Analysis of Full Waveform Acoustic Logging Data in "Soft" Formations

ANALYSIS OF FULL WAVEFOIDl ACOUSTIC LOGGING DATA

IN "SOFT" FOIDlATIONS

by

C.Barton.C.R Cheng andlioN. Tolaroz

EarthResources Laboratory

Department ofEarth,Atmospheric. and Planetary Sciences lIasBachusetta InBtitute of Technology

Cambridge. llA 02139

ABSTRACT

Direct recording

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tormation shear wave travel time is not possible in "soft" tormations where the shear velocity is lower than the borehole tluid velocity. The borehole Stoneley wave is quite sensitive to changes in tormation shear wave properties and may be used to indirectly determine shear velocity. This paper presents a method to calculate tormation shear velocity through inversion

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the dispersion equation for the propagation

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borehole Stoneley waves. The Stoneley wave group velocity and etrective attenuation are also computed in this data analysis.

INTRODUCTION

The simultaneous measurement of compressional and shear wave velocities in a borehole Is possible wIth the full wavetorm acoustic logging technique. This extension

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the conventional sonic log can provide tormation compressional and shear velocities as well as attenuation. Compressional and shear wave veloclty data have been extracted from a variety of lithologies with various tool contlgurations (Paillet, 1980; Cheng and Toksoz, 1981; Ingramet al., 1981; Willis and Toksoz, 1983). There remain some obvious limitations in the determination

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tormation properities in certain geologic settings, tor example, thinly interbedded sediments. highly tractured zones. or, for the case addressed in this paper. "sott" formations where the shear wave velocities are lower than the borehole tluid velocity. The borehole shear wave is actually a compressional wave in the borehole tluid that is converted to an SV wave at the borehole wall. It is critically refracted into the tormation at this intertace, travels in the tormation, and is retracted back Into the borehole tluid as a P wave. Critical refractions of shear waves do not exist in "sort" formations and thus it is impossible to directly measure the tormation shear velocity in such cases. Tools with non-axisymmetric sources and receivers have been developed to excite formation shear waves in "sott" formations (Kitsunezaki. 1980; Zemanek et Cll .• 1984), however, these are not yet commonly aVailable tor routine logging operations.

168 _{Barton etal.}

For conventional full waveform acoustic logs, it has been established that borehole guided waves are qUite sensitive to formation properities (Cheng

et

a.L., 1982). Formation shear wave velocities and attenuation appear to have a major etrect on the propagation of guided waves. The intl.uence of shear velocity and attenuation on the Stoneley wave is especially pronounced in "sort" sediments and provides a means of calculating shear formation parameters. Cheng and Toksoz (1983) presented a study of the intl.uence of formation shear wave velocity and attenuation on the Stoneley waves in "soft" formations and a method to determine formation shear wave properties from the Stoneley wave properties. In this paper, their method is used to determine formation shear wave velocity and attenuation from full waveform acoustic logging data obtained in a "soft" formation.

THEORY

Velocity Dispersion

The period equation that detl.nes the dispersion characteristics of seismic wave propagation in an open borehole is given by (Biot, 1952; Cheng

et

a.L., 1982): ( ( 1) where c2 1 1 L

=.1:

(1-- ) *

=

eJ(---)*; 0.2 c2 0.2 c2 _{1 1} m =k(1--)*

_p2

=

Col(---)*. c2

p2

'

c2 1 1 If =k(1-- ) *

=

Col( - --)*;

a'j

c e

a'j

Col is the angular frequency; c is the phase velocity; k

=

Coli c is the axial wave

number; a,

p,

and a/ are the P and S wave velocity of the formation and the borehole tl.uid velocity, respectively; R is the borehole radius; p and Pf are the formation and fiuid density; and

1i.

and .Ii:; are the moditl.ed Bessel functions of the il

/\ order. The roots of the period equation as a function of frequency define the dispersion characteristics of the seismic waves propagating in an open borehole. For Stone ley waves, the propagation characteristics are detl.ned by those roots of the period equation that correspond to phase velocities less than both the formation shear wave velocity and the borehole tl.uid velocity.

