Relationship Between Compressional-wave and Shear-wave Velocities in Clastic Silicate Rocks

8/12/2019 Relationship Between Compressional-wave and Shear-wave Velocities in Clastic Silicate Rocks

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572 Castagna et al.OBSERVATIONS IN MUDROCKS

We define mudrock as clas tic silicate r oc k c om po se d primarily of clay- or silt-sized particles Blatt et al., 1972),Lithifiedmu ds are c om po se d pr im ar il y of quartz and clay minerals,Owi ng to the difficulty associated with handl ing of mostmudrocks, laboratory m ea su re me nt s on these ro cks are no tcommonly found in the literature. Measurements that do existare generally biased toward highly lithified samples.

Figure 3 is a ~ - v e r s u s - ~ p lo t of laboratory measurementsfor a variety of water-saturated mudrocks. For reference, linesare drawn from the c la y- po in t velocities e xt ra po la te d fromTosaya s data Vp = 3.4 km/s, ~ = 1.6 krn/s) to ca lc it e andquartz points. The data are scattered about the quartz-clay line,suggesting that p and ~ are principally controlled by mineralogy.

In-situ sonic and field seismic measurements in mudrocks Figure 4)form a well-defined line given by

1504010 120 130ll V s SECIFT

100

l iMESTONE DOLOMITEo CLEAN SANDS VERY l iMY SAND

50

9 O - - - - . - - - - . . . - - - . - - - - - r - - - - - - , ~ - - - , . . . _ . . . J90

eo

60

owcq 7>

FIG. 1. Laboratory measurements on limestones, dolomites,and sandstones from Pickett 1963). p = compressional velocity, ~ = shear velocity.p = 1 . l 6 ~ + 1.36, I)

where the velocities are in km/s, In view of the highly variablecomposition and texture of mudrocks, the uniform distributionof these data is s urpris ing. We believe this l ine ar trend isexplained in part by the l oc at io n of the clay point near a linejoining the quartz point with the velocity of water. We hypothesize t hat , as the poros it y of a pure clay increases, compressional and shear velocities decrease in a nearly linear fashion asthe water point is approached. Similarly, as quartz is added topure clay, velocities i nc re ase in a n ea rl y l in ea r f ashi on as thequartz point is approached. These bounds generally agree withthose inferred from the empirical relations of Tosaya 1982); theexception is for behavior at very high porosities. The net resultis that quartz-clay-water ternary mixtures are spread along an

o CLAYo QUARTZ CALCITE DOLOMITE

6.0

1.0

2.0

_ 5.01rl 40

Q> 3.0

8.0 . . . . . ~ ~7.0

0.0 r r . r r l0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Vs (KMSEC)FIG,2. Compressional and shear velocities for some minerals.

1.0 1.5 2.0 2.5 3.0 3.5 4.0VS KMI SEC

. . .... .QU...RTZ.0TO CALCITE 5.0/ ,QUARTZ6.0

~ ~ t 4.05.0 v 0o ~ ~ o , t w

0 ...>. 0 :l; 3.04.0 j-.J . x.K. ....0 ) aw > 2.0i 3.0 o x CLAY WATER - 1.0> 2.0

0.01.0 0.0 0.5

0.0 +--r--,.---.-----.--,.--,.-.....,----10.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0VS KMI SECGREEN RIVER SHALE; PODIO, GREGORY,AND GRAY 968AXIAL LOADING 10,000 PSI Vp=4 39 Vs =Vs =2 42 HYDROSTATIC LOADING,10,000PSI Vp = 4.4,VS, = 2.68,Vs, = 2.64TOSAYA (1982)CLAY POINT Vp =3 4 Vs=1.6o OTTO VALLEY SILTSTONED PIERRE SHALEARCO D T

