193
DETERMINATION OF SHEAR WAVE VELOCITY AND ATTENUATION
FROM WAVEFORMS IN LOW VELOCITY FORMATIONS
by
M. Nafi Toksi5z, R.H. Wilkens and C.H. Cheng
Earth Resources Laboratory
Department of Earth, Atmospheric, and Planetary Sciences
Massachusetts Institute of Technology
Cambridge, llA 02139
ABSTRACT
In boreholes where formation shear velocity is lower than borehole tluid
velocity neither refracted shear waves nor pseudo-Rayleigh waves can
propagate. When frequency response of the sonde does not extend to low
frequencies (e.g. 2 kHz) Stoneley waves are not excited efficiently. In such
cases refracted P, leaking modes (PL) and tluid waves become dominant phases
on a full waveform acoustic log. The P wave velocity can be determined from
the first arrivals. Then, using synthetic microseismograms and a waveform
matching technique, formation shear wave velocity and attenuation can be
determined. This method· is demonstrated using data from a well in the
Baltimore Canyon Trough area of the Atlantic margin.
INTRODUCTION
The determination of shear wave velocity in "soft" formations where shear
wave velocities are less than the fluid velocity in the. borehole is an important
application of full waveform acoustic logs. The usual approach for low velocity
formations has been to derive the shear velocity from the Stoneley wave phase
velocities (Cheng and Toksi:iz, 1983; Barton et at., this report). Stoneley waves
are efficiently excited by low-frequency sources. In a typical borehole with a
diameter of eight inches, most commonly used logging tools do not excite
Stone ley waves when the shear wave velocity is below the fluid velocity.
Mathematically this can be demonstrated in terms of the eigenfunctions of the
borehole-formation system (see Figure 3, Toksi:iz et at., 1983). Physically, as the
formation shear wave velocity decreases, the phase velocity of the Stone ley
wave, and hence its wavelength, decreases also. This implies that the amplitUde
of the Stoneley wave falls off more rapidly away from the borehole boundary. As
a result, a source at the center of the borehole cannot excite the Stone ley
waves as efficiently as its wavelength decreases.
In this paper we demonstrate an approach with which both shear velocity
and attenuation values may be obtained from the detailed analysis of the P
wave train. We apply these to full waveform acoustic logging data obtained from
a drill hole in the Baltimore Canyon region of the Atlantic Ocean.
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TokBiiz et al.
FULL WAVEFORII LOGS IN LOW VELOCITY SEDIMENTS
(
The data used in this study are from the Baltimore Canyon Trough, DSDP
drilling Site 612 (Figure 1). The seismic section and the well location are shown
in Figure 2. In addition to the logs, approximately 600 m of sediments were
recovered at this site using the hydraulic piston corer (HPC) in the softer,
unlithified sediments, and the extended core barrel (XCB) in the lower, more
indurated sections. The stratigraphic column consists of an upper section of
muds and glauconitic sands (135 m) overlying, on an erosional contact, a
section of siliceous nannofossil oozes and chalks. At a very distinct level the
biogenic silica in the sediments vanishes and is replaced by amorphous silica
cement, creating a distinctive chalk-porcellanite unit. There is an excellent
correlation between lithological units and the seismic retl.ectors (Figure 3).
At this time we have only a limited data set. The data was collected with
the Schlumberger SLS-TA sonde. The Schlumberger logging tool has two
sources and two receivers. The separation between the sources and between
the receivers is 0.61 m (2 It), with a distance of 2.44 m (8 It) between the
source and receiver arrays. Figure 4 shows typical full waveform acoustic logs.
These sample traces are selected from actual data recorded at 60 em depth
intervals, with source-receiver separation of 2.44 m (8 It). In this section of
semiconsolidated oceanic sediments the P wave velocity is generally near 2.0
km/ sec or less. The shear wave velocities measured on recovered cores are
generally about 1.0 km/ sec, much less than water velocity. In such cases
there are no refracted shear waves, nor pseudo-Rayleigh waves.
The full waveform logs show a clear beginning of P waves followed by a long
train that indicates the presence of a number of phases. In this case the
borehole wavegUide can propagate refracted P waves, leaky modes, tl.uid waves,
and Stoneley waves.
The Schlumberger logging tool used at this site has a peak frequency
response between 10 kHz and 15 kHz. In this frequency range the PL (Leaking
p) modes are efficiently excited while Stoneley waves are not. The dispersions
of these waves are best illustrated by the frequency wavenumber response of
the borehole shown in Figure 5. This figure shows the refracted P wave (P), the
tl.rst and second leaking PL modes (PL I , PL 2 ), borehole "tl.uid" mode (FL) and
Stone ley wave (ST). With the peak frequency response of the logging tool
between 10 kHz and 15 kHz we expect to see primarily the P, PL. and FL
modes.
A synthetic microselsmogram calculated using formation velocities
(Vp = 2.0 km/ sec and V. = 1.0 km/ sec) and logging tool properties similar to
those used in Site 612 is shown in Figure 6. P. PL and FL phases are indicated.
The ST (Stone ley) phase is outside the time window because of its slow velocity
(VST'" 0.7 km/ sec). The theoretical log is sirrular to the traces shown in Figure
1.