There are significant ditrerences in full waveform acoustic micro seismograms recorded in "fast" and in "slow" formations. Specifically, the P wave train appears to be of longer duration, the pseUdo-Rayleigh waves (or normal mode) no longer exist, and the Stoneley waves are more dispersive and are shifted to lower frequencies (Cheng and Toksoz, 1983). The dispersion

(

shown in Figure 1. The dispersion curve for Stoneley waves in "fast" formations (Figure 1a) shows very little' change in velocity with frequency. In "soft" sediments (Figure 1b) the Stoneley wave is more dispersive. For this particular set of formation and tluid parameters, the phase and group velocities start at the tube wave velocity (White, 1983), which is about 0.75 the tluid compressional velocity and decrease with increasing frequency. Since the frequency of the Stoneley wave in "soft" formations observed in full waveform acoustic logs is of the order of 1 to 5 kHz, it is clear that the calculation of shear velocities through Stoneley wave data in "soft" formations cannot be accomplished using either a high or low frequency approximation due to these dispersion characteristics. The frequency of the Stoneley wave must be determined for a valid analysis.

The Importance of variations in formation and tluid parameters on the Stoneley wave velocity has been examined in detal! by Cheng and Toksoz (1983). There is an almost one to one relationship between formation shear wave velocity and the Stoneley wave phase velocity in a "solt" formation. The Stoneley wave phase velocity Is seen to increase with increasini formation to tluid density ratio and to decrease with increasing borehole radius. Changes in formation compressional wave velocity appear to have relatively little effect on the Stoneley wave velocity.

Attenuation

The attenuation of the Stoneley wave is a linear sum of the formation and tluid body wave attenuations multiplied by their respective partition coefficients (Cheng at cU., 1982). The partition coefficients are the normalized partial derivatives of the phase velocity of the Stoneley wave with respect to the formation and tluid body wave velocities. The relative etrects of the formation and tluid attenuation on the the Stoneley wave attenuation in a "soft" formation are clearly shown on the plot of the partition coefficients versus frequency (Figure 2). The effects of the formation shear wave and fluid attenuation are similar at lower frequencies and the formation shear wave attenuation has an increasing effect with increasing frequency, becoming the dominant etrect at higher frequencies. The formation compressional wave attenuation has very little effect on the Stoneley wave attenuation at all frequencies.

DATAANALYSIS

Full waveform data and companion logs from a sandstone sequence that has a compressional velocity of approximately 10,000 ft/sec were analyzed in this study. The stratigraphic section used to test the inversion of the dispersion equation for formation shear velocities includes 300 feet of the data at an unspecified depth where there is some variation in lithology from sand to shale (Figure 3). In this paper all depths are referenced to the top of the data set. A 10 foot shale layer occurs at depth 60 feet and a 25 foot layer at ZOO feet. Both compressional and shear wave velocities measured in this analysis may retlect a sensitivity to the associated changes in lithology at these depths.

170 BartonetaL

(

kHz. although no significant signal is recorded beyond about 12 kHz. probably because of attenuation. The recording interval is 5 microseconds/foot. Details of the tooi are given in Williams st

at.

(1964). The compressional wave arrival can be easily traced on the variable density plot (Figure 4) as can the Stoneley wave arrival. k; expected. there is no distinguishable shear wave arrival.

Figure 4 clearly shows the sensitivity of the Stone ley wave to changes in lithology. The Stoneley wave essentially disappears at depth 220 feet where there is a 25 foot layer of shale. This phenomenon could be due to high formation shear wave attenuation.

Velocity Determination

Shear wave velocities were determined for this data set by solving the period equation (Eq. 1) given the compressional velocity and the Stone ley wave phase velocity as well as certain parameters from the companion logs. The borehole radius was taken from the caliper log (Figure 5) which indicates the borehole radius is approximately 4 inches. The formation density was determined from the compensated density log (Figure 5). The density recorded for this sandstone varies between 2.0 and 2,3 gms/cc. The borehole fiuid velocity was assumed constant at 5000 ft/sec. as was the tluid density at 1.1 gms/cc. The formation compressional velocities were measured using the threshold detection semblance correlation technique developed by Willis and Toksoz (1963).

A frequency domain analysis was performed between the waveforms recorded at the tlrst and second receivers and between the second and third receivers to measure the Stoneley wave phase velocities. The routine developed to accomplish this analysis windows each waveform around the Stoneley wave to isolate this pulse from interference from the other wave types recorded on the trace. A sine taper is applied to the endpoints of the windowed waveform. Figure 6 shows a typical waveform from this data set and the corresponding windowed Stoneley wave pulse.

