks,because the P-wave velocity in water is less than the P-wavevelocity in mineral skeleton.

Although several researchers have investigated the effectof saturation on P-wave velocity of different rocks, none of them has derived an empirical equation between dry- andwet-rock P-wave velocities. A correlation equation betweendry- and wet-rock P-wave velocities for the estimation pur-pose will be useful for the rock engineering applications. Inthis study, the predictability of wet-rock P-wave velocityfrom the dry-rock P-wave velocity was studied.

2. Sampling

Sound velocity tests were performed on 41 different rocktypes, 11 of which were igneous, 15 of which were sedimen-tary and 15 of which was metamorphic. Rock blocks were

collected from the stone processing plants, quarries and

natural outcrops in Turkey. Each block sample wasinspected for macroscopic defects so that it would providetest specimens free from fractures, partings or alterationzones. The name, location and class of the rocks are givenin Table 1.

3. Experimental studies

NX (54 mm) samples were cored from the block samplesin the laboratory. End surfaces of the core samples were cutand polished sufficiently smooth plane to provide good cou-pling. A good acoustic coupling between the transducer faceand the soil surface is necessary for the accuracy of transittime measurement. Stiffer grease was used as a couplingagent in this study. Transducers were pressed to either endof the sample and the pulse transit time was recorded. P-

wave velocity values were calculated by dividing the length

Table 1The name, location and class of the rocks tested

Sample code Rock type Location Rock class

1 Travertine Mut/Icel Sedimentary2 Travertine (Limra) Finike/Antalya Sedimentary3 Travertine Godene/Konya Sedimentary4 Travertine (Limra) Bucak/Burdur Sedimentary

5 Limestone Sogutalan/Bursa Sedimentary6 Limestone Korkuteli/Antalya Sedimentary7 Travertine (Limra) Demre/Antalya Sedimentary8 Limestone Hazra/Diyarbakir Sedimentary9 Travertine Karaman/Konya Sedimentary

10 Travertine (DemreTasi) Demre/Antalya Sedimentary11 Limestone Bunyan/Kayseri Sedimentary12 Limestone Fethiye/Mugla Sedimentary13 Travertine Yildizeli/Sivas Sedimentary14 Sandstone Kavlaktepe/Nigde Sedimentary15 Sandstone Kolsuz/Nigde Sedimentary16 Marble Altintas/Kutahya Metamorphic17 Marble (Afyon Sekeri) Iscehisar/Afyon Metamorphic18 Marble Yatagan/Mugla Metamorphic19 Marble Uckapili/Nigde Metamorphic

20 Marble Gumusler/Nigde Metamorphic21 Marble Marmara island Metamorphic22 Marble (Kaplan postu) Iscehisar/Afyon Metamorphic23 Marble Kemalpasa/Bursa Metamorphic24 Marble Milas/Mugla Metamorphic25 Migmatite Gumusler/Nigde Metamorphic26 Quartzite Gumusler/Nigde Metamorphic27 Gneiss Gumusler/Nigde Metamorphic28 Amphibolite Gumusler/Nigde Metamorphic29 Micaschist Gumusler/Nigde Metamorphic30 Serpentinite Kilavuzkoy/Nigde Metamorphic31 Granite (Anadolu grey) Ortakoy/Aksaray Igneous32 Granite Kaman/Kirsehir Igneous33 Granite (Kircicegi) Ortakoy/Aksaray Igneous34 Granite Uckapili/Nigde Igneous35 Basalt Altinhisar/Nigde Igneous36 Andesite Yesilburc/Nigde Igneous37 Volcanic bomb Meke/Konya Igneous38 Granite (King rosa) Unknown Igneous39 Granite (Rosa Porrino) Porrino/Spain Igneous40 Granite (Pink Porrino) Porrino/Spain Igneous41 Granite Kozak/Balikesir Igneous

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of core to the pulse transit time. In the measurements, thePUNDIT and two transducers (a transmitter and a receiver)having a frequency of 1 MHz were used.

Firstly, the samples were saturated with distilled waterfor 48 h. After weighting a sample, P-wave velocity mea-surement was carried out on the sample. The method was

repeated for each sample. Then, the samples were allowedto dry in the atmosphere over a period of 32 h. During thedrying period, P-wave velocity measurements were per-formed for the 2nd, 4th, 8th, 16th and 32nd hours. Afterthat, the samples were oven dried at a temperature of 105 C for 24 h. Finally, weight and P-wave velocity mea-surements were carried out on the dry samples. In addition,

S-wave velocity measurements were carried out on the drysamples.