KOERPERICH, 1979, SILTSTONE, SONIC LOG (15 KHz)o EASTWOODAND CASTAGNA, 1983, WOLFCAMP SHALE, SONIC LOG (10 KHz) OIL SHALE, SONIC LOG,(25 KHz)+ liNGLE AND JONES, 1977, DEVONIAN SHALE, SONIC LOG* HAMILTON, 1979, PIERRE SHALEo HAMILTON, 1979, GRAYSON SHALE8 HAMILTON, 1979, JAPANESE SHALE LASH, 1980, GULF COAST S E I M E ~ T S VERTICAL SEISMIC PROFILE6 SHALE, SONIC LOG, INVERTED ST0r lElEY WAVE VELOCITIES, 1 KHz)

HAMILTON, 1979, MUDSTONES EBENIRO. 1981, GULF COAST SEDIMENTS, SURFACE WAVE INVERSION TOSAYA S CLAY POINT (EXTRAPOLATION FROM LABORATORY DATA)

FIG. 3. Ultrasonic laboratory measurements for various mud-rocks. FIG. 4. Compressional and shear wave velocities for mudrocksfrom in-situ sonic and field seismic measurements.

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waveand S wave Velocities in Clastic Rocks 7

1.0

o o-t--- --.----r---r---r---r- --r---l0.0 05 1.0 15 2.0 2.5 3.0 3.5 4,0

Vs. KMiSEC

~ a u A R T . :.0

5.0

40ow::;; 3.0 ,) i - o ,f.> ,,,,0


4/11

7 st gn et l6.0 . . . .----------------::>15.0

4.0s 3.0> 2.0

6.0

5.0

4.0CJw

3.0> 2.0o

1.0 1.0

0.0 -+- T - ......- - r - - . - - - r - - - r - - r - - - - -l0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Vs, KM SE EASTWOOD CASTAGNA {l983l, ORTHOQUARTZITE, SONIC LOG, 10 KHza FRIO FORMATION SANDSTONES, SONIC LOG 15 KHz)

-- HAMILTON 1979), SANDS

0.0 - - r - - - r - - . - - - - - - r - - . . . - .- - - - I0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Vs, KM SEFIG. 10. Com pi la ti on of laboratory data for water-saturatedsandstones, including ARC a and literature data.

FIG.8. Sonic log velocities in sandstones.

Some a lge bra ic m an ip ul at io n yields e qu at io ns which explicitly reveal the dependence of ViI ,. on porosity and volumeof clay. From equations 2a) and 2b) we get

Vp/I . = 1.33 + .63/ 3.89 - 7 7 2.0

1.0

0.0 - - - . - - - r - - . - - .- - - - - - - - - - - - I0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

VB' KMISE

a)

6.0 ~5.0

4.0ow' 3.0> 2.0

A cc or di ng to G re go ry 1977), Poi sson s r at io is about 0.1 corresponding to ViI .:::; 1.5) for most dry rocks and unconsolidated sands, and it is independent of pressure. Figure l lis a cross plot of Vp/v versus r ; for dr y and water-saturatedBerea sandstone. Note that the water-saturated points are reasonably close to the relationship defined by e qua ti on I),whereas the dry p oi nt s are n ea rl y constant at a Vp/I . of abouti.5. Figure 12 isa compilation of laboratory compressional ands he ar wave velocities for dry s an ds to ne s. The field data ofWhi te 1965) for loose san ds also are i nc lu de d. The data fit aline having a constant Vp/V ratio of 1.5.

We gain some i nsigh t int o the b eh av io r of dry sandstones byconsidering various regular packings of spheres. The reader isreferred to W hi te 1965) and Murphy i982) for a detaileddiscussion. The dry compressional to s he ar Vf) velocityratio, as a function of Poisson s ratio (v) of solid spheres, is

1.0

0.0 -t-- -- --.--- --- ---.---r--l0.0 0.5 . 1.0 1.5 2.0 2.5 3.0 3.5 4.0

VS' KM ISEC

= [ 2 - v)/ i - vW 2for a simple cubic packing SC) of spheres;

= [4 3 - v)/ 6 - 5V JI 2

4a)

4b) b) for a hexagonal close packing HCP) of spheres; and

V ~ ; V f = 4c)FIG. 9. Sonic log velocities for clean w at er -s at ur at ed s an dstones. a) Backus et al. 1979), b) Leslie and Mons 1982).

for a face-centered cubic FCC) packing. Fo r HCP and FCCpackings propagation directions are I, 0, 0).