The windowed time series are transformed to obtain the Fourier phase between the receiver pairs. The resulting phase spectra are then phase unwrapped through the adaptive integration routine of Tribolet (1977). Figure 7 is a plot of typical power spectra for the windowed portion of the three receivers. The amplitude spectra for the windowed Stone ley wave pulse is consistently between 1 and 2.5 kHz. The peak amplitude frequency of the Stoneley wave is used in the computation of the phase velocity by:

( ( ( ( ( ( (2)

where

f

is the frequency. I"r 1 and I"r2 are the unwrapped phase spectra for the

nrst and second receivers. tiz the receiver spacing, and n an arbitrary constant. The peak amplitude frequency is usually about 1 kHz.

The algorithm developed to perform this velocity analysis also computes the group velocity of the Stoneley wave through a straight cross correlation with sync interpolation of the Stone ley waveforms. The optimum lag. or

coefficient. The group velocity is calculated from:

IJ.z u : :

-IJ.t (3)

The phase velocity is computed via Eq. 2 for n::O, 1 and 2. These values are then tested against the group velocity to isolate the closest value above the group velocity. This value is considered the Stoneley wave phase velocity for that depth. Should the test fail to provide a reasonable value the routine displays the waveforms again so that the window picks may be adjusted and the phase velocity recalculated.

Etfectift Attenuation

Etrective attenuation or quality factor, Q, values for the Stoneley wave at each depth were calculated using the spectral ratio method. The log ratio of the amplitude spectra of the receiver pairs is first determined and Q is given by (Johnston and Toksoz, 1981):

1TIJ.z

I

Qc([) (4)

where

A.o

is the amplitude at the il_{/\ receiver, Q the quality factor, and G, the} geometrical spreading factor at the il/\ receiver. Again, the peak amplitude frequency of the Stoneley wave power spectrum is used for the values of the frequency for each computation. There is no geometrical spreading in borehole gulded waves and Eq. 4 is simplified to;

rrllJ.z

Qc([) (5)

The attenuation or Q of the Stoneley wave as a function of frequency can be determined from the measured log amplitude ratio using Eq. 5. However, in order to determine the formation shear wave attenuation or Q" we need to know the Q of the borehole t1uld. Alternatively, we can determine the Stoneley wave Q at a number of frequencies, and assuming there is little frequency dependence of the body wave Q's, we can then solve for the formation shear wave Q, by a least squares technique. However, in this paper, the t1uld attenuation was not available, and the Stoneley wave pulse is not broad banded enough to allow a measurement of its attenuation as a function of frequency. As a result, only the Stoneley wave Qwill be presented and not the formation shear wave Q,. Assuming that the t1uid attenuation is relatively constant over the 300 foot interval, the etrective Stoneley wave attenuation should correlate very well with the ac tual formation shear wave attenuation.

RESULTS

172 _{Barton et al.}

(Figure 8). The Stoneley wave is difficult to identify between depths 205 and 230 teet and it was necessary to manually window the wavetorms within this depth interval to obtain the expected low phase velocity values. Figure 8 shows the phase velocity analysis results

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the Rl/R2 receiver pair depth-corrected to the R2/R3 receiver pair. There is very good agreement between the separate computations

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the Stoneley wave phase velocity at each depth. The analysis successtully measured Stoneley wave phase velocities that are typical

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a sott sediment.

Results

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the Stoneley wave group velocity calculation are very close to, and show excellent correlation with, the phase velocity determined tor each depth. These results are theoretically predicted tor Stone ley waves that propagate at trequencies ot 1.0 kHz. Figure 9 is a depth profile ot the phase and group velocities determinedtor the Rl/R2 .receiver pair.

The solution ot the dispersion equation tor tormation shear velocities ot

the RlIR2 receiver pair depth corrected to the R2/R3 receiver pair is shown on the depth protlle in Figure 10. Again there is relatively good agreement between the two computations at each depth. The shear velocities vary trom 3500 to 4300 tt/sec in the upper part

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the section and are 3300 tt/sec below depth 240 teet. The variations in the calculated shear velocities match the variations in lithology quite well. The lower velocities calculated in the lower section show a sensitivity to an overall 10% increase in porosity below depth 240 teet. With caretul consideration ot depth intervals where the wavetorms are ot low qUality due to attenuation ot the medium, this technique proves to be generally very good at discriminating variations in shear velocities.