Some of the tested rocks had bedding or schistoseplanes. It is known that weakness planes reduce the veloc-ity. In this study, experiments were carried out on the sam-ples cored perpendicular to any visible bedding or schistose

plane in the laboratory.Porosity values of each sample were determined fromthe saturated and dry weights. Measured dry- and wet-rockP-wave velocity values and porosity values are given inTable 2.

4. Evaluation of the test results

To see the P-wave velocity changing on the samplesallowed to dry in the atmosphere over a period of 32 h,Fig. 1 was plotted. As shown in Fig. 1, a rapid decreaseon P-wave velocity was occurred between 2 and 4 h. How-ever, after 4 h there are no remarkable changes until 32 h.

When the P-wave velocity plots as a function of satura-tion degree was examined, it was shown that after initialincreasing with increasing saturation degree, P-wave veloc-ity values were remained approximately same up to a satu-ration degree value depending on the rock properties. Aftera value defined as threshold saturation degree (SDt), it wasseen that P-wave velocity values were rapidly increased.The P-wave velocity plots as a function of saturationdegree for some rocks are given in Fig. 2. As shown inFig. 2, the SDt values vary between approximately 20%and 85%. The reason why the SDt differs from rock to rockwas investigated. It was found that the SD t values largely

depend on the velocity difference (DtP), i.e. the differencebetween wet- and dry-rock P-wave velocities. There is anexponential relation between SDt and DtP as shown inFig. 3. SDt values decrease with increasing DtP values.

The P-wave velocity plots as a function of saturationdegree show some similarities to the results obtained byWyllie et al. [28] for sandstones and Gregory [28] for sedi-mentary rocks. The differences are probably due to the fact

Table 2Dry- and saturated P-wave velocity and porosity values of the tested rocks

Sample

code

Dry-rock P-wave

velocity (km/s)

Wet-rock P-wave

velocity (km/s)

Velocity

difference(km/s)

Porosity

(%)

1a 4.23 5.60 1.4 9.902 4.31 5.89 1.6 6.143a 4.98 6.92 1.9 2.854 4.26 5.65 1.4 13.055 5.63 7.65 2.0 0.356 5.34 6.72 1.4 0.297 4.57 5.77 1.2 13.448 5.40 6.72 1.3 2.489 4.78 6.26 1.5 15.51

10a 4.56 6.55 2.0 1.8511 5.11 6.57 1.5 1.3812 5.45 7.22 1.8 0.2113a 5.24 7.00 1.8 1.1614 4.67 6.24 1.6 1.4015 4.85 6.25 1.4 1.7816 4.99 6.90 1.9 0.1817 5.58 7.91 2.3 0.1918 3.44 5.73 2.3 0.3419 4.98 7.12 2.1 0.2320 4.60 6.88 2.3 0.2621 3.81 6.23 2.4 0.3722 4.71 7.52 2.8 0.4323 4.55 6.86 2.3 0.4124 3.40 5.52 2.1 0.2425 5.50 7.56 2.1 0.6526 5.15 7.17 2.0 0.3927a 4.01 5.98 2.0 0.4628a 3.73 5.61 1.9 1.0529a 3.42 5.28 1.9 0.9830 5.46 7.17 1.7 0.2731 5.59 7.43 1.8 0.6932 4.76 6.51 1.8 0.7133 4.94 6.85 1.9 0.6234 4.38 6.04 1.7 0.4735 4.38 6.15 1.8 2.1036 5.12 6.46 1.3 5.2037 4.11 5.90 1.8 3.2038 4.79 6.54 1.8 0.3539 3.87 5.82 2.0 1.0140 4.20 5.74 1.5 3.5941 4.74 6.26 1.5 0.98

a Anisotropic rocks. Ultrasonic measurements were carried out per-

pendicular to the bedding or schistosity plane.

1

2

3

4

5

6

7

8

9

0 5 10 15 20 25 30 35

Time after saturation (hours)

P - w a v e v e l o c i t y ( k m / s )

Sample 2

Sample 5

Sample 20

Sample 24

Sample 36

Sample 40

Fig. 1. P-wave velocities of some samples initially saturated with water as

a function of time.

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that the rocks tested in this study are different from therocks tested by Wyllie et al. [28] and Gregory [28]. Gregory

[28] stated that, in general, DtP is large for low porosity

rocks and is small for high porosity rocks. In this study,a correlation between DtP and porosity was found(Fig. 4). DtP decreases with increasing porosity as statedby Gregory [28].