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P-wave and S-wave Velocities in Clastic Rocks 575

1.4 ~ = = = = = = = = = = = l

FIG. 12. Laboratory measurements for ; and Vp for dry san dstones. Note that one sandstone with calcite cement plots wellabove the line.

DOMENICO (1976) WHITE (1965)LOOSE SANDS ARGOo GREGORY 976+ KING (1966)o MURPHY (1982)

.5

SC

HCP

.41 .2 .3GRAIN POISSON S RATIO

1.8

1.7

DRYROCK 16Vp I Vs

15

6.0

) 5.0UJ 0J) +::;; CALCAREOUS 4.0 -, .j D0>-f-aS 3.0 0UJ>- 2.00iiio

rr2.0

czo[ 1.0o

FIG. 11. Ultrasonic measurements of V I for a dry and watersaturated Berea s an ds to ne sample. The va ri ous p oi nt s wereobtained at different effective pressures.FIG. 14. The results of Aktan and Farouq Ali 1975) for severaldry sandstones before and after heat cycling. Data are plottedfor measurements at high and low confining pressures.



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astagna et alsure conditions. Qualitatively, the data from water-saturatedsan dsto ne s are c on si ste nt with e qu at io n 1) but tend t ow ardhigher for a given Vp Given the compressional and shear wave velocities obtainedin the laboratory for dry sandstones, we use Gassmann s 1951)equations to compute velocities when these rocks are saturatedwith water. Gassmann s equations are:

76.0

5.0

4.0ow ,,::Ii 3.0 /; .


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waveand S wave Velocities in Clastic Rocks

0.0 - - - - - . . . - - ~ - r _ - r _ - r _ _ _ - - i0.0 0.5 1.0 15 2.0 2.5 3.0 3.5 4.0

Vs, KM/ SEC

1.0

2.0

60 :> 1

3.0

4.0

5.0

0.0 - - . - - - . - - ~ - r _ - r _ - . _ _ - . _ _ _ _ _ l0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

VS KM JSEC

1.0

>

6.0

5.0

4.0 )w::0 3.0> 2.0

FIG. 19. Calculated v: and Vp for Boise sandstone based on theformulation ofCli.eng and Toksoz 1979).

FIG. 18. Calculated and Vp for saturated regular packings ofquartz sph er es using the c al cu la te d dry velocities and Gassmann s equations.

(9)

11)

(10)Equations 9)and 10)and Gassmann s equations [ Sa) through 5d)J allow computation of v: given Vp < > and the g ra in andfluid densities and bulk moduli.

We computed shear-wave velocities for sandstone core porosities and sonic log compressional velocities given by Gregory et al. 1980) for d ep th s from 2 500 to 14 500 ft in two wells500 ft apart in Bra zo ri a Cou nt y, Texas. Fig ur e 20 shows t ha tthe resulting Vp- v: relationship is in excellent agreement withour sandstone observations.

Similarly, in Table 1 wecompare the calculated shear velocities to the m ea su re d l ab or at or y values. The differences areusually less than 5 percent, demonstrating excellent agreementwith the theory. Since part of these differences must be due toexperimental error and to our a ss um pt io n t ha t the m at ri x is100 p er ce nt q ua rt z, we c on si de r the a gr ee me nt r em ar ka bl e.Additionally, Gassmann s equations are strictly valid only atlow frequencies. Further corrections can be applied to accountfor dispersion. The Holt sand sample, which gives the largestdiscrepancy in Table I, i llus trat es the i mp or ta nc e of the assumption that dry bulk m od ul us is e qu al to dry rigidity [ eq ua tion 6)]. The dry Vp V for this H ol t san d sam pl e is 2.17 Table2), far di ffe ren t from the r at io of 1.53 r eq ui re d for e qu al it y ofdry bulk and s he ar moduli. This va ri at ion is p ro ba bl y due tothe high c ar bo na te cement c om po ne nt of this rock. H ow eve r,given this m ea su re d dry r at io , we can still apply G assm an n sequations to calculate the water-saturated values. As shown inTa bl e 2, these pre di ct ed values are vi rtuall y identical to themeasured velocities.