Figure 11 is the depth protlle

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the compressional and shear velocities determined trom the RlIR2 receiver pair tor the depth interval studied. FigJll"e 12 shows this information tor the R2/R3 receiver pair. Compressional velocities range between 9500 and 11,000 tt/sec above depth 240 teet and are 9000 tt/sec below depth 240 teet. There is good correspondence between the two measurements with both receivel' combinations.

The depth pl'ofiles ot compl'essional and shear wave velocity slownesses tor the two receivel' pairs (Figures 13 and 14) contorm to the defiection sense

ot

the other logs and pl'ovide a bettel' means rol' comparison with the lithologic and companion logs. Decreases in porosity are mOl'e apparent on the shear wave slowness pl'ofiles. Once the shear velocity pl'ofile has been determined, calculation ot engineering properties such as Poisson's !'atio is stl'aight torward. Figures 15 and 16 are the depth protlles ot Poisson's I'atio tOI' each ot

the I'eceivel' pail'S. Poisson's I'atio tor this section is appl'oximately 0.42 which is a value chal'acteristic

ot

sort sediments.

A depth protlle ot the et!ective attenuation ot the Stoneley wave phase velocity calculated between the Rl /R2 I'eceiver pairs is shown in Figure 17. The Stoneley wave Q obtained is I'elatively stable at 10 tOI' most ot the depth pl'otile With a slight increase with depth. Due to the low signal level, the Q value measul'ed at the shale intel'val tl'om200 to 225 teet is unl'eliable.

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CONCLUSIONS

In this paper we have obtained formation shear wave velocity and attenuation from full waveform acoustic logs in a "sort" formation using the phase velocity and spectral amplitude of the Stoneley wave. This method provides formation shear wave information from data that would otherwise be inappropriate for standard full waveform analysis. The velocity and attenuation obtained are stable and consistent with local lithology.

This method requires the proper identification and isolation of the Stoneley wave pulse. A total loss in the energy of the Stoneley wave signal is not unco=on in full waveform data that has been recorded in relatively unconsolldated sediments, regions where the borehole has caved in, and in formations with high attenuation (such as the shale section in this stUdy). An

improper tool response (no low frequency energy in the source or inadequate low frequency response of the receiver) will also significantly diminish the Stone ley wave amplitude. These areas will require more attention during analysis regardless of the technique used to calculate shear wave velocities.

ACKNOWLEDGEMENTS

The study is supported by the Full Waveform Acoustic Logging Consortium at M.LT. Colleen Barton was also supported by a Chevron Fellowship. We would like to thank Mobil Research and Development Corporation for the use of their data.

174 Barton etaI.

Biot, M. A., 1952, Propagation ot elastic waves in a cylindrical bore containing a fluid: Jour.ot Appl. Phys., v.23, p.977-1005.

Cheng, C.H. and Toksoz, M.N., 1961, Elastic wave propagation in a fluid-filled borehole and synthetic acoustic logs: Geophysics, v.46, p.1042-1053.

Cheng, C.H., Toksoz, M.N., and Willis, M.E., 1962, Determination ot in situ attenuation tromtull wavetorm acoustic logs: J. Geophys. Res .. v.67, p.5477-54!\4.

Cheng, C.H.and Toksoz, M.N., 1963, Determination ot shear wave velocities in "slow" tormations; Trans. 24th Ann. Logging Symp. ot SPWLA, Paper Y.

Ingram, J.D., Morris, C.F., MacKnight, E.E.. and Parks, T.W., 1961, Shear velocity logs using direct phase determination: Presented at 51st Annual International Meeting ot the Society ot Exploration Geophysicists, October 11-15, Los Angeles, CA.

Johnston, D.H. and Toksoz. M.N., 1961, Definitions and terminology: in Seismic

Wave Attenuatian, Toksoz, M.N. and Johnston, D.H. editors; Geophysics Reprint Series, No.2, Societyot Exploration Geophysicists, Tulsa. OK.

Kitsunezaki, C., 1960. A new method tor shear-wave logging: Geophysics, v.45, p.1469-1506.