5. Evaluation of the test results using Gassmann’s theory

Several petro-elastical models have been proposed bythe different researchers. The most obvious and simplemodel is Gassmann’s theory according to Carcione[35,36]. Gassmann [37] wet-rock P-wave velocity is

twP ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi K G þ ð4=3Þlm

q

s ð1Þ

where

K G ¼ K m þ a2 M ð2Þ

is Gassmann’s bulk modulus,

K m ¼ qd td 2

P 43td

2

S

ð3Þ

is the dry-rock bulk modulus,

lm ¼ qdtd

2

S ð4Þ

is the dry-rock shear modulus,

a ¼ 1 K m

K sð5Þ

1

M ¼

a /

K sþ /

K f ð6Þ

where / is the porosity, K s and K f are the bulk modulus of

mineral and fluid, and

q ¼ qd þ /qf ð7Þ

qd ¼ ð1 /Þqs ð8Þ

where q is the bulk density, qd is the dry density, and qs andqf are the densities of the mineral and fluid, respectively.

One of the results of Gassmann’s theory is that the wet-and dry-rock shear moduli are the same, so the wet- anddry-rock S-wave velocities are

twS ¼

ffiffiffiffiffiffilmq

r ð9Þ

td S ¼ ffiffiffiffiffiffilmqd

r ð10Þ

Moreover, Gassmann’s theory implies

twStd S

¼

ffiffiffiffiffiqdq

r

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does not fit the data. The unconformity between the mea-sured data and the estimated data from the theories isdue to the fact that Gassmann [37] and derived his equa-tions for high-porosity unconsolidated sediments at lowfrequencies. Gassmann’s theory assumes that porous mate-rial is isotropic, elastic and homogeneous, fully saturatedwith fluid, and the pore spaces are well connected. Therocks tested in this study do not match the material speci-fied by Gassmann’s theory.

Although Gassmann’s theory does not fit the data,there is a good correlation between Gassmann wet-rockP-wave velocity and measured wet-rock P-wave velocity(Fig. 5). For this reason, using the two data a constant(c) can be obtained. Measured wet-rock P-wave velocityvalues were divided by Gassmann wet-rock P-wave veloc-

ity values. It was seen that division results differ for each

rock class. c constant values are 1.34 ± 0.05, 1.49 ± 0.11,1.38 ± 0.06 for sedimentary, metamorphic and igneousrocks, respectively. Gassmann’s equation (Eq. (1)) can bemodified including c constant as follows:

twP ¼ c

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi K G þ ð4=3Þlm

q

s ð12Þ

It can be said that Eq. (12) is valid for the rocks excepthigh-porosity unconsolidated sediments.

As stated in Eq. (11), Gassmann’s theory implies thatthe ratio between wet- and dry-rock S-wave velocity islower than 1. As shown in Table 3, some of the ratiosbetween wet- and dry-rock S-wave velocity are equal to 1and the other ratios can be accepted as 1. Therefore, Eq.

(11) does not completely fit the data.

Table 3Some properties of the tested rocks, Gassmann wet-rock P-wave velocity and S-wave velocity ratio

Samplecode

Bulkdensity(g/cm3)

Drydensity(g/cm3)

Mineraldensity(g/cm3)

Mineral bulk modulus(GPa)

Shear modulus(GPa)

Gassmann wet-rockP-wave velocity(km/s)

Gassmann wet-rock S-wavevelocity/dry-rock S-wavevelocity

1 2.16 2.07 2.29 24.9 9.91 4.14 0.9772 2.46 2.39 2.55 33.8 8.68 4.26 0.987

3 2.32 2.30 2.36 43.7 10.34 4.95 0.9944 2.20 2.07 2.38 30.1 6.85 4.13 0.9705 2.69 2.69 2.70 56.1 21.95 5.63 0.9996 2.68 2.67 2.68 32.6 32.76 5.34 0.9997 2.34 2.20 2.55 26.1 16.06 4.44 0.9718 2.66 2.63 2.70 40.8 27.24 5.38 0.9959 1.98 1.82 2.15 28.9 11.25 4.60 0.960

10 2.47 2.46 2.50 38.3 9.73 4.54 0.99611 2.68 2.66 2.70 34.5 26.45 5.10 0.99712 2.69 2.69 2.70 47.6 24.23 5.44 1.00013 1.83 1.82 1.84 34.2 11.99 5.22 0.99714 2.43 2.42 2.45 30.8 16.59 4.65 0.99715 2.50 2.48 2.52 37.6 15.70 4.83 0.99616 2.72 2.72 2.72 31.5 27.09 4.99 1.00017 2.56 2.56 2.57 57.6 23.50 5.89 1.000