For clean san dsto ne s at high p re ssur es and with m od er at ep or osit ie s, p or osit y is often e st im at ed by the e mp ir ic al timeaverage formula Wyllie et aI., 1956),

I/Vp - I/V - I V ~

2 KDV s ~ -

The wet bulk modulus isgiven bys ; = Pw V; V ;

where is the grain compressional velocity and is the fluidvelocity. Figure 21 shows the Vp- v: relationship predicted by

60 - ---------------.... .

6.0 . . . . . . . . . 50

0.0 - - - - - . . . - - ~ - r _ - r _ - r _ _ _ r _ _ 10.0 5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

SHEAR W VE VELOCITY(KM JSEC)

FIG. 17. Measured open symbols) versus computed solid symbols) v: and Vp using the dry data from Figure 12 and Ga ssmann s equations.

2.0c,>

::2: 3.0

00 0.5 1.0 1.5 2.0 2.5 3.0 35 4.0Vs, KM/ SEC

00 - - - . - - . - - ~ - r _ - . _ _ - r _ _ _ _ - i

40

1.0

FIG. 20. Com pa ri so n of m ea su re d Vp with calculated v: forsandstones from two wells as reported by Gregory et al. 1980).Calculations are based on measured wet Vp and porosity usingGassmann s equations and dry bulk modulus equal to dryrigidity.

o

o LAB DATA OMPUTED

65 0

::0> 4 0

3 0-zQ 2.0a:0..::0 1.08



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8 st gn et lTable t. Holt sand: Comparison of observed water-saturated shear velocities with those calculated using the measured water-saturated com-pressional velocities and porosities. The calculations were based on Gassmann's equations and the assumption that Ko 11

Predicted Observed PercentRock Reference Porosity ErrorBerea Johnston 1978) 3.888 18.4 2.330 2.302 1.2Berea Johnston 1978) 4.335 18.4 2.700 2.590 4.2Navajo Johnston 1978) 4.141 16.4 2.520 2.430 3.7Navajo Johnston 1978) 4.584 16.4 2.890 2.710 6.6Gulf Coast sand Gregory 1976) 3.927 21.7 2.380 2.367 0.5Gulf Coast sand Gregory 1976) 3.185 21.7 1.730 1.975 -12.4Boise Gregory 1976) 3.402 26.8 1.970 1.960 .5Boise Gregory 1976) 3.533 26.8 2.080 2.073 .3Travis peak Gregory 1976) 4.732 4.45 2.860 2.581 10.8Travis peak Gregory 1976) 4.990 4.45 3.110 3.284 -5.3Travis peak Gregory 1976) 4.342 8.02 2.590 2.667 -2.9Travis peak Gregory 1976) 5.001 8.02 3.180 3.391 -6.2Bandera Gregory 1976) 3.492 17.9 1.970 2.032 -3.1Bandera Gregory 1976) 3.809 17.9 2.250 2.240 .4Ottawa Domenico 1976) 2.072 37.74 .740 .801 -7.6Sample no. MAR ARCO data 5.029 1.0 3.200 3.315 -3.5Sample no. MAR ARCO data 5.438 1.0 3.420 3.496 -2.2Sample no. MDP ARCO data 3.377 21.0 1.900 2.047 -7.2Sample no. MDP ARCO data 3.862 21.0 2.320 2.350 -1.3Berea ARCO data 3.642 19.0 2.120 1.992 6.4Berea ARCO data 3.864 19.0 2.310 2.267 4.3Berea ARCO data 3.510 19.0 2.000 1.680 19.0Berea ARCO data 3.740 19.0 2.200 2.130 3.8St. Peter Tosaya 1982) 5.100 6.6 3.250 3.420 -5.0St. Peter Tosaya 1982) 4.880 7.2 3.060 3.060 0.0St. Peter Tosaya 1982) 4.500 4.2 2.610 2.680 -2.6St. Peter Tosaya 1982) 4.400 7.5 2.630 2.600 1.2St. Peter Tosaya 1982) 4.400 5.0 2.540 2.600 -2.3St. Peter Tosaya 1982) 3.950 18.8 2.380 2.420 -1.6St. Peter Tosaya 1982) 3.600 19.6 2.090 2.070 1.0St. Peter Tosaya 1982) 3.170 14.5 1.580 1.560 1.3Holt sand ARCO data 3.546 16.3 1.990 1.539 29.3