Paillet, F., 1960, Acoustic propagation in the vicinity ot 'tractures which intersect a fiuid-filled borehole: Trans. ot 21st Ann. Logging Symp. of SPWLA, Paper DD.

Tribolet, J.M., 1977. A new phase unwrapping algorithm: IEEE Trans. ot Acoustic, Speech and Signal Processing, vol. ASSP-25, no.2.

White, J.E., 1963, Un.d.rn-gTovlnd. Sound., Applicatian 01 Seismic Waves; Elsevier, Holland.

Williams, D.M., Zemanek, J., Dennis, C.L., Angona, F.A., and Caldwell, R.L.. 1964, The long-spaced acoustic logging tool: Trans. 25th Ann. Logging Symp. of SPWLA, in press.

Willis, M.E. and Toksoz, M.N., 1963, Automatic P and S velocity determination fromtull wavetorm digital acoustic logs: Submitted to Geophysics.

Zemanek, J., Angona, F.A., Williams, D.M., and Caldwell, R.L., 1984, Continuous shear wave logging: Trans. 25th Ann. Logging Symp. ot SPWLA, In press.

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Group Phase

-

---...

"-r',

PSEUDO-

"-

"'-RAYLEIGH ' -

_...

....

--...

---...

'-

_{' -}

---

--

_-

_---

--

-

--I STONELEY 1.0 1 . 1

1.5

1.3

1.4

1.2

0.9

>- f-()

o

-l ll.J

>

o

ll.J N -l oCt ~ CC

o

Z

0.8

0.7

o

5

10

WAVE NUMBER

x

RADIUS

Figure la Stoneley wave phase and group velocity dispersion for hard sed-iments.

( 176 _{Barton etaI.}

STONELEY

SOFT SEDIMENT

-( (

10

8

4

6

FREQUENCY (kHz)

2

0.78

>-

_0.76

I-<.)

0

...J

_0.74

w

>

a

_0.72

w

N ...J

-<

0.70

::2:

CC

0

0.68

z

0.66

0

Figure lb Stoneley wave phase and group velocity dispersion for soft sedi-ments.

1.0

r - - r - - - , . . . - - . . , - - - , - - - . , . - - - , - - - - , - - - - , - - - , . . - - - - ,

STONELEY

~ Z l.LJ <..:l

u.

U. l.LJ

o

<..:l Z

o

~ ~

cc

<C

a.

0.8

0.6

0.4

0.2

/

-

--

S_

-/ . / / ' /

SOFT SEDIMENT

5

10

FREQUENCY (kHz)

p

---

---o

'---_-=--'=~_=-.=..-.=.-.=L.-_ - - - J_ _. l . . - _ . . . l . . - _ - l . - _ - l - _ - - l . . _ - - L _ - - l

o

178

-..-..-

..

Barton et &1.

-( (

Figure 3 Study borehole lithologic section

(i) ~.

~

DEPTH

eft)

.~

Figure 4 Variable density plot of borehole full waveform acoustic data

-

C) CD (/J

E

-

w

:2

-

I-180 Barton et aI. ( ( (, 0)

o

DENSITY CALIPER gm/cc inches

...

...

... ... ... ...

OJ OJ OJ OJ OJ

w

m

--J Cll fD ~

. .

•

.

.

• •

.

.

•

.

•

.

.

•

.

~ OJ .l>.

m

Cll ~ OJ .:..

m

Cll ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ IS ~ .s> ~ ~ ~ ~ -~ ~ ~ 0

,

F ~

w

o

o

...l. I\J 0 C m -0 -; ::I: (

....

-

co

-

0 (

,.-.. . , . - - - . , - - - t

r

I

.

....

'oU'

..

~

..

..

~~:.,of_"'--~-~---~-__;.

,.,.I

l

i

;

I

h _

i

""if---IJ

V'vr---

I

•·..1,

_~~

_ _

~---..Jlf

...1-

t.«'

"

•.•,.

:l

,.,"('----1\

.,J

I

.,."JI-_~--_-~,~----J-•. ".. ' .•11 I.a. t •1.. [ "J

..

'.llS •• tt1'' -I

~

.•.

_~

I

-1 ••,01-.-_--~_~_ _-__l_ t.

'.iI"

...