18 2.70 2.70 2.71 14.5 13.06 3.44 0.99919 2.73 2.73 2.74 34.7 24.77 4.98 1.00020 2.70 2.70 2.71 39.6 13.20 4.60 1.00021 2.68 2.67 2.68 22.3 12.42 3.81 0.99922 2.58 2.58 2.59 40.6 12.46 4.70 0.99923 2.71 2.71 2.72 30.1 19.50 4.54 0.99924 2.59 2.58 2.59 16.2 10.34 3.40 1.00025 2.76 2.75 2.77 52.5 23.03 5.49 0.99926 2.70 2.70 2.71 32.6 29.39 5.15 0.99927 2.68 2.68 2.69 29.0 10.65 4.01 0.99928 2.79 2.78 2.81 19.6 14.32 3.72 0.99829 2.69 2.68 2.71 17.5 10.41 3.41 0.99830 2.71 2.71 2.72 49.3 23.72 5.46 1.00031 2.64 2.64 2.65 58.8 17.82 5.58 0.99932 2.69 2.68 2.70 33.6 20.34 4.75 0.99933 2.55 2.55 2.56 35.5 19.96 4.93 0.99934 2.60 2.60 2.61 28.3 16.16 4.37 0.99935 2.59 2.57 2.63 34.4 11.39 4.36 0.99636 2.58 2.52 2.66 34.8 24.06 5.07 0.99037 2.42 2.39 2.47 24.7 12.11 4.09 0.99338 2.66 2.66 2.67 34.9 19.56 4.78 0.99939 2.63 2.62 2.64 18.2 15.84 3.86 0.99840 2.57 2.54 2.63 24.5 15.49 4.17 0.99341 2.67 2.66 2.69 34.3 19.21 4.73 0.998


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To model partial saturation Wood’s theory [38] wasused. Wood suggested following equations:

1

K f ¼ S w

K wþ

1 S w K a

ð13Þ

where K f is the fluid bulk modulus, S w is water saturation,K w and K a are the bulk modulus of water and air.

q ¼ qd þ /½S wqw þ ð1 S wÞqa ð14Þ

where q is the bulk density, qd is the dry density, / is theporosity, qw and qa are the density of water and air,respectively.

For the modeling of partial saturation, the data in the2nd and the 16th hour during the drying period after satu-ration were used. Figs. 6 and 7 indicate the comparisonbetween the measured P-wave velocity and the P-wavevelocity calculated using Wood’s and Gassmann’s theory.As shown in Fig. 6, the data in the 2nd hour during thedrying period after saturation does not fit the theories.

However, the most data in the 16th hour during the dryingperiod after saturation approach to the 1:1 diagonal line(Fig. 7). Although Wood’s and Gassmann’s theories donot fit the data, there is a good correlation between mea-sured and estimated data (Figs. 6 and 7). Similarly above,using the two data a constant (c) can be obtained for par-tial saturation. Measured data were divided by estimateddata and c constant values were obtained. For the 2ndand the 16th hour during the drying period after satura-tion, c values are 1.34 ± 0.06 and 1.09 ± 0.04, respectively.The average of the two c values is 1.22 ± 0.01. This con-stant value can be used for the partial saturation.

6. Derivation of the estimation equations

Dry- and wet-rock P-wave velocity values were evalu-ated using the method of least squares regression. Linear,logarithmic, exponential and power curve fitting approxi-mations were tried and the best approximation equationwith highest correlation coefficient (R2) was determinedfor each regression.

The correlation between the dry- and wet-rock P-wavevelocity values is indicated in Fig. 8. There is a strong cor-relation between the dry- and wet-rock P-wave velocities.The relation follows a linear function. The equation of the line is

twP ¼ 0:94td

P þ 2:10; R2 ¼ 0:74 ð15Þ

where twP is the wet-rock P-wave velocity (km/s) and td

P isthe dry-rock P-wave velocity (km/s).

To see how the rocks classes affect the correlation,regression analysis were performed for sedimentary, meta-morphic and igneous rocks, respectively (Fig. 9). The cor-relation coefficients for the rock classes are higher than

Eq. (14). The equations of the lines are

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

P- wave velocity Vp measured in 2nd hour during the drying

period (km/s)

P - w a v e v e l o c i t y c a l c u l a t e d f r o m W o o d ' s a n d

G a s s m a n n ' s t h e o r y ( k

m / s )

Fig. 6. The comparison between the measured P-wave velocity and theP-wave velocity calculated using Wood’s and Gassmann’s theory for the

2nd hour during the drying period after saturation.