Table 2. Water-saturated sandstones:A recalculation of velocities forthe Holt Sand (Table 1) for which Ko - liD, New water-saturatedvalues are computed using both the V and V, measured for the dryrock.

equations (5), (9), 10), and (11). This time-average line describes the laboratory data from water-saturated conditionspresented in Figure 10 extremely well. Recalling the results ofcrack modeling shown in Figure 19, one explanation for thevalidity of this empirical formula would be the dominance ofpores ofhigh aspect ratio.

Holt SandPorosityWater-saturated (laboratory)Water-saturated (laboratory)Water-saturated (predicted from porosityand water-saturated p Percent errorDry (laboratory)Dry (laboratory)Dry Vp V (laboratory)Water-saturated p (predicted from dry data)Percent errorWater-saturated (predicted from dry data)Percent error

16.33.546krn/s1.539 krn/s1.990 km/s29.3%3.466 krn/s1.599 km/s2.17 krn/s3.519 krn/s-.81.540krn/s.1%

DISCUSSION OF RESULTS:DYNAMIC ELASTIC MODULI RELATIONSHIPSCompressional and shear velocities, along with the density,

provide sufficient information to determine the elastic parameters of isotropic media (Simmons and Brace, 1965). These parameters proved useful in estimating the physical properties ofsoils and characteristics of formations (see, for example, Richart, 1977). However, the relationships given by equation (1)for mudrocks or Gassmann's equations and equation (6) forsandstones fix in terms of V Hence, the elastic parameterscan be determined for clastic silicate rocks from conventionalsonic and density logs. This explains in part why Stein 1976)was successful in empirically determining the properties ofsands from conventional logs.In this discussion we assumed that equation (1) holds to first

order for all clastic silicate rocks, with the understanding thatGassmann's equat ions might be used to obtain more preciseresults in clean porous sandstones if necessary. For many rocks,particularly those with high clay content, the addition of watersoftens the frame, thereby reducing the bulk elastic moduli. Thefollowing empirical relationships are, therefore, not entirelygeneral but are useful for describing the wide variety of datapresented here. As shown in Figure 22, bulk and shear moduliare about equal for dry sandstones. Adding water causes thebulk modulus to increase. This effect is most pronounced at



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579

MBULK MODULUS I DENSITY ..cm3

gm

/

/

f O ~:./

./

18.0

I E 1 50:;;.c 12.0f-iiizwo 9.0;;;3::>c 60::;0: 3I-f-iiiai 80:> 6.0---::>00::; 4::>CD 2

0.0-0

FIG.23. The computed relationships between the bulk modulus normalized by density) and Vp based on the observed V and Vptrends.

In recent years there has been i ncre as ed use of Vp andin seismic exploration for estimation of porosity, lithology, and saturating fluids in particular statigraphic intervals.The above analysis both complicates and enlightens such interpretation. It is clear that clay content increases the ratio V p ~as does porosity. The analyses of Tosaya 1982)and Eastwoodand Castagna 1983) and e qu at io ns 3a) and 3b) i nd ic at e t ha t

is less sensitive to v ar ia ti on of clay c on te nt t ha n to variation of porosity. However, the range of variation in clayc on te nt may be larger. Thus, Vp V can be grossly d ep en de ntupon clay content.

Figure 25 shows c om pu te d as a f un ct ion of d ep th in theG ul f C oa st for n on ca lc are ous shales and clean p or ou s s an dsto ne s t ha t are w at er -sat ur at ed . The c om pr essi on al velocityand porosity data given in Gregory 1977) are used to establishthe v ar ia ti on with d ep th . E qu at i on I ) is used to p re di ct forshales, and Gassmann s equations are used for sandstones. At agiven depth, shale velocity ratios are on the order of I )percenthigher than sandstone velocity ratios.