'.eN ... 1.1" l:' 10K ~I ttt,of"O"""'~_~_~_~_-t

.J

. . . ,. .0 1 - - - - 1

~,.~

..," ... ... ..n.

1.1M \~ t.~'"'_J l:a1'" ..)

r - - '

c.ln l.:~J

,

..

:J

-1.nJI--_-_c,-~,

". ".~GIJ ... '.6'.

Figure 6 Typical full waveform acoustic waveforms and windowed Stoneley waveform

( 182 Barton et aI. ( I: :l: 10E ~J 5.60 0=300.00 ~.20 RI ( 2.80 1.~0 0.

"

..

1.26 2.52 3..78 5.•0~ 6.30 ( l: :l: lOE ~J -4.00

o ...

J00.00 3.00 R2

,

, 2.00 1.00 O. ,,~ _{1.26 2.52 3.78 5.•0~ e.~0} I: _,~J 0-300.00 R3 ( 0.Si-0.78 0.65 0.52 0.3S" 0.26 00133 ( 0. -... -._,...-~~ 1.26 2.52 3.• 78 5.. 04 6.•~a frequency kHz

5 U R1..-R2 E R2"-R3 :.. - ---1. 0 4 C I T '-I _:3 K F T

..-

S S E C 1 _I

_I

_{I I}

_r-rl

_{I I Irr~1 I}

₁

0 50 100 150 200 a50 300

DEPTH FEET.

Figure 8 Depth profile of calculated Stoneley wave phase velocities for the RlIR2 receiver pair depth corrected to the R2/R3 receiver pair

( 184 Barton et al. ( 5 V

PHASE VELOCITY

E

GROWP VELOCITY

-

- --... L 0 ( C I T

-.

Y _:3 K F T / 2 S c:'

-C 1 ( -13 50 100 150 200 250 :300

DEPTH FEET

(

Figure 9 Depth profiie of Stoneley wave phase and group velocities for the Rl/R2 receiver pair

5 V RVR2 -E R2/R3 -

---t.

0

"'

C I T y ₃

•

K

..

..

F' T / S E C 1

_'TIl

I

_I

r I I I

_I

I I I 0 S0 100 150 200 250 3130

OEPTH FEET

Figure 10 Depth profile of calculated shear wave velocities for the R1/R2 receiver pair depth corrected to the R2/R3 receiver pair

( 186 Barton et81. ( ( 15 R1/R2 V E T-O 10 C I T y K F T 5 + t / _S 5 E C

,

I ₍

I

0

_....1

I

r1

_{I I}

_I

_I

,

I

_{I I}

I

_I

I

0 50 100 150 200 250 300

DEPTH, Fi

(

Figure 11 Compressional and shear wave velocity profiles for the R1/R2 re-ceiver pair

Figure 12 Compressional and shear wave velocity profiles for the R2/R3 re-ceiver pair

188

Barton et al.

o

50 100 150 200 250 300

IJt;PTH, FT

Figure 13 Compressional and shear wave slowness profiles lor the R1/R2 receiver pair

,

600 R2"-R3

5OO

S L 0 W _"!00 N E S S

s

:300 M I C _ae0

s

..-F P T ₁₀₀

o

50 100 150

DEPTH, FT

2130 250 :3013

Figure 14 Compressional and shear wave slowness profiles for the R2/R3 receiver pair

190 _{Barton etaI.}

a . 5 - . , . . . - - - ,

F' 0 I ( S

_a.'!

s

0 N S R A T

_a.3

I 0 300 250

20a

150

a.2

rrrf-r

I I

f-r.-r-r...-l-...-r~..,...,...~--r--r-...-1

a

5a

10a

DEF'TH. F'T (

0.5~---_:"""""_---,

RS/R3

F' 0 I S 0."! S 0 N

_,

S R A T _0.3 I 0

o

50 100 150 DEPTH, FT 200 250 300

192 ( Barton etai. ( ( ( 2513 2130 150

DEPTH FEET

o

-l---'-""""'-'-lr-"T"l--.-.,..,..,.I-r·-.-..,...,-.-....-.,....,--r--r--r--T-.-~.,...,.

...

-.-,...,..-l

50 100 (

Figure 17 Depth profile of quality factor determined from the Rl/R2 re-ceiver pairs