This is demonstrated more clearly in Figure 7 where synthetic
microscismograms are plotted with the observed data.
The amplitUdes of P and PL modes strongiy depend on the shear velocities
of the formation. This is illustrated in Figure 8, where V. is varied
systematically while all other parameters are held constant. Note that for
lower formation shear wave velocity the PL mode becomes longer and more
8-2
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Vs from Leaky modes
195
dominant. Even for very small changes in shear wave velocity, the change in
wave train is obvious. Zhang and Cheng (1984), using contour integrals to
generate synthetic P waves and PL modes, have found that the amplitude of
the P wave packet depends strongly on the Poisson's ratio of the formation.
This is due to the conversion of the P head wave into shear wave energy at the
borehole boundary, as evidenced by the "snapshots," generated by the finite
difference technique, of the propagating waves In the formation (Stephen and
Pardo-Casas, 1984).
In Figure 9 we show the effects of the attenuation properties of the
formation (Q", Q.) on the waveforms. Increasing formation attenuation
decreases the amplitudes of P and PL waves, but does not affect the fiuid
waves. The duration of the wave train is not affected. Based on these
calculations, the parameters that best fit the observed data shown In Figure 4
are Vp = 2.0 kml sec, Yo = 1.0 kml sec, Qp = Q. = 20 for formation and
Q/luw = 100 for borehole fluid.
DISCUSSION
This short paper is a simple demonstration of how to determine formation
shear wave velocity and attenuation using waveform matching in a low shear
velocity formation in the absence of Stoneley waves. Since only a limited
amount of logging data are available at this time, no systematic Inversion was
carried out. For routine applications a formal inver~ion algorithm needs to be
developed.
An unusual character of these logs not normally seen in typical data is the
presence of a prominent fiuid arrival. This phase is generally attenuated by the
drilling mud in typical cases where Q/ '" 15. However, when mud attenuation is
low relative to formation attenuation, and when there are no Stone ley or
pseudo-Rayleigh waves to mask it, a fluid arrival can be seen if the frequency
response of the tool is high, The fiuid arrival can be an important phase for
calibrating the relative amplitudes and determining the formation Q.
ACKNOWLEDGEMENT
This research was partially supported by the full waveform acoustic logging
consortium. Roy Wilkens was supported by the Deep Sea Drilling Project during
the cruise.
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Toksoz et aL
REFERENCES
(
Barton, C.A.. Cheng C.H. and Toksiiz M.N., Determination of formation properties
in a "slow" formation by the use of Stoneley Waves: in this volume.
Cheng, C.H. and M.N. Toksiiz, 1983, Determination of shear wave velocities in
"slow" formations: Trans. SPWLA 24th Ann. Lagging symp., Paper V.
(
Stephen, R.A. and Pardo-Casas, F., 1984, Applications of finite difference
synthetic acoustic logs: in this volume.
Toksoz, M.N., Cheng C.H. and Willis M.E., 1983, Seismic waves in a borehole - a
review: M.J T. Pull Waveform Acoustic Lagging Consortium Annual Report,
Paper 1.
(
Zhang, Jinzhong and Cheng, C.H., 1984, Numerical studies of body wave
amplitudes in full waveform acoustic logs: in this volume.
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8-4
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197
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Figure 1: Locations of DSDP Sites 612 and 613. The sites are located along the
U.S.G.S. multichannel seismic line 25 and downslope from the COST B-2 and
B-3 wells.
6-5
198
Toksilz et aL
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USGS Line 25
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Figure 2: A portion of U.S.G.S. line 25 indicatmg the location of the COST B-3
well and DSDP Site 612. Vertical scale is 2-way travel time.
8-6
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Figure 3: A preliminary correlation between reflectors at Site 612 and physical
properties measured onboard the Glomar Challenger. Depths are below
seafloor.
6-7
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Toksoz et al.
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Figure .;,: Full waveform acoustic log traces (microseismograms) from Site 612.
Source receiver separation is 2.44 m (8 tt). Depth is below sea level.
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shear wave velocity (V. < Vf'uid) formation, K
wavenumber, R
borehole
radius (10 cm), P
refracted P waves, PL l , PL 2
leaking PL modes, FL =
fluid wave, ST = Stone ley wave.
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Figure 6: Theoretical full waveform acoustic log calculated using the method
described in Toksoz et al. (1983). Parameters used Ip = 2 km/ sec,
V.=1.0km/see,p=2.0g/em s , R
12.5 em, LIZ
2.44 m (8 fl),
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Figure 7: Fuil waveform acoustic logs from Site 612 and their comparison with
theoretical logs calculated using parameters given in Figure 6. Depth below
se a level.
8-11
Toksoz et aL
204
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Figure B: Variation of full waveform acoustic logs with change in formation
shear wave velocity. All other parameters are held constant, same as those
in Flgure 6.
8-12
Vs from Leaky modes
205
Q=10
20
100
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Figure 9: Effects of formation attenuation parameters on full waveform logs.
Ail parameters except formalin Q are the same as those in Figure 6. Q
values are the same for both Qp and Q•. The borehole fluid Q is 100.
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