50---.-- -------------------,6

5

4.0Uw::; 3.0> TIMEAVERAGE LINE2.0

40

of- 30


10/11

580 Castagna et al

SUMMARY AND CONCLUSIONS

where V; is the g ra in shear wave velocity. The c on st an t 1.12s/krn is used in place of fluid transit time. This equation shouldbe superior to the compressional wave time-average equationfor porosity estimation when there is significant residual gassaturation in the flushed zone.

REFERENCES

To first order, we conelude that shear wave velocity is nearlylinearly related to compressional wave velocity for both watersaturated and dry clastic silicate sedimentary rocks. For a given mudrocks tend toward slightly higher VP v t ha n do cleanporous sandstones.

For dry sandstones, v /V is nearly constant. For wet sandstones and mudstones, Vp/V decreases with increasing VpWater-saturated sandstone shear wave velocities are consistentwith those obtained from Gassmann s equations. The watersaturated linear v,,-versus- trend begins at Vp slightly less thanwater velocity and = 0, and it ter minates at the compressional and shear wave velocities of quartz. The dry sandstonelinear Vp versus trend begins at zero velocity and terminatesat q ua rt z velocity. Dry rigidity and bulk mod ul us are a bo utequal.

Theoretical models based on regular packing arrangementsof spheres and on cracked solids yield Vp versus trends consistent with observed dry and wet trends.

We believe that the observed Vp versus V,-relationship forwet clastic silicate rocks results from the coincidental locationof the quartz and clay points. The simple sphere-pack modelsindicate that the low-velocity, high-porosity trends are largelyindependent of the mineral elastic properties. As the porosityapproaches zero, however, the velocities must necessarily approa ch the values for the pure mineral. In this case, clay andquartz fall on the extrapolated low-velocity trend.

Aktan, T and F ar ou q Ali, C. M., 1975, Effect of cyclic and in situheating on the absolute permeabilities, elastic constants, and electrical resistivities of rocks: Soc. Petr. Eng., 5633.Backus, M. M., Castagna, 1. P., and Gregory, A. R., 1979,Sonic logwaveforms from geothermal well, Brazoria Co., Texas: Presented at49th Annual International SEG Meeting, New Orleans.Birch, F., 1966, Compressibility; elastic constants, in Handbook ofphysical constants, Clark, S. P., Jr., Ed., Geol. Soc. Am., Memoir 97,97-174.Blatt , H., Middleton, G. Y.,and Murray, R. C 1972, Origin of sedimentary rocks: Prentice-Hall, Inc.Cheng, C. H., and Toksoz, M. N., 1976, Inversion of seismic velocitiesfor the pore aspect ratio s pec tru m of a rock: J. Geophys. Res., 84,7533-7543.Christensen, N. 1., 1982, Seismic velocities, in Carmichael, R. S., Ed.,Handbook ofphysical properties of rocks, II: 2-227,CRC Press, Inc.Domenico, S. N., 1976, Effect of brine-gas mixture on velocity in anunconsolidated sand reservoir: Geophysics, 41,887-894.Eastwood, R. L and Castagna, 1. P., 1983, Basis for interpretation ofv ;v ratios in complex lithologies: Soc. Prof. Well Log Analysts24th Annual Logging Symp.Ebeniro, 1., Wilson, C. R., and D or ma n, 1., 1983, Propagation ofdispersed compressional and Rayleigh waves on the Texas coastalplain: Geophysics, 48,27-35.G as sm an n, F., 1951, Elastic waves t hr ou gh a packing of spheres:Geophysics, 16,673-685.Gregory, A. R., 1977, Fluid s at ur at io n effects on d yn ami c elasticproperties of sedimentary rocks: Geophysics, 41,895-921. 1977,Aspects of rock physics from laboratory and log data thatare important to seismic interpretation, in Seismic stratigraphy-application to hydrocarbon exploration: Am. Assn. Petr. Geol.,Memoir 26. 15)

5.0 . .

4.0

3.0

2.0

o 4,000 8,000 12,000 16,000 20,000DEPTH FEET

>

IG 25. Vp v computed as a function of depth for selected GulfCoast shales and water-saturated sands.

0.0 - ----r--. --- ----r----f

1.0

These conclusions are somewhat at odds with conventionalwisdom that Vp/V equals 1.5 to 7in sandstones and is greaterthan 2 in shales. Clearly, mapping net sand from Vp/V is not asstraightforward as conventional wisdom would imply.

In clastic silicates, shear wave velocities for elastic moduliestimation or seismic velocity control may be estimated fromequation 1) and or Gassmann s equations and conventionallogs. Alternatively, our relationships indicate that when p and are used together, they can be sensitive indicators of both gassat urat io n and no nel asti c c ompo ne nt s in the rock. Gas saturat io n will move the v /V towar d the dry line in Figure 16.N on el asti c c ompo ne nt s can also move the rat io off the mudrock line, as shown by the Holt s an d sample m ar ke d as calcareous in Figure 16.The possibly ambiguous interpretation of lithology and porosity from Vp v and Vp/V in seismic exploration also appliesto log analysis. However, because sonic logs are generally apart of usual logging programs, the interpretation of full waveform sonic logs should be made in the context of other logginginformation as wedid) to obtain equations 2a) and 2b).Othe rlogs which are sensitive to clay co nt en t and por os ity e.g.,neutron and gamma-ray) are needed to evaluate the details ofhow porosity and clay content separately affect clastic rocks. Ingas-bearing and highly porous zones where the time-averageequation fails, combined and information may potentiallybe used in porosity determination.

Assuming that the time-average equation works for compressional transit times and that dry incompressibility equals dryrigidity, Gassmann s equations yield a nearly linear relationship between she ar wave t ra nsit time and porosity. This relationship is welldescribed by a time-average equation

1/V - = 1.12 s/km -



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waveand S wave Velocities in Clastic Rocks 8Gregory, A. R., Kendall, K. K., and Lawai, S. S., 19RO, Study effects ofgeopressured-geothermal subsurface environment of elastic properties of Texas Gulf Coast sandstones and shales using welllogs, coredata, and velocity surveys: Bureau of Econ. Geol. Rep.. Univ. Texas.Austin.Hamilton, E. L 1971. Elastic properties of marine sediments J Geophys. Res., 76,579-604. 1979, pl and Poisson s ratios in marine sediments and rocks:J. Acoust. Soc. Arn., 66,1093-1101.Johnston, D. H., 1978, The attenuation of seismic waves in dry andsaturated rocks: PhD. thesis, Mass. Inst. of Tech.Jones, L. E. A., and Wang, H. F.. 1981. Ultrasonic velocities in Cretaceous shales from the Williston Basin: Geophysics, 46, 288 297.King, M. S., 1966,Wave velocitiesin rocks as a function of changes ofo ver bu rd en pressure and pore fluid s at ur an ts : Geophysics, 31.50-73.Kithas, B A., 1976,Lithology, gas detection. and rock properties fromacoustic logging systems: Trans., Soc. Prof. Well Log Analvsts 17thAnnual Logging Symp.Koerperich, E. A., 1979, Shear wave velocities determined from longand short-spaced borehole acoustic devices: Soc. Petr. Eng.. R237.Lash, C. E., 1980, Shear waves, multiple reflections, and convertedwaves found by a deep vertical wave test vertical seismic profiling):Geophysics, 45, 1373-1411.Leslie, H. D. and Mons, F., 1982, Sonic waveform analysis applications: Trans., Soc. Prof. Well Log Analysts 23rd Annual LoggingSymp.Lingle, R., and Jones, A. H., 1977.Comparison of log and laboratorymeasured P-wave and S-wave velocities: Trans ..Soc. Prof. Well LogAnalysysts 18th Annual Logging SympMurphy, W. F.. III, 1982, Effects of microstructure and pore fluids on

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Relationship Between Compressional-wave and Shear-wave Velocities in Clastic Silicate Rocks

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