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

P- wave velocity Vp measured in 16th hour during

drying period (km/s)

G a s s m a n n ' s t h e o r y ( k m / s )

p - w a v e v e l o c t i y c a l u c u

l a t e d f r o m W o o d ' s a n d

Fig. 7. The comparison between the measured P-wave velocity and theP-wave velocity calculated using Wood’s and Gassmann’s theory for the16th hour during the drying period after saturation.

1

2

3

0

4

5

6

7

8

9

10

0 2 4 6 8 10

Measured wet-rock P-wave velocity (km/s)

G a s s m a n n w e t - r o c k P - w

a v e v e l o c i t y ( k m / s )

Fig. 5. The comparison between measured and Gassmann wet-rockP-wave velocity.


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For sedimentary rocks:

twP ¼ 1:19td

P þ 0:67; R2 ¼ 0:83 ð16Þ

For metamorphic rocks:

twP ¼ 1:02td

P þ 2:06; R2 ¼ 0:90 ð17Þ

For igneous rocks:

tw

P ¼ 0:94td

P þ 1:99; R2

¼ 0:87 ð18Þ

As shown in Fig. 9, DtP is large for metamorphic rocksand is small for sedimentary and igneous rocks. This isbecause the water saturation effect on P-wave velocity ismuch larger in low porosity rocks than in high porosityrocks as stated above. Comparing to sedimentary and igne-ous rocks, metamorphic rocks have small porosity values(generally less than 1%) and therefore has large DtP.

In addition, the correlations between dry- and wet-rockP-wave velocity values were investigated for the rockgroups having a porosity value of lower and higher than1%. It was found that, conforming to the above statements,

while DtP is large for the rocks having a porosity value of

lower than 1%, whereas DtP is small for the rocks having aporosity value of higher than 1% (Fig. 10).

7. Conclusions

Dry- and wet-rock P-wave velocity and dry-rock S-wavevelocity measurements were carried out on 41 differentrock types. The results were evaluated and following con-clusions were obtained:

• The threshold saturation degree (SDt) after whichP-wave velocity values rapidly increases largely dependson the velocity difference (DtP). An exponential relationbetween SDt and DtP was found.

• A general correlation between DtP and porosity wasfound.

• The modeling of fully and partial saturation using Gass-mann’s and Wood’s theory showed that the theories didnot fit the data. This is because Gassmann derived hisequations for high-porosity unconsolidated sedimentsat low frequencies.

• Gassmann’s equation was modified for the rocks excepthigh-porosity unconsolidated sediments.

• Regression analysis indicated that wet-rock P-wavevelocity values were strongly correlated with the dry-rock P-wave velocity values. When the regression analy-ses were repeated for the rock classes respectively, it wasseen that correlation coefficients were increased. Thederived equations can be used for the prediction of wet-rock P-wave velocity from the dry-rock P-wavevelocity.

Acknowledgements

Author thanks to Professor J.M. Carcione for com-ments and suggestions. This study has been supported bythe Turkish Academy of Sciences (TUBA), in the frame-work of the Young Scientist Award Program (EA-

TUBA-GEBIP/2001-1-1).

y = 0.94x + 2.10

R2 = 0.74

3

4

5

6

7

8

9

10

3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0

Dry-rock P-wave velocity (km/s)

W e t - r o c k P - w a

v e v e l o c i t y ( k m / s )

Fig. 8. The relation between dry- and wet-rock P-wave velocity values.

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

8.5

9.0

3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5


W e t - r o c k P - w a v e v e l o c i t y ( k m / s )

Sedimantary rocks

Metamorphic rocks

Igneous rocks

Fig. 9. The relation between dry- and wet-rock P-wave velocity values forsedimentary, metamorphic and igneous rocks, respectively.

y = 0.80x + 2.5

R2 = 0.78

y = 0.88x + 2.63

R2 = 0.80

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

8.5

9.0

3.0 3 .5 4.0 4.5 5.0 5.5 6.0 6 .5


W e t - r o c k P - w

a v e v e l o c i t y ( k m / s )

Porosity > 1 %

Porosity < 1 %

Fig. 10. The correlations between dry- and wet-rock P-wave velocity forthe rocks having porosity value of lower and higher than 1%